Drawing of hands soldering a wire in a radio.


So far, generators and motors are the only instruments described as using the principle of induction. COILS and TRANSFORMERS, while much simpler in design and containing NO MOVING parts, also depend upon INDUCTION for their operation.

Radios use hundreds of coils and transformers. Some are large, over a foot long, and several inches in diameter, while others are so small that a dozen could be placed inside a cigarette pack.

Many coils and transformers have special names, such as CHOKES, POWER TRANSFORMERS, INTERMEDIATE TRANSFORMERS, INPUT TRANSFORMERS, and many others. It will not be unusual to hear all coils and transformers called by a general name of INDUCTANCE or INDUCTOR.


One characteristic of induction is the ability of a COIL to INDUCE a voltage in ITSELF-SELF INDUCTION.


Look at figure 73. A coil of two turns is connected to a battery through a switch. When the switch is closed, the conductors will be surrounded by a magnetic field.

If only a SINGLE loop of wire were present, the magnetic fields would have little influence on the operation of the circuit. But it follows naturally that the field surrounding loop 2 also cuts across loop 1.

Self induction.
Figure 73.-Self induction.
When the switch is FIRST closed, the fields surrounding the loops are being CREATED. As long as the current is INCREASING the field is EXPANDING-in other words MOVING.

Now here is the situation. You have a MOVING magnetic field and conductors-loops 1 and 2-so what will take place?

Right! The field of loop 1 will induce a voltage in loop 2, and the field of loop 2 will induce a voltage in loop 1.

When the current through the coil becomes constant, the fields become stationary and no INDUCTION takes place. The field is SUSTAINED at a constant strength.

When the switch is opened, the SUSTAINING current falls. The field BEGINS to collapse, moving in a direction OPPOSITE to its motion when it was being created. In


collapsing, the field again induces a voltage in the turns of the coil. Thus, whenever the magnetic field of a coil is either EXPANDING or CONTRACTING, a VOLTAGE is INDUCED in its own TURNS.


What happens to the voltage that is INDUCED in the turns of the coil ? Does it AID, or OPPOSE the battery voltage ?

Look at drawing A of figure 74. The switch has just been closed and the current is rising. The INDUCED VOLTAGE is ALWAYS in OPPOSITION to the voltage that CREATED IT. Thus, if the emf of the battery is 10 volts, and the induced emf is 2 volts, the resulting emf tending to cause the current to flow through the coil is-

10 - 2 = 8 volts.

After the current has reached a steady value, the INDUCED VOLTAGE becomes zero, and the resulting emf is-

10 - 0 = 10 volts.

As long as a steady current is maintained, no induced COUNTER EMF is present, and the magnetic field remains constant.

Counter emf.
Figure 74.-Counter emf.
When the switch is suddenly opened, figure 74B, the magnetic field will collapse and induce a voltage in a DIRECTION OPPOSITE to the COUNTER emf, the SAME direction



as the APPLIED Voltage. Hence, on the collapse of a field, the INDUCED emf ADDS to the APPLIED emf.

If the switch is opened SUDDENLY, the induced emf from the collapsing field added to the battery voltage will cause a SPARK to jump between the terminals of the switch.


Here is something to remember. In any inductance, the INDUCED voltage is always in OPPOSITION to the VOLTAGE THAT CREATED it. When the current caused by the applied emf is rising, the induced voltage tends to reduce the current; but when the current from the applied voltage is falling, the induced voltage tends to keep it going. This statement is known as LENZ'S LAW.


In figures 73 and 74 you learned what happens when d.c. is applied to a coil. Now observe what takes place when a.c. is applied to a coil.

Counter emf created by a.c.
Figure 75.-Counter emf created by a.c.
In figure 75 an a.c. generator is delivering an emf to the inductance. During one half of the alternation, the current will be flowing in direction A, and during the other half-cycle, the current will flow in direction B. Since a.c. is never steady, a counter emf will be present at all times. The DIRECTION of this counter emf will always be opposed to the emf of the half-cycle that created it.

As an example, in figure 75, if the applied emf is in the direction indicated by arrow A, the counter emf will be in direction X, while on the next half alteration, the counter emf will be in direction Y.


The magnitude of the counter emf depends upon two factors-the construction of the coil, and the FREQUENCY of the current.

The construction of the coil includes such factors as the NUMBER of TURNS per inch of the coil's length, the DIAMETER of the coil, the NUMBER of LAYERS of windings, and the KIND of CORE. All these factors are combined in a single unit and referred to as the INDUCTANCE of the coil.

The UNIT of inductance is the HENRY, and the SYMBOL used to designate INDUCTANCE is the letter L.

The actual calculation of a coil's inductance is an involved and difficult process. But here's all you need to remember-the GREATER the number of turns, and the TIGHTER the winding, the HIGHER the INDUCTANCE. And a coil with an IRON CORE has a GREATER inductance than a coil with an air core.

Inductance is a PHYSICAL property of a coil, and it DOES NOT CHANGE with an increase or decrease of frequency. A certain type of coil, known as a "swing choke," is designed to have a HIGH INDUCTANCE with low current, and LOW INDUCTANCE with HIGH CURRENT. While the second statement seems to contradict the first, the cause of the CHANGEABLE INDUCTANCE is in the CORE and not in the COIL itself.

Coils used with audio frequencies may run higher than 30 Henries, while those used with high radio frequencies may be as small as a few MILLIHENRIES (thousandths of a Henry).


The REACTANCE of a coil is the OPPOSITION to the flow of current caused by the counter emf. The AMOUNT OF


REACTANCE depends upon the INDUCTANCE of the coil, and the FREQUENCY of the a.c. applied.

Since a counter emf is induced each time the current reverses its direction, the greater the number of reversals-the higher the frequency-the greater the counter emf will be.

The formula for finding the reactance of a coil is simple-

XL = 2πfL

The symbol XL designates the reactance in OHMS; f is the frequency of the a.c. in cycles per second; and L is the inductance of the coil in HENRIES.

The factor 2 X π is derived from the ANGULAR rotation of a cycle. Don't let it bother you. Just think of it as equal to 2 X 3.14, or 6.28. So now the equation above becomes-

XL = 6.28 fL

Suppose you have a coil of two Henries inductance, carrying a 50-cycle current. What is the reactance? Substitute in the formula, and you get-

XL = 6.28 X 50 x 2
XL = 628 ohms

But suppose the current is of an r.f. frequency of 2,000,000 cycles (2 mc). The reactance of the coil will now be-

XL = 6.28 X 2,000,000 X 2
XL = 25,120,000 ohms

Remember, the HIGHER the FREQUENCY the HIGHER the REACTANCE. This feature is used extensively in radio work. You will hear a lot about it.



The coils used in radio circuits are divided into two classes-those designed to be used with AUDIO FREQUENCIES, and the others to be used with RADIO FREQUENCIES.

Audio frequency coils, usually called A.F. CHOKES, have IRON CORES to increase their inductance. Figure 76 shows the schematic symbol and one example of an audio

Audio frequency choke.
Figure 76.-Audio frequency choke.
frequency choke. While this example is one of the most common types, don't be surprised to find them of other designs.

Radio frequency coils, R.F. CHOKES, usually don't have iron cores. If they did, so much heat would be produced in making and destroying the field in the core that the coil would burn up.

R.F. coils have a greater variety of shapes and sizes than a.f. types. Some of the windings are of fine wire; others are made of large copper tubing with the individual turns widely spaced. Figure 77 shows the schematic symbol and one example of an r.f. choke.


Radio frequency choke.
Figure 77.-Radio frequency choke.


When a coil is placed close enough to another coil so that the magnetic field of the first induces a voltage in the second. you have MUTUAL INDUCTION.


In figure 78, the magnetic field of coil A induces a voltage in coil B. If the coils are far apart, coil A will induce a small voltage in B. Moving the coils closer together INCREASES the emf induced in B. When the coils are very close together, the magnetic field of the induced current in B will induce an emf in A.

The relative position of the two coils is expressed as the DEGREE of COUPLING. If the first coil is just able to

Mutual induction.
Figure 78.-Mutual induction.
induce an emf in the second, the coils are LOOSELY coupled. When coil A induces a maximum voltage in B, without B inducing a voltage in A, the coupling is CRITICAL. Any coupling greater than critical is CLOSE.

To keep the TYPES of INDUCTION straight in your mind, remember that MUTUAL induction requires TWO coils, while SELF induction needs but ONE.


Mutual inductive devices are called TRANSFORMERS. In figure 78, coil A is the PRIMARY winding and B the SECONDARY. You can always tell which is the PRIMARY because it is the coil WINDING that receives the APPLIED voltage. The SECONDARY is the winding receiving the INDUCED voltage.

Transformers are used with both a.f. and r.f. Audio frequency transformers have iron cores, and the windings


are usually of heavier wire. Most radio frequency transformers DO NOT have iron cores. The wires used for the lower r.f. coils are fine and are wound on plastic tubes.
Audio and radio frequency transformers.
Figure 79.-Audio and radio frequency transformers.
In figure 79, the schematic symbols for both a.f and r.f. transformers are given. You will see each type with different numbers of loops, but the identifying feature is the absence of the iron core with r.f. types.

Transformers operate on only a.c., because with d.c. induction takes place only when the circuit furnishing the applied emf is made or broken. Certain transformers are used with rapidly pulsating d.c., but these cases are few. You may never see one used.


The core in audio frequency transformers is used to increase its efficiency. The iron core forms a LOW

A. F. transformer.
Figure 80.-A. F. transformer.

RELUCTANCE path for the flux to couple the primary and secondary windings together.

In figure 80, the iron core forms a complete circle for the flux to follow. In this way, any change in the primary current will be quickly carried to the secondary.

Not all transformers have cores and windings like the one in figure 80. In figure 31, four types of cores and windings are given. In drawing A, the core is circular,

Transformer cores and windings.
Figure 81.-Transformer cores and windings.
but PART of the PRIMARY and PART of the SECONDARY is wound on each side of the core. Both primary and secondary windings of drawing B are made on the CENTRAL LEG of the core. Core C is just double that of B, and core D is the one illustrated in figure 80.


The transformer's ability either to increase or decrease the voltage is probably its most valuable feature.

Step up and step down transformers.
Figure 82.-Step up and step down transformers.
If there are MORE windings on the SECONDARY than on the primary, figure 82, the transformer is a STEP UP. If the windings are reversed, with MORE on the PRIMARY, the transformer is a STEP DOWN.

The amount of step up or step down is directly proPortional to the TURNS RATIO between primary and secondary. Thus, in drawing 82A with 11 primary and 22 secondary turns, the voltage will be stepped up by a ratio of 1:2. Therefore, if 10 volts are applied to the primary, 20 volts will appear across the secondary.

With a step down transformer, if 22 turns are on the primary and 11 on the secondary, the step down is 2 to 1. Thus if 100 volts are applied to the primary, only 50 will appear across the secondary.

The step up and step down feature of transformers holds true for all ratios within reason. While, in theory, one turn on the primary and a thousand on the secondary should increase 10 volts to 10,000, ACTUALLY you would get much less. The difference between the THEORETICAL and ACTUAL performances is due to loss of efficiency with extreme ratios.


Efficient transformers with ratios as large as 20:1 are not uncommon, but when step up or step down ratios as large as 100 to 1 are desired, it is more efficient to use two 10 to 1 transformers.

Radio frequency also employs the step up and step down principle, but it is less commonly used because of the desire to obtain resonance in r.f. circuits. You will learn more about resonance in chapter 11.

Radios use many transformers that are both step up and step down at the same time. Look at figure 83. The top secondary winding is step up and lower secondary winding step down. It is not unusual to have a single

Step up, step down transformer.
Figure 83.-Step up, step down transformer.
transformer in a radio receiver's power supply deliver potentials like 600, 6.3, and 5 volts from three secondary windings.


It may seem at first that you are getting more out of a transformer than you put in, but if you look a little further you will see this is not true.

First, you know that it is impossible to take more power out of a device than you put in. That also holds true for transformers. The power you take out of the secondary


is EXACTLY equal to the power put -in the secondary. Thus-

Primary power = Secondary power

or by using the power formula W = Ep X Ip = Es X Is

If the transformer is step up with a ratio of 1:2, and 50 volts with 10 amperes is applied to the primary, the secondary will have an emf of 100 voltage but a current of only 5 amperes because-

50 X 10 = 100 X 5



While most radio frequency transformers have primary and secondary windings, they are called COILS. Don't let that confuse you. If only one winding is present, it usually will be called an r.f choke.

You were told that most of the r.f. transformers don't have cores, but a few do have cores, made of IRON FILINGS imbedded in a piece of PLASTIC. The symbol for transformers with iron cores is given in figure 84.

Symbol for iron core r.f. transformers.
Figure 84.-Symbol for iron core r.f. transformers.
The windings of many r.f. transformers are of copper tubing and are held in place by strips of some special insulation material.

Intermediate frequency transformer
Figure 85.-Intermediate frequency transformer
Two of the many types of r.f. transformers are given in figures 85 and 86. The one in 85 is small, only 2 or 3
Transformer used with transmitters.
Figure 86.-Transformer used with transmitters.

inches long and about 1/2 inch in diameter. It is used in the INTERMEDIATE stage of a SUPERHETERODYNE receiver. You will hear more of these transformers later.

The transformer given in figure 86 is used with a low frequency, high power transmitter. The coil is large, over a foot long, and several inches in diameter.


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