1. OSCILLATORS

2. Oscillators Objectives Describe the basic concept of an oscillator
Discuss the basic principles of operation of an oscillator
Analyze the operation of RC, LC and crystal oscillators
Describe the operation of the basic relaxation oscillator circuits

3. Oscillators Introduction
Oscillators are circuits that produce a continuous signal of some type without the need of an input. These signals serve a variety of purposes. Communications systems, digital systems (including computers), and test equipment make use of oscillators.

4. Oscillators
An oscillator is a circuit that produces a repetitive signal from a dc voltage.
The feedback oscillator relies on a positive feedback of the output to maintain the oscillations.
The relaxation oscillator makes use of an RC timing circuit to generate a nonsinusoidal signal such as square wave.

5. Oscillators

6. Oscillators Types of oscillators 1. RC oscilators 2. LC oscillators
- Wien Bridge
- Phase Shift
2. LC oscillators
- Hartley
- Colpitts
3. Relaxation oscilators

7. Oscillators Basic principles for oscillation
An oscillator is an amplifier with positive feedback.

8. Oscillators

9. Oscillators
The closed loop gaind is;

10. Oscillators
In general A and  are functions of frequency and thus may be written as;
is known as loop gain

11. Oscillators
Writing
the loop gain becomes;
Replacing s with j;
and

12. Oscillators At a specific frequency f0;
At this frequency, the closed loop gain;
will be infinite, i.e. the circuit will have finite output for zero input signal - oscillation

13. Oscillators
Thus, the condition for sinusoidal oscillation of frequency f0 is;
This is known as Barkhausen criterion.
The frequency of oscillation is solely determined by the phase characteristic of the feedback loop – the loop oscillates at the frequency for which the phase is zero.

14. Oscillators
The feedback oscillator is widely used for generation of sine wave signals. The positive (in phase) feedback arrangement maintains the oscillations. The feedback gain must be kept to unity to keep the output from distorting.

15. Oscillators

16. Oscillators Design Criteria for Oscillators
1. The magnitude of the loop gain must be unity or slightly larger i.e.
– Barkhaussen criterion
2. Total phase shift, of the loop gain must be 0° or 360°.

17. Oscillators Factors determining the frequency of oscillation
Oscillators can be classified into many types depending on the feedback components, amplifiers and circuit topologies used.
RC components generate a sinusoidal waveform at a few Hz to kHz range.
LC components generate a sine wave at frequencies of 100 kHz to 100 MHz.
Crystals generate a square or sine wave over a wide range,i.e. about 10 kHz to 30 MHz.

18. Oscillators
1. RC Oscillators

19. Oscillators 1. RC Oscillators
RC feedback oscillators are generally limited to frequencies of 1 MHz or less.
The types of RC oscillators that we will discuss are the Wien-bridge and the phase-shift.

20. Oscillators – Wien-bridge
It is a low frequency oscillator which ranges from a few kHz to 1 MHz.
Structure of this oscillator is shown below;

21. Oscillators – Wien-bridge
The loop gain for the oscillator is
where;
and;

22. Oscillators – Wien-bridge
Hence;
Substituting for s;

23. Oscillators – Wien-bridge
For oscillation frequency f0;
Since at the frequency of oscillation, T(j) must be real (for zero phase condition), the imaginary component must be zero i.e.;

24. Oscillators – Wien-bridge
Which gives us;

25. Oscillators – Wien-bridge
From the previous equation;
the magnitude condition is;
or;
To ensure oscillation, the ratio R2/R1 must be slightly greater than 2.

26. Oscillators – Wien-bridge
With the ratio;
then;
K = 3 ensures the loop gain of unity – oscillation.
- K > 3 : growing oscillations
- K < 3 : decreasing oscillations

27. Oscillators – Wien-bridge
The lead-lag circuit of a Wien-bridge oscillator reduces the input signal by 1/3 and yields a response curve as shown. The frequency of resonance can be determined by the formula below.

28. Oscillators – Wien-bridge

29. Oscillators – Wien-bridge

30. Oscillators – Wien-bridge
The lead-lag circuit is in the positive feedback loop of Wien-bridge oscillator. The voltage divider limits the gain. The lead lag circuit is basically a band-pass with a narrow bandwidth.

31. Oscillators – Wien-bridge
Since there is a loss of about 1/3 of the signal in the positive feedback loop, the voltage-divider ratio must be adjusted such that a positive feedback loop gain of 1 is produced. This requires a closed-loop gain of 3. The ratio of R1 and R2 can be set to achieve this.

32. Oscillators – Wien-bridge

33. Oscillators – Wien-bridge
To start the oscillations an initial gain greater than 1 must be achieved.

34. Oscillators – Wien-bridge
The back-to-back zener diode arrangement is one way of achieving this.

35. Oscillators – Wien-bridge

36. Oscillators – Wien-bridge
When dc is first applied the zeners appear as opens. This allows the slight amount of positive feedback from turn on noise to pass.

37. Oscillators – Wien-bridge
The lead-lag circuit narrows the feedback to allow just the desired frequency of these turn transients to pass. The higher gain allows reinforcement until the breakover voltage for the zeners is reached.

38. Oscillators – Wien-bridge
Automatic gain control is necessary to maintain a gain of exact unity. The zener arrangement for gain control is simple but produces distortion because of the nonlinearity of zener diodes. A JFET in the negative feedback loop can be used to precisely control the gain. After the initial startup and the output signal increases, the JFET is biased such that the negative feedback keeps the gain at precisely 1.

39. Oscillators – Wien-bridge

40. Oscillators – Phase-shift

41. Oscillators – Phase-shift
The phase shift oscillator utilizes three RC circuits to provide 180º phase shift that when coupled with the 180º of the op-amp itself provides the necessary feedback to sustain oscillations. The gain must be at least 29 to maintain the oscillations. The frequency of resonance for the this type is similar to any RC circuit oscillator.

42. Oscillators – Phase-shift
The transfer function of the RC network is

43. Oscillators – Phase-shift
If the gain around the loop equals 1, the circuit oscillates at this frequency. Thus for the oscillations we want,
or;

44. Oscillators – Phase-shift
Putting s = j and equating the real parts and imaginary parts, we obtain;
(1)
(2)

45. Oscillators – Phase-shift
From equation (1);
Substituting into equation (2);
The gain must be at least 29 to maintain the oscillations

46. Oscillators – Phase-shift
The last R has been incorporated into the summing resistors at the input of the inverting op-amp.

47. Oscillators – Phase-shift

48. Oscillators
2. LC Oscillators

49. Oscillators Oscillators With LC Feedback Circuits
For frequencies above 1 MHz, LC feedback oscillators are used.
We will discuss the Colpitts, Hartley and crystal-controlled oscillators.
Transistors are used as the active device in these types.

50. Oscillators Oscillators With LC Feedback Circuits
Employs BJTs (or FETs) instead of op-amps and are therefore useful at high frequencies.
Consider the general BJT circuit:

51. Oscillators Oscillators With LC Feedback Circuits
Using the small signal equivalent circuit this becomes;

52. Oscillators Oscillators With LC Feedback Circuits (1)
Applying KVL around loop (1), and let
we will have;
or;
(1)

53. Oscillators Oscillators With LC Feedback Circuits (2)
Applying KVL around loop (2);
(2)

54. Oscillators Oscillators With LC Feedback Circuits
Substituting (2) into (1);

55. Oscillators Oscillators With LC Feedback Circuits
If the Z’s are purely imaginary and hie is real, then;
Substituting (3) into the expression

56. Oscillators Oscillators With LC Feedback Circuits
Z2 and Z1 are the same type of component
Z3 is the opposite type (-ve). If Z2 and Z1 are inductors, then Z3 is a capacitor and vice versa.

57. Oscillators
Oscillators With LC Feedback Circuits

58. Oscillators
Oscillators With LC Feedback Circuits

59. Oscillators – Colpitts
The Colpitts oscillator utilizes a tank circuit (LC) in the feedback loop as shown in the following figure.

60. Oscillators – Colpitts

61. Oscillators – Colpitts
The resonant frequency can be determined by the formula below.

62. Oscillators – Colpitts
Conditions for oscillation and start up

63. Oscillators – Hartley
The Hartley oscillator is similar to the Colpitts. The tank circuit has two inductors and one capacitor

64. Oscillators – Hartley
The calculation of the resonant frequency is the same.

65. Oscillators – Crystal
The crystal-controlled oscillator is the most stable and accurate of all oscillators. A crystal has a natural frequency of resonance. Quartz material can be cut or shaped to have a certain frequency. We can better understand the use of a crystal in the operation of an oscillator by viewing its electrical equivalent.

66. Oscillators – Crystal

67. Oscillators – Crystal
Since crystal has natural resonant frequencies of 20 MHz or less, generation of higher frequencies is attained by operating the crystal in what is called the overtone mode

68. Oscillators
3. Relaxation Oscillators

69. Oscillators – Relaxation
Relaxation oscillators make use of an RC timing and a device that changes states to generate a periodic waveform (non-sinusoidal).
1. Triangular-wave
2. Square-wave
3. Sawtooth

70. Oscillators – Relaxation
Triangular-wave oscillator
Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit.

71. Oscillators – Relaxation
Triangular-wave oscillator

72. Oscillators – Relaxation
Triangular-wave oscillator

73. Oscillators – Square-wave
A square wave relaxation oscillator is like the Schmitt trigger or Comparator circuit.
The charging and discharging of the capacitor cause the op-amp to switch states rapidly and produce a square wave.
The RC time constant determines the frequency.

74. Oscillators – Square-wave

75. Oscillators – Square-wave

76. Oscillators – Sawtooth voltage controlled oscillator (VCO)
Sawtooth VCO circuit is a combination of a Programmable Unijunction Transistor (PUT) and integrator circuit.

77. Oscillators – Sawtooth VCO
OPERATION
Initially, dc input = -VIN
Vout = 0V, Vanode < VG
The circuit is like an integrator.
Capacitor is charging.
Output is increasing positive going ramp.

78. Oscillators – Sawtooth VCO
OPERATION

79. Oscillators – Sawtooth VCO
OPERATION
When Vout = VP
Vanode > VG , PUT turns ‘ON’
The capacitor rapidly discharges.
Vout drop until Vout = VF.
Vanode < VG , PUT turns ‘OFF’
VP – maximum peak value
VF – minimum peak value

80. Oscillators – Sawtooth VCO
OPERATION
Oscillation frequency

81. Oscillators – Sawtooth VCO
EXAMPLE
In the following circuit, let VF = 1V.
a) Find;
(i) amplitude;
(ii) amplitude;
b) Sketch the output waveform

82. Oscillators – Sawtooth VCO
EXAMPLE (cont’d)

83. Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (i) Amplitude
and
So, the peak-to-peak amplitude is;

84. Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (ii) Frequency

85. Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (ii) Frequency

86. Oscillators – Sawtooth VCO
EXAMPLE – Solution
b) Output waveform

87. Oscillators
The 555 timer as an oscillator

88. Oscillators The 555 Timer As An Oscillator
The 555 timer is an integrated circuit that can be used in many applications. The frequency of output is determined by the external components R1, R2, and C. The formula below shows the relationship.

89. Oscillators The 555 Timer As An Oscillator
Duty cycles can be adjusted by values of R1 and R2. The duty cycle is limited to 50% with this arrangement. To have duty cycles less than 50%, a diode is placed across R2. The two formulas show the relationship;
Duty Cycle > 50 %

90. Oscillators
The 555 Timer As An Oscillator
Duty Cycle < 50 %

91. Oscillators
The 555 Timer As An Oscillator

92. Oscillators The 555 Timer As An Oscillator
The 555 timer may be operated as a VCO with a control voltage applied to the CONT input (pin 5).

93. Oscillators
Summary
Sinusoidal oscillators operate with positive feedback.
Two conditions for oscillation are 0º feedback phase shift and feedback loop gain of 1.
The initial startup requires the gain to be momentarily greater than 1.
RC oscillators include the Wien-bridge, phase shift, and twin-T.
LC oscillators include the Colpitts, Clapp, Hartley, Armstrong, and crystal.

94. Oscillators Summary (cont’d)
The crystal actually uses a crystal as the LC tank circuit and is very stable and accurate.
A voltage controlled oscillator’s (VCO) frequency is controlled by a dc control voltage.
A 555 timer is a versatile integrated circuit that can be used as a square wave oscillator or pulse generator.