OSCILLATORS

Amplifiers are extremely important in the world of electronics. Oscillators are perhaps equally important. No matter what field of electronics you may be involved in, you will encounter Oscillators.

Oscillators are used in computers, communications systems, television systems, industrial control and manufacturing processes, and even in electric watches as the basic time-keeping device. Probably one of the most common uses of the high-frequency oscillator is in the television tuner or "channel selector." Here, the oscillator helps select the channel to be viewed. A faulty tuner oscillator can result in a "no reception" condition, where no stations are received and the television screen is blank, making the television useless. The oscillator is an important part of television systems and most other electronic equipment. Therefore, how well you understand oscillators may affect your success in electronics.

The term oscillator naturally implies an oscillating or revolving motion. One example of mechanical oscillation is the pendulum in a typical grandfather clock. The pendulum "oscillates" back and forth, ticking away the minutes. In this sense, the pendulum is the basic timing mechanism for the clock. Electronic oscillators operate in a similar manner, generating a continuously repetitive output signal that is sometimes used to time or synchronize operations.

We will study common electronic oscillators; how they work and how they are identified. Each oscillator has its own distinct characteristics of identification and operation. It is important to remember these characteristics. You will also examine different oscillators and discover how they function to maintain oscillation at a set frequency.

OSCILLATOR FUNDAMENTALS

Frequently, electronic circuits require AC signals that can range from a few hertz to many millions of hertz. Oscillators are usually used to generate these frequencies. Furnishing this wide range of frequencies requires many different oscillators, and there are literally hundreds. However, all oscillators operate on the same basic principles and, if you thoroughly understand these basic principles, you should be able to analyze the operation of most common oscillators.

What is an Oscillator?

An oscillator is a circuit that generates a repetitive AC signal. As mentioned previously, the frequency of this AC signal may be a few hertz, a thousand hertz, a million hertz, or even higher, in the giga-hertz range. The 50 hertz AC signal available at the normal wall outlet is produced by an AC generator or alternator at the power station and is then transmitted through the power lines to your home or office. Since AC can be transmitted easily with subsequent low power losses, it is quite suitable for use in power systems. .

The 50 hertz AC signal from the wall outlet is a convenient source of a relatively constant 50 hertz signal. However, except for supplying operating power (its primary purpose), this 50 hertz sine wave has few applications in electronic circuits. So, other means are required to supply AC signals of different frequencies.

Why not use an AC generator? Generators are relatively large and expensive. Also, they would be satisfactory only for low frequency applications because generator output frequency depends on the number of poles in the generator field and the speed of rotation. Generator frequency is limited since, at high speeds, the generator will fly apart. Therefore, the AC generator is not a feasible solution.

The electronic generator or "oscillator" is an alternative to the mechanical generator. It has no moving parts and is capable of producing AC signals ranging from a few hertz to many millions of hertz. Such an oscillator is shown below. It operates from the DC power supply and generates an AC signal. Oscillator output can be a sine wave, rectangular wave, or a sawtooth, depending on the type of oscillator. The major requirement of a good oscillator is that the output is uniform, not varying in

frequency or amplitude. In this course, our major concern is with the sinusoidal or sine wave oscillator.

The Basic Oscillator

When a tank circuit is "excited" by a DC source, it has a tendency to oscillate. Circulating current flows inside the "tank" producing a back and forth oscillatory motion. However, resistance of the tank circuit dissipates energy and oscillations are damped.

For the tank circuit to continue oscillation, lost energy must be replaced. A crude method of replacing energy is to close the power switch once each cycle. It is important for the switch to close so the energy is replaced at exactly the instant that reinforces the charge on capacitor C. Replacement energy then has a reinforcing effect and is in phase with the tank waveform. Reinforcing energy that "adds to" circuit action is a type of "positive feedback." Positive feedback is the most important requisite for oscillation. There is nothing unique about oscillation or positive feedback, especially in high frequency circuits. Distributed capacitance of these circuits "feeds back" signals that can cause high frequency circuits to break into oscillation. Of course this is undesirable, so circuit designers "neutralize" such circuits.

One form of positive feedback is common in public address systems. If the microphone is placed too close to the loudspeaker, positive feedback results, as shown below. Speaker output is fed back to the microphone, amplified, and again applied to the speaker. This sets up a continual cycle and the loudspeaker emits a high-pitched acoustical squeal.

From this example, it may seem that an oscillator can be created by simply taking a portion of amplifier output and feeding it back to the input. In some cases this is true, but not in all. For the circuit to oscillate, the feedback signal must be in phase with the input signal. See below.

This is a common-emitter amplifier, where a portion of the output signal is fed back to the input. Remember, in the common-emitter arrangement, output is 180º out of phase with input. So in this circuit, the feedback signal opposes the input signal, resulting in reduced input. Such feed- back is degenerative or negative in nature, and is used in amplifier circuits to reduce distortion. This circuit will not oscillate.

However, if you place a 180º phase-shift network between the output and input, feedback will be of the correct phase. Notice that the feedback signal is in phase with the input signal, adding to the input. The result is positive or regenerative feedback.

Once the amplifier begins to operate, the input signal can be removed and the circuit will continue to oscillate. The gain of the amplifier replaces energy lost in the circuit and positive feedback sustains oscillation. This circuit meets all of the requirements of an oscillator, except one …. the frequency of oscillation. This circuit could oscillate on any number of frequencies. Even minor noise pulses could change oscillator frequency. An oscillator should have a constant output so a means of setting frequency is necessary.

Here, the frequency selectivity of the parallel LC network is useful because the network resonates at a specific frequency determined by the values of inductance and capacitance. Also, because the inductor and capacitor are reactive, they can produce the required 180 º phase shift. Therefore, a tank circuit in the positive feedback loop, as shown below, controls the frequency. The tank resonates at its natural frequency and amplifier gain replaces energy lost in the tank.

A similar result is obtained if the regenerative feedback loop contains enough RC networks to produce the desired 180 º phase shift. Here, RC time constants determine oscillator frequency and the amplifier replaces energy lost across the RC networks.

Up to this point, the oscillators were amplifiers with input signals applied to start the circuit. In actual practice, oscillators must start on their own. This is a natural phenomenon. When a circuit is first turned on, energy levels do not instantly reach maximum, but gradually approach it. This produces many noise pulses that can be phase shifted and fed back to the input.

The amplifier steps up these pulses, which are again supplied to the input. This action continues and oscillation is underway.

Therefore, the oscillator is naturally "self-excited", meaning it starts on its own.

The basic oscillator, and a breakdown of circuit parameters, is shown below.

In this simplified drawing, A represents amplifier gain, B is the feedback factor (the percentage of output returned to the input) and A´ is overall stage gain. These parameters are illustrated mathematically in the stage gain formula below:

A´ = A / (1-AB)

Where, A´ = stage gain

A = amplifier gain

B = feedback factor (%)

Since the oscillator must produce its own input signal and this condition must occur continuously, the product of amplifier gain (A) and feedback factor (B) must equal 1, or a condition of unity. Plug this value into the stage gain formula :

A´ = A / (1-AB) = A / (1- 1) = A / 0 = ∞

When the product of amplifier gain and feedback factor is equal to 1, the denominator of the gain equation is 0, resulting in infinite stage gain. This may seem impractical, but it is very practical, even desirable for oscillators. Infinite stage gain implies that a signal is present at the output, without an input. This is one of the conditions required for an oscillator. The qualification that AB = + 1 for oscillation is known as the "Barkhausen Criterion"

With infinite stage gain, you might think that output would continually increase. This happens when the oscillator initially starts, but after a few oscillations, the amplifier saturates and brings the oscillator quickly under control. When an amplifier is saturated, it is providing maximum gain. This has a damping effect, returning the feedback product (AB) to one.

Oscillator designers strive for a feedback product (AB) of slightly greater than 1. When AB is at this point, maximum stability and the cleanest output waveform results. If the feedback product is too small, the circuit cannot sustain oscillation. If it is too large, output waveform clipping results. Clipping is desirable in some oscillators but not in sine wave oscillators.

THE TRANSFORMER OSCILLATOR

The simplest oscillator that applies the principle of positive feedback, a tuned LC circuit and shock excitation, is the Armstrong or “tickler coil" oscillator shown above. This oscillator requires a phase shift for positive feedback. One of the easiest methods to obtain the 180 º phase shift is to use a transformer. The 180 º phase shift between primary and secondary makes the transformer ideal.

Coils L1 and L2 are the primary and secondary windings of transformer T1. The primary winding L1 is connected between the collector of Q1 and the supply, +Vcc. Capacitor C1 and the primary winding form a parallel resonant circuit that determines the oscillator frequency. L2 is loosely coupled to L1 and is known as a tickler coil. As mentioned previously, the transformer is wound so that the voltage induced into L2 is 180 º out of phase with the voltage across the tank circuit. This provides the positive feedback necessary for oscillation. For simplicity, bias components and coupling capacitors are eliminated.

The bias components make the oscillator "self-starting." When the circuit is initially energized, the bias circuit (not shown) establishes emitter-to-base current in transistor Q1. This turns on Q1 and collector current is through L1 to +Vcc as shown below. This changing current through L1 produces a magnetic field around L2 and induces a voltage that is 180 º out of phase with the voltage across L1. The voltage across L2 is applied directly to the base of Q1. This positive voltage increases the emitter-to-base current and Q1 is biased further into conduction. This action continues, as the feedback voltage developed across L2 increases base-emitter bias, resulting in more Q1 collector current. Capacitor C1 is charging through transistor Q1 to the polarity shown.

Finally, Q1 saturates. Except for the voltage dropped across the transistor, C1 is charged to source potential. At saturation, Q1 is conducting its maximum current with no further increase possible. Since current is no longer changing, the field around L1 stops expanding and no voltage is induced into the L2 winding. Remember, to induce a voltage there must be motion. ...the changing magnetic field of L1 provides this motion. The overall effect removes forward bias from Q1. Q1 ceases conduction.

So, the following conditions are present in the circuit:

C1 is charged to source potential and Q1 is no longer forward biased. The field around L1 collapses and capacitor C1 begins to discharge through L1 as shown. The flywheel effect of the tank circuit has begun.

When capacitor C1 completely discharges its energy is stored in L1. The field collapses and capacitor C1 charges in the direction shown. The base of L1 is now biased in the negative direction as Q1 is further driven into cutoff.

Now capacitor C1 discharges through L1 in the opposite direction and the field around L1 builds up again.

The base bias of Q1, although still negative, is going in a positive direction. When C1 completely discharges, L1 stores tank energy in its field. This field collapses and C1 begins to charge to its original potential.

The collapsing field of L1 induces a voltage into L2 that biases Q1 on again. Q1 conducts and charges C1 to source potential, Q1 saturates, the tank takes over and the cycle repeats. At this point, the circuit is oscillating and the tank is providing transistor bias. Transistor Q1 acts like a switch, conducting to replace energy lost in the tank. This action is similar to manually closing the switch

in the basic tank circuit, as the energy is replaced by charging C1.

The Tuned-Collector Oscillator

The Figure below is the circuit just discussed with bias components added. Since the tuned circuit is connected in the collector of Q1 this is known as a tuned-collector oscillator. The parallel network of L1 and C1 determine oscillator frequency. C1 is variable so the frequency can be changed. Oscillator output is taken off by adding a winding on the transformer.

The Tuned-Base Oscillator

Another variation of the Armstrong oscillator is shown below. In this configuration, the tuned circuit is across the base of Q1, hence the name "tuned-base oscillator." Component functions are similar to those in the tuned-collector oscillator. Transformer winding L1 and capacitor C1 form the tuned circuit that determines oscillator frequency. C1 is variable to permit frequency adjustment. Tickler coil L2 is in the collector circuit and is inductively coupled to L1 to provide positive feedback. Again, the output is taken off by adding another transformer secondary winding.

LC OSCILLATORS

Most oscillators work on the feedback principle, which means that feed-back is necessary to sustain oscillation. Therefore, oscillators are generally classified according to the frequency determining components. The three classifications are:

L-C Oscillators

R-C Oscillators

Crystal Oscillators

LC oscillators use a tuned circuit consisting of either a parallel-connected or series-connected capacitor and inductor to set the frequency. The Armstrong oscillator just discussed is an LC oscillator, since the transformer primary and shunt capacitor form a parallel resonant circuit. We will continue to examine LC oscillators that produce sine wave outputs.

The Series-Fed Hartley

One of the undesirable features of the Armstrong oscillator is that the tickler coil has a tendency to resonate with the distributed capacitance in the circuit. This results in oscillator frequency variations. If the tickler coil is made a part of the tuned circuit, the unstable effect of the tickler coil can be overcome. In the Hartley oscillator, below, the tickler coil becomes a part of the tuned circuit. The inductor is tapped to form two coils. L1A and L1B. Tuning capacitor C1 is connected across inductor L1, making the entire coil part of a tuned circuit.

Resistors R1 and R2 forward bias the base-emitter junction of Q1 when the circuit is initially turned on. Transistor Q1 conducts and collector current is through the lower section of coil L1 (L1B), through Q1 and collector load resistor R3. The current through L1B induces current into L1A because of the mutual inductance of the two coils. The result is a positive potential at the top of L1A, that is coupled to the base of Q1 by capacitor C2. This increases the forward bias on Q1 and Q1 quickly saturates.

Once Q1 saturates, the current through L1A is no longer changing and no voltage is induced into L1A. This removes forward bias from Q1 and conduction rapidly decreases. The field around L1B collapses and again induces current into L1A. The polarity of this induced current is such that the top of L1A is negative. This negative potential is felt on the base of Q1, reverse biasing Q1 and quickly driving it into cutoff. During this time, tank capacitor C1 charges to a negative potential. When Q1 is completely cut off, capacitor C1 begins to discharge and tank action begins.

During the cycle of tank oscillation when the upper plate of C1 begins to accumulate a positive charge, Q1 is again forward biased and conducts through section L1B of the tank coil. Conduction through the lower section of the tank coil replaces energy lost in the tank, providing the positive feedback necessary for oscillation. The amount of feedback can be controlled by varying the position of the coil tap.

Since emitter current flows through a portion of the tank coil, the oscillator is said to be "series-fed." This series-fed arrangement and the tapped coil are the identifying features of a series-fed Hartley oscillator.

The disadvantage of the series-fed Hartley is that DC current flows through a portion of the tank, increasing power losses in the circuit. This results in a lower circuit Q and causes the oscillator to become unstable.

The Shunt-Fed Hartley

Below is a schematic of another type of Hartley oscillator known as the shunt-fed Hartley. The tapped coil, L1, immediately identifies this as a Hartley oscillator. Unlike the series-fed Hartley, no DC current passes through the tank coil, hence the name "shunt-fed." This keeps circuit Q high, resulting in better frequency stability.

The bias circuit, which is similar to the series-fed Hartley, has been deleted for simplicity. The parallel network of L1 and C1 set the frequency at which the circuit oscillates. Capacitor C1 is variable so the oscillator frequency can be adjusted. Capacitor C2 is a coupling capacitor between the resonate tank and the base of Q1. The radio frequency choke (RFC) acts as a collector load and effectively blocks high frequency AC oscillations from the power supply. Collector AC variations are coupled to the tank by capacitor C3.

When the circuit is initially energized, the bias circuit (not shown) forward biases Q1. Q1 conducts and the change in current through RFC results in a drop in collector voltage. Capacitor C3 couples this change in voltage to the bottom of the tank, supplying energy to the tank. Since the tap on L1 is grounded, opposite ends of L1 will be at different potentials, placing a positive potential at the top of coil L1. This positive potential is coupled to the base of Q1, further forward biasing the transistor. Q1 quickly saturates.

With Q1 saturated, there is no change in collector current. Therefore, AC is no longer coupled to the bottom of the tank. The field around the inductor collapses, charging the top plate of capacitor C1 to a negative potential. At this point, C1 is charged negative and the field around L1 has completely collapsed. C1 discharges through the tank, simultaneously reverse biasing Q1. Q1 is rapidly cut off. Tank flywheel action takes over for one oscillation. When tank action charges the top plate of C1 positive, Q1 is turned on again and the cycle continues.

Follow the solid arrow in Figure and trace the path of DC current through the oscillator. DC current is through transistor Q1 and RFC, returning to the power supply. Follow the dashed arrow for the AC current path and notice that AC current is through Q1, coupling capacitor C3 and the lower section of coil L1. Therefore, no DC current passes through the tank and positive feedback is AC coupled through C3.

Remember, Hartley oscillators are easily identified by the tapped coil in the tuned circuit. If DC collector current passes through a portion of the tank circuit, the oscillator is "series-fed". If feedback is AC coupled through a capacitor, the oscillator is "shunt-fed".

The Colpitts Oscillator

The Colpitts oscillator is similar to the shunt-fed Hartley except two capacitors are used instead of a tapped coil. Essentially, the Colpitts is shunt-fed , so DC collector current does not pass through the choke. Since the Colpitts is more stable than the Hartley, it is used in many signal generators. Below is the schematic of a Colpitts oscillator. Bias networks, eliminated for simplicity, are similar to other transistor oscillators discussed. The tapped capacitor arrangement identifies the Colpitts oscillator. As with all LC oscillators, frequency is determined by inductor L1 and the series combination of capacitors C1 and C2. Capacitor C3 couples AC collector voltage to the tank, while blocking DC.

Since the oscillator is a common-emitter configuration, collector voltage is 180º out of phase with base voltage. The arrangement of capacitors C1 and C2 in a voltage-divider network produces the desired 180º phase shift across capacitor C1, resulting in regenerative or positive feedback. The feedback factor, usually 0.1 to 0.5, is determined by the ratio of C1 to C2. Feedback increases if the value of C1 is lowered. Although the combination of C1 and C2 determines oscillator frequency, C2 has the most pronounced effect on frequency.

The Colpitts is shock-excited into oscillation much like the other oscillators. Initial forward bias is furnished by the bias network and Q1 begins to conduct. The DC collector current path is from emitter to collector, through the RFC, returning to the power supply. This initial surge of current causes a negative voltage drop across the RFC, since the change is rapid. Capacitor C3 couples this negative voltage to the lower plate of capacitor C2. For simplicity, the following discussion will cover only the AC current path in the tank circuit.

Figure A shows the tank circuit with a negative potential at the bottom plate of C2. This negative potential is felt across the entire tank, charging the top plate of C1 to a positive potential through inductor L1. The end result is that the feedback voltage across C1 is phase shifted 180°, producing regenerative feedback. Q1 is further forward biased and quickly saturates. With Q1 saturated, there is no voltage drop across RFC, because current is no longer changing. The flywheel effect of the tank then takes over (Figure B) as C1 and C2 act as one capacitor discharging through L1 and building up the magnetic field.

When the capacitors are completely discharged, the field collapses and charges the top plate of C1 negative, reverse biasing Q1. Q1 is driven into cutoff. When feedback capacitor C1 is fully charged, it discharges through L1. Again, a field is built up around L1 that subsequently collapses and charges C1 in the opposite direction (Figure C). Transistor Q1 is now forward biased and conducts. Thus, energy lost in the tank is replaced. A similar action occurs each cycle as positive feedback replenishes energy expended.

As mentioned previously, the series combination of C1 and C2 determines oscillator frequency. However, C1, the feedback capacitor, controls the amount of feedback. This is the result of the series voltage-divider arrangement of C1 and C2. If the capacitance of C1 is decreased, the amount of feedback is increased. Remember the formula for capacitive reactance (Xc):

↑Xc = 1 / (2 π F C↓)

A decrease in capacitance C, results in an increase in opposition (Xc). Therefore, a larger feedback voltage is developed across this increased opposition. As mentioned previously, the feedback factor is determined by the ratio or the two capacitors.

Feedback Factor (B) = C2/C1

The feedback factor for the Colpitts is typically 0.1 to 0.5, or 10 to 50%. Too much feedback distorts the output waveform, as transistor Q1 is saturated for long periods of time. A feedback factor of less than 10% may not be sufficient to sustain oscillation.

Usually the tapped capacitors are variable and frequently are ganged together. This arrangement permits adjustment of oscillator frequency. But, the ganged capacitor arrangement has a disadvantage; as frequency is varied, feedback changes. At one end of the frequency range, there is too much feedback and the output waveform is distorted. At the other end, feedback is small and cannot sustain oscillation. These factors, combined with the distributed capacitance of the circuit, limit the adjustable frequency range of the Colpitts oscillator.

The Clapp Oscillator

The Clapp oscillator, below, is a variation of the Colpitts. The only difference is the addition of variable capacitor C3. Capacitor C3 forms a series-resonant circuit with inductor L1 and allows capacitor tuning without affecting the feedback ratio. C3 is small, in relation to C1 and C2. Therefore, C3 effectively determines oscillator frequency. The theory of operation is identical to the Colpitts discussed in the previous section.

CRYSTAL CONTROLLED OSCILLATORS

LC oscillators, such as those just discussed, are widely used. However, in applications where extreme oscillator stability is required, the LC oscillator is unsatisfactory. Temperature changes, component aging and load fluctuations cause oscillator drift, which makes the oscillator unstable. When a high degree of stability is required, crystal oscillators are generally used.

What is meant by a high degree of stability? Suppose an acceptable frequency change is one part per million (ppm). The allowable oscillator drift then would be 0.0001%. Compare this with the stability of the LC oscillators, where 1 % frequency drift is common. If an electronic clock had a timing oscillator that drifts 1%, the clock could either gain or lose 14 minutes each day and still be within oscillator tolerance. However, if the clock oscillator is stable to within 0.0001 %, the maximum time lost or gained each day is 0.09 seconds, or 32 seconds each year. To achieve this accuracy, electronic clocks use crystal oscillators as the basic timing device.

Crystal Characteristics

Crystal materials produce piezoelectricity. That is, when mechanical pressure is applied to a crystal, a difference in potential is developed. Figures below illustrates this point. A normal crystal has changes evenly distributed and is therefore neutral. If force is applied to the sides of the crystal, the crystal is compressed and opposite changes accummulate on the sides ..... a difference in potential is developed.

Crystal microphones use this principle. Rochelle salt, a crystalline material, is alternately compressed and stretched by sound waves. The salt crystals in the microphone generate a small voltage corresponding to sound wave variations. Just the opposite effect occurs if AC voltage is applied to a crystal. The electrical energy from the voltage source is converted to mechanical energy in the crystal, see below. The AC input signal causes the crystal to stretch and compress, which creates mechanical vibrations that correspond to the frequency of the AC signal.

Because of their structure, crystals have a natural frequency of vibration. If the frequency of the applied AC signal matches this natural frequency, the crystal will stretch and compress a large amount. However, if the frequency of the exciting voltage is slightly different than the crystal's natural frequency, little vibration is produced. The crystal, therefore, is extremely frequency selective, making it desirable for filter circuits. The crystal's mechanical frequency of vibration is extremely constant, which makes it ideal for oscillator circuits.

Many crystals produce piezoelectricity, but three types are the most useful: Rochelle salt, Tourmaline, and Quartz. Rochelle salt has the greatest electrical activity, but it is also the weakest and fractures easily. Tourmaline has the least electrical activity, yet it is the strongest of the three. Quartz is a compromise, since it is inexpensive, rugged, and has good electrical activity. Therefore, Quartz is the most commonly used crystal in oscillator circuits.

The natural shape of quartz is a hexagonal prism with pyramids at the ends. Slabs are cut from the natural crystal, or "mother stone," to obtain a usable crystal. There are many ways to cut a crystal, all with different names; such as the X cut, Y cut, X- Y cut, and AT cut. Each cut has a different piezoelectric property. For example, the AT cut has a good temperature coefficient, meaning the frequency changes very little with temperature changes. The other cuts also have characteristics that are desirable for specific applications.

The natural frequency of a crystal is usually determined by its thickness. The thinner the crystal, the higher its natural frequency. Conversely, the thicker a crystal, the lower its natural frequency. To obtain a specific frequency, the crystal slab is ground to the required dimensions. Of course, there are practical limits on just how thin a crystal can be cut, without it becoming extremely fragile. This places an upper limit on the crystal's natural frequency, around 50 MHz.

To reach higher frequencies, crystals are mounted in such a way that they vibrate on "overtones" or harmonics of the fundamental frequency. For example, a 10 MHz crystal can be mounted so it vibrates at 20 MHz, the first overtone. The same crystal could be mounted to operate on the second overtone, 30 MHz.

Equivalent Crystal Circuits

A crystal is usually mounted between two metal plates and a spring applies mechanical pressure on the plates. The metal plates secure the crystal and also provide electrical contact. The crystal is then placed in a metal casing or holder. The schematic symbol for a crystal is derived from the way it is mounted and represents the crystal slab held between two plates. The word crystal is often abbreviated "XTAL" or "Y" on schematics.

The crystal alone looks electrically like a series-resonant circuit. In the series equivalent circuit, inductance (L), represents the crystal mass that effectively causes vibration; C represents crystal stiffness, which is the equivalent of capacitance; R is the electrical equivalent of internal resistance caused by friction. Therefore, at the crystal's natural mechanical resonant frequency, the electrical circuit is series resonant and offers minimum impedance to current flow. When the circuit's characteristics are plotted on an impedance-frequency curve, it shows sharp skirts and minimum impedance at the series- resonant frequency. The sharp skirts indicate the highly-selective frequency characteristic of the crystal.

When the crystal is mounted between metal plates, the equivalent circuit is modified. The metal mounting plates now appear as a capacitor, Cp, in parallel with the series-resonant circuit of the crystal. The value of Cp is relatively high and, at lower frequencies, does not appreciably affect the series-resonant circuit of the crystal. However, at frequencies above the crystal's series-resonant frequency, the inductive reactance of the crystal is greater than the crystal's capacitive reactance, and the crystal appears inductive. At these higher frequencies, a point is reached where the inductive reactance of the crystal equals the capacitive reactance of the mounting plates (XL = XC). Here, equivalent circuit is parallel-resonant and impedance is maximum. The electrical equivalent of the crystal at this frequency is a parallel-tuned LC circuit. Therefore, a crystal has two resonant frequencies.

At the natural mechanical frequency of the crystal, the crystal is series- resonant and impedance is minimum. At a slightly higher frequency, the crystal and the capacitance of its mounting plates form a parallel- resonant circuit and impedance is maximum. The overall crystal response curve is illustrated below.

As mentioned before, a crystal is highly frequency selective as indicated by the sharp skirts in the response curve. This is natural, since a crystal has an extremely high Q, sometimes approaching a Q of 50,000. When Q's of this value are compared with the Q of an LC circuit, usually 100, it is clear why crystal oscillators are more stable than normal LC oscillators. You will also find that crystal oscillators use either the series-resonant or parallel-resonant characteristic.

The Hartley Crystal Oscillator

The circuits below are shunt-fed Hartley oscillator. The bias network is eliminated for simplicity. The Hartley is a typical LC oscillator and, although fairly stable, frequency drifts of 1 % are common. If the Hartley oscillator is to be operated at a specific frequency and a high-degree of stability is required, a crystal can be inserted in the circuit. However, if the frequency of this oscillator is to be changed, even by a fraction of a percent, the crystal must be replaced.

Notice that in Hartley crystal oscillators, the crystal is connected in series with the feedback path. Therefore, the crystal operates at its series- resonant frequency. Also, the LC tank network must be tuned to the series-resonant frequency of the crystal.

When the oscillator is operating at the crystal frequency, the crystal's equivalent series-resonant circuit offers minimum opposition to current and feedback is maximum. If the oscillator drifts away from the crystal frequency, the impedance of the crystal increases drastically, reducing feedback. This forces the oscillator to return to the natural frequency of the crystal. Therefore, when the crystal is series-connected, it controls feedback.

The Colpitts Crystal Oscillator

The Colpitts oscillator can be crystal controlled in the same manner as the Hartley. Again, crystal Y1 is connected in series with the feedback path, as shown below. Biasing networks are also eliminated from this circuit. Since the crystal is series-connected, it controls feedback and the LC tank circuit is tuned to the crystal frequency. Otherwise, operation is identical to the basic Colpitts oscillator you studied earlier.

The Pierce Oscillator

The Pierce oscillator is similar to the basic Colpitts, except the tank inductor is replaced with a crystal operating at is parallel resonant frequency. Crystal Y1 replacing the tank coil. Remember, the crystal's parallel-resonant frequency is slightly higher than its series-resonant frequency and appears as an inductor.

The voltage divider arrangement of capacitors C1 and C2 provides the 180° phase shift between the collector and emitter of Q1, resulting in positive feedback. The ratio of these two capacitors also determines the feedback ratio and therefore, the crystal excitation voltage. Since the crystal's response is extremely sharp, it will vibrate only over a narrow range of frequencies, producing a stable output.

The crystal operates in its parallel-resonant mode, and controls the tuned circuit impedance. At resonance, tank impedance is maximum and a large feedback voltage is developed across capacitor C1. If frequency drifts above or below resonance, crystal impedance decreases rapidly, and decreases feedback. By controlling tank impedance, the crystal effectively determines feedback and stabilizes the oscillator,

The Butler Oscillator

The Butler crystal oscillator combines a tuned LC circuit with the frequency selectivity of a crystal. The Butler is a two transistor oscillator. Transistor Q2 operates as a common-base amplifier with a tuned collector circuit, while Q1 functions as an emitter follower. Crystal Y1 is connected between the emitters of the two transistors and operates in its series-resonant mode to control feedback. Bias components have been omitted for simplicity.

When the circuit is first energized, transistor Q2 is forward biased by the initial bias circuit (not shown). Q2 conducts, developing a negative-going voltage at the bottom of the collector tank circuit. Capacitor C3 couples this negative potential to the base of Q1, cutting Q1 off. Transistor Q2 quickly saturates. At this point, transistor Q1 begins to conduct. The resulting positive voltage drop across the emitter resistor R2 is coupled to the emitter of Q2 by the crystal and is developed across resistor R1. This positive potential on the emitter of Q2 reverse biases Q2 and it begins to cut off. Consequently, the collector voltage of Q2 starts to go more positive. This change is coupled to Q1 through C3, increasing the forward bias on Q1. Q1 conducts harder and Q2 is driven into cutoff. The tank action of the tuned LC circuit takes over and reverse biases Q1, cutting it off. As Q1 ceases conduction, Q2 is forward biased and the cycle repeats.

Since positive feedback is through crystal Y1, the oscillator is operating at the crystal's series-resonant frequency. At its series resonant frequency, the crystal presents a low impedance path between the emitters and feedback is maximum. If frequency drifts, however, the crystal decreases feedback and forces the oscillator back on frequency.

The tuned LC circuit is important because, if the tank circuit is not tuned to the crystal frequency, the oscillator will not work. The combined effect of the tuned circuit and the crystal results in good oscillator performance.

One advantage of the Butler oscillator is that very small voltages exist across the crystal, reducing crystal strain and contributing to stable operation. The Butler oscillator is very versatile and can easily be tuned to operate at one of the crystal's overtone frequencies. Of course, this usually requires replacing the tank components.

RC OSCILLATORS

Up to this point, LC and crystal oscillators that are commonly used in RF applications have been discussed. However, in the low and audio frequency ranges, these oscillators are usually not practical. For example, inductors for the low frequency range, around 50 Hz, would be large and expensive. And, the practical low limit on crystals is usually around 50 kHz. So an inexpensive approach to oscillator design in these low frequency ranges is the RC oscillator. The RC oscillator uses resistance-capacitance networks to determine oscillator frequency. This makes the oscillator inexpensive, easy to construct and relatively stable. There are basically two types of RC oscillators that produce sine wave outputs; the phase-shift oscillator and the Wien bridge oscillator. Many other RC oscillators, such as the multivibrator and Schmitt trigger, produce non-sinusoidal outputs.

The Phase-Shift Oscillator

The phase-shift oscillator is a conventional amplifier and a phase shifting RC feedback network. It is typically used in fixed frequency applications. As in the conventional LC oscillator, the collector output signal must be shifted 180° to produce the required regenerative feedback. The phase-shift oscillator accomplishes this with a series of RC networks connected in the collector-to-base feedback loop.

Briefly review the basic principles of an RC phase-shift network. Remember that in a purely capacitive circuit, current leads voltage by 90°, However, in an RC network the phase difference between current and voltage falls between 0° and 90°, because resistance now affects the phase relationship. Thus, the phase difference in an RC circuit is a function of the capacitive-reactance (Xc) and resistance of the network. By carefully selecting the resistance and capacitive values, the amount of phase shift across an RC network can be controlled.

Resistance does not vary with frequency. However, the capacitor is frequency sensitive, since its reactance changes with frequency. Therefore, any change in frequency, changes Xc. As Xc changes, the phase shift of the RC network also varies. Hence, the capacitor is the frequency sensitive component in the RC network.

Below is an RC network with a 55 Hz AC input signal applied The output is taken across the resistor and therefore the output voltage leads the input by 60°. It is important to note that, if the frequency increases or decreases from 55 Hz, Xc changes, resulting in a different phase shift. The 60° phase shift is the result of R, C, and the 55 Hz frequency of the applied signal as shown by the voltage vectors.

If three such 60° phase-shift networks are cascaded, as shown above, the combined phase shift is 180°. Each network contributes 60° to the total phase shift of 180°. This condition only occurs for a 55 Hz input signal. If the frequency of the input signal increases, the total phase shift decreases. Likewise, a decrease in frequency results in an increase in phase shift.

Since one requirement of an oscillator is a 180° phase shift between input and output, placing this network between the collector and base of a common-emitter amplifier results in a phase-shift oscillator, see below. The phase-shift network comprised of R1C1, R2C2, and R3C3 is connected between the collector and base of Q1, providing the 180° phase shift that makes the circuit regenerative. Since there is a considerable power loss across the RC networks, transistor gain must be high enough to compensate for these losses. Usually a voltage gain of between 30 and 50 is required.

Transistor Q1 operates between saturation and cutoff. The bias network is omitted for simplicity. Initial conduction causes a decrease in collector voltage. Collector voltage is shifted 180° by the RC networks, placing a positive potential on the base of Q1, further biasing it into saturation. When Q1 saturates, the forward bias of Q1 decreases, with the process continuing until Q1 is cut off. This action is repeated continually. As a result, the collector voltage varies in a sinusoidal manner, producing a slightly distorted sine wave output.

Since each phase-shift network must produce a 60° phase shift, the circuit will naturally oscillate at the frequency at which this phase shift occurs. The approximate frequency of oscillation can be determined with the formula:

F₀ = 1/ (19RC)

where, R is the value of one resistor and C is the value of one capacitor.

The phase-shift oscillator functions best at fixed frequencies, since any variation of resistance or capacitance upsets the phase shift. However, it is possible to change the frequency over a small range by varying the resistance or capacitance of the RC networks. Stability can be improved by increasing the number of RC networks, thereby reducing the phase shift across each network.

The Wien-Bridge Oscillator

Like the phase-shift oscillator, the Wien-Bridge uses RC networks. However, in the Wien-Bridge oscillator, the RC networks are part of a bridge circuit that produces both regenerative and degenerative feedback. The result is an excellent sine wave oscillator that can be used to generate frequencies ranging from 5 Hz to 1 MHz. In the phase-shift oscillator, the RC networks produce the desired 180° phase shift for regenerative feedback. In the Wien-Bridge oscillator, the RC networks select the frequency at which feedback occurs, but do not shift the phase of the feedback voltage. It is easy to understand the bridge oscillator if you understand the regenerative feedback network.

The circuit below includes a lead-lag network. It is a simple bandpass filter comprised of a series RC network, R1C1, and a parallel RC network, R2C2. The output phase angle leads for some frequencies and lags for others. However, at the resonant frequency, the phase shift is exactly 0°. This allows the lead-lag network to determine oscillator frequency in the Bridge oscillator.

The resonant frequency of the lead-lag network is calculated using the formula:

If the two resistors are equal in value and the two capacitors are also equal, which is frequently the case, the resonant frequency formula is simplified:

We apply this lead-lag network to the Wien-bridge oscillator above an operational amplifier as the active device. The lead-lag network makes up one side of the bridge. A voltage divider, R3 and R4, is the remaining leg of the bridge. The inverting and non-inverting inputs of the op amp make it ideal for use in the Wien-bridge oscillator, since regenerative and degenerative feedback are required. The op amp's high gain is also very useful in offsetting circuit losses.

Op amp output is fed back to the bridge input. Regenerative feedback is developed across the lead-lag network and is applied to the non-inverting input. Therefore, regenerative feedback is in phase with the output signal. Degenerative feedback is developed across resistors R3 and R4 and is applied to the inverting input. Of course, for the circuit to oscillate, regenerative feedback must be greater than degenerative feedback.

Degenerative feedback remains constant regardless of the frequency, since the resistance values do not change. However, regenerative feedback depends on the frequency response of the lead-lag network which is frequency sensitive.

Component values are selected so that, at the desired oscillator frequency, regenerative feedback is larger than degenerative feedback and oscillation occurs. If however, oscillator frequency attempts to increase, the reactance of capacitor C2 will decrease and shunt more voltage to ground, reducing regenerative feedback. Likewise, a decrease in frequency increases the reactance of C1. Less voltage is developed across the R2C2 network and again regenerative feedback is reduced. Only over a narrow range of frequencies, set by the lead-lag network, will regenerative feedback be great enough to sustain oscillation. Thus, the oscillator is forced on frequency by this network.

Oscillator frequency may be varied by changing either the resistance or capacitance in the lead-lag network. Usually resistors R1 and R2 are ganged potentiometers, permitting frequency variations. The formula shows that an increase in resistance or capacitance decreases oscillator frequency. Conversely, a reduction in resistance or capacitance increases oscillator frequency.

The IC Wien-Bridge oscillator is simple to construct and relatively inexpensive. Before integrated circuits were widely used for electronic design, Wien-Bridge oscillators were assembled from discrete components, see below circuit.