Energy Research

CAPACITANCE

Recall that inductance is the property of a coil that causes electrical energy to be stored in a magnetic field about the coil. The energy is stored in such a way as to oppose any change in current. CAPACITANCE is similar to inductance in that it also causes a storage of energy.

A CAPACITOR is a device that stores electrical energy in an ELECTROSTATIC FIELD. The energy is stored in such a way as to oppose any change in voltage. Just how capacitance opposes a change in voltage I will explain presently. However, it is first necessary to explain the principles of an electrostatic field as it is applied to capacitance.

THE ELECTROSTATIC FIELD

Recall that opposite electrical charges attract each other while like electrical charges repel each other. The reason for this is the existence of an electrostatic field. Any charged particle is surrounded by invisible lines of force, called electrostatic lines of force. These lines of force have some interesting characteristics:

They are polarized from positive to negative. They radiate from a charged particle in straight lines and do not form closed loops. They have the ability to pass through any known material. They have the ability to distort the orbits of tightly bound electrons.

Examine figure 1. This figure represents two unlike charges surrounded by their electrostatic field. Because an electrostatic field is polarized positive to negative, arrows are shown radiating away from the positive charge and toward the negative charge. Stated another way, the field from the positive charge is pushing, while the field from the negative charge is pulling. The effect of the field is to push and pull the unlike charges together.

Figure 1. - Electrostatic field attracts two unlike charged particles.

In figure 2, two like charges are shown with their surrounding electrostatic field. The effect of the electrostatic field is to push the charges apart.

Figure 2. - Electrostatic field repels two like charged particles.

If two unlike charges are placed on opposite sides of an atom whose outermost electrons cannot escape their orbits, the orbits of the electrons are distorted as shown in figure 3. Figure 3 (A) shows the normal orbit. Part (B) of figure 3 shows the same orbit in the presence of charged particles. Since the electron is a negative charge, the positive charge attracts the electrons, pulling the electrons closer to the positive charge. The negative charge repels the electrons, pushing them further from the negative charge. It is this ability of an electrostatic field to attract and to repel charges that allows the capacitor to store energy.

Figure 3. - Distortion of electron orbital paths due to electrostatic force.

THE SIMPLE CAPACITOR

A simple capacitor consists of two metal plates separated by an insulating material called a dielectric, as illustrated in figure 4. Note that one plate is connected to the positive terminal of a battery; the other plate is connected through a closed switch (S1) to the negative terminal of the battery. Remember, an insulator is a material whose electrons cannot easily escape their orbits. Due to the battery voltage, plate A is charged positively and plate B is charged negatively. (How this happens is explained later in this chapter.) Thus an electrostatic field is set up between the positive and negative plates. The electrons on the negative plate (plate B) are attracted to the positive charges on the positive plate (plate A).

Figure 4. - Distortion of electron orbits in a dielectric.

Notice that the orbits of the electrons in the dielectric material are distorted by the electrostatic field. The distortion occurs because the electrons in the dielectric are attracted to the top plate while being repelled from the bottom plate.

This is the key feature for the operation of Stan Meyer’s Water Fuel Cell wherein the dielectric material is the water molecule itself composed of Hydrogen (-) and Oxygen (+) atoms being pulled apart in a strong electrostatic field. For more about this see earlier post: http://www.alexpetty.com/2010/09/17/water-as-fuel-with-puharich-and-meyer .

When switch S1 is opened, the battery is removed from the circuit and the charge is retained by the capacitor. This is the basic operation of a capacitor, a device that stores the energy of charge as electrostatic field.

This occurs because the dielectric material is an insulator, and the electrons in the bottom plate (negative charge) have no path to reach the top plate (positive charge). The distorted orbits of the atoms of the dielectric plus the electrostatic force of attraction between the two plates hold the positive and negative charges in their original position. Thus, the energy which came from the battery is now stored in the electrostatic field of the capacitor. Two slightly different symbols for representing a capacitor are shown in figure 5. Notice that each symbol is composed of two plates separated by a space that represents the dielectric. The curved plate in (B) of the figure indicates the plate should be connected to a negative polarity.

Figure 5. - Circuit symbols for capacitors.

THE FARAD

Capacitance is measured in units called FARADS. A one-farad capacitor stores one coulomb (a unit of charge (Q) equal to 6.28 X 10¹⁸electrons) of charge when a potential of 1 volt is applied across the terminals of the capacitor. This can be expressed by the formula:

The farad is a very large unit of measurement of capacitance. For convenience, the microfarad (abbreviated mF) or the picofarad (abbreviated pF) is used. One (1.0) microfarad is equal to 0.000001 farad or 1 X 10^-6 farad, and 1.0 picofarad is equal to 0.000000000001 farad or 1.0 X 10^-12 farad. Capacitance is a physical property of the capacitor and does not depend on circuit characteristics of voltage, current, and resistance. A given capacitor always has the same value of capacitance (farads) in one circuit as in any other circuit in which it is connected.

FACTORS AFFECTING THE VALUE OF CAPACITANCE

• The value of capacitance of a capacitor depends on three factors:
• The area of the plates.
• The distance between the plates.
• The dielectric constant of the material between the plates.

PLATE AREA affects the value of capacitance in the same manner that the size of a container affects the amount of water that can be held by the container. A capacitor with the large plate area can store more charges than a capacitor with a small plate area. Simply stated, “the larger the plate area, the larger the capacitance”.

The second factor affecting capacitance is the DISTANCE BETWEEN THE PLATES. Electrostatic lines of force are strongest when the charged particles that create them are close together. When the charged particles are moved further apart, the lines of force weaken, and the ability to store a charge decreases.

The third factor affecting capacitance is the DIELECTRIC CONSTANT of the insulating material between the plates of a capacitor. The various insulating materials used as the dielectric in a capacitor differ in their ability to respond to (pass) electrostatic lines of force. A dielectric material, or insulator, is rated as to its ability to respond to electrostatic lines of force in terms of a figure called the DIELECTRIC CONSTANT. A dielectric material with a high dielectric constant is a better insulator than a dielectric material with a low dielectric constant. Dielectric constants for some common materials are given in the following list:

Notice the dielectric constant for a vacuum. Since a vacuum is the standard of reference, it is assigned a constant of one. The dielectric constants of all materials are compared to that of a vacuum. Since the dielectric constant of air has been determined to be approximately the same as that of a vacuum, the dielectric constant of AIR is also considered to be equal to one.

The formula used to compute the value of capacitance is:

For example, find the capacitance of a parallel plate capacitor with paraffin paper as the dielectric.

By examining the above formula you can see that capacitance varies directly as the dielectric constant and the area of the capacitor plates, and inversely as the distance between the plates.

VOLTAGE RATING OF CAPACITORS

In selecting or substituting a capacitor for use, consideration must be given to (1) the value of capacitance desired and (2) the amount of voltage to be applied across the capacitor. If the voltage applied across the capacitor is too great, the dielectric will break down and arcing will occur between the capacitor plates. When this happens the capacitor becomes a short-circuit and the flow of direct current through it can cause damage to other electronic parts. Each capacitor has a voltage rating (a working voltage) that should not be exceeded.

The working voltage of the capacitor is the maximum voltage that can be steadily applied without danger of breaking down the dielectric. The working voltage depends on the type of material used as the dielectric and on the thickness of the dialectic. (A high-voltage capacitor that has a thick dielectric must have a relatively large plate area in order to have the same capacitance as a similar low-voltage capacitor having a thin dielectric.) The working voltage also depends on the applied frequency because the losses, and the resultant heating effect, increase as the frequency increases.

A capacitor with a voltage rating of 500 volts dc cannot be safely subjected to an alternating voltage or a pulsating direct voltage having an effective value of 500 volts. Since an alternating voltage of 500 volts (rms) has a peak value of 707 volts, a capacitor to which it is applied should have a working voltage of at least 750 volts. In practice, a capacitor should be selected so that its working voltage is at least 50 percent greater than the highest effective voltage to be applied to it.

CAPACITOR LOSSES

Power loss in a capacitor may be attributed to dielectric hysteresis and dielectric leakage. Dielectric hysteresis may be defined as an effect in a dielectric material similar to the hysteresis found in a magnetic material. It is the result of changes in orientation of electron orbits in the dielectric because of the rapid reversals of the polarity of the line voltage. The amount of power loss due to dielectric hysteresis depends upon the type of dielectric used. A vacuum dielectric has the smallest power loss.

Dielectric leakage occurs in a capacitor as the result of LEAKAGE CURRENT through the dielectric. Normally it is assumed that the dielectric will effectively prevent the flow of current through the capacitor. Although the resistance of the dielectric is extremely high, a minute amount of current does flow. Ordinarily this current is so small that for all practical purposes it is ignored. However, if the leakage through the dielectric is abnormally high, there will be a rapid loss of charge and an overheating of the capacitor.

The power loss of a capacitor is determined by loss in the dielectric. If the loss is negligible and the capacitor returns the total charge to the circuit, it is considered to be a perfect capacitor with a power loss of zero.

CHARGING AND DISCHARGING A CAPACITOR

CHARGING

In order to better understand the action of a capacitor in conjunction with other components, the charge and discharge actions of a purely capacitive circuit are analyzed first. For ease of explanation the capacitor and voltage source shown in figure 6 are assumed to be perfect (no internal resistance), although this is impossible in practice.

In figure 6(A), an uncharged capacitor is shown connected to a four-position switch. With the switch in position 1 the circuit is open and no voltage is applied to the capacitor. Initially each plate of the capacitor is a neutral body and until a difference of potential is impressed across the capacitor, no electrostatic field can exist between the plates.

Figure 6. - Charging a capacitor.

To CHARGE the capacitor, the switch must be thrown to position 2, which places the capacitor across the terminals of the battery. Under the assumed perfect conditions, the capacitor would reach full charge instantaneously. However, the charging action is spread out over a period of time in the following discussion so that a step-by-step analysis can be made.

At the instant the switch is thrown to position 2 of Figure 6 (B), a displacement of electrons occurs simultaneously in all parts of the circuit. This electron displacement is directed away from the negative terminal and toward the positive terminal of the source (the battery). A brief surge of current will flow as the capacitor charges.

You can observe the motion of the individual electrons (the electric current) in video 1 below. This surge of electron motion is the charging effect.

Video 1. – the operation of a capacitor

At the instant the switch is closed, the positive terminal of the battery extracts an electron from the bottom conductor. The negative terminal of the battery forces an electron into the top conductor. At this same instant an electron is forced into the top plate of the capacitor and another is pulled from the bottom plate. Thus, in every part of the circuit a clockwise DISPLACEMENT of electrons occurs simultaneously.

As electrons accumulate on the top plate of the capacitor and others depart from the bottom plate, a difference of potential develops across the capacitor. Each electron forced onto the top plate makes that plate more negative, while each electron removed from the bottom causes the bottom plate to become more positive. Notice that the polarity of the voltage which builds up across the capacitor is such as to oppose the source voltage. The source voltage (emf) forces current around the circuit  in a clockwise direction, ie. the flow foes from battery terminal Vss (-) to battery terminal Vdd (+). The emf developed across the capacitor, however, has a tendency to force the current in a counterclockwise direction, opposing the source emf. As the capacitor continues to charge, the voltage across the capacitor rises until it is equal to the source voltage. Once the capacitor voltage equals the source voltage, the two voltages balance one another and current ceases to flow in the circuit.

In studying the charging process of a capacitor, you must be aware that NO current flows THROUGH the capacitor. The material between the plates of the capacitor must be an insulator. However, to an observer stationed at the source or along one of the circuit conductors, the action has all the appearances of a true flow of current, even though the insulating material between the plates of the capacitor prevents the current from having a complete path. The current which appears to flow through a capacitor was named by Maxwell as DISPLACEMENT CURRENT.

If the switch is now opened as shown in figure 8(A),the electrons on the upper plate are isolated. The electrons on the top plate are attracted to the charged bottom plate. Because the dielectric is an insulator, the electrons can not cross the dielectric to the bottom plate. The charges on both plates will be effectively trapped by the electrostatic field and the capacitor will remain charged indefinitely. You should note at this point that the insulating dielectric material in a practical capacitor is not perfect and small leakage current will flow through the dielectric. This current will eventually dissipate the charge. However, a high quality capacitor may hold its charge for a month or more.

Figure 7. - Discharging a capacitor.

To review briefly, when a capacitor is connected across a voltage source, a surge of charging current flows. This charging current develops a cemf across the capacitor which opposes the applied voltage. When the capacitor is fully charged, the cemf is equal to the applied voltage and charging current ceases. At full charge, the electrostatic field between the plates is at maximum intensity and the energy stored in the dielectric is maximum. If the charged capacitor is disconnected from the source, the charge will be retained for some period of time. The length of time the charge is retained depends on the amount of leakage current present. Since electrical energy is stored in the capacitor, a charged capacitor can act as a source emf.

DISCHARGING

To DISCHARGE a capacitor, the charges on the two plates must be neutralized. This is accomplished by providing a conducting path between the two plates as shown in figure 7(B). With the switch in position (4) the excess electrons on the negative plate can flow to the positive plate and neutralize its charge. When the capacitor is discharged, the distorted orbits of the electrons in the dielectric return to their normal positions and the stored energy is returned to the circuit. It is important for you to note that a capacitor does not consume power. The energy the capacitor draws from the source is recovered when the capacitor is discharged.

CHARGE AND DISCHARGE OF AN RC SERIES CIRCUIT

Ohm’s law states that the voltage across a resistance is equal to the current through the resistance times the value of the resistance. This means that a voltage is developed across a resistance ONLY WHEN CURRENT FLOWS through the resistance.

A capacitor is capable of storing or holding a charge of electrons. When uncharged, both plates of the capacitor contain essentially the same number of free electrons. When charged, one plate contains more free electrons than the other plate. The difference in the number of electrons is a measure of the charge on the capacitor. The accumulation of this charge builds up a voltage across the terminals of the capacitor, and the charge continues to increase until this voltage equals the applied voltage. The charge in a capacitor is related to the capacitance and voltage as follows:

in which Q is the charge in coulombs, C the capacitance in farads, and E the emf across the capacitor in volts.

CHARGE CYCLE

A voltage divider containing resistance and capacitance is connected in a circuit by means of a switch, as shown at the top of figure 8. Such a series arrangement is called an RC series circuit.

Figure 8. - Charge of an RC series circuit.

In explaining the charge and discharge cycles of an RC series circuit, the time interval from time t₀ (time zero, when the switch is first closed) to time t₁ (time one, when the capacitor reaches full charge or discharge potential) will be used. (Note that switches S1 and S2 move at the same time and can never both be closed at the same time.)

When switch S1 of the circuit in figure 8 is closed at t₀, the source voltage (E_S) is instantly felt across the entire circuit. Graph (A) of the figure shows an instantaneous rise at time t₀ from zero to source voltage (E_S = 6 volts). The total voltage can be measured across the circuit between points 1 and 2. Now look at graph (B) which represents the charging current in the capacitor (i_c). At time t ₀, charging current is MAXIMUM. As time elapses toward time t ₁, there is a continuous decrease in current flowing into the capacitor. The decreasing flow is caused by the voltage buildup across the capacitor. At time t₁, current flowing in the capacitor stops. At this time, the capacitor has reached full charge and has stored maximum energy in its electrostatic field. Graph (C) represents the voltage drop (e _r) across the resistor (R). The value of e_r is determined by the amount of current flowing through the resistor on its way to the capacitor. At time t₀ the current flowing to the capacitor is maximum. Thus, the voltage drop across the resistor is maximum (E = IR). As time progresses toward time t₁, the current flowing to the capacitor steadily decreases and causes the voltage developed across the resistor (R) to steadily decrease. When time t ₁ is reached, current flowing to the capacitor is stopped and the voltage developed across the resistor has decreased to zero.

You should remember that capacitance opposes a change in voltage. This is shown by comparing graph (A) to graph (D). In graph (A) the voltage changed instantly from 0 volts to 6 volts across the circuit, while the voltage developed across the capacitor in graph (D) took the entire time interval from time t_o to time t₁ to reach 6 volts. The reason for this is that in the first instant at time t ₀, maximum current flows through R and the entire circuit voltage is dropped across the resistor. The voltage impressed across the capacitor at t₀ is zero volts. As time progresses toward t ₁, the decreasing current causes progressively less voltage to be dropped across the resistor (R), and more voltage builds up across the capacitor (C). At time t₁, the voltage felt across the capacitor is equal to the source voltage (6 volts), and the voltage dropped across the resistor (R) is equal to zero. This is the complete charge cycle of the capacitor.

As you may have noticed, the processes which take place in the time interval t₀ to t₁ in a series RC circuit are exactly opposite to those in a series LR circuit.

For your comparison, the important points of the charge cycle of RC and LR circuits are summarized in the table shown in figure 9.

Figure 9. - Summary of Capacitive and Inductive Characteristics.

DISCHARGE CYCLE

In figure 10 at time t₀, the capacitor is fully charged. When S1 is open and S2 closes, the capacitor discharge cycle starts. At the first instant, circuit voltage attempts to go from source potential (6 volts) to zero volts, as shown in graph (A). Remember, though, the capacitor during the charge cycle has stored energy in an electrostatic field.

Figure 10. - Discharge of an RC Series circuit.

Because S2 is closed at the same time S1 is open, the stored energy of the capacitor now has a path for current to flow. At t₀, discharge current (i_d) from the bottom plate of the capacitor through the resistor (R) to the top plate of the capacitor (C) is maximum. As time progresses toward t₁, the discharge current steadily decreases until at time t₁ it reaches zero, as shown in graph (B).

The discharge causes a corresponding voltage drop across the resistor as shown in graph (C). At time t₀, the current through the resistor is maximum and the voltage drop (e_r) across the resistor is maximum. As the current through the resistor decreases, the voltage drop across the resistor decreases until at t₁ it has reached a value of zero. Graph (D) shows the voltage across the capacitor (e_c) during the discharge cycle. At time t ₀ the voltage is maximum and as time progresses toward time t ₁, the energy stored in the capacitor is depleted. At the same time the voltage across the resistor is decreasing, the voltage (e _c) across the capacitor is decreasing until at time t ₁ the voltage (e_c) reaches zero.

By comparing graph (A) with graph (D) of figure 10,you can see the effect that capacitance has on a change in voltage. If the circuit had not contained a capacitor, the voltage would have ceased at the instant S1 was opened at time t₀. Because the capacitor is in the circuit, voltage is applied to the circuit until the capacitor has discharged completely at t₁. The effect of capacitance has been to oppose this change in voltage.

RC TIME CONSTANT

The time required to charge a capacitor to 63 percent (actually 63.2 percent) of full charge or to discharge it to 37 percent (actually 36.8 percent) of its initial voltage is known as the TIME CONSTANT (TC) of the circuit. The charge and discharge curves of a capacitor are shown in figure 11. Note that the charge curve is like the curve in figure 8, graph (D), and the discharge curve like the curve in figure 8, graph (B).

Figure 11. - RC time constant.

The value of the time constant in seconds is equal to the product of the circuit resistance in ohms and the circuit capacitance in farads. The value of one time constant is expressed mathematically as t = RC. Some forms of this formula used in calculating RC time constants are:

UNIVERSAL TIME CONSTANT CHART

Because the impressed voltage and the values of R and C or R and L in a circuit are usually known, a UNIVERSAL TIME CONSTANT CHART (fig. 12) can be used to find the time constant of the circuit. Curve Ec-X is a plot of both capacitor voltage during charge and inductor current during growth. Curve Ec-Y is a plot of both capacitor voltage during discharge and inductor current during decay.

Figure 12. - Universal time constant chart for RC and RL circuit.

The time scale (horizontal scale) is graduated in terms of the RC or L/R time constants so that the curves may be used for any value of R and C or L and R. The voltage and current scales (vertical scales) are graduated in terms of percentage of the maximum voltage or current so that the curves may be used for any value of voltage or current. If the time constant and the initial or final voltage for the circuit in question are known, the voltages across the various parts of the circuit can be obtained from the curves for any time after the switch is closed, either on charge or discharge. The same reasoning is true of the current in the circuit.

The graphs shown in figure 11 and 12 are not entirely complete. That is, the charge or discharge (or the growth or decay) is not quite complete in 5 RC or 5 L/R time constants. However, when the values reach 0.99 of the maximum (corresponding to 5 RC or 5 L/R), the graphs may be considered accurate enough for all practical purposes.

CAPACITORS IN SERIES AND PARALLEL

Capacitors may be connected in series or in parallel to obtain a resultant value which may be either the sum of the individual values (in parallel) or a value less than that of the smallest capacitance (in series).

CAPACITORS IN SERIES

The overall effect of connecting capacitors in series is to move the plates of the capacitors further apart. This is shown in figure 13. Notice that the junction between C1 and C2 has both a negative and a positive charge. This causes the junction to be essentially neutral. The total capacitance of the circuit is developed between the left plate of C1 and the right plate of C2. Because these plates are farther apart, the total value of the capacitance in the circuit is decreased. Solving for the total capacitance (C_T) of capacitors connected in series is similar to solving for the total resistance(R_T)of resistors connected in parallel.

Figure 13. - Capacitors in series.

Note the similarity between the formulas for R_T and C_T:

If the circuit contains more than two capacitors, use the above formula. If the circuit contains only two capacitors, use the below formula:

Note: All values for C_T, C1, C2, C3,… C _n should be in farads. It should be evident from the above formulas that the total capacitance of capacitors in series is less than the capacitance of any of the individual capacitors.

CAPACITORS IN PARALLEL

When capacitors are connected in parallel, one plate of each capacitor is connected directly to one terminal of the source, while the other plate of each capacitor is connected to the other terminal of the source. Figure 14 shows all the negative plates of the capacitors connected together, and all the positive plates connected together. C _T, therefore, appears as a capacitor with a plate area equal to the sum of all the individual plate areas. As previously mentioned, capacitance is a direct function of plate area. Connecting capacitors in parallel effectively increases plate area and thereby increases total capacitance.

Figure 3-14. - Capacitors in parallel.

 

For capacitors connected in parallel the total capacitance is the sum of all the individual capacitances. The total capacitance of the circuit may by calculated using the formula:

where all capacitances are in the same units.

FIXED CAPACITOR

A fixed capacitor is constructed in such manner that it possesses a fixed value of capacitance which cannot be adjusted. A fixed capacitor is classified according to the type of material used as its dielectric, such as paper, oil, mica, or electrolyte.

A PAPER CAPACITOR is made of flat thin strips of metal foil conductors that are separated by waxed paper (the dielectric material). Paper capacitors usually range in value from about 300 picofarads to about 4 microfarads. The working voltage of a paper capacitor rarely exceeds 600 volts. Paper capacitors are sealed with wax to prevent the harmful effects of moisture and to prevent corrosion and leakage.

Many different kinds of outer covering are used on paper capacitors, the simplest being a tubular cardboard covering. Some types of paper capacitors are encased in very hard plastic. These types are very rugged and can be used over a much wider temperature range than can the tubular cardboard type. Figure 15(A) shows the construction of a tubular paper capacitor; part 15(B) shows a completed cardboard-encased capacitor.

Figure 15. - Paper capacitor.

A MICA CAPACITOR is made of metal foil plates that are separated by sheets of mica (the dielectric). The whole assembly is encased in molded plastic. Figure 16(A) shows a cut-away view of a mica capacitor. Because the capacitor parts are molded into a plastic case, corrosion and damage to the plates and dielectric are prevented. In addition, the molded plastic case makes the capacitor mechanically stronger. Various types of terminals are used on mica capacitors to connect them into circuits. These terminals are also molded into the plastic case.

Mica is an excellent dielectric and can withstand a higher voltage than can a paper dielectric of the same thickness. Common values of mica capacitors range from approximately 50 picofarads to 0.02 microfarad. Some different shapes of mica capacitors are shown in figure 16(B).

Figure 16. - Typical mica capacitors.

A CERAMIC CAPACITOR is so named because it contains a ceramic dielectric. One type of ceramic capacitor uses a hollow ceramic cylinder as both the form on which to construct the capacitor and as the dielectric material. The plates consist of thin films of metal deposited on the ceramic cylinder.

A second type of ceramic capacitor is manufactured in the shape of a disk. After leads are attached to each side of the capacitor, the capacitor is completely covered with an insulating moisture-proof coating. Ceramic capacitors usually range in value from 1 picofarad to 0.01 microfarad and may be used with voltages as high as 30,000 volts. Some different shapes of ceramic capacitors are shown in figure 17.

Figure 17. - Ceramic capacitors.

An ELECTROLYTIC CAPACITOR is used where a large amount of capacitance is required. As the name implies, an electrolytic capacitor contains an electrolyte. This electrolyte can be in the form of a liquid (wet electrolytic capacitor). The wet electrolytic capacitor is no longer in popular use due to the care needed to prevent spilling of the electrolyte.

A dry electrolytic capacitor consists essentially of two metal plates separated by the electrolyte. In most cases the capacitor is housed in a cylindrical aluminum container which acts as the negative terminal of the capacitor (see fig. 18). The positive terminal (or terminals if the capacitor is of the multisection type) is a lug (or lugs) on the bottom end of the container. The capacitance value(s) and the voltage rating of the capacitor are generally printed on the side of the aluminum case.

Figure 18. - Construction of an electrolytic capacitor.

An example of a multisection electrolytic capacitor is illustrated in figure 18(B). The four lugs at the end of the cylindrical aluminum container indicates that four electrolytic capacitors are enclosed in the can. Each section of the capacitor is electrically independent of the other sections. It is possible for one section to be defective while the other sections are still good. The can is the common negative connection to the four capacitors. Separate terminals are provided for the positive plates of the capacitors. Each capacitor is identified by an embossed mark adjacent to the lugs, as shown in figure 18(B). Note the identifying marks used on the electrolytic capacitor are the half moon, the triangle, the square, and no embossed mark. By looking at the bottom of the container and the identifying sheet pasted to the side of the container, you can easily identify the value of each section.

Internally, the electrolytic capacitor is constructed similarly to the paper capacitor. The positive plate consists of aluminum foil covered with an extremely thin film of oxide. This thin oxide film (which is formed by an electrochemical process) acts as the dielectric of the capacitor. Next to and in contact with the oxide is a strip of paper or gauze which has been impregnated with a paste-like electrolyte. The electrolyte acts as the negative plate of the capacitor. A second strip of aluminum foil is then placed against the electrolyte to provide electrical contact to the negative electrode (the electrolyte). When the three layers are in place they are rolled up into a cylinder as shown in figure 18(A).

An electrolytic capacitor has two primary disadvantages compared to a paper capacitor in that the electrolytic type is POLARIZED and has a LOW LEAKAGE RESISTANCE. This means that should the positive plate be accidentally connected to the negative terminal of the source, the thin oxide film dielectric will dissolve and the capacitor will become a conductor (i.e., it will short). The polarity of the terminals is normally marked on the case of the capacitor. Since an electrolytic capacitor is polarity sensitive, its use is ordinarily restricted to a dc circuit or to a circuit where a small ac voltage is superimposed on a dc voltage. Special electrolytic capacitors are available for certain ac applications, such as a motor starting capacitor. Dry electrolytic capacitors vary in size from about 4 microfarads to several thousand microfarads and have a working voltage of approximately 500 volts.

The type of dielectric used and its thickness govern the amount of voltage that can safely be applied to the electrolytic capacitor. If the voltage applied to the capacitor is high enough to cause the atoms of the dielectric material to become ionized, arcing between the plates will occur. In most other types of capacitors, arcing will destroy the capacitor. However, an electrolytic capacitor has the ability to be self-healing. If the arcing is small, the electrolytic will regenerate itself. If the arcing is too large, the capacitor will not self-heal and will become defective.

WATER CAPACITORS are an emerging new technology which act at once as a capacitor and also a fuel cell. When energized in the correct manner, water capacitors use pulsing electrostatic and magnetic  fields to electrically stress the covalent bonding that holds  Hydrogen and Oxygen atoms together as water. The result is the thermodynamically efficient release of Hydrogen fuel gases from water.

Water Capacitor

 

To learn more about water fuel cell technology see me earlier writings on this topic: http://www.alexpetty.com/2010/09/17/water-as-fuel-with-puharich-and-meyer/

OIL CAPACITORS are often used in high-power electronic equipment. An oil-filled capacitor is nothing more than a paper capacitor that is immersed in oil. Since oil impregnated paper has a high dielectric constant, it can be used in the production of capacitors having a high capacitance value. Many capacitors will use oil with another dielectric material to prevent arcing between the plates. If arcing should occur between the plates of an oil-filled capacitor, the oil will tend to reseal the hole caused by the arcing. Such a capacitor is referred to as a SELF-HEALING capacitor.

A VARIABLE CAPACITOR  is constructed in such manner that its value of capacitance can be varied. A typical variable capacitor (adjustable capacitor) is the rotor-stator type. It consists of two sets of metal plates arranged so that the rotor plates move between the stator plates. Air is the dielectric. As the position of the rotor is changed, the capacitance value is likewise changed. This type of capacitor is used for tuning most radio receivers. Its physical appearance and its symbol are shown in figure 19.

Figure 19. - Rotor-stator type variable capacitor.

Another type of variable capacitor (trimmer capacitor) and its symbol are shown in figure 20. This capacitor consists of two plates separated by a sheet of mica. A screw adjustment is used to vary the distance between the plates, thereby changing the capacitance.

Figure 20. - Trimmer capacitor.

 

SUMMARY

Before going on to the next chapter, study the below summary to be sure that you understand the important points of this chapter.

THE ELECTROSTATIC FIELD – When a charged body is brought close to another charged body, the bodies either attract or repel one another. (If the charges are alike they repel; if the charges are opposite they attract). The field that causes this effect is called the ELECTROSTATIC FIELD. The amount by which two charges attract or repel each other depends upon the size of the charges and the distance between the charges. The electrostatic field (force between two charged bodies) may be represented by lines of force drawn perpendicular to the charged surfaces. If an electron is placed in the field, it will move toward the positive charge.

CAPACITANCE – Capacitance is the property of a circuit which OPPOSES any CHANGE in the circuit VOLTAGE. The effect of capacitance may be seen in any circuit where the voltage is changing. Capacitance is usually defined as the ability of a circuit to store electrical energy. This energy is stored in an electrostatic field. The device used in an electrical circuit to store this charge (energy) is called a CAPACITOR. The basic unit of measurement of capacitance is the FARAD (F). A one-farad capacitor will store one coulomb of charge (energy) when a potential of one volt is applied across the capacitor plates. The farad is an enormously large unit of capacitance. More practical units are the microfarad (mF) or the picofarad (pF).

CAPACITOR – A capacitor is a physical device consisting of two pieces of conducting material separated by an insulating material. This insulating material is referred to as the DIELECTRIC. Because the dielectric is an insulator, NO current flows through the capacitor. If the dielectric breaks down and becomes a conductor, the capacitor can no longer hold a charge and is useless. The ability of a dielectric to hold a charge without breaking down is referred to as the dielectric strength. The measure of the ability of the dielectric material to store energy is called the dielectric constant. The dielectric constant is a relative value based on 1.0 for a vacuum.

CAPACITORS IN A DC CIRCUIT – When a capacitor is connected to the terminals of a battery, each plate of the capacitor becomes charged. The plate connected to the positive terminal loses electrons. Because this plate has a lack of electrons, it assumes a positive charge. The plate connected to the negative terminal gains electrons. Because the plate has an excess of electrons, it assumes a negative charge. This process continues until the charge across the plates equals the applied voltage. At this point current ceases to flow in the circuit. As long as nothing changes in the circuit, the capacitor will hold its charge and there will be no current in any part of the circuit. If the leads of the capacitor are now shorted together, current again flows in the circuit. Current will continue to flow until the charges on the two plates become equal. At this point, current ceases to flow. With a dc voltage source, current will flow in the circuit only long enough to charge (or discharge) the capacitor. Thus, a capacitor does NOT allow dc current to flow continuously in a circuit.

FACTORS AFFECTING CAPACITANCE – There are three factors affecting capacitance. One factor is the area of the plate surfaces. Increasing the area of the plate increases the capacitance. Another factor is the amount of space between the plates. The closer the plates, the greater will be the electrostatic field. A greater electrostatic field causes a greater capacitance. The plate spacing is determined by the thickness of the dielectric. The third factor affecting capacitance is the dielectric constant. The value of the dielectric constant is dependent upon the type of dielectric used.

WORKING VOLTAGE – The working voltage of a capacitor is the maximum voltage that can be steadily applied to the capacitor without the capacitor breaking down (shorting). The working voltage depends upon the type of material used as the dielectric (the dielectric constant) and the thickness of the dielectric.

CAPACITOR LOSSES – Power losses in a capacitor are caused by dielectric leakage and dielectric hysteresis. Dielectric leakage loss is caused by the leakage current through the resistance in the dielectric. Although this resistance is extremely high, a small amount of current does flow. Dielectric hysteresis may be defined as an effect in a dielectric material similar to the hysteresis found in a magnetic material.

RC TIME CONSTANT – The time required to charge a capacitor to 63.2 percent of the applied voltage, or to discharge the capacitor to 36.8 percent of its charge. The time constant (t) is equal to the product of the resistance and the capacitance. Expressed as a formula:

where t is in seconds, R is in ohms, and C is in farads.

CAPACITORS IN SERIES – The effect of wiring capacitors in series is to increase the distance between plates. This reduces the total capacitance of the circuit. Total capacitance for series connected capacitors may be computed by the formula:

If an electrical circuit contains only two series connected capacitors, C_T may be computed using the following formula:

CAPACITORS IN PARALLEL – The effect of wiring capacitors in parallel is to increase the plate area of the capacitors. Total capacitance (C_T) may be found using the formula:

TYPES OF CAPACITORS – Capacitors are manufactured in various forms and may be divided into two main classes-fixed capacitors and variable capacitors. A fixed capacitor is constructed to have a constant or fixed value of capacitance. A variable capacitor allows the capacitance to be varied or adjusted.

 

 

A TRANSFORMER is a device that transfers electrical energy from one circuit to another by electromagnetic induction (transformer action). The electrical energy is always transferred without a change in frequency, but may involve changes in magnitudes of voltage and current. Because a transformer works on the principle of electromagnetic induction, it must be used with an input source voltage that varies in amplitude. There are many types of power that fit this description; for ease of explanation and understanding, transformer action will be explained using an ac voltage as the input source.

Alternating current has certain advantages over direct current. One important advantage is that when AC is used, the voltage and current levels can be increased or decreased by means of a transformer.

As you may know, the amount of power used by the load of an electrical circuit is equal to the current (I) in the load times the voltage (V) across the load, or P = VI. If, for example, the load in an electrical circuit requires an input of 2 amperes at 10 volts (20 watts) and the source is capable of delivering only 1 ampere at 20 volts, the circuit could not normally be used with this particular source. However, if a transformer is connected between the source and the load, the voltage can be decreased (stepped down) to 10 volts and the current increased (stepped up) to 2 amperes. Notice in the above case that the power remains the same. That is, 20 volts times 1 ampere equals the same power as 10 volts times 2 amperes.

BASIC OPERATION OF A TRANSFORMER

In its most basic form a transformer consists of:

• A primary coil or winding.
• A secondary coil or winding.
• A core that supports the coils or windings.

Refer to the transformer circuit in video 1 as you read the following explanation: The primary winding is connected to a 60 hertz ac voltage source. The magnetic field (flux) builds up (expands) and collapses (contracts) about the primary winding. The expanding and contracting magnetic field around the primary winding cuts the secondary winding and induces an alternating voltage into the winding. This voltage causes alternating current to flow through the load. The voltage may be stepped up or down depending on the design of the primary and secondary windings.

Video 1. – Basic transformer action.

THE COMPONENTS OF A TRANSFORMER

Two coils of wire (called windings) are wound on some type of core material. In some cases the coils of wire are wound on a cylindrical or rectangular cardboard form. In effect, the core material is air and the transformer is called an AIR-CORE TRANSFORMER. Transformers used at low frequencies, such as 60 hertz and 400 hertz, require a core of low-reluctance magnetic material, usually iron. This type of transformer is called an IRON-CORE TRANSFORMER. Most power transformers are of the iron-core type. The principle parts of a transformer and their functions are:

• The CORE, which provides a path for the magnetic lines of flux.
• The PRIMARY WINDING, which receives energy from the ac source.
• The SECONDARY WINDING, which receives energy from the primary winding and delivers it to the load.
• The ENCLOSURE, which protects the above components from dirt, moisture, and mechanical damage.

CORE CHARACTERISTICS

The composition of a transformer core depends on such factors as voltage, current, and frequency. Size limitations and construction costs are also factors to be considered. Commonly used core materials are air, soft iron, and steel. Each of these materials is suitable for particular applications and unsuitable for others. Generally, air-core transformers are used when the voltage source has a high frequency (above 20 kHz). Iron-core transformers are usually used when the source frequency is low (below 20 kHz). A soft-iron-core transformer is very useful where the transformer must be physically small, yet efficient. The iron-core transformer provides better power transfer than does the air-core transformer. A transformer whose core is constructed of laminated sheets of steel dissipates heat readily; thus it provides for the efficient transfer of power. The majority of transformers you will encounter in Navy equipment contain laminated-steel cores. These steel laminations (see figure 1) are insulated with a nonconducting material, such as varnish, and then formed into a core. It takes about 50 such laminations to make a core an inch thick. The purpose of the laminations is to reduce certain losses which will be discussed later in this chapter. An important point to remember is that the most efficient transformer core is one that offers the best path for the most lines of flux with the least loss in magnetic and electrical energy.

Figure 1. - hallow laminated transformer core

There are two main shapes of cores used in laminated-steel-core transformers. One is the HOLLOW-CORE, so named because the core is shaped with a hollow square through the center. Figure 1 illustrates this shape of core. Notice that the core is made up of many laminations of steel. Figure 2 illustrates how the transformer windings are wrapped around both sides of the core.

Figure 2. - Windings wrapped around laminations.

Shell-Core Transformers

The most popular and efficient transformer core is the SHELL CORE, as illustrated in figure 3. As shown, each layer of the core consists of E- and I-shaped sections of metal. These sections are butted together to form the laminations. The laminations are insulated from each other and then pressed together to form the core.

Figure 3. - E and I Laminations of the Shell Core

TRANSFORMER WINDINGS

As stated above, the transformer consists of two coils called WINDINGS which are wrapped around a core. The transformer operates when a source of ac voltage is connected to one of the windings and a load device is connected to the other. The winding that is connected to the source is called the PRIMARY WINDING. The winding that is connected to the load is called the SECONDARY WINDING. (Note: In this chapter the terms “primary winding” and “primary” are used interchangeably; the term: “secondary winding” and “secondary” are also used interchangeably.)

Figure 4 shows an expanded view of a shell-type transformer. The primary is wound in layers directly on a rectangular cardboard form.

Figure 4. - Expanded view of shell-type transformer construction.

In the transformer shown in the cutaway view in figure 5, the primary consists of many turns of relatively small wire. The wire is coated with varnish so that each turn of the winding is insulated from every other turn. In a transformer designed for high-voltage applications, sheets of insulating material, such as paper, are placed between the layers of windings to provide additional insulation.

Figure 5. - Cutaway view of shell-type core with windings.

When the primary winding is completely wound, it is wrapped in insulating paper or cloth. The secondary winding is then wound on top of the primary winding. After the secondary winding is complete, it too is covered with insulating paper. Next, the E and I sections of the iron core are inserted into and around the windings as shown.

The leads from the windings are normally brought out through a hole in the enclosure of the transformer. Sometimes, terminals may be provided on the enclosure for connections to the windings. The figure shows four leads, two from the primary and two from the secondary. These leads are to be connected to the source and load, respectively.

SCHEMATIC SYMBOLS FOR TRANSFORMERS

Figure 6 shows typical schematic symbols for transformers. The symbol for an air-core transformer is shown in figure 6(A). Parts (B) and (C) show iron-core transformers. The bars between the coils are used to indicate an iron core. Frequently, additional connections are made to the transformer windings at points other than the ends of the windings. These additional connections are called TAPS. When a tap is connected to the center of the winding, it is called a CENTER TAP. Figure 6(C) shows the schematic representation of a center-tapped iron-core transformer.

Figure 6. - Schematic symbols for various types of transformers.

HOW A TRANSFORMER WORKS

Up to this point the chapter has presented the basics of the transformer including transformer action, the transformer’s physical characteristics, and how the transformer is constructed. Now you have the necessary knowledge to proceed into the theory of operation of a transformer.

NO-LOAD CONDITION

You have learned that a transformer is capable of supplying voltages which are usually higher or lower than the source voltage. This is accomplished through mutual induction, which takes place when the changing magnetic field produced by the primary voltage cuts the secondary winding.

A no-load condition is said to exist when a voltage is applied to the primary, but no load is connected to the secondary, as illustrated by video 2. Because of the open switch, there is no current flowing in the secondary winding. With the switch open and an ac voltage applied to the primary, there is, however, a very small amount of current called EXCITING CURRENT flowing in the primary. Essentially, what the exciting current does is “excite” the coil of the primary to create a magnetic field. The amount of exciting current is determined by three factors: (1) the amount of voltage applied (E_a), (2) the resistance (R) of the primary coil’s wire and core losses, and (3) the X_L which is dependent on the frequency of the exciting current. These last two factors are controlled by transformer design.

Video 2. – Transformer under no-load conditions.

This very small amount of exciting current serves two functions:

• Most of the exciting energy is used to maintain the magnetic field of the primary.
• A small amount of energy is used to overcome the resistance of the wire and core losses which are dissipated in the form of heat (power loss).

Exciting current will flow in the primary winding at all times to maintain this magnetic field, but no transfer of energy will take place as long as the secondary circuit is open.

PRODUCING A COUNTER EMF

When an alternating current flows through a primary winding, a magnetic field is established around the winding. As the lines of flux expand outward, relative motion is present, and a counter emf is induced in the winding. This is the same counter emf that you learned about in the chapter on inductors. Flux leaves the primary at the north pole and enters the primary at the south pole. The counter emf induced in the primary has a polarity that opposes the applied voltage, thus opposing the flow of current in the primary. It is the counter emf that limits exciting current to a very low value.

INDUCING A VOLTAGE IN THE SECONDARY

To visualize how a voltage is induced into the secondary winding of a transformer, again refer to video 2. As the exciting current flows through the primary, magnetic lines of force are generated.

During the time current is increasing in the primary, magnetic lines of force expand outward from the primary and pass over the  secondary windings. As you remember, a voltage is induced into a coil when magnetic lines moves over windings. Therefore, the a charge pressure (voltage) moving current in the primary causes a charge pressure (voltage) to be induced in the secondary by the action of the magnetic fields relative movement over the windings of the secondary side.

PRIMARY AND SECONDARY PHASE RELATIONSHIP

The secondary voltage of a simple transformer may be either in phase or out of phase with the primary voltage. This depends on the direction in which the windings are wound and the arrangement of the connections to the external circuit (load). Simply, this means that the two voltages may rise and fall together or one may rise while the other is falling.

Transformers in which the secondary voltage is in phase with the primary are referred to as LIKE-WOUND transformers, while those in which the voltages are 180 degrees out of phase are called UNLIKE-WOUND transformers.

Dots are used to indicate points on a transformer schematic symbol that have the same instantaneous polarity (points that are in phase).

The use of phase-indicating dots is illustrated in figure 7. In part (A) of the figure, both the primary and secondary windings are wound from top to bottom in a clockwise direction, as viewed from above the windings. When constructed in this manner, the top lead of the primary and the top lead of the secondary have the SAME polarity. This is indicated by the dots on the transformer symbol. A lack of phasing dots indicates a reversal of polarity.

Figure 7. - Instantaneous polarity depends on direction of winding.

Part (B) of the figure illustrates a transformer in which the primary and secondary are wound in opposite directions. As viewed from above the windings, the primary is wound in a clockwise direction from top to bottom, while the secondary is wound in a counterclockwise direction. Notice that the top leads of the primary and secondary have OPPOSITE polarities. This is indicated by the dots being placed on opposite ends of the transformer symbol. Thus, the polarity of the voltage at the terminals of the secondary of a transformer depends on the direction in which the secondary is wound with respect to the primary.

COEFFICIENT OF COUPLING

The COEFFICIENT OF COUPLING of a transformer is dependent on the portion of the total flux lines that cuts both primary and secondary windings.

Ideally, all the flux lines generated by the primary should cut the secondary, and all the lines of the flux generated by the secondary should cut the primary.

The coefficient of coupling would then be one (unity), and maximum energy would be transferred from the primary to the secondary. Practical power transformers use high-permeability silicon steel cores and close spacing between the windings to provide a high coefficient of coupling.

Lines of flux generated by one winding which do not link with the other winding are called LEAKAGE FLUX. Since leakage flux generated by the primary does not cut the secondary, it cannot induce a voltage into the secondary.

The voltage induced into the secondary is therefore less than it would be if the leakage flux did not exist. Since the effect of leakage flux is to lower the voltage induced into the secondary, the effect can be duplicated by assuming an inductor to be connected in series with the primary. This series

LEAKAGE INDUCTANCE is assumed to drop part of the applied voltage, leaving less voltage across the primary.

TURNS AND VOLTAGE RATIOS

The total voltage induced into the secondary winding of a transformer is determined mainly by the RATIO of the number of turns in the primary to the number of turns in the secondary, and by the amount of voltage applied to the primary. Refer to figure 8. Part (A) of the figure shows a transformer whose primary consists of ten turns of wire and whose secondary consists of a single turn of wire. You know that as lines of flux generated by the primary expand and collapse, they cut BOTH the ten turns of the primary and the single turn of the secondary. Since the length of the wire in the secondary is approximately the same as the length of the wire in each turn in the primary, EMF INDUCED INTO THE SECONDARY WILL BE THE

SAME AS THE EMF INDUCED INTO EACH TURN IN THE PRIMARY. This means that if the voltage applied to the primary winding is 10 volts, the counter emf in the primary is almost 10 volts. Thus, each turn in the primary will have an induced counter emf of approximately one-tenth of the total applied voltage, or one volt. Since the same flux lines cut the turns in both the secondary and the primary, each turn will have an emf of one volt induced into it. The transformer in part (A) of figure 8 has only one turn in the secondary, thus, the emf across the secondary is one volt.

Figure 8. - Transformer turns and voltage ratios.

The transformer represented in part (B) of figure 8 has a ten-turn primary and a two-turn secondary. Since the flux induces one volt per turn, the total voltage across the secondary is two volts. Notice that the volts per turn are the same for both primary and secondary windings.

Since the counter emf in the primary is equal (or almost) to the applied voltage, a proportion may be set up to express the value of the voltage induced in terms of the voltage applied to the primary and the number of turns in each winding. This proportion also shows the relationship between the number of turns in each winding and the voltage across each winding. This proportion is expressed by the equation:

relationship between the number of turns in each winding and the voltage across each winding

Notice the equation shows that the ratio of secondary voltage to primary voltage is equal to the ratio of secondary turns to primary turns.

The equation can be written as:

ratio of secondary voltage to primary voltage is equal to the ratio of secondary turns to primary turns

The following formulas are derived from the above equation:

transposition equations

So, if any three of the quantities in the above formulas are known, the fourth quantity can be calculated.

Example: A transformer has 200 turns in the primary, 50 turns in the secondary, and 120 volts applied to the primary (E_p). What is the voltage across the secondary (E _s)?

solving for secondary voltage

Example: There are 400 turns of wire in an iron-core coil. If this coil is to be used as the primary of a transformer, how many turns must be wound on the coil to form the secondary winding of the transformer to have a secondary voltage of one volt if the primary voltage is five volts?

determining needed number of turns on secondary side given primary side characteristics

Note: The ratio of the voltage (5:1) is equal to the turns ratio (400:80). Sometimes, instead of specific values, you are given a turns or voltage ratio. In this case, you may assume any value for one of the voltages (or turns) and compute the other value from the ratio. For example, if a turn ratio is given as 6:1, you can assume a number of turns for the primary and compute the secondary number of turns (60:10, 36:6, 30:5, etc.).

The transformer in each of the above problems has fewer turns in the secondary than in the primary. As a result, there is less voltage across the secondary than across the primary. A transformer in which the voltage across the secondary is less than the voltage across the primary is called a STEP-DOWN transformer. The ratio of a four-to-one step-down transformer is written as 4:1. A transformer that has fewer turns in the primary than in the secondary will produce a greater voltage across the secondary than the voltage applied to the primary. A transformer in which the voltage across the secondary is greater than the voltage applied to the primary is called a STEP-UP transformer. The ratio of a one-to-four step-up transformer should be written as 1:4. Notice in the two ratios that the value of the primary winding is always stated first.

EFFECT OF A LOAD

When a load device is connected across the secondary winding of a transformer, current flows through the secondary and the load. The magnetic field produced by the current in the secondary interacts with the magnetic field produced by the current in the primary. This interaction results from the mutual inductance between the primary and secondary windings.

MUTUAL FLUX

The total flux in the core of the transformer is common to both the primary and secondary windings. It is also the means by which energy is transferred from the primary winding to the secondary winding. Since this flux links both windings, it is called MUTUAL FLUX. The inductance which produces this flux is also common to both windings and is called mutual inductance.

Figure 9 shows the flux produced by the currents in the primary and secondary windings of a transformer when source current is flowing in the primary winding.

Figure 9. - Simple transformer indicating primary- and secondary-winding flux relationship.

Video 3. Step-down transformer with 20:1 turns ratio.

When a load resistance is connected to the secondary winding, the voltage induced into the secondary winding causes current to flow in the secondary winding. This current produces a flux field about the secondary (shown as broken lines) which is in opposition to the flux field about the primary (Lenz’s law). Thus, the flux about the secondary cancels some of the flux about the primary. With less flux surrounding the primary, the counter emf is reduced and more current is drawn from the source. The additional current in the primary generates more lines of flux, nearly reestablishing the original number of total flux lines.

TURNS AND CURRENT RATIOS

The number of flux lines developed in a core is proportional to the magnetizing force (IN AMPERE-TURNS) of the primary and secondary windings.

The ampere-turn (I X N) is a measure of magnetomotive force; it is defined as the magnetomotive force developed by one ampere of current flowing in a coil of one turn. The flux which exists in the core of a transformer surrounds both the primary and secondary windings. Since the flux is the same for both windings, the ampere-turns in both the primary and secondary windings must be the same.

Therefore:

The ampere-turn (I X N) is a measure of magnetomotive force

By dividing both sides of the equation by I_pN _s, you obtain:

Notice the equations show the current ratio to be the inverse of the turns ratio and the voltage ratio. This means, a transformer having less turns in the secondary than in the primary would step down the voltage, but would step up the current. Example: A transformer has a 6:1 voltage ratio.

current ratio is the inverse of the turns ratio and the voltage ratio

For example:

Find the current in the secondary if the current in the primary is 200 milliamperes

solving for current in the secondary given current in the primary

The above example points out that although the voltage across the secondary is one-sixth the voltage across the primary, the current in the secondary is six times the current in the primary.

The above equations can be looked at from another point of view.

The expression:

transformer turns ratio

is called the transformer TURNS RATIO and may be expressed as a single factor. Remember, the turns ratio indicates the amount by which the transformer increases or decreases the voltage applied to the primary. For example, if the secondary of a transformer has two times as many turns as the primary, the voltage induced into the secondary will be two times the voltage across the primary. If the secondary has one-half as many turns as the primary, the voltage across the secondary will be one-half the voltage across the primary. However, the turns ratio and the current ratio of a transformer have an inverse relationship. Thus, a 1:2 step-up transformer will have one-half the current in the secondary as in the primary. A 2:1 step-down transformer will have twice the current in the secondary as in the primary.

Example: A transformer with a turns ratio of 1:12 has 3 amperes of current in the secondary. What is the value of current in the primary?

solve for current in primary given turns ratio and current in secondary

POWER RELATIONSHIP BETWEEN PRIMARY AND SECONDARY WINDINGS

As just explained, the turns ratio of a transformer affects current as well as voltage. If voltage is doubled in the secondary, current is halved in the secondary. Conversely, if voltage is halved in the secondary, current is doubled in the secondary. In this manner, all the power delivered to the primary by the source is also delivered to the load by the secondary (minus whatever power is consumed by the transformer in the form of losses). Refer again to the transformer illustrated in figure 9 and video 3.

The turns ratio is 20:1. If the input to the primary is 0.1 ampere at 300 volts, the power in the primary is P = E X I = 30 watts. If the transformer has no losses, 30 watts is delivered to the secondary. The secondary steps down the voltage to 15 volts and steps up the current to 2 amperes. Thus, the power delivered to the load by the secondary is P = E X I = 15 volts X 2 amps = 30 watts.

The reason for this is that when the number of turns in the secondary is decreased, the opposition to the flow of the current is also decreased.

Hence, more current will flow in the secondary. If the turns ratio of the transformer is increased to 1:2, the number of turns on the secondary is twice the number of turns on the primary. This means the opposition to current is doubled. Thus, voltage is doubled, but current is halved due to the increased opposition to current in the secondary. The important thing to remember is that with the exception of the power consumed within the transformer, all power delivered to the primary by the source will be delivered to the load. The form of the power may change, but the power in the secondary almost equals the power in the primary.

power in the secondary almost equals the power in the primary

TRANSFORMER LOSSES

Practical power transformers, although highly efficient, are not perfect devices. Small power transformers used in electrical equipment have an 80 to 90 percent efficiency range, while large, commercial powerline transformers may have efficiencies exceeding 98 percent.

The total power loss in a transformer is a combination of three types of losses. One loss is due to the dc resistance in the primary and secondary windings. This loss is called COPPER loss or I²R loss.

The two other losses are due to EDDY CURRENTS and to HYSTERESIS in the core of the transformer. Copper loss, eddy-current loss, and hysteresis loss result in undesirable conversion of electrical energy into heat energy.

Copper Loss

Whenever current flows in a conductor, power is dissipated in the resistance of the conductor in the form of heat. The amount of power dissipated by the conductor is directly proportional to the resistance of the wire, and to the square of the current through it. The greater the value of either resistance or current, the greater is the power dissipated. The primary and secondary windings of a transformer are usually made of low-resistance copper wire.

The resistance of a given winding is a function of the diameter of the wire and its length. Copper loss can be minimized by using the proper diameter wire. Large diameter wire is required for high-current windings, whereas small diameter wire can be used for low-current windings.

Eddy-Current Loss

The core of a transformer is usually constructed of some type of ferromagnetic material because it is a good conductor of magnetic lines of flux.

Whenever the primary of an iron-core transformer is energized by an alternating-current source, a fluctuating magnetic field is produced. This magnetic field cuts the conducting core material and induces a voltage into it. The induced voltage causes random currents to flow through the core which dissipates power in the form of heat. These undesirable currents are called

EDDY CURRENTS.

To minimize the loss resulting from eddy currents, transformer cores are LAMINATED. Since the thin, insulated laminations do not provide an easy path for current, eddy-current losses are greatly reduced.

Hysteresis Loss

When a magnetic field is passed through a core, the core material becomes magnetized. To become magnetized, the domains within the core must align themselves with the external field. If the direction of the field is reversed, the domains must turn so that their poles are aligned with the new direction of the external field.

Power transformers normally operate from either 60 Hz, or 400 Hz alternating current. Each tiny domain must realign itself twice during each cycle, or a total of 120 times a second when 60 Hz alternating current is used. The energy used to turn each domain is dissipated as heat within the iron core. This loss, called HYSTERESIS LOSS, can be thought of as resulting from molecular friction. Hysteresis loss can be held to a small value by proper choice of core materials.

TRANSFORMER EFFICIENCY

To compute the efficiency of a transformer, the input power to and the output power from the transformer must be known. The input power is equal to the product of the voltage applied to the primary and the current in the primary. The output power is equal to the product of the voltage across the secondary and the current in the secondary. The difference between the input power and the output power represents a power loss. You can calculate the percentage of efficiency of a transformer by using the standard efficiency formula shown below:

transformer efficiency

Example: If the input power to a transformer is 650 watts and the output power is 610 watts, what is the efficiency?

transformer efficiency given input and output power

Hence, the efficiency is approximately 93.8 percent, with approximately 40 watts being wasted due to heat losses

TRANSFORMER RATINGS

When a transformer is to be used in a circuit, more than just the turns ratio must be considered. The voltage, current, and power-handling capabilities of the primary and secondary windings must also be considered.

The maximum voltage that can safely be applied to any winding is determined by the type and thickness of the insulation used. When a better (and thicker) insulation is used between the windings, a higher maximum voltage can be applied to the windings.

The maximum current that can be carried by a transformer winding is determined by the diameter of the wire used for the winding. If current is excessive in a winding, a higher than ordinary amount of power will be dissipated by the winding in the form of heat. This heat may be sufficiently high to cause the insulation around the wire to break down. If this happens, the transformer may be permanently damaged.

The power-handling capacity of a transformer is dependent upon its ability to dissipate heat. If the heat can safely be removed, the power-handling capacity of the transformer can be increased. This is sometimes accomplished by immersing the transformer in oil, or by the use of cooling fins. The power-handling capacity of a transformer is measured in either the volt-ampere unit or the watt unit.

Two common power generator frequencies (60 hertz and 400 hertz) have been mentioned, but the effect of varying frequency has not been discussed.

If the frequency applied to a transformer is increased, the inductive reactance of the windings is increased, causing a greater ac voltage drop across the windings and a lesser voltage drop across the load. However, an increase in the frequency applied to a transformer should not damage it. But, if the frequency applied to the transformer is decreased, the reactance of the windings is decreased and the current through the transformer winding is increased. If the decrease in frequency is enough, the resulting increase in current will damage the transformer. For this reason a transformer may be used at frequencies above its normal operating frequency, but not below that frequency.

TYPES AND APPLICATIONS OF TRANSFORMERS

The transformer has many useful applications in an electrical circuit. A brief discussion of some of these applications will help you recognize the importance of the transformer in electricity and electronics.

POWER TRANSFORMERS

Power transformers are used to supply voltages to the various circuits in electrical equipment. These transformers have two or more windings wound on a laminated iron core. The number of windings and the turns per winding depend upon the voltages that the transformer is to supply. Their coefficient of coupling is 0.95 or more.

You can usually distinguish between the high-voltage and low-voltage windings in a power transformer by measuring the resistance. The low-voltage winding usually carries the higher current and therefore has the larger diameter wire. This means that its resistance is less than the resistance of the high-voltage winding, which normally carries less current and therefore may be constructed of smaller diameter wire.

So far you have learned about transformers that have but one secondary winding. The typical power transformer has several secondary windings, each providing a different voltage. The schematic symbol for a typical power-supply transformer is shown in figure 5-12. For any given voltage across the primary, the voltage across each of the secondary windings is determined by the number of turns in each secondary. A winding may be center-tapped like the secondary 350 volt winding shown in the figure. To center tap a winding means to connect a wire to the center of the coil, so that between this center tap and either terminal of the winding there appears one-half of the voltage developed across the entire winding. Most power transformers have colored leads so that it is easy to distinguish between the various windings to which they are connected. Carefully examine the figure which also illustrates the color code for a typical power transformer. Usually, red is used to indicate the high-voltage leads, but it is possible for a manufacturer to use some other color(s).

Figure 10. - Schematic diagram of a typical power transformer.

There are many types of power transformers. They range in size from the huge transformers weighing several tons-used in power substations of commercial power companies-to very small ones weighing as little as a few ounces-used in electronic equipment.

AUTOTRANSFORMERS

It is not necessary in a transformer for the primary and secondary to be separate and distinct windings. Figure 11 is a schematic diagram of what is known as an AUTOTRANSFORMER. Note that a single coil of wire is “tapped” to produce what is electrically a primary and secondary winding. The voltage across the secondary winding has the same relationship to the voltage across the primary that it would have if they were two distinct windings. The movable tap in the secondary is used to select a value of output voltage, either higher or lower than E _p, within the range of the transformer. That is, when the tap is at point A, E_s is less than E_p; when the tap is at point B, E_s is greater than E _p.

Figure 11. – Schematic diagram of an autotransformer.

There are many types of power transformers. They range in size from the huge transformers weighing several tons-used in power substations of commercial power companies-to very small ones weighing as little as a few ounces-used in electronic equipment.

AUTOTRANSFORMERS

It is not necessary in a transformer for the primary and secondary to be separate and distinct windings. Figure 5-13 is a schematic diagram of what is known as an AUTOTRANSFORMER. Note that a single coil of wire is “tapped” to produce what is electrically a primary and secondary winding. The voltage across the secondary winding has the same relationship to the voltage across the primary that it would have if they were two distinct windings. The movable tap in the secondary is used to select a value of output voltage, either higher or lower than E _p, within the range of the transformer. That is, when the tap is at point A, E_s is less than E_p; when the tap is at point B, E_s is greater than E _p.

Figure 11. – Schematic diagram of an autotransformer.

Figure 11. - Schematic diagram of an autotransformer.

AUDIO-FREQUENCY TRANSFORMERS

Audio-frequency (af) transformers are used in af circuits as coupling devices. Audio-frequency transformers are designed to operate at frequencies in the audio frequency spectrum (generally considered to be 15 Hz to 20kHz).

They consist of a primary and a secondary winding wound on a laminated iron or steel core. Because these transformers are subjected to higher frequencies than are power transformers, special grades of steel such as silicon steel or special alloys of iron that have a very low hysteresis loss must be used for core material. These transformers usually have a greater number of turns in the secondary than in the primary; common step-up ratios being 1 to 2 or 1 to 4. With audio transformers the impedance of the primary and secondary windings is as important as the ratio of turns, since the transformer selected should have its impedance match the circuits to which it is connected.

RADIO-FREQUENCY TRANSFORMERS

Radio-frequency (rf) transformers are used to couple circuits to which frequencies above 20,000 Hz are applied. The windings are wound on a tube of nonmagnetic material, have a special powdered-iron core, or contain only air as the core material. In standard broadcast radio receivers, they operate in a frequency range of from 530 kHz to 1550 kHz. In a short-wave receiver, rf transformers are subjected to frequencies up to about 20 MHz – in radar, up to and even above 200 MHz.

IMPEDANCE-MATCHING TRANSFORMERS

For maximum or optimum transfer of power between two circuits, it is necessary for the impedance of one circuit to be matched to that of the other circuit. One common impedance-matching device is the transformer.

To obtain proper matching, you must use a transformer having the correct turns ratio. The number of turns on the primary and secondary windings and the impedance of the transformer have the following mathematical relationship

relationship between turns ratio and impedance

Because of this ability to match impedances, the impedance-matching transformer is widely used in electronic equipment.

SAFETY

EFFECTS OF CURRENT ON THE BODY

Before learning safety precautions, you should look at some of the possible effects of electrical current on the human body. The following table lists some of the probable effects of electrical current on the human body.

Note in the above chart that a current as low as 4 mA can be expected to cause a reflex action in the victim, usually causing the victim to jump away from the wire or other component supplying the current. While the current should produce nothing more than a tingle of the skin, the quick action of trying to get away from the source of this irritation could produce other effects (such as broken limbs or even death if a severe enough blow was received at a vital spot by the shock victim).

It is important for you to recognize that the resistance of the human body cannot be relied upon to prevent a fatal shock from a voltage as low as 115 volts or even less. Fatalities caused by human contact with 30 volts have been recorded. Tests have shown that body resistance under unfavorable conditions may be as low as 300 ohms, and possibly as low as 100 ohms (from temple to temple) if the skin is broken. Generally direct current is not considered as dangerous as an equal value of alternating current. This is evidenced by the fact that reasonably safe “let-go currents” for 60 hertz, alternating current, are 9.0 milliamperes for men and 6.0 milliamperes for women, while the corresponding values for direct current are 62.0 milliamperes for men and 41.0 milliamperes for women. Remember, the above table is a fist of probable effects. The actual severity of effects will depend on such things as the physical condition of the work area, the physiological condition and resistance of the body, and the area of the body through which the current flows. Thus, based on the above information, you MUST consider every voltage as being dangerous.

ELECTRIC SHOCK

Electric shock is a jarring, shaking sensation you receive from contact with electricity. You usually feel like you have received a sudden blow. If the voltage and resulting current are sufficiently high, you may become unconscious. Severe burns may appear on your skin at the place of contact; muscular spasms may occur, perhaps causing you to clasp the apparatus or wire which caused the shock and be unable to turn it loose.

RESCUE AND CARE OF SHOCK VICTIMS

The following procedures are recommended for rescue and care of electric shock victims:

Remove the victim from electrical contact at once, but DO NOT endanger yourself. You can do this by:

1) Throwing the switch if it is nearby

2) Cutting the cable or wires to the apparatus, using an ax with a wooden handle while taking care to protect your eyes from the flash with the wires are severed

3) Using a dry stick, rope, belt, coat, blanket, shirt or any other electrically non-conductive material to drag or push the victim to safety.

Determine whether the victim is breathing. If the victim is not breathing, you must apply artificial ventilation (respiration) without delay, even though the victim may appear to be lifeless. DO NOT STOP ARTIFICIAL RESPIRATION UNTIL MEDICAL AUTHORITY PRONOUNCES THE VICTIM DEAD.

Lay the victim face up. The feet should be about 12 inches higher than the head. Chest or head injuries require the head to be slightly elevated. If there is vomiting or if facial injuries have occurred which cause bleeding into the throat, the victim should be placed on the stomach with the head turned to one side and 6 to 12 inches lower than the feet.

Keep the victim warm. The injured person’s body heat must be conserved. Keep the victim covered with one or more blankets, depending on the weather and the person’s exposure to the elements. Artificial means of warming, such as hot water bottles should not be used.

Drugs, food, and liquids should not be administered if medical attention will be available within a short time. If necessary, liquids may be administered. Small amounts of warm salt water, tea or coffee should be used. Alcohol, opiates, and other depressant substances must never be administered.

Send for medical personnel (a doctor if available) at once, but do NOT under any circumstances leave the victim until medical help arrives.

SAFETY PRECAUTIONS FOR PREVENTING ELECTRIC SHOCK

You must observe the following safety precautions when working on electrical equipment:

• Never work alone. Another person may save your life if you receive an electric shock.
• Work on energized circuits ONLY WHEN ABSOLUTELY NECESSARY.
• Power should be tagged out, using approved tagout procedures, at the nearest source of electricity.
• Stand on an approved insulating material, such as a rubber mat.
• Discharge power capacitors before working on deenergized equipment. Remember, a capacitor is an electrical power storage device.
• When you must work on an energized circuit, wear rubber gloves and cover as much of your body as practical with an insulating material
• (such as shirt sleeves). This is especially important when you are working in a warm space where sweating may occur.
• Deenergize equipment prior to hooking up or removing test equipment.
• Work with only one hand inside the equipment. Keep the other hand clear of all obstacles that may provide a path, such as a ground, for current to flow.
• Wear safety goggles. Sparks could damage your eyes, as could the cooling liquids in some components such as transformers should they overheat and explode.
• Keep a cool head and think about the possible consequences before performing any action. Carelessness is the cause of most accidents.
• Remember the best technician is NOT necessarily the fastest one, but the one who will be on the job tomorrow.

SUMMARY

For future reference, the important points given above have been summarized below:

BASIC TRANSFORMER – The basic transformer is an electrical device that transfers alternating-current energy from one circuit to another circuit by magnetic coupling of the primary and secondary windings of the transformer. This is accomplished through mutual inductance (M). The coefficient of coupling (K) of a transformer is dependent upon the size and shape of the coils, their relative positions, and the characteristic of the core between the two coils. An ideal transformer is one where all the magnetic lines of flux produced by the primary cut the entire secondary. The higher the K of the transformer, the higher is the transfer of the energy.

The voltage applied to the primary winding causes current to flow in the primary.

This current generates a magnetic field, generating a counter emf (cemf) which has the opposite phase to that of the applied voltage. The magnetic field generated by the current in the primary also cuts the secondary winding and induces a voltage in this winding.

TRANSFORMER CONSTRUCTION – A TRANSFORMER consists of two coils of insulated wire wound on a core. The primary winding is usually wound onto a form, then wrapped with an insulating material such as paper or cloth. The secondary winding is then wound on top of the primary and both windings are wrapped with insulating material. The windings are then fitted onto the core of the transformer. Cores come in various shapes and materials. The most common materials are air, soft iron, and laminated steel.

The most common types of transformers are the shell-core and the hollow-core types. The type and shape of the core is dependent on the intended use of the transformer and the voltage applied to the current in the primary winding.

EXCITING CURRENT – When voltage is applied to the primary of a transformer, exciting current flows in the primary.

The current causes a magnetic field to be set up around both the primary and the secondary windings. The moving flux causes a voltage to be induced into the secondary winding, countering the effects of the counter emf in the primary.

PHASE – When the secondary winding is connected to a load, causing current to flow in the secondary, the magnetic field decreases momentarily. The primary then draws more current, restoring the magnetic field to almost its original magnitude. The phase of the current flowing in the secondary circuit is dependent upon the phase of the voltage impressed across the primary and the direction of the winding of the secondary.

If the secondary were wound in the same direction as the primary, the phase would be the same. If wound opposite to the primary, the phase would be reversed.

This is shown on a schematic drawing by the use of phasing dots. The dots mean that the leads of the primary and secondary have the same phase. The lack of phasing dots on a schematic means a phase reversal.

TURNS RATIO – The TURNS RATIO of a transformer is the ratio of the number of turns of wire in the primary winding to the number of turns in the secondary winding. When the turns ratio is stated, the number representing turns on the primary is always stated first. For example, a 1:2 turns ratio means the secondary has twice the number of turns as the primary. In this example, the voltage across the secondary is two times the voltage applied to the primary.

POWER AND CURRENT RATIOS – The power and current ratios of a transformer are dependent on the fact that power delivered to the secondary is always equal to the power delivered to the primary minus the losses of the transformer. This will always be true, regardless of the number of secondary windings. Using the law of power and current, it can be stated that current through the transformer is the inverse of the voltage or turns ratio, with power remaining the same or less, regardless of the number of secondaries.

TRANSFORMER LOSSES – Transformer losses have two sources-copper loss and magnetic loss. Copper losses are caused by the resistance of the wire (I²R). Magnetic losses are caused by eddy currents and hysteresis in the core. Copper loss is a constant after the coil has been wound and therefore a measureable loss. Hysteresis loss is constant for a particular voltage and current. Eddy-current loss, however, is different for each frequency passed through the transformer.

TRANSFORMER EFFICIENCY – The amplitude of the voltage induced in the secondary is dependent upon the efficiency of the transformer and the turns ratio. The efficiency of a transformer is related to the power losses in the windings and core of the transformer. Efficiency (in percent) equals P_out/P_in X 100. A perfect transformer would have an efficiency of 1.0 or 100%.

POWER TRANSFORMER – A transformer with two or more windings wound on a laminated iron core. The transformer is used to supply stepped up and stepped down values of voltage to the various circuits in electrical equipment.

AUTOTRANSFORMER – A transformer with a single winding in which the entire winding can be used as the primary and part of the winding as the secondary, or part of the winding can be used as the primary and the entire winding can be used as the secondary.

AUDIO-FREQUENCY TRANSFORMER – A transformer used in audio-frequency circuits to transfer af signals from one circuit to another.

RADIO-FREQUENCY TRANSFORMER – A transformer used in a radio-frequency circuit to transfer rf signals from one circuit to another.

IMPEDANCE-MATCHING TRANSFORMER – A transformer used to match the impedance of the source and the impedance of the load. The mathematical relationship of the turns and impedance of the transformer is expressed by the equation:

USEFUL AC FORMULAS

PERIOD TIME (t)

FREQUENCY (f)

AVERAGE VOLTAGE OR CURRENT

EFFECTIVE VALUE OF VOLTAGE OR CURRENT

MAXIMUM VOLTAGE OR CURRENT

OHM’S LAW OF AC CIRCUIT CONTAINING ONLY RESISTANCE

L/R TIME CONSTANT (TC)

MUTUAL INDUCTANCE (M)

TOTAL INDUCTANCE (L_T) Series without magnetic coupling

TOTAL INDUCTANCE (L_T) PARALLEL (No magnetic coupling)

CAPACITANCE (C)

RC TIME CONSTANT (t)

TOTAL CAPACITANCE (C_T) SERIES

TOTAL CAPACITANCE (C_T) PARALLEL

INDUCTIVE REACTANCE (X_L)

CAPACITIVE REACTANCE (X_C)

IMPEDANCE (Z)

OHM’S LAW FOR REACTIVE CIRCUITS

OHM’S LAW FOR CIRCUITS CONTAINING RESISTANCE AND REACTANCE

REACTIVE POWER

APPARENT POWER

POWER FACTOR (PF)

VOLTAGE ACROSS THE SECONDARY (E_s)

VOLTAGE ACROSS THE PRIMARY (E_p)

CURRENT ACROSS THE SECONDARY (I_s)

CURRENT ACROSS THE PRIMARY (I_p)

TRANSFORMER EFFICIENCY

TRIGONOMETRIC FUNCTIONS

In a right triangle, there are several relationships which always hold true. These relationships pertain to the length of the sides of a right triangle, and the way the lengths are affected by the angles between them.

An understanding of these relationships, called trigonometric functions, is essential for solving problems in AC circuits such as power factor, impedance, voltage drops, and so forth.

To be a RIGHT triangle, a triangle must have a “square” corner; one in which there is exactly 90° between two of the sides. Trigonometric functions do not apply to any other type of triangle.

By use of the trigonometric functions, it is possible to determine the UNKNOWN length of one or more sides of a triangle, or the number of degrees in UNKNOWN angles, depending on what is presently known about the triangle.

The first basic fact of triangles is that IN ANY RIGHT TRIANGLE, THE SUM OF THE THREE ANGLES FORMED INSIDE THE TRIANGLE MUST ALWAYS EQUAL 180°. If one angle is always 90° (a right angle) then the sum of the other two angles must always be 90°.

thus, if angle Theta  is known, angle Phi may be quickly determined.

The second basic fact you must understand is that FOR EVERY DIFFERENT COMBINATION OF ANGLES IN A TRIANGLE, THERE IS A DEFINITE RATIO BETWEEN THE LENGTHS OF THE THREE SIDES.

In applying trigonometry to AC circuits, these units of measure will be values given in ohms, amperes, volts, and watts. Angle Theta will be the phase angle between (source) voltage and circuit current.

euclid elements: book1 proposition 3 in greek

To cut off from the greater of two given unequal straight lines a straight line equal to the less.

Let AB and C be the two given unequal straight lines, and let AB be the greater of them.

book1 - proposition3 - step1

It is required to cut off from AB the greater a straight line equal to C the less.

Place AD at the point A equal to the straight line C

book1 - proposition3 - step2

and describe the circle DEF with center A and radius AD.

book1 - proposition3 - step3

Now, since the point A is the center of the circle DEF, therefore AE equals AD.

But C also equals AD, therefore each of the straight lines AE and C equals AD, so that AE also equals C.

Therefore, given the two straight lines AB and C, AE has been cut off from AB the greater equal to C the less.

book1 - proposition3 - final

.:.

I have discovered that the very first patent Stan Meyer ever submitted is actually the  key to all of his subsequent water fuel related inventions.

Meyer titled this patent “Electrical Particle Generator”,  a name which would not attract too much attention to itself.  Furthermore,  Meyer never  patented this device in the USA. He only patented it in the Canadian patent office which had far less traffic. I believe that Stan Meyer wanted to place this key invention into the public record while in some sense  keeping the “secret” hidden in plain sight.

The patent for this invention can be downloaded from my site:  http://www.singularics.com/docs/patents/meyer_ca1213671.pdf

What Stan developed in the Electrical Particle Generator is quite incredible. It’s a highly efficient transformer whose primary can be powered with AC, pulsed DC and even pure Direct Current! The most important feature of this device is that it, once operating at speed,  functions in a highly efficient manner. Stan always referred to this device in his subsequent patents as the “Unipolar Pulsing Core Transformer”, a name which anyone who has spent time on Meyer’s work will recognize.

But what exactly is this device?  (read my annotated copy of the patent at the above link to dig into this more fully).

Below is a drawing I have made of it.

Alex Petty's design for Meyer's Gas Core Transformer

Here is how it is used in operation:

Alex Petty's approach to operating Meyer's Unipolar Pulsing Core

How can we get magnetized gas into the core?

Here is the approach that I took:

Alex Petty's Pressurization Unit for the Meyer Unipolar Pulsing Core

Parts Listing for Alex Petty's Pressurization Unit for the Meyer Unipolar Pulsing Core

Here are pictures of my first implementation of this device.

alex petty's magnetized gas core pressurization unit

When one adds primary and secondary windings to this core and then energizes the primary with a flow of charge, a  magnetic field is produced. The magnetized oxyhydrogen gas particles which have been added into the core are attracted to the S end of the primary magnetic field and repelled by the N end of the same field. The effect is accelerative upon the particles. As the gas flow velocity increases, the particles move ever faster around the core. The faster the particles are accelerated, the greater the charge amplitude induced on the  secondary side as the “tiny magnets” pass in a fluid aggregate over these windings.

Alex Petty's drawing of Meyer's Unipolar Pulsing Core in operation

In conventional transformers, iron cores can only amplify the field of the primary coil to a limited degree. The flux flow communicated to the secondary windings through the flux of the primary field alone is very low in comparison to what can be done with Meyer’s fluid core concept.

Also, PVC or flexible vinyl tubing works far better for fluid core construction then copper or aluminum. The first core I made (shown above) was made out of  copper, but in subsequent cores I have used PVC.
The reason for this is that you don’t want the field emanated by the primary coil or the magnetized particles hindered or affected in any way. It is the case that both  copper and aluminum have a dampening effect upon magnetic fields with relative velocity to these materials.

In many of Meyer’s patents (such as seen below),  he refers to a Unipolar Magnetic Field Coupling and uses his “Loop” symbol notation.

Magnetic Coupling "Loops" in Meyer drawings refer to magnetized gas particles

Here Meyer refers to the gas filled “pulsing core”, and it’s “unipolar magnetic field coupling” action. He always used the cryptic circles on his block diagrams to indicate the effect. Of course, he never disclosed this notation explicitly. Through years of thinking about Meyer’s work through my own primary research effort, I have discovered that what his little circles actually represent are the magnetic fields of tiny magnetized gas ions which when accelerated by the primary coil on the gas core, move at tremendous speeds  across the secondary windings inducing significant charge amplitudes. You can see what this looks like in my drawing below.

Alex Petty's Implementation of the Meyer WFC environment

When the input frequency is tuned so that the vortex coils are resonant with the water capacitor, it is then that the charging will reach its highest instantaneous voltage. It is also at this point that the magnetically negative side of the water molecule (H) is pulled hardest by the anode and the positive side of the water molecule (O) is pulled hardest by the cathode. The result is that the water molecule is electrically drawn and quartered into ions of hydrogen and oxygen which, once broken free from their molecular bondage, can be used as a clean source of energy in the form of gaseous fuel.

Splitting water molecules with strong magnetic polarity

I am also developing multi-loop cores to allow the gas particles to be more greatly accelerated before returning to the cell.

Here is an image of a multi-loop gas core I and my friend/colleague Paul Oberman have built together.

Petty/Oberman Multi-loop Gas Core

More to come!

In addition to my love of math and physics, I also love to write and perform music.

I am very happy to announce that tonight I will be releasing my latest CD titled “Memoirs” at a performance in Vienna Virgina with my band drumfish.

Facebook page: http://www.facebook.com/pages/drumfish/59713930924

You can listen to / obtain the music here:

http://drumfish.bandcamp.com/album/memoirs

For those interested, I will here provide a walk through of the music on this new album.

This is the album cover

memoirs album cover

without my light

poetry in motion

it just dont matter

listen:

http://drumfish.bandcamp.com/track/flood

flood

about “flood”

This song is full of water imagery. It breathes of the idea that within us there is some kind of well. And that at some point, when one is ready, the waters of this well stir a higher instinct, an inexplicable compulsion to seek a further understanding and to reconsider one’s personal situation and the general human condition. “The rest is up to me” the song states numerous times realizing that despite the numerous and onerous obstacles in his way he must do something. The protagonist in our “Memoirs” story has finally turned a corner in his journey.

There is even a “shout-out” to Nikola Tesla in the song. In the middle section the line goes “On the rocks with Tesla’s boxes”. This is a tribute to Alex’s work with energy physics and his admiration of Tesla. Alex’s work incorporates new theories on math and their relationship to spirituality and physics. The rest of us have embraced his theories and have used it as part of the decision making process for the sequencing of the songs. Each number, zero through 9, has a particular meaning and we lined up the track numbers of the songs to match.

listen:

http://drumfish.bandcamp.com/track/earthworms

earthworms

about “earthworms”

In this song our protagonist is making the first steps towards completing his journey. He has accepted that the journey is difficult. He notices many things around him in the world that are leading to a potentially apocalyptic ending…. “Hell fire in the mother’s breast”, “Lightning in the distance”, “Thunder in the middle sky”…. He feels like an “Earthworm in the eagle’s nest” meaning that the challenge facing him seems overwhelming and seemingly unbeatable. He is a tiny person in a vast world. He mentally challenges himself by facetiously saying, “You are listening to me, watching as the whole world dies”. Yet he summons his courage and “Puts one foot in front of the other”….he takes his first step.

listen:

http://drumfish.bandcamp.com/track/no-hesitation

no hesitation

about “no hesitation”

One of the lines in the first verse says, “I am what I am, zero to nine”. What exactly does it mean to be “zero to nine”? Alex does a lot of work with numerology as it relates to physics and spirituality. And much of the numerological work settles around new theories on math involving the intrinsic meaning of enumeration as it relates to conciousness. The numbers one through nine are represented on a circle and through these representations many deeper truths may be approached. On the circle, nine is also in the same place as zero. So when the protagonist in our story says this line, it is referring to all parts of himself, beginning to end.

This is the song where our protagonist has begun to fully make a change. He says, “I have already gone, no hesitation”. Yet he still struggles with himself by following that up saying, “I have long way to run, have some patience”. He has internalized the need for spiritual re-emergence but is battling himself. It is a battle against his ego which all of us are destined to one day dispel. It could be said that life itself is a struggle to defeat this inner adversary.

listen:

http://drumfish.bandcamp.com/track/all-for-you

all for you

about “all for you”

In this song our protagonist is experiencing the intense psychological pressures that can accompany inner transformation. Still all around him in the world there are things that he cannot change and an inner sense of self-doubt and so he falls into acute despair even contemplating suicide. He goes from questioning in the first verse, to angry in the second, to slightly insane in the third and finally he’s suicidal in the final tag section of the song. As we’ll see in the next song, “Already Home”, he makes his way through this desperate state and emerges from this intensely negative state transformed with true realization of the nature of self, like a dreamer waking from a nightmare.

listen:

http://drumfish.bandcamp.com/track/already-home

already home

about “already home”

One of the main harmonic themes on the record is to start in the home key and then move to the 6th scale degree. We do this in 4 or 5 different ways on the record but you can hear this happening over and over. We began to align the songs in an order such that the keys of the songs would line up in the same way. The record starts in D for the first two songs and then the third song is in B-flat minor….again 1 to 6. In fact if you line up the keys for the entire record, it makes a progression very similar to what a lot of the individual songs are doing. It even goes full circle and arrives back at D for the last song, “Remember”.

Another pattern that we saw emerging was that a lot of the songs aligned very closely with Alex’s numerology work (for more on this see the back stories for “Flood” and “No Hesitation”). The numbers 1 through 9 can be place on a circle moving around clockwise. 9 is just to the left of 1 and could also be represented with a 0. The number 9 in this way represents returning back to the beginning or back home, the starting point. And so this track “Already Home” became track 9. Other songs on the record have similar stories about placement due to the track numbering.

In addition to the song keys and numerical meanings, the songs were placed in order for lyrical reasons as well. In “Already Home” our protagonist has just gone through a very difficult emotional experience in “All For You”. He has passed through his long journey of transformation and has emerged changed. Through a moment of acceptance forced upon him by the nightmarish intensity reached in “All For You”, he realizes that what he searched for throughout his journey was already within himself the whole time and in this way he has connected with the source of his own life. He now understands that he is “Already Home”.

remember

Throughout the history of the band we have had many songs that toy around with key changing, in particular we like the interplay between major and minor. In “Remember” that idea is taken to a new extreme. The first moments of the song are definitely in D-minor but then slowly elements are bro…ught in to change it. Alex sings an F# in the verse which is the major third. By the time the chorus hits, we’re all playing a full D-major chord instead of D-minor. At the end of the chorus, on the lines “remain, always”, we’re in both major and minor simultaneously. The instrumentation has switched back to D-minor but the vocals are in D-major. You can hear the tension between the F# in the vocals and the F-natural in the guitar. Another interesting musical element to this song is the section that comes right after each chorus. Similar to the polytonality of the harmonic structure, we have a polyrhythm when Aaron continues playing in 4/4 time while the rest of the instrumentation is playing in 5/4.

In the story arc, this song is a reflection of our protagonist’s journey. In it he is “remembering”, the steps of his path to the attainment of inner peace having realized that he was “already home”. This return home is also reflected by a return to the original key from the first song on the record (“Motion” was also in D). He says “life is but a dream” in his understanding that this human life is not the absolute level of reality but only relatively true. He knows now that the physical world we experience as human beings is a merely a construct of mind fortified by senses, a beautiful illusion manifested for the benefit of the collective consciousness, so that the Universe, through us, can experience love as self. The protagonist, having experientially realized this is no longer questioning. He says, “I can guide you by the hand; I can make you realize how you and I remain, always”. This certainty comes from having passed through his journey and living now in the state of clarity which accompanies attunement to higher vibrations of consciousness.

At the very end of the song, if you let it play for about 10 seconds you’ll hear one last tag for the record. It was spontaneously recorded as Alex was tracking his acoustic guitar part in “Earthworms”. Our engineer/producer Kevin “131” Gutierrez tracked it and kept it as part of the recording. Alex is playing the guitar by himself and singing, “I am trying to make a difference with everything I do and say.” As we were listening to playbacks of “Earthworms” during the recording process we all really took to it. We decided that it was the perfect tag line to the CD, a simple yet profound statement that summarizes the entire work.

Here are some pictures of the band.

alex

larry

aaron

Here is a live performance from the band’s November 2009 performance:

For those of you who are interested, here is the bands bio:

drumfish was formed in 1992 by Alex Petty, Larry France, Neil Richardson and Aaron Bertoglio. From its inception, the band has always melded a wide variety of musical sounds, cultures and genres. This approach has led the band to develop a signature sound forged in the fires of cross genre innovation, harnessed by an acoustic modern rock feel.
The band has always focused on writing and distributing their original music. In 1997 drumfish released its first self-titled CD. Before long the band was attracting the attention of various record labels and playing venues all across the United States and Canada. As the excitement for the band grew, the demand for a follow up CD grew with it. The band released “Ra’s Zoo” in 1998 to critical acclaim.

In 1999, due to uncontrollable circumstances, the band parted ways before their full potential was realized. However, there was still unfinished business, a message that needed to be sent. There was more music that had to be created and shared. In 2000, a year after the official breakup, drumfish recorded their third CD, “Under Under Hill”. Not to be outdone by their earlier releases, the CD “Under Under Hill” went on to win a nationwide song writing contest and received strong praise from critics.

But this third CD remained dormant for nine years, without artwork, labeling or packaging. This weighed on the foursome leading to attempted reunions in 2005 and 2007. Finally, in early 2009, the band decided it was time to release this long over due work.

While the band was preparing for the release of the 3rd CD, they began writing new music. The material the band wrote during this period was fresh and invigorating, drumfish was now writing at a new level and doing its best work yet. More than that, there was an underlying message emerging from this new music, a message carrying a call to action for needed change in the world. The new work is filled with images of light and life.

In early 2010, drumfish began recording its 4th CD at Assembly Line Studios near Washington, DC with double-platinum producer Kevin “131″ Gutierrez. At around this time, the band signed up bassist James Hansford to fill the position left by departing bassist and founding member Neil Richardson. The band spent the spring and early summer recording new material and Memoirs” was completed in early June.

The group is now embarking on an international promotional campaign of the new record. Boosted by early reviews, France, Bertoglio, Hansford and Petty are now preparing for their live CD Release Concert on September 11th at Jammin’ Java in Vienna, VA.

For more information about the band please visit:
www.drumfishmusic.com

I have been taking a closer look at the affect of base on numbers in terms of  understanding the intrinsic significance of base 10 mod 9 as elements of the organizing principles which  give rise to the “physical world”.

Below I have taken a close look at 33 incrementations around the following number systems

Base 9 MOD 8

Base 8, MOD 7

Base 7, MOD 6

Base 6, MOD 5

Base 5, MOD 4

Base 4, MOD 3

Base 3, MOD 2

Base 2, MOD 1

My investigation has so far shown me that whenever a mind  elects to subdivide the consciousness field of One into myriad parts, that no matter which number base system is used, the numbers will always  take on the pattern of in-flow and out-flow. They will always exhibit the cyclonic vortex form.

However, because at least three parts are required for balanced motion, you see base 2 mod 1 as a mirror in stillness.

Balanced stillness: http://www.alexpetty.com/wp-content/uploads/2009/11/ying-yang-on-8.png

Balanced motion: http://www.alexpetty.com/wp-content/uploads/2009/11/ying-yang-in-motion1.png

Red is used to indicate expansion or out-flow (+)

Grey is used to indicate contraction or in-flow (-)

Notice how both the  contractive  and expansive paths always form mirrored palindromes in every base.

I find this to be remarkable.

FNS Table for Base 9 Modulus 8

FNS Web for Base 9 Modulus 8

FNS Table for Base 8 Modulus 7

FNS Web for Base 8 Modulus 7

FNS Table for Base 7 Modulus 6

FNS Web for Base 7 Modulus 6

FNS Table for Base 6 Modulus 5

FNS Web for Base 6 Modulus 5

FNS Table for Base 5 Modulus 4

FNS Web for Base 5 Modulus 4

FNS Table for Base 4 Modulus 3

FNS Web for Base 4 Modulus 3

FNS Table for Base 3 Modulus 2

FNS Web for Base 3 Modulus 2

FNS Table for Base 2 Modulus 1

FNS Web for Base 2 Modulus 1

More to come!

Magic Squares are expressions of balance in the Creation and are keystones for mapping to deeper truths hidden in  plain sight everywhere in nature.

For base 10, this square seems to be fundamental.  It is balanced horizontally, vertically and diagonally – summing to 15 in every direction as shown below.

balanced square of nine

balanced square of nine

circle of nine

There is a relationship between this arrangement and the circle of 11.

foundational field glyph of 11

foundational field table of 11

Here is an interesting page scanned from a dusty old book.

Fundamental Magic Square

Here is a bit of visual analysis in terms of the understanding I’ve  developed of the magnetic nature of numbers.

As per my usual color coding schema, yellow and red are positive (expansive), green and gray are negative (contractive), blue is neutral (still).

Numeric Polarity within the Magic Square

magicsquare path

Interestingly, here we see negatively charged field elements (1, 5, 7) proceeding counter clockwise around the center cone while positively charged field elements (2, 4, 8)  proceed in a clockwise path.

magic square rotation step 1

magic square rotation step 2

magic square rotation step 3

magic square rotation step 4

Opposing flows, in flow and out flow, arising directly from the numeric fields when they are aligned in a balanced way, ie. in the manner that nature arranges.

opposing rotational paths

There will be more to come on this topic.