1. En. Rosemizi Bin Abd Rahim
EMT212 – Analog Electronic II
Chapter 4 Oscillator By
En. Rosemizi Bin Abd Rahim

2. 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. 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. The Oscillator
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.
Fig 16-1 Oscillator

5. Types of Oscillator RC Oscillator - Wien Bridge Oscillator
- Phase Shift Oscillator
2. LC Oscillator - Hartley Oscillator
- Colpitts Oscillator
- Clapp Oscillator
- Crystal Oscillator
Fig 16-1 Oscillator
3. Relaxation Oscillator

6. Feedback Oscillator Principles
An oscillator is an amplifier with positive feedback.
Ve = Vi + Vf (1)
Vo = Ave (2)
Vf = Vo (3)
From (1), (2) and (3), we get

7. Feedback Oscillator Principles
Hence the closed loop gain, Vo/Vi = A/(1 - A)
The closed loop gain can be very large if (1 - A)= 0
A small signal value at the input can produce an output of reasonable magnitude. Thus the amplifier will be unstable when (1 - A) = 0, or when the loop gain A = 1
In polar form, A = 1 0° or 1 360°

8. Feedback Oscillator Principles
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.
Fig 16-3 Pos. Feedback

9. Design Criteria for oscillators
1) |A| equal to unity or slightly larger at the desired oscillation frequency.
- Barkhaussen criterion, |A|=1
2) Total phase shift, of the loop gain must be 0° or 360°.

10. Factors that determine 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 sin wave at frequencies of 100 kHz to 100 MHz.
Crystals generate a square or sin wave over a wide range,i.e. about 10 kHz to 30 MHz.

11. 1. RC Oscillators

12. Oscillators With RC Feedback Circuits
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.

13. Wien-Bridge Oscillator
It is a low frequency oscillator which ranges from a few kHz to 1 MHz.
Structure of this oscillator is

14. Wien-Bridge Oscillator

15. Wien-Bridge Oscillator
Multiply the top and bottom by jωC1,
we get
Divide the top and bottom by C1 R1 C2 R2

16. Wien-Bridge Oscillator
Now the amp gives
Furthermore, for steady state oscillations, we want the feedback
V1 to be exactly equal to the amplifier input, V1’. Thus

17. Wien-Bridge Oscillator
Hence
Equating the real parts,

18. Wien-Bridge Oscillator
If R1 = R2 = R and C1 = C2 = C
- Gain > 3 : growing oscillations
- Gain < 3 : decreasing oscillations

19. Wien-Bridge Oscillator
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.
fr = 1/2RC
Fig 16-6a&b

20. Wien-Bridge Oscillator
The lead-lag circuit is in the positive feedback loop of Wien-bridge oscillator. The voltage divider limits gain. The lead lag circuit is basically a band-pass with a narrow bandwidth.
Fig. 16-7b Wien-bridge

21. Wien-Bridge Oscillator
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.
Fig 16-8a&b

22. Wien-Bridge Oscillator
To start the oscillations an initial gain greater than 1 must be achieved. The back-to-back zener diode arrangement is one way of achieving this. When dc is first applied the zeners appear as opens. This allows the slight amount of positive feedback from turn on noise to pass.
Fig Wien-bridge w/zeners

23. Wien-Bridge Oscillator
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.

24. Wien-Bridge Oscillator
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.
Fig JFET AGC

25. Phase Shift Oscillator
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.
fr = 1/26RC
Fig phase shift osc.

26. Phase Shift Oscillator
The transfer function of the RC network is
Fig phase shift osc.

27. Phase Shift Oscillator
If the gain around the loop equals 1, the circuit oscillates at this
frequency. Thus for the oscillations we want,
Putting s=jω and equating the real parts and imaginary parts,
we obtain
Fig phase shift osc.

28. Phase Shift Oscillator
From equation (1) ;
Substituting into equation (2) ;
Fig phase shift osc.
# The gain must be at least 29 to maintain the oscillations.

29. Phase Shift Oscillator – Practical
The last R has been incorporated into the summing resistors
at the input of the inverting op-amp.
Fig phase shift osc.

30. 2. LC Oscillators

31. 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.

32. 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:

33. Oscillators With LC Feedback Circuits
Using the small signal equivalent circuit this becomes
Applying KVL around loop (1), and let ZT = Z1 + Z2 + Z3

34. Oscillators With LC Feedback Circuits
Using KVL in loop (2) ;
Substituting (2) into (1) ;

35. Oscillators With LC Feedback Circuits
If the Z’s are purely imaginary and hie is real, then
Substituting (3) into the expression ZT = Z1 + Z2 + Z3 = 0 ;
Z2 and Z1 are the same type of component

36. Oscillators With LC Feedback Circuits
Z3 is the opposite type (-ve)
if Z2 and Z1 are inductors, then Z3 is a capacitor and vice versa.

37. Oscillators With LC Feedback Circuits

38. Colpitts Oscillators
The Colpitts oscillator utilizes a tank circuit (LC) in the feedback loop. The resonant frequency can be determined by the formula below.
Fig BJT Colpitts

39. Colpitts Oscillators Conditions for oscillation and start up
Fig BJT Colpitts

40. Hartley Oscillators
The Hartley oscillator is similar to the Colpitts. The tank circuit has two inductors and one capacitor. The calculation of the resonant frequency is the same.
Fig Hartley osc.

41. Crystal Oscillators
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.
Fig abc&d crystal

42. Oscillators With LC Feedback Circuits
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.
Fig 16-26a xtal osc.

43. 3. Relaxation Oscillators

44. Relaxation Oscillators
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
Fig op-amp gen
Fig output waveforms

45. Triangular-wave Oscillator
Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit.
Fig op-amp gen
Fig output waveforms

46. Square-wave Oscillator
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.
Fig basic square wave
Fig waveforms

47. Sawtooth Voltage-Controlled Oscillator (VCO)
Sawtooth VCO circuit is a combination of a Programmable Unijunction Transistor (PUT) and integrator circuit.

48. Sawtooth Voltage-Controlled Oscillator (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.

49. Sawtooth Voltage-Controlled Oscillator (VCO)
Operation
When Vout = VP
Vanode > VG , PUT turn ‘ON’
The capacitor rapidly discharges.
Vout drop until Vout = VF.
Vanode < VG , PUT turn ‘OFF’
VP-maximum peak value
VF-minimum peak value

50. Sawtooth Voltage-Controlled Oscillator (VCO)
Oscillation frequency is

51. Sawtooth Voltage-Controlled Oscillator (VCO)
Example
Let VF = 1V, find
Amplitude
Frequency
Sketch the output waveform

52. Sawtooth Voltage-Controlled Oscillator (VCO)
Solution
Amplitude
So, peak – to- peak Amplitude is

53. Sawtooth Voltage-Controlled Oscillator (VCO)
ii) Frequency

54. Sawtooth Voltage-Controlled Oscillator (VCO)
iii) Output Waveform

55. 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.
Fig timer

56. 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 %
Duty Cycle <50 %

57. The 555 Timer As An Oscillator
Fig w/diode

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

59. 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.

60. Summary
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.