SECTION OUTLINE
_1 The Oscillator
_2 Feedback Oscillators
_3 Oscillators with RC Feedback Circuits
_4 Oscillators with LC Feedback Circuits
_5 Relaxation Oscillators
_6 The 555 Timer as an Oscillator Application Activity Programmable Analog
Technology
GOALS
 Describe the operating principles of an oscillator
 Discuss the principle on which feedback oscillators is based
 Describe and analyze the operation of RC feedback oscillators
 Describe and analyze the operation of LC feedback oscillators
 Describe and analyze the operation of relaxation oscillators
 Discuss and analyze the 555 timer and use it in oscillator applications
TERMS USED
 Oscillator
 Positive feedback
 Voltagecontrolled oscillator (VCO)
 Astable
APPLICATION ACTIVITY PREVIEW
The application in this Section is a circuit that produces an ASK signal
for testing the RFID reader developed in the last Section.
The ASK test generator uses an oscillator, a 555 timer, and a JFET analog
switch to produce a 125 kHz carrier signal modulated at 10 kHz by a digital
signal. The output amplitude is adjustable down to a low level to simulate
the RFID tag signal.
INTRODUCTION
Oscillators are electronic circuits that generate an output signal without
the necessity of an input signal. They are used as signal sources in all
sorts of applications. Different types of oscillators produce various types
of outputs including sine waves, square waves, triangular waves, and sawtooth
waves.
In this Section, several types of basic oscillator circuits using both
discrete transistors and opamps as the gain element are introduced. Also,
a popular integrated circuit, the 555 timer, is discussed in relation to
its oscillator applications.
Sinusoidal oscillator operation is based on the principle of positive
feedback, where a portion of the output signal is fed back to the input
in a way that causes it to reinforce itself and thus sustain a continuous
output signal. Oscillators are widely used in most communications systems
as well as in digital systems, including computers, to generate required
frequencies and timing signals. Also, oscillators are found in many types
of test instruments like those used in the laboratory.
1. THE OSCILLATOR
An oscillator is a circuit that produces a periodic waveform on its output
with only the dc supply voltage as an input. A repetitive input signal
is not required except to synchronize oscillations in some applications.
The output voltage can be either sinusoidal or nonsinusoidal, depending
on the type of oscillator. Two major classifications for oscillators are
feedback oscillators and relaxation oscillators.
After completing this section, you should be able to:
 Describe the operating principles of an oscillator
 Discuss feedback oscillators
 List the basic elements of a feedback oscillator ? Show a test setup
 Briefly describe a relaxation oscillator
 State the difference between a feedback oscillator and a relaxation
oscillator
Essentially, an oscillator converts electrical energy from the dc power
supply to periodic waveforms. A basic oscillator is shown in FIG. 1.
FIG. 1 The basic oscillator concept showing three common types of output
wave forms: sine wave, square wave, and sawtooth.
Feedback Oscillators
One type of oscillator is the feedback oscillator,
which returns a fraction of the output signal to the input with no net
phase shift, resulting in a reinforcement of the output signal. After
oscillations are started, the loop gain is maintained at 1.0 to maintain
oscillations. A feedback oscillator consists of an amplifier for gain (either
a discrete transistor or an opamp) and a positive feedback circuit that
produces phase shift and provides attenuation, as shown in FIG. 2.
FIG. 2 Basic elements of a feedback oscillator.
Relaxation Oscillators
A second type of oscillator is the relaxation oscillator. Instead of feedback,
a relaxation oscillator uses an RC timing circuit to generate a waveform
that is generally a square wave or other nonsinusoidal waveform. Typically,
a relaxation oscillator uses a Schmitt trigger or other device that changes
states to alternately charge and discharge a capacitor through a resistor.
Relaxation oscillators are discussed in SECTION 5.
1. What is an oscillator?
2. What type of feedback does a feedback oscillator require?
3. What is the purpose of the feedback circuit?
4. Name the two types of oscillators.
_2 FEEDBACK OSCILLATORS
Feedback oscillator operation is based on the principle of positive feedback.
In this section, we will examine this concept and look at the general conditions
required for oscillation to occur. Feedback oscillators are widely used
to generate sinusoidal waveforms.
After completing this section, you should be able to:
 Discuss the principle on which feedback oscillators is based
 Explain positive feedback
 Define oscillation
 Describe the conditions for oscillation
 Define closed loop gain
 Discuss the conditions required for oscillator startup
Positive Feedback
Positive feedback is characterized by the condition wherein a portion
of the output voltage of an amplifier is fed back to the input with no
net phase shift, resulting in a reinforcement of the output signal. This
basic idea is illustrated in FIG. 3(a). As you can see, the in phase feedback
voltage, Vf is amplified to produce the output voltage, which in turn produces
the feedback voltage. That is, a loop is created in which the signal sustains
itself and a continuous sinusoidal output is produced. This phenomenon
is called oscillation. In some types of amplifiers, the feedback circuit
shifts the phase and an inverting amplifier is required to provide another
phase shift so that there is no net phase shift. This is illustrated in
FIG. 3(b).
FIG. 3 Positive feedback produces oscillation.
Conditions for Oscillation
Two conditions, illustrated in FIG. 4, are required for a sustained state
of oscillation:
1. The phase shift around the feedback loop must be effectively
2. The voltage gain, around the closed feedback loop (loop gain) must
equal 1 (unity).
FIG. 4 General conditions to sustain oscillation.
The voltage gain around the closed feedback loop, is the product of the
amplifier gain, and the attenuation, B, of the feedback circuit.
Acl = Av B
If a sinusoidal wave is the desired output, a loop gain greater than 1
will rapidly cause the output to saturate at both peaks of the waveform,
producing unacceptable distortion. To avoid this, some form of gain control
must be used to keep the loop gain at exactly 1 once oscillations have
started. For example, if the attenuation of the feedback circuit is 0.01,
the amplifier must have a gain of exactly 100 to overcome this attenuation
and not create unacceptable distortion.
An amplifier gain of greater than 100 will cause the oscillator to limit
both peaks of the waveform.
StartUp Conditions
So far, you have seen what it takes for an oscillator to produce a continuous
sinusoidal out put. Now let's examine the requirements for the oscillation
to start when the dc supply voltage is first turned on. As you know, the
unitygain condition must be met for oscillation to be sustained. For oscillation
to begin, the voltage gain around the positive feedback loop must be greater
than 1 so that the amplitude of the output can build up to a desired level.
The gain must then decrease to 1 so that the output stays at the desired
level and oscillation is sustained. Ways that certain amplifiers achieve
this reduction in gain after startup are discussed in later sections of
this Section. The voltage gain conditions for both starting and sustaining
oscillation are illustrated in FIG. 5.
A question that normally arises is this: If the oscillator is initially
off and there is no out put voltage, how does a feedback signal originate
to start the positive feedback buildup process? Initially, a small positive
feedback voltage develops from thermally produced broadband noise in the
resistors or other components or from power supply turnon transients.
The feedback circuit permits only a voltage with a frequency equal to the
selected oscillation frequency to appear in phase on the amplifier's input.
This initial feedback voltage is amplified and continually reinforced,
resulting in a buildup of the output voltage as previously discussed.
FIG. 5 When oscillation starts at t0, the condition Acl > 1 causes
the sinusoidal output voltage amplitude to build up to a desired level.
Then Acl decreases to 1 and maintains the desired amplitude.
SECTION 2 CHECKUP
1. What are the conditions required for a circuit to oscillate?
2. Define positive feedback.
3. What is the voltage gain condition for oscillator startup?
_3 OSCILLATORS WITH RC FEEDBACK CIRCUITS
Three types of feedback oscillators that use RC circuits to produce sinusoidal
outputs are the Wienbridge oscillator, the phaseshift oscillator, and
the twinT oscillator.
Generally, RC feedback oscillators are used for frequencies up to about
1 MHz. The Wienbridge is by far the most widely used type of RC feedback
oscillator for this range of frequencies.
After completing this section, you should be able to
 Describe and analyze the operation of RC feedback oscillators
 Identify and describe the Wienbridge oscillator
 Discuss the response of a leadlag circuit
 Discuss the attenuation of the leadlag circuit
 Calculate the resonant frequency
 Discuss the positive feedback conditions for oscillation
 Describe the startup conditions
 Discuss a JFET stabilized Wienbridge oscillator
 Describe and analyze the phaseshift oscillator
 Discuss the required value of feedback attenuation
 Calculate the resonant frequency
 Discuss the twinT oscillator
The WienBridge Oscillator
One type of sinusoidal feedback oscillator is the Wienbridge oscillator.
A fundamental part of the Wienbridge oscillator is a leadlag circuit
like that shown in FIG. 6(a).R1 and C1 together form the lag portion of
the circuit; and form the lead portion. The operation of this leadlag
circuit is as follows. At lower frequencies, the lead circuit dominates
due to the high reactance of As the frequency increases, decreases, thus
al lowing the output voltage to increase. At some specified frequency,
the response of the lag circuit takes over, and the decreasing value of
causes the output voltage to decrease.
FIG. 6 A leadlag circuit and its response curve.
The response curve for the leadlag circuit shown in FIG. 6(b) indicates
that the out put voltage peaks at a frequency called the resonant frequency,
fr. At this point, the attenuation (Vout/Vin) of the circuit is 1/3 if
R and X_c1 = X_c2 as stated by the following equation:
EQN. 1
The formula for the resonant frequency (also derived on the companion
website) is:
EQN. 2
To summarize, the leadlag circuit in the Wienbridge oscillator has a
resonant frequency fr, at which the phase shift through the circuit is
and the attenuation is 1/3.
Below the lead circuit dominates and the output leads the input. Above
fr, the lag circuit dominates and the output lags the input.
FIG. 7 The Wienbridge oscillator schematic drawn in two different but
equivalent ways.
The Basic Circuit
The leadlag circuit is used in the positive feedback loop of an op amp,
as shown in FIG. 7(a). A voltage divider is used in the negative feedback
loop.
The Wienbridge oscillator circuit can be viewed as a noninverting amplifier
configuration with the input signal fed back from the output through the
leadlag circuit. Recall that the voltage divider determines the closedloop
gain of the amplifier.
Acl = 1 / B = 1 / [R2>(R1 + R2)] = [R1 + R2] / R2
The circuit is redrawn in FIG. 7(b) to show that the opamp is connected
across the bridge circuit. One leg of the bridge is the leadlag circuit,
and the other is the voltage divider.
Positive Feedback Conditions for Oscillation
As you know, for the circuit
to produce a sustained sinusoidal output (oscillate), the phase shift
around the positive feedback loop must be 0° and the gain around the loop
must equal unity (1). The 0° phaseshift condition is met when the frequency
is fr because the phase shift through the leadlag circuit is 0° and
there is no inversion from the noninverting (+_) input of the opamp to
the output. This is shown in FIG. 8(a).
FIG. 8 Conditions for sustained oscillation. (b) The voltage gain around
the loop is 1. (a) The phase shift around the loop is 0°.
The unitygain condition in the feedback loop is met when:
Acl = 3
This offsets the 1/3 attenuation of the leadlag circuit, thus making
the total gain around the positive feedback loop equal to 1, as depicted
in FIG. 8(b). To achieve a closedloop gain of 3,
R1 = 2R2
Then:
Acl = [R1 + R2]/ R2 = [2R2 + R2]/ R2 = 3R2/R2 = 3

HISTORY NOTE
Max Wien (18661938) was a German physicist. He theoretically developed
the concept of the Wienbridge oscillator in 1891. At that time, Wien did
not have a means of developing electronic gain, so a workable oscillator
could not be achieved. Based on Wien's work, William Hewlett, cofounder
of HewlettPackard, was successful in building a practical Wienbridge
oscillator in 1939.

FIG. 9 Conditions for startup and sustained oscillations. (a) Loop gain
greater than 1 causes output to build up. (b) Loop gain of 1 causes a sustained
constant output.
FIG. 10 Selfstarting Wienbridge oscillator using backtoback zener
diodes.
StartUp Conditions
Initially, the closedloop gain of the amplifier itself must be more than
3 (Acl > 3) until the output signal builds up to a desired level. Ideally,
the gain of the amplifier must then decrease to 3 so that the total gain
around the loop is 1 and the output signal stays at the desired level,
thus sustaining oscillation. This is illustrated in FIG. 9.
The circuit in FIG. 10 illustrates a method for achieving sustained oscillations.
Notice that the voltagedivider circuit has been modified to include an
additional resistor in parallel with a backtoback zener diode arrangement.
When dc power is first applied, R3 both zener diodes appear as opens. This
places R3, in series with R1 thus increasing the closedloop gain of the
amplifier as follows (R1 = 2R2):
Acl =R1 + R2 + R3 R2 = 3R2 + R3 R2 = 3 + R3 R2
Initially, a small positive feedback signal develops from noise or turnon
transients. The leadlag circuit permits only a signal with a frequency
equal to fr to appear in phase on the noninverting input. This feedback
signal is amplified and continually reinforced, resulting in a buildup
of the output voltage. When the output signal reaches the zener breakdown
voltage, the zeners conduct and effectively short out R3. This lowers the
amplifier's closed loop gain to 3. At this point, the total loop gain is
1 and the output signal levels off and the oscillation is sustained.
All practical methods to achieve stability for feedback oscillators require
the gain to be selfadjusting. This requirement is a form of automatic
gain control (AGC). The zener diodes in FIG. 10 limit the gain at the onset
of nonlinearity, in this case, zener conduction. Although the zener feedback
is simple, it suffers from the nonlinearity of the zener diodes that occurs
in order to control gain. It is difficult to achieve an undistorted sinusoidal
output waveform. In some older designs, a tungsten lamp was used in the
feed back circuit to achieve stability.
A better method to control the gain uses a JFET as a voltagecontrolled
resistor in a negative feedback path. This method can produce an excellent
sinusoidal waveform that is stable. A JFET operating with a small or zero
is operating in the ohmic region. As the gate voltage increases, the drainsource
resistance increases. If the JFET is placed in the negative feedback path,
automatic gain control can be achieved because of this voltagecontrolled
resistance.
A JFET stabilized Wien bridge is shown in FIG. 11. The gain of the opamp
is con trolled by the components shown in the green box, which include
the JFET. The JFET's drainsource resistance depends on the gate voltage.
With no output signal, the gate is at zero volts, causing the drainsource
resistance to be at the minimum. With this condition, the loop gain is
greater than 1. Oscillations begin and rapidly build to a large output
signal. Negative excursions of the output signal forwardbias D1, causing
capacitor C3 to charge to a negative voltage. This voltage increases the
drainsource resistance of the JFET and reduces the gain (and hence the
output). This is classic negative feedback at work. With the proper selection
of components, the gain can be stabilized at the required level. Example
161 illustrates a JFET stabilized Wienbridge oscillator.
FIG. 11 Selfstarting Wienbridge oscillator using a JFET in the negative
feedback loop.
The PhaseShift Oscillator
FIG. 13 shows a sinusoidal feedback oscillator
called the phaseshift oscillator.
Each of the three RC circuits in the feedback loop can provide a maximum
phase shift approaching 90°. Oscillation occurs at the frequency where
the total phase shift through the three RC circuits is 180°. The inversion
of the opamp itself provides the additional 180° to meet the requirement
for oscillation of a 360° (or 0°) phase shift around the feedback loop.
FIG. 13 Phaseshift oscillator.
The attenuation, B, of the threesection RC feedback circuit is
EQN. 3
EQN. 4
where B=R3/Rf. To meet the greaterthanunity loop gain requirement, the
closedloop voltage gain of the opamp must be greater than 29 (set by
and ). The frequency of oscillation is also derived on the companion website
and is stated in the following equation, where R1 = R2 = R3 = R and C1
= C2 = C3 = C.
TwinT Oscillator
Another type of RC feedback oscillator is called the twinT because of
the two Ttype RC filters used in the feedback loop, as shown in FIG. 15(a).
One of the twinT filters has a lowpass response, and the other has a
highpass response. The combined parallel filters produce a bandstop or
notch response with a center frequency equal to the desired frequency of
oscillation, as shown in FIG. 15(b).
Oscillation cannot occur at frequencies above or below fr because of the
negative feedback through the filters. At fr, however, there is negligible
negative feedback; thus, the positive feedback through the voltage divider
(R1 and R1) allows the circuit to oscillate.
FIG. 15 TwinT oscillator and twinT filter response.
SECTION 3 CHECKUP
1. There are two feedback loops in the Wienbridge oscillator. What is
the purpose of each?
2. A certain leadlag circuit has R1 = R2 and C1 = C2. An input voltage
of 5 V rms is applied. The input frequency equals the resonant frequency
of the circuit. What is the rms output voltage?
3. Why is the phase shift through the RC feedback circuit in a phaseshift
oscillator 180°?
_4 OSCILLATORS WITH LC FEEDBACK CIRCUITS
Although the RC feedback oscillators, particularly the Wien bridge, are
generally suitable for frequencies up to about 1 MHz, LC feedback elements
are normally used in oscillators that require higher frequencies of oscillation.
Also, because of the frequency limitation (lower unitygain frequency)
of most opamps, discrete transistors (BJT or FET) are often used as the
gain element in LC oscillators. This section introduces several types of
resonant LC feedback oscillators: the Colpitts, Clapp, Hartley, Armstrong,
and crystalcontrolled oscillators.
After completing this section, you should be able to:
 Describe and analyze the operation of LC feedback oscillators
 Identify and analyze a Colpitts oscillator
 Determine the resonant frequency
 Describe the conditions for oscillation and startup
 Discuss and analyze loading of the feedback circuit
 Identify and analyze a Clapp oscillator
 Determine the resonant frequency
 Identify and analyze a Hartley oscillator
 Determine the resonant frequency and attenuation of the feedback circuit
 Identify and analyze an Armstrong oscillator
 Determine the resonant frequency
 Describe the operation of crystalcontrolled oscillators
 Define piezoelectric effect
 Discuss the quartz crystal
 Discuss the modes of operation in the crystal
The Colpitts Oscillator
One basic type of resonant circuit feedback oscillator is the Colpitts,
named after its inventoras are most of the others we cover here. As shown
in FIG. 16, this type of oscillator uses an LC circuit in the feedback
loop to provide the necessary phase shift and to act as a resonant filter
that passes only the desired frequency of oscillation.
FIG. 16 A basic Colpitts oscillator with a BJT as the gain element.
The approximate frequency of oscillation is the resonant frequency of
the LC circuit and is established by the values of C1, C2, and L according
to this familiar formula:
EQN. 5
where C_T is the total capacitance. Because the capacitors effectively
appear in series around the tank circuit, the total capacitance is
C_T = C1C2/C1+C2
Conditions for Oscillation and StartUp The attenuation, B, of the resonant
feedback circuit in the Colpitts oscillator is basically determined by
the values of and FIG. 17 shows that the circulating tank current is through
both and (they are effectively in series). The voltage developed across
is the oscillator's output voltage and the voltage developed across is
the feedback voltage as indicated. The expression for the attenuation (B)
is […]
p818
Cancelling the 2 pi fr terms gives Since B = C2/C1
As you know, a condition for oscillation is:
AvB = C1/C2
... where is the voltage gain of the amplifier, which is represented by
the triangle in FIG. 17. With this condition met, Actually, for the oscillator
to be selfstarting, must be greater than 1 (that is, Therefore, the voltage
gain must be made slightly greater than
Loading of the Feedback Circuit Affects the Frequency of Oscillation
As
indicated in FIG. 18, the input impedance of the amplifier acts as a
load on the resonant feed back circuit and reduces the Q of the circuit.
The resonant frequency of a parallel resonant circuit depends on the Q,
according to the following formula:
EQN. 7
As a rule of thumb, for a Q greater than 10, the frequency is approximately
as stated in EQN. 5. When Q is less than 10, however, is reduced significantly.
FIG. 18 Zin of the amplifier loads the feed back circuit and lowers its
Q, thus lowering the resonant frequency.

HISTORY NOTE
Edwin H. Colpitts was involved in the development of oscillators and vacuum
tube pushpull amplifiers at Western Electric in the early 1900s. Western
Electric research laboratories became part of Bell Laboratories in 1925,
and Colpitts became vicepresident of Bell Labs before retirement. The
Colpitts oscillator is named in his honor.

FIG. 17 The attenuation of the tank circuit is the output of the tank
(Vf) divided by the input to the tank (Vout). B _ Vf /Vout _ C2/C1. For
AvB _ 1, Av must be greater than C1/C2.

A FET can be used in place of a BJT, as shown in FIG. 19, to minimize
the loading effect of the transistor's input impedance. Recall that FETs
have much higher input impedances than do bipolar junction transistors.
Also, when an external load is connected to the oscillator output, as shown
in FIG. 20(a), fr may decrease, again be cause of a reduction in Q. This
happens if the load resistance is too small. In some cases, one way to
eliminate the effects of a load resistance is by transformer coupling,
as indicated in FIG. 20(b).
FIG. 19 A basic FET Colpitts oscillator.
FIG. 20 Oscillator loading.
The Clapp Oscillator
The Clapp oscillator is a variation of the Colpitts. The basic difference
is an additional capacitor, in series with the inductor in the resonant
feedback circuit, as shown in FIG. 22. Since is in series with and around
the tank circuit, the total capacitance is
p821
and the approximate frequency of oscillation is:
p821b
If C3 is much smaller than C1 and C2 then C3 almost entirely controls
the resonant frequency.
Since and are both connected to ground at one end, the junction capacitance
of the transistor and other stray capacitances appear in parallel with
C1 and C2 to ground, altering their effective values. C3 is not affected,
however, and thus provides a more accurate and stable frequency of oscillation.
FIG. 22 A basic Clapp oscillator.
The Hartley Oscillator
The Hartley oscillator is similar to the Colpitts except that the feedback
circuit consists of two series inductors and a parallel capacitor as shown
in FIG. 23.
FIG. 23 A basic Hartley oscillator.

HISTORY NOTE
Ralph Vinton Lyon Hartley (18881970) invented the Hartley oscillator
and the Hartley transform, a mathematical analysis method, which contributed
to the foundations of information theory.
In 1915 he was in charge of radio receiver development for the Bell System
transatlantic radiotelephone tests. During this time he developed the Hartley
oscillator. A patent for the oscillator was filed in 1915 and awarded in
1920.

In this circuit, the frequency of oscillation for is Q > 10
fr = 1/2p _/LT C
...where LT = L1 + L2. The inductors act in a role similar to C1 and C2
in the Colpitts to determine the attenuation, B, of the feedback circuit.
B _ L1 / L2
To assure startup of oscillation, must be greater than 1/B.
Av = L2 / L1
EQN. 8
Loading of the tank circuit has the same effect in the Hartley as in the
Colpitts; that is, the Q is decreased and thus decreases.
The Armstrong Oscillator
This type of LC feedback oscillator uses transformer coupling to feed
back a portion of the signal voltage, as shown in FIG. 24. It is sometimes
called a "tickler" oscillator in reference to the transformer
secondary or "tickler coil" that provides the feedback to keep
the oscillation going. The Armstrong is less common than the Colpitts,
Clapp, and Hartley, mainly because of the disadvantage of transformer size
and cost. The frequency of oscillation is set by the inductance of the
primary winding (Lpri) in parallel with C1.
EQN. 9
FIG. 24 A basic Armstrong oscillator.

HISTORY NOTE
Edwin Howard Armstrong (18901954) was an American electrical engineer
and inventor. He was the inventor of the FM radio.
Armstrong also invented the regenerative circuit (patented 1914), the
superheterodyne receiver (patented 1918) and the superregenerative circuit
(patented 1922). Many of Armstrong's inventions were ultimately claimed
by others in patent lawsuits. The Armstrong oscillator is named in his
honor.

CrystalControlled Oscillators
The most stable and accurate type of feedback oscillator uses a piezoelectric
crystal in the feedback loop to control the frequency.
The Piezoelectric Effect
Quartz is one type of crystalline substance found
in nature that exhibits a property called the piezoelectric effect. When
a changing mechanical stress is applied across the crystal to cause it
to vibrate, a voltage develops at the frequency of mechanical vibration.
Conversely, when an ac voltage is applied across the crystal, it vibrates
at the frequency of the applied voltage. The greatest vibration occurs
at the crystal's natural resonant frequency, which is determined by the
physical dimensions and by the way the crystal is cut.
FIG. 25 A quartz crystal.  (c) Symbol (a) Typical packaged crystal
(b) Basic construction (without case) (d) Electrical equivalent
FIG. 26 Basic crystal oscillators.
Crystals used in electronic applications typically consist of a quartz
wafer mounted be tween two electrodes and enclosed in a protective "can" as
shown in FIG. 25(a) and (b).
A schematic symbol for a crystal is shown in FIG. 25(c), and an equivalent
RLC circuit for the crystal appears in FIG. 25(d). As you can see, the
crystal's equivalent circuit is a seriesparallel RLC circuit and can operate
in either series resonance or parallel resonance. At the series resonant
frequency, the inductive reactance is cancelled by the reactance of Cs.
The remaining series resistor Rs, determines the impedance of the crystal.
Parallel resonance occurs when the inductive reactance and the reactance
of the parallel capacitance Cp, are equal. The parallel resonant frequency
is usually at least 1 kHz higher than the series resonant frequency. A
great advantage of the crystal is that it exhibits a very high Q (Qs with
values of several thousand are typical).
An oscillator that uses a crystal as a series resonant tank circuit is
shown in FIG. 26(a). The impedance of the crystal is minimum at the series
resonant frequency, thus providing maximum feedback. The crystal tuning
capacitor, CC, is used to "fine tune" the oscillator frequency
by "pulling" the resonant frequency of the crystal slightly up
or down.
FIG. 26 Basic crystal oscillators.
A modified Colpitts configuration is shown in FIG. 26(b) with a crystal
acting as a parallel resonant tank circuit. The impedance of the crystal
is maximum at parallel resonance, thus developing the maximum voltage across
the capacitors. The voltage across C1 is fed back to the input.
Modes of Oscillation in the Crystal
Piezoelectric crystals can oscillate in either of two modesfundamental
or overtone. The fundamental frequency of a crystal is the lowest frequency
at which it is naturally resonant. The fundamental frequency depends on
the crystal's mechanical dimensions, type of cut, and other factors, and
is inversely proportional to the thickness of the crystal slab. Because
a slab of crystal cannot be cut too thin without fracturing, there is an
upper limit on the fundamental frequency. For most crystals, this upper
limit is less than 20 MHz. For higher frequencies, the crystal must be
operated in the overtone mode. Overtones are approximate integer multiples
of the fundamental frequency. The overtone frequencies are usually, but
not always, odd multiples of (3,5,7,...) the fundamental. Many crystal
oscillators are available in integrated circuit packages.
SECTION 4 CHECKUP
1. What is the basic difference between the Colpitts and the Hartley oscillators?
2. What is the advantage of a FET amplifier in a Colpitts or Hartley oscillator?
3. How can you distinguish a Colpitts oscillator from a Clapp oscillator?
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