**NEETS Module 9 — Introduction to Wave- Generation and Wave-Shaping**Pages

i - ix,

1-1 to 1-10,

1-11 to 1-20,

1-21 to 1-30,

1-31 to 1-40,

1-41 to 1-52,

2-1 to 2-10,

2-11 to 2-20,

2-21 to 2-30,

2-31 to 2-38,

3-1 to 3-10,

3-11 to 3-20,

3-21 to 3-30,

3-31 to 3-40,

3-41 to 3-50,

3-51 to 3-56,

4-1 to 4-10,

4-11 to 4-20,

4-21 to 4-30,

4-31- to 4-40,

4-41 to 4-50,

4-51 to 4-61, Index

frequency selection to be accomplished in a different manner. It gives the circuit different characteristics.
The first of these characteristics is the ability to store energy.

**The Characteristics of a
Typical Parallel-Resonant Circuit** Look at figure 1-11. In this circuit, as in other parallel
circuits, the voltage is the same across the inductor and capacitor. The currents through the components vary
inversely with their reactances in accordance with Ohm's law. The total current drawn by the circuit is the vector
sum of the two individual component currents. Finally, these two currents, IL and IC, are 180 degrees out of
phase because the effects of L and C are opposite. There is not a single fact new to you in the above. It is all
based on what you have learned previously about parallel AC circuits that contain L and C.

Figure 1-11.—Curves of impedance and current in an RLC parallel-resonant circuit.

Now, at resonance, X

_{L} is still equal to X

_{C}. Therefore, I

_{L} must equal I

_{C}.
Remember, the voltage is the same; the reactances are equal; therefore, according to Ohm's law, the currents must
be equal. But, don't forget, even though the currents are equal, they are still opposites. That is, if the current
is flowing "up" in the capacitor, it is flowing "down" in the coil, and vice versa. In effect, while the one
component draws current, the other returns it to the source. The net effect of this "give and take action" is that
zero current is drawn from the source at resonance. The two currents yield a total current of zero amperes because
they are exactly equal and opposite at resonance.

A circuit that is completed and has a voltage applied,
but has zero current, must have an INFINITE IMPEDANCE (apply Ohm's law — any voltage divided by zero yields
infinity).

1-21

By now you know that we have just ignored our old friend resistance from previous discussions. In an
actual circuit, at resonance, the currents will not quite counteract each other because each component will have
different resistance. This resistance is kept extremely low, but it is still there. The result is that a
relatively small current flows from the source at resonance instead of zero current. Therefore, a basic
characteristic of a practical parallel-LC circuit is that, at resonance, the circuit has MAXIMUM impedance which
results in MINIMUM current from the source. This current is often called line current. This is shown by the peak
of the waveform for impedance and the valley for the line current, both

occurring at f

_{r} the
frequency of resonance in figure 1-11.

There is little difference between the circuit pulsed by the battery in figure 1-8 that oscillated at its resonant
(or natural) frequency, and the circuit we have just discussed. The equal and opposite currents in the two
components are the same as the currents that charged and discharged the capacitor through the coil.

For a
given source voltage, the current oscillating between the reactive parts will be stronger at the resonant
frequency of the circuit than at any other frequency. At frequencies below resonance, capacitive current will
decrease; above the resonant frequency, inductive current will decrease. Therefore, the oscillating current (or
circulating current, as it is sometimes called), being the lesser of the two reactive currents, will be maximum at
resonance.

If you remember, the basic resonant circuit produced a "damped" wave. A steady amplitude wave
was produced by giving the circuit energy that would keep it going. To do this, the energy had to be at the same
frequency as the resonant frequency of the circuit.

So, if the resonant frequency is "timed" right, then
all other frequencies are "out of time" and produce waves that tend to buck each other. Such frequencies cannot
produce strong oscillating currents.

In our typical parallel-resonant (LC) circuit, the line current is
minimum (because the impedance is maximum). At the same time, the internal oscillating current in the tank is
maximum. Oscillating current may be several hundred times as great as line current at resonance.

In any
case, this circuit reacts differently to the resonant frequency than it does to all other frequencies. This makes
it an effective frequency selector.

**Summary of Resonance** Both series- and
parallel-LC circuits discriminate between the resonant frequency and all other frequencies by balancing an
inductive reactance against an equal capacitive reactance.

In series, these reactances create a very low
impedance. In parallel, they create a very high impedance. These characteristics govern how and where designers
use resonant circuits. A low- impedance requirement would require a series-resonant circuit. A high-impedance
requirement would require the designer to use a parallel-resonant circuit.

**Tuning a Band of
Frequencies** Our resonant circuits so far have been tuned to a single frequency - the resonant
frequency. This is fine if only one frequency is required. However, there are hundreds of stations on many
different frequencies.

Therefore, if we go back to our original application, that of tuning to different
radio stations, our resonant circuits are not practical. The reason is because a tuner for each frequency would be
required and this is not practical.

1-22

What is a practical solution to this problem? The answer is simple. Make either the capacitor or the
inductor variable. Remember, changing either L or C changes the resonant frequency.

Now you know what has
been happening all of these years when you "pushed" the button or "turned" the dial. You have been changing the L
or C in the tuned circuits by the amount necessary to adjust the tuner to resonate at the desired frequency. No
matter how complex a unit, if it has LC tuners, the tuners obey these basic laws.

Q-9. What is the term
for the number of times per second that tank circuit energy is either stored in the inductor or capacitor?

Q-10. In a parallel-resonant circuit, what is the relationship between impedance and current? Q-11. When is
line current minimum in a parallel-LC circuit?

**RESONANT CIRCUITS AS FILTER CIRCUITS**

The principle of series- or parallel-resonant circuits have many applications in radio, television,
communications, and the various other electronic fields throughout the Navy. As you have seen, by making the
capacitance or inductance variable, the frequency at which a circuit will resonate can be controlled.

In
addition to station selecting or tuning, resonant circuits can separate currents of certain frequencies from those
of other frequencies.

Circuits in which resonant circuits are used to do this are called FILTER CIRCUITS.

If we can select the proper values of resistors, inductors, or capacitors, a FILTER NETWORK, or "frequency
selector," can be produced which offers little opposition to one frequency, while BLOCKING or ATTENUATING other
frequencies. A filter network can also be designed that will "pass" a band of frequencies and "reject" all other
frequencies.

Most electronic circuits require the use of filters in one form or another. You have already
studied several in modules 6, 7, and 8 of the NEETS.

One example of a filter being applied is in a
rectifier circuit. As you know, an alternating voltage is changed by the rectifier to a direct current. However,
the DC voltage is not pure; it is still pulsating and fluctuating. In other words, the signal still has an AC
component in addition to the DC voltage. By feeding the signal through simple filter networks, the AC component is
reduced. The remaining DC is as pure as the designers require.

Bypass capacitors, which you have already
studied, are part of filter networks that, in effect, bypass, or shunt, unwanted AC components to ground.

**THE IDEA OF "Q"** Several times in this chapter, we have discussed "ideal" or theoretically
perfect circuits. In each case, you found that resistance kept our circuits from being perfect. You also found
that low resistance in tuners was better than high resistance. Now you will learn about a factor that, in effect,
measures just how close to perfect a tuner or tuner component can be. This same factor affects BANDWIDTH and
SELECTIVITY. It can be used in figuring voltage across a coil or capacitor in a series-resonant circuit and the
amount of circulating (tank) current in a parallel-resonant circuit. This factor is very important

1-23

and useful to designers. Technicians should have some knowledge of the factor because it affects so many
things. The factor is known as Q. Some say it stands for quality (or merit). The higher the Q, the better the
circuit; the lower the losses (I

^{2}R), the closer the circuit is to being perfect.

Having studied
the first part of this chapter, you should not be surprised to learn that resistance (R) has a great effect on
this figure of merit or quality.

**Q Is a Ratio** Q is really very simple to
understand if you think back to the tuned-circuit principles just covered. Inductance and capacitance are in all
tuners. Resistance is an impurity that causes losses. Therefore, components that provide the reactance with a
minimum of resistance are "purer" (more perfect) than those with higher resistance. The actual measure of this
purity, merit, or quality must include the two basic quantities, X and R.

The ratio

does the job for us. Let's take a look at it and see just why it measures quality.

First, if a perfect circuit has zero resistance, then our ratio should give a very high value of Q to reflect the
high quality of the circuit. Does it?

Assume any value for X and a zero value for R.

Then:

Remember, any value divided by zero equals infinity. Thus, our ratio is infinitely high for a
theoretically perfect circuit.

With components of higher resistance, the Q is reduced. Dividing by a
larger number always yields a smaller quantity. Thus, lower quality components produce a lower Q. Q, then, is a
direct and accurate measure of the quality of an LC circuit.

Q is just a ratio. It is always just a number
— no units. The higher the number, the "better" the circuit. Later as you get into more practical circuits, you
may find that low Q may be desirable to provide certain characteristics. For now, consider that higher is better.

Because capacitors have much, much less resistance in them than inductors, the Q of a circuit is very often
expressed as the Q of the coil or:

The answer you get from using this formula is very near correct for most purposes. Basically, the Q of a
capacitor is so high that it does not limit the Q of the circuit in any practical way. For that reason, the
technician may ignore it.

1-24

**The Q of a Coil** Q is a feature that is designed into a coil. When the coil is
used within the frequency range for which it is designed, Q is relatively constant. In this sense, it is a
physical characteristic.

Inductance is a result of the physical makeup of a coil - number of turns, core,
type of winding, etc. Inductance governs reactance at a given frequency. Resistance is inherent in the length,
size, and material of the wire. Therefore, the Q of a coil is mostly dependent on physical characteristics.

Values of Q that are in the hundreds are very practical and often found in typical equipment.

**
Application of Q** For the most part, Q is the concern of designers, not technicians. Therefore,
the chances of you having to figure the Q of a coil are remote. However, it is important for you to know some
circuit relationships that are affected by Q.

**Q Relationships in Series Circuits**
Q can be used to determine the "gain" of series-resonant circuits. Gain refers to the fact that at resonance, the
voltage drop across the reactances are greater than the applied voltage. Remember, when we applied Ohm's law in a
series-resonant circuit, it gave us the following characteristics:

· Low impedance, high current.

· High current; high voltage across the comparatively high reactances.

This high voltage is usable
where little power is required, such as in driving the grid of a vacuum tube or the gate of a field effect
transistor (F.E.T.). The gain of a properly designed series-resonant circuit may be as great or greater than the
amplification within the amplifier itself. The gain is a function of Q, as shown in the following example:

E = the input voltage to the tuned circuit

E_{L} = the voltage drop across the
coil at resonance Q.

Q = the Q of the coil.

Then:

E_{L} = EQ

If the Q of the coil were 100, then the gain would be 100; that is, the voltage of the coil would be 100 times
that of the input voltage to the series circuit.

Resistance affects the resonance curve of a series
circuit in two ways — the lower the resistance, the higher the current; also, the lower the resistance, the
sharper the curve. Because low resistance causes high Q, these two facts are usually expressed as functions of Q.
That is, the higher the Q, the higher and sharper the curve and the more selective the circuit.

The lower
the Q (because of higher resistance), the lower the current curve; therefore, the broader the curve, the less
selective the circuit. A summary of the major characteristics of series RLC-circuits at resonance is given in
table 1-1.

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Table 1-1.—Major Characteristics of Series RLC Circuits at Resonance

**Q Relationships in a Parallel-Resonant Circuit** There is no voltage gain in a
parallel-resonant circuit because voltage is the same across all parts of a parallel circuit. However, Q helps
give us a measure of the current that circulates in the tank.

1-26

Given:

I_{LINE} = current drawn from the source

I_{L} = current through the
coil (or circulating current

Q = the Q of the coil

Then:

I_{L}
= I_{LINE} Q

Again, if the Q were 100, the circulating current would be 100 times the value of the line current. This
may help explain why some of the wire sizes are very large in high-power amplifying circuits.

The
impedance curve of a parallel-resonant circuit is also affected by the Q of the circuit in a manner similar to the
current curve of a series circuit. The Q of the circuit determines how much the impedance is increased across the
parallel-LC circuit. (Z = Q x X

_{L})

The higher the Q, the greater the impedance at resonance and
the sharper the curve. The lower the Q, the lower impedance at resonance; therefore, the broader the curve, the
less selective the circuit. The major characteristics of parallel-RLC circuits at resonance are given in table
1-2.

1-27

Table 1-2.—Major Characteristics of Parallel RLC Circuits at Resonance

**Summary of Q** The ratio that is called Q is a measure of the quality of resonant
circuits and circuit components. Basically, the value of Q is an inverse function of electrical power dissipated
through circuit resistance. Q is the ratio of the power stored in the reactive components to the power dissipated
in the resistance. That is, high power loss is low Q; low power loss is high Q.

Circuit designers provide
the proper Q. As a technician, you should know what can change Q and what quantities in a circuit are affected by
such a change.

1-28

**BANDWIDTH**

If circuit Q is low, the gain of the circuit at resonance is relatively small. The circuit does not
discriminate sharply (reject the unwanted frequencies) between the resonant frequency and the frequencies on
either side of resonance, as shown by the curve in figure 1-12, view (A). The range of frequencies included
between the two frequencies (426.4 kHz and 483.6 kHz in this example) at which the current drops to 70 percent of
its maximum value at resonance is called the BANDWIDTH of the circuit.

Figure 1-12A.—Bandwidth for high- and low-Q series circuit. LOW Q CURRENT CURVE.

Figure 1-12B.—Bandwidth for high- and low-Q series circuit. HIGH Q CURRENT CURVE.

It is often necessary to state the band of frequencies that a circuit will pass. The following standard
has been set up: the limiting frequencies are those at either side of resonance at which the curve falls to a
point of .707 (approximately 70 percent) of the maximum value. This point is called the HALF-POWER point. Note
that in figure 1-12, the series-resonant circuit has two half-power points, one above and one

1-29

below the resonant frequency point. The two points are designated upper frequency cutoff (fco) and
lower frequency cutoff (f

_{co}) or simply f

_{1} and f

_{2}. The range of frequencies
between these two points comprises the bandwidth. Views (A) and (B) of figure 1-12 illustrate the bandwidths for
low- and high-Q resonant circuits. The bandwidth may be determined by use of the following formulas:

Where:

BW = bandwidth of a circuit in units of frequency

f_{r}
= resonant frequency

f_{2} = the upper cutoff frequency

f_{1} = the lower cutoff
frequency

For example, by applying the formula we can determine the bandwidth for the curve shown in figure 1-12,
view (A).

Solution:

BW= f_{2} - f_{1}

BW = 483.6 kHz - 426.4 kHz

BW = 57.2 kHz

If the Q of the circuit represented by the curve in figure 1-12, view (B), is 45.5, what would be the
bandwidth?

Solution:

If Q equals 7.95 for the low-Q circuit as in view (A) of figure 1-12, we can check our original
calculation of the bandwidth.

1-30

Introduction to Matter, Energy, and Direct Current, Introduction
to Alternating Current and Transformers,

Introduction to Circuit Protection,
Control, and Measurement,

Introduction to Electrical Conductors, Wiring Techniques,
and Schematic Reading,

Introduction to Generators and Motors,

Introduction to Electronic Emission, Tubes, and Power Supplies,
Introduction to Solid-State Devices and Power Supplies,

Introduction to Amplifiers, Introduction to
Wave-Generation and Wave-Shaping Circuits,

Introduction to Wave Propagation, Transmission
Lines, and Antennas,

Microwave Principles,
Modulation Principles, Introduction to Number Systems and Logic Circuits, Introduction
to Microelectronics,

Principles of Synchros, Servos, and Gyros,

Introduction to Test Equipment,

Radio-Frequency
Communications Principles,

Radar Principles, The Technician's Handbook,
Master Glossary,

Test Methods and Practices, Introduction to Digital Computers,
Magnetic Recording, Introduction to Fiber Optics