Know the oscillator circuit design

1. UNIT V
AMPLIFIERS AND OSCILLATORS
ANALOG ELECTRONICS

2. FEEDBACK AMPLIFIERS
 Basic Concept of Feedback
 A block diagram of an amplifier with feedback is
shown in figure.
 The output quantity (either voltage or current) is
sampled by a suitable sampler which is of two
types, namely, voltage sampler and current sampler
and fed to the feedback network.

3.  The output of feedback network which has a
fraction of the output signal is combined with
external source signal фs through a mixer and fed
to the basic amplifier.
 Mixer, also known as comparator, is of two types,
namely, series mixer and shunt mixer.
 There are two types of feedback
 (i) Positive feedback and
 (ii) Negative feedback

4. Positive feedback:
 If the feedback signal фf, is in phase with input signal
фs,then the net effect of the feedback will increase the
input signal given to the amplifier, i.e. фi =фs + фf
 Hence, the input voltage applied to the basic amplifier
is increased thereby increasing o exponentially.
 This type of feedback is said to be positive or
regenerative feedback. Gain of the amplifier with
positive feedback is

5.  Here,Af > A.The product of the open loop gain
and the feedback factor is called the loop gain,
i.e. loop gain = Aβ.
 If, then. Hence, the gain of the amplifier with
positive feedback is infinite and the amplifier
gives an a.c. output without a.c. input signal.
Thus, the amplifier acts as an oscillator.
 The positive feedback increases the instability of
an amplifies, reduces the bandwidth and
increases the distortion and noise.
 The property of the positive feedback is utilised in
oscillators.

6.  Here, Af < A. If then ,where Aβ>>1 β is a
feedback ratio. Hence, the gain depends less on
the operating potentials and the characteristics of
the transistor or vacuum tube.
 The gain may be made to depend entirely on the
feedback network.
 If the feedback network contains only stable
passive elements, the gain of the amplifier using
negative feedback is also stable.

7. Negative feedback:
 If the feedback signal фf is out of phase with the input
signal фs, then фi =фs - фf
 So the input voltage applied to the basic amplifier is
decreased and correspondingly the output is
decreased.
 Hence, the voltage gain is reduced. This type of
feedback is known as negative or degenerative
feedback. Gain of the amplifier with negative feedback
is

8. Effects of Negative Feedback
 1. Stabilisation of Gain
 The term dAf/dA represents the fractional change in
amplifier voltage gain with feedback and dA/A denotes the
fractional change in voltage gain without feedback.
 The term 1/(1 + Aβ) is called sensitivity.

9.  Therefore, the sensitivity is defined as the ratio of
percentage change in voltage gain with feedback to the
percentage change in voltage gain without feedback.
 The reciprocal of the term sensitivity is called desensitivity,
i.e., desensitivity = (1 + Aβ)

10.  2. Increase of Bandwidth (Cut-off Frequencies)
 The bandwidth of an amplifier is the difference between the
upper cut-off frequency f2 and the lower cut-off frequency f1.
 The product of voltage gain and bandwidth of an amplifier
without feedback and with feedback remains the same,
 i.e., Af x BWf = A x BW.
 As the voltage gain of a feedback amplifier reduces by the
factor , its bandwidth would be increased by (1 + Aβ),
 i.e., BWf = BW (1 + Aβ),
 where A is the mid band gain without feedback.
 Due to the negative feedback in the amplifier, the upper cut-off
frequency f2f is increased by the factor (1 + Aβ) and the lower
cut-off frequency f1f, is decreased by the same factor (1 + Aβ).
 These upper and lower 3dB frequencies of an amplifier with
negative feedback are given by the relations,

11.  3. Decreased Distortion
 Consider an amplifier with an open loop voltage gain and a
total harmonic distortion D.
 Then, with the introduction of negative feedback with the
feedback ratio, β.
 The distortion will reduce to
 4. Decreased Noise
 There are many sources of noise in an amplifier depending
upon the active device used.
 With using the negative feedback with the feedback ratio,
β, the noise, N, can be reduced by a factor of in a similar
manner to non-linear distortion.
 Thus, the noise with feedback is given by

12.  5. Increase in Input Impedance
 An amplifier should have high input impedance (resistance)
so that it will not load the preceding stage or the input
voltage source.
 Such a desirable characteristic can be achieved with the
help of negative series voltage feedback.
 The input impedance with feedback is given by
 Thus, the input impedance is increased by a factor of (1
+Aβ).
 6. Decrease in Output Impedance
 An amplifier with low output impedance (resistance) is
capable of delivering power (or voltage) to the load without
much loss.
 Such a desirable characteristics is achieved by employing
negative series voltage feedback in an amplifier.
 The output impedance with feedback is expressed by

13. TYPES OF NEGATIVE FEEDBACK
CONNECTIONS
 There are four different combinations in which negative
feedback may be accomplished, as given below.
1. Voltage-series feedback
2. Voltage-shunt feedback
3. Current-series feedback
4. Current-shunt feedback.

14. 1. Voltage-Series Feedback
 A block diagram of a voltage-series feedback is
illustrated in figure
 Here, the input to the feedback network is in parallel
with the output of the amplifier. A fraction of the output
voltage through the feedback network is applied in
series with the input voltage of the amplifier. The shunt
connection at the output reduces the output resistance
R0. The series connection at the input increases the
input resistance. It is also known as series-shunt
amplifier (or) voltage amplifier. In this case, the amplifier

15.  Input and output resistances
 Fig shows the voltage-series feedback circuit used to
calculate input and output resistances

16.  Hence, the input resistance of a voltage-series feedback
amplifier is given by
 For measuring the output resistance, RL is disconnected
and Vs is set to zero.
 Then an external voltage V is applied across the output
terminals and the current I delivered by V is calculated.
 Then, Rof = V/I.
 Due to feedback, input voltage Vf reduces output voltage
AVi, which opposes V. Therefore,

17.  Emitter follower
 The Common collector or Emitter follower as shown in
figure
 It is an example of voltage-series feedback since the
voltage developed in the output is in series with the input
voltage as far as the base-emitter junction is concerned.
 This is a single stage RC coupled amplifier without emitter
bypass capacitor across RE. R1 and R2 provide the base
bias.
 The emitter follower inherently exhibits 100% negative

18.  Characteristics of an emitter follower:

19. 2. Voltage-Shunt Feedback
 A voltage-shunt feedback is illustrated in figure.
 It is called a shunt derived, shunt-fed feedback
connection.
 Here, a fraction of the output voltage is supplied in
parallel with the input voltage through the feedback
network.
 The feedback signal If is proportional to the output
voltage V0.

20.  The voltage-shunt feedback provides a stabilised
overall gain and decreases both input and output
resistances by a factor (1 + Aβ)
 Common emitter amplifier with voltage-shunt
feedback
 The collector feedback biased common emitter amplifier
as shown in figure is an example of voltage-shunt
feedback.

21.  Here, a current which is proportional to the output
voltage is feedback to the input.
 Since Vo >> Vi, the feedback current If = Vo/RB, So that
the feedback ratio β =1/RB .
 The reduction in input and output resistances occurs
due to Miller effect with RB.

22. 3. Current-Series Feedback
 A block diagram of a current-series feedback is
illustrated in figure.
 In current-series feedback, a voltage is developed
which is proportional to the output current.
 This is called current feedback even though it is a
voltage that subtracts from the input voltage.
 Because of the series connection at the input and
output, the input and output resistances get increased.
 This type of amplifier is called transconductance

23.  One of the most common method of applying the
current-series feedback is to place a resistor Re, between
the emitter lead of a common emitter amplifier and
ground.
 As the common emitter amplifier has a high gain, this is
most often used with series negative feedback so that it
can afford to lose some gain. Such a circuit is illustrated
in figure

24.  Feedback Ratio (β)
 Referring to the figure, it is possible to calculate the
approximate value of feedback ratio β.

25.  Input Resistance (Rif)

26.  Input resistance without feedback, Ri = hie
 We find that there is a increase in input resistance due
to negative feedback.

27.  Voltage Gain (Af)
 We find that there is a large decrease in voltage gain due
to negative feedback.
 Output resistance (Rof)

28. 4. Current-Shunt Feedback
 A current-shunt feedback is illustrated in figure
 It is called a series-derived, shunt-fed feedback.
 The shunt connection at the input reduces the input
resistance and the series connection at the output
increases the output resistance.
 This is true current amplifier also known as shunt-series
feedback amplifier.

29.  Input and output resistances
 Figure shows the current-shunt feedback circuit used to
calculate input and output resistances.

30.  For measuring the output resistance, RL is disconnected
and Vs is set to zero.
 Then external voltage V is applied across the output
terminals and the current I delivered by V is calculated.
 Then, Rof = V/I

31. 31
Classifications of Power Amplifiers:
 Class AAmplifier
 Class B Amplifier
 Class C Amplifier
 Class AB Amplifier
 Class D Amplifier
 Class S Amplifier

32. Class A Amplifiers
 Select Q-point and i/p signal such that o/p signal obtained for
a full i/p cycle.
 Position of Q-point as mid point of load line as shown
1–32

33.  All value of i/p signal transistor
remains in active region and never
comes under cut-off or saturation
region.
 i/p signal applied, then Vc varies
sinusoidally and also Ic varies
sinusoidally. Ic flows 360 deg of
i/p signal.
 Here o/p produced without any
distortion. Small efficiency.
1–33

34. Class B Amplifier
 Select Q-point and i/p signal such that o/p signal obtained for a one
half cycle of full i/p cycle.
 Position of Q-point on X-axis as shown and transistor biased in
cutoff region.
1–34

35.  Due to selection of Q-point on X-axis, transistor remains in active
region only for half cycle of the i/p signal. Hence this half cycle is
reproduced at o/p.
 For –ve half cycle of i/p signal transistor remains in cutoff region
and no signal reproduced at the o/p
 Ic flows only for 180 deg (half cycle) of the i/p signal.
 So o/p signal distorted in this mode of operation.
 Eliminate this distortion, two transistor used in alternate half cycle
of i/p signal. Each transistor conducts only for half cycle of i/p
signal.
 Efficiency of Class B operation is much higher than Class A
operation.
1–35

36.  Current and voltage waveform as shown
1–36

37. Class C amplifier
 Select Q-point and i/p signal such that o/p signal obtained for a less
than a half cycle of full i/p cycle.
 Position of Q-point is below the X-axis as shown
1–37

38.  Transistor remains in active
region only less than a half
cycle. Hence that much part
only reproduced at the o/p.
 Remaining cycle of i/p cycle,
transistor remains in cut-off
region and no signal produced
at o/p. Ic flows less then 180
deg.
 Here o/p is much more distorted
1–38

39. Application
 Class C operation is not suitable for audio frequency power
amplifiers.
 Class C amplifiers are used in tuned circuits used in
communication areas and in radio frequency (RF) amplifier. There
are also used in mixer or converter circuits used in radio receivers
and wireless communication system.
Class C tuned amplifier
1–39

40.  The LC parallel circuit is a parallel resonant circuit. This circuit
acts as a load impedance.
 Due to Class C operation, the collector current consists of a series
of pulses containing harmonics.
 The parallel tuned circuit is designed to be tuned to the
fundamental i/p frequency.
 Hence it eliminates the harmonics and produce a sine wave of
fundamental component of i/p signal.
 As the transistor and coil losses are small, the most of the d.c i/p
power is converted to a a.c load power. Hence efficiency of class C
is very high.
1–40

41. Class AB Amplifier
 Select Q-point and i/p signal such that o/p signal obtained for a
more than 180 deg but less than 360 deg of full i/p cycle.
 Position of Q-point is above the X-axis but below the midpoint of
load line as shown
1–41

42.  Here o/p signal is distorted.
Efficiency is more than Class
A but less than Class B
operation.
 Class AB operation is
important to eliminate cross
over distortion.
 In general, as Q-point moves
away from center of the load
line below towards the X-axis,
the efficiency of class of
operation increases.
1–42

43. 43
Comparison of Amplifier Classes:
Class A B C AB
Operating
cycle
360o 180o
Less than
180o
180o to 360o
Position of
Q point
Centre of Load
line
On X-axis Below X-axis
Above X-axis below
the centre of load
line
Efficiency
Poor 25% to
50%
Better 78.5% High
Higher than A but
less than B
Distortion
Absent
No distortion
Present more
than Class A
Highest Present
The amplifiers discussed above are linear amplifiers whereas Class-D and
Class-S are non-linear amplifiers.

44. Class D amplifier
 In Class D amplifier, transistor are used as switch instead of current
sources.
 Power dissipation in a switch is ideally zero, the efficiency of class
D amplifier approaches 100%
 It is widely used in transmitters.
 Class D amplifier used in two push pull transistor switches to
produced a square wave, which is then filtered to recover the
fundamental frequency.
 RF transformer couples the i/p signal to the base of both transistor.
 During +ve half cycle
 Upper transistor driven into the cut-off region
 Lower transistor driven into the saturation.
1–44

45.  During +ve half cycle
 Upper transistor driven into the saturation region
 Lower transistor driven into the cut-off region.
 Result as o/p voltage alternate between 0 and Vcc.
 Square wave transmit such that it allows only fundamental
frequency and it blocks the harmonics.
 The square wave at the o/p of push pull amplifier can be expressed
as
 The voltage o/p from the circuit is almost sine wave is given by
 Max value of o/p sine wave is 0.636 Vcc.
1–45

46. 46
Class D Amplifier:

47. Class S Amplifier
 Circuit as shown
 Class S operation of a transistor is mostly used in switching
regulators.
 Continues string of pulses of an amplitude Vcc drives the
transistor in emitter followers connection
1–47

48.  Because of VBE drop, voltage driving the LC filter is a train of
pulses with an amplitude of Vcc-VBE
 If XL is much greater than Xc at the switching frequency, the o/p is
a d.c voltage of
 Vdc= D(Vcc-VBE)
 D- duty cycle of i/p waveform. Higher the duty cycle larger will
be d.c o/p.
 The switching regulator uses a Class S amplifier in which by
varying the duty cycle one can regulate the d.c o/p
 Transistor is switched into either cut-off or saturation its power
dissipation is much lower.
 Power dissipation by the transistor is given by
 PD=VCE(sat). Idc
 Since VCE(sat) (=0.3V) is closer to zero, the power dissipation is very
low.
1–48

49. OSCILLATORS
 Any circuit which is used to generate a periodic voltage
without an a.c. input signal is called an oscillator.
 To generate the periodic voltage, the circuit is supplied
with energy from a d.c. source.
 If the output voltage is a sine wave function of time, the
oscillator is called a "Sinusoidal” or “Harmonic”
oscillator.
 There is another category of oscillators which generate
non-sinusoidal waveforms such as square, rectangular,
triangular or sawtooth waves.

50. CLASSIFICATION OF
OSCILLATORS
 1. According to the waveforms generated:
 (a) Sinusoidal oscillator- Generate sinusoidal waveform
 (b) Relaxation oscillator- Generate non- sinusoidal
waveform
 2. According to the fundamental mechanisms involved:
 (a) Negative resistance oscillators
 (b) Feedback oscillators
 3. According to the frequency generated:
 (a) Audio frequency oscillator (AFO): up to 20 kHz
 (b) Radio frequency oscillator (RFO): 20 kHz to 30 MHz
 (c) Very high frequency (VHF) oscillator: 30 MHz to 300
MHz
 (d) Ultra high frequency (UHF) oscillator: 300 MHz to 3
GHz

51.  4. According to the type of circuit used, sine-wave
oscillators may be classified as
 (a) LC tuned oscillator
 (b) RC phase shift oscillator.

52. CONDITIONS FOR OSCILLATION
(BARKHAUSEN CRITERION)
 The essential conditions for maintaining oscillations are:
 |Aβ| = 1, i.e., the magnitude of loop gain must be unity.
 The total phase shift around the closed loop is zero or 360
degrees.
 Practical considerations

53. GENERAL FORM OF AN LC
OSCILLATOR
 Vacuum tube, Transistor, FET and Operational amplifier
may be used in the amplifier section. Z1, Z2 and Z3 are
reactive elements constituting the feedback tank circuit
which determines the frequency of oscillation.
 Here, Z1 and Z2 serve as an a.c. voltage divider for the
output voltage and feedback signal. Therefore, the
voltage across Z1 is the feedback signal.
 The frequency of oscillation of the LC oscillator is

54. General form of an oscillator and
its equivalent circuit
 The inductive or capacitive reactances are represented
by Z1, Z2 and Z3.
 In figure, the output terminals are 2 and 3, and input
terminals are 1 and 3.

55. Load impedance
 Since Z1 and the input resistance hie of the transistor are
in parallel, their equivalent impedance Z1 is given by

56.  Now the load impedance ZL between the output
terminals 2 and 3 is the equivalent impedance of Z2 in
parallel with the series combination of Z1 and Z3.

57.  Voltage gain without feedback
 Feedback fraction β

58.  Equation for the oscillator

59. HARTLEY OSCILLATOR
 In the Hartley oscillator shown in figure, Z1 and Z2 are
inductors and Z3 is a capacitor. Resistors R1, R2 and RE
provide the necessary d.c. bias to the transistor.
 CE is a bypass capacitor. CC1 and CC2 are coupling
capacitors. The feedback network consisting of inductors
L1 and L2, and capacitor C determines the frequency of
the oscillator.

60.  When the supply voltage +Vcc is switched ON, a
transient current is produced in the tank circuit and
consequently, damped harmonic oscillations are set up
in the circuit.
 The oscillatory current in the tank circuit produces a.c.
voltages across L1 and L2. As terminal 3 is earthed, it is
at zero potential.
 If terminal 1 is at a positive potential with respect to 3 at
any instant, terminal 2 will be at a negative potential with
respect to 3 at the same instant. Thus, the phase
difference between the terminals 1 and 2 is always 180°.
 In the CE mode, the transistor provides the phase
difference of 180° between the input and output.
Therefore, the total phase shift is 360°.

61. Analysis
 Z1 and Z2 are inductive reactance and Z3, is the
capacitive reactance.
 Substituting the values in below equation and simplifying
 The frequency of oscillation can be determined by
equating the imaginary part of above equation

62. The condition for maintenance of oscillation is obtained by the real part becomes
zero and hence
Substituting equation into the above equation and simplifying, we get

63. COLPITTS OSCILLATOR
 In the Colpitts oscillator shown in figure, Z1 and Z2 are
capacitors and Z3 is an inductor. The resistors R1, R2
and RE provide the necessary d.c. bias to the transistor.
 CE is a bypass capacitor. CC1 and CC2 are coupling
capacitors. The feedback network consisting of
capacitors C1 and C2 and an inductor L determines the
frequency of the oscillator.

64.  When the supply voltage +Vcc is switched ON, a
transient current is produced in the tank circuit and
consequently, damped harmonic oscillations are set up
in the circuit.
 The oscillatory current in the tank circuit produces a.c.
voltages across C1 and C2. As terminal 3 is earthed, it is
at zero potential.
 If terminal 1 is at a positive potential with respect to 3 at
any instant, terminal 2 will be at a negative potential
with respect to 3 at the same instant.
 Thus, the phase difference between the terminals 1 and
2 is always 180°.
 In the CE mode, the transistor provides the phase
difference of 180° between the input and output.
Therefore, the total phase shift is 360°.

65.  The frequency of oscillation is
 Analysis:
 Substituting the values in below equation and simplifying

66.  The frequency of oscillation can be determined by
equating the imaginary part of above equation
 The condition for maintenance of oscillation as

67. RC OSCILLATORS
 All the oscillators using tuned LC circuits operate
well at high frequencies.
 At low frequencies, as the inductors and
capacitors required for the time circuit would be
very bulky, RC oscillators are found to be more
suitable.
 Two important RC oscillators are
 (i) RC Phase shift oscillator and
 (ii) Wien Bridge oscillator.

68. cascade connection of high pass
filter
 In this oscillator the required phase shift of 180° in the
feedback loop from output to input is obtained by using
R and C components
 Here, a common emitter amplifier is followed by three
sections of RC phase shift network, the output of the
last section being returned to the input.

69.  The phase shift Φ, given by each RC section is Φ = 1/
ꞶCR.
 If R is made zero, then Φ will become 90°.
 But making R = 0 is impracticable because if R is zero,
then the voltage across it will become zero.
 Therefore, in practice the value of R is adjusted such
that Φ becomes 60°.
 If the values of R and C are so chosen that, for the
given frequency f0, the phase shift of each RC section is
60°.
 Thus, such a RC ladder network produces a total phase
shift of 180°
 Therefore, at the specific frequency f0, the total phase
shift will be exactly 360° or 0°
 The frequency of oscillation is given by

70.  Analysis:

71.  Solving the above simultaneous equations, we get
 For determining the frequency of oscillation, the phase
shift, i.e., the imaginary part must be equal to zero.

72. cascade connection of low pass
filter
 In practice, the resistor R of the last section is adjusted
in such a way that the total phase shift produced by the
cascade connection of RC network is exactly equal to
180°. The transistor in the amplifier circuit gives a
phase shift of another 180°. Hence, the total phase shift
around the circuit is 360° i.e., 0°.

73. From above equation , the value of I3 becomes
---------------------- (1)
---------------------- (2)

74.  Substituting I3 value in 2nd equation
 By substituting the values of I2 and I3 into equation (1),
we get

75.  To determine the frequency of oscillation, the imaginary
part is equated to zero
 By substituting the values of fo into β , we get
 Thus, sustained oscillation is obtained by having the
gain of transistor amplifier greater than 29

76. Cascade connection of one RC and
one CR filters
 A two stage oscillator uses the phase-shifting network is
shown in figure

77.  Solving the above simultaneous equations, we get the
feedback factor (β) of the network given by
 As should not be less than unity, it is necessary that the
amplifier gain must be greater than 3 for the operation of

78. WIEN-BRIDGE OSCILLATOR
 The circuit consists of a two-stage RC coupled amplifier
which provides a phase shift of 360° or 0°. A balanced
bridge is used as the feedback network which has no
need to provide any additional phase shift.

79.  If the bridge is balanced,
 Simplifying above equation and equating the real and
imaginary parts on both sides, we get the frequency of
oscillation as,

80. bridge oscillator using BJT
amplifier:

81.  We know that Aβ = 1
 Therefore, the gain of the amplifier,
 Substituting,
 A = 3. Hence the gain of the Wien bridge oscillator using
BJT amplifier is at least equal to 3 for oscillators to
occur.

82. CRYSTAL OSCILLATORS
 Here, it is a Colpitts crystal oscillator in which the
inductor is replaced by the crystal.
 In this type, a piezo-electric crystal, usually quartz, is
used as a resonant circuit replacing an LC circuit.

83. Quartz Crystal Construction
 In order to obtain high degree of frequency stability,
crystal oscillators are essentially used.
 Generally, the crystal is a ground wafer of translucent
quartz or tourmaline stone placed between two metal
plates and housed in a stamp sized package.
 There are two different methods of cutting this crystal
wafer from the crude quartz.
 The method of cutting determines the natural resonant
frequency and temperature coefficient of the crystal.

84.  When the wafer is cut in such a way that its flat
surfaces are perpendicular to its electrical axis (X-axis),
it is called an X-cut crystal as shown in figure (b).
 When the wafer is cut in such a way that its flat
surfaces are perpendicular to its mechanical axis (Y-
axis), it is called Y-cut crystal as shown in figure (c).

85.  The frequency of vibration is
 where Y is the Young modulus, p is the density of the
material and P = 1, 2, 3, ...

86.  The reactance function
 Serious resonant frequency
 Parallel resonant frequency
 Oscillation frequency

87. MILLER OSCILLATOR
 The Miller crystal controlled oscillator circuit is
shown

88.  The crystal has two resonant frequencies. In between
the series-resonant frequency and parallel resonant
frequency, the reactance of the crystal becomes
inductive and hence the crystal can be used as an
inductor.
 One of the inductors in Hartley Oscillator is replaced by
the crystal, which acts as an inductor when the
frequency is greater than the series resonant
frequency.
 The inter electrode capacitance of the transistor acts as
a capacitor to generate oscillations in the circuit.

89. PIERCE CRYSTAL
OSCILLATOR
 The transistor Pierce Crystal Oscillator is shown
 Here the crystal is connected as a series element in the
feedback path from the collector to the base.

90.  The resistor R1, R2 and R3 provide the necessary d.c.
bias to the transistor and CE is an emitter by pass
capacitor.
 The radio frequency (RF) choke coil provides d.c. bias
while decoupling any a.c. signal on the power lines from
affecting the output signal.
 The coupling capacitor C blocks any d.c. between
collector and base, and has negligible impedance at the
operating frequency of the oscillator.
 The frequency of oscillation set by the series-resonant
frequency of the crystal is given by,