1. Part 1

2. Sinusoidal Oscillators, Wave-shaping Circuits
Unit 6
Sinusoidal Oscillators, Wave-shaping Circuits

3. Objectives: Sinusoidal Oscillators Wave-shaping circuits
Classification of oscillators
Conditions for oscillations
Barkhausen’s criteria
Types of oscillators
Crystal oscillators
Voltage-controlled oscillators
Frequency stability
Wave-shaping circuits
RC, RL low-pass & high-pass circuits
RC, RL integrator & differentiator circuits
Multivibrators
IC Multivibrators

4. Sinusoidal Oscillators:
Classification:
Oscillator (AC generating circuits)
Sinusoidal:
Generate sine wave
Non-Sinusoidal (Multivibrators):
Generate square wave or pulsed waveforms
TON << TOFF

5. 12.2 Conditions for oscillations: Barkhausen's Criterion
Types of feedback systems:
Negative feed back system
Positive feed back system
Notes:
β is gain of frequency selective feedback network, which uses resonant circuit.

6. Negative feedback system:

7. Positive feedback system:

8. Barkhausen's Criterion:

9. Initialization of oscillations:
Generation of oscillations is initialized due to some inevitable noise at input
The amplified output due to noise has all frequency components
Feedback network is frequency selective
Barkhausen’s criterion is satisfied
Oscillations start

10. 12.3 Types of oscillators: RC oscillators LC oscillators
Crystal oscillator

11. RC oscillators:
A single RC or RL section provides a maximum of 90° phase shift
Multiple RC sections are used to provide the required phase shift
3 RC sections  3 x 60° =180°
CE amplifier  180°
Total = 360°

12. LC oscillators: A single LC section provides 180°
CE amplifier provides 180 °
Total 360 °

13. 15.15 Crystal oscillator:
A quartz crystal with the desired value of the resonant frequency forms the frequency-selective feedback network
More accuracy and stability

14. AC equivalent circuit of Quartz crystal:

15. Resonant frequencies:
Series resonant frequency: 1
fs =
2 Π  LCS
Parallel resonant frequency:
fp =
2 Π  LCp
Where Cp = (CM x CS) / (CM + CS) in the above figure

16. Crystal controlled Colpitt oscillator:
Resonant / tank circuit
Crystal in feedback path to control frequency

17. Crystal based Colpitt oscillator:
Resonant / tank circuit
Crystal in resonant / tank track to decide frequency

18. 12.16 Voltage controlled oscillator (VCO):
A VCO is an oscillator circuit in which the frequency can be varied by an applied voltage
This is achieved by “varicap”, whose capacitance varies with applied voltage.
Varicap is used in tank circuit, which determines frequency

19. Voltage-controlled Hartley oscillator:
Varicap used as voltage controlled capacitance in resonant / tank circuit
FET used as common-drain amplifier (Av little < 1)
Feedback factor β is large
To avoid noise effect 2 varicaps are used
Fine tuning the frequency is easy with VCO
Feedback path

20. 12.17 Frequency stability:
Oscillators ability to maintain constant frequency, for as long a period as possible
Frequency depends on: (large set of elements)
Circuit components
Stray elements (inter-electrode reactance)
Supply voltages
Active device’s characteristics
But largely frequency depends on RC or LC values (small set of elements)

21. Frequency stability criterion:
θ=phase-shift
Ω=2Πf=frequency
Frequency stability criterion:
A small set of elements (RC / RL) introduces a large change of phase-shift dθ for a given change in frequency dω, then higher the value of dθ
------, dω
more will be the dependence on the these (RC / RL) circuit features

22. When dθ
------ dω
approaches infinity, ω is independent of other circuit features (large set of elements)
More the above ratio more the stability

23. 13.1 Basic RC low pass circuit:
Xc = R 1
XC =
2 Π f C

24. Step & pulse response of LP circuit:

25. 13.2 RC low pass circuit as integrator:
Basics / fundas:
C=Q / V  C= dq / dv ---- in integral form
I=Q / T  i = dq / dt
from 1  dv = dq / C
from 2  = (1/C) i dt 1
v = ∫ i dt C

27. Positive feedback system:

28. Barkhausen's Criterion:

29. Initialization of oscillations:
Generation of oscillations is initialized due to some inevitable noise at input
The amplified output due to noise has all frequency components
Feedback network is frequency selective
Barkhausen’s criterion is satisfied
Oscillations start

30. 12.3 Types of oscillators: RC oscillators LC oscillators
Crystal oscillator

31. RC oscillators:
A single RC or RL section provides a maximum of 90° phase shift
Multiple RC sections are used to provide the required phase shift
3 RC sections  3 x 60° =180°
CE amplifier  180°
Total = 360°

32. LC oscillators: A single LC section provides 180°
CE amplifier provides 180 °
Total 360 °

33. 15.15 Crystal oscillator:
A quartz crystal with the desired value of the resonant frequency forms the frequency-selective feedback network
More accuracy and stability

34. AC equivalent circuit of Quartz crystal:

35. Resonant frequencies:
Series resonant frequency: 1
fs =
2 Π  LCS
Parallel resonant frequency:
fp =
2 Π  LCp
Where Cp = (CM x CS) / (CM + CS) in the above figure

36. Crystal controlled Colpitt oscillator:
Resonant / tank circuit
Crystal in feedback path to control frequency

37. Crystal based Colpitt oscillator:
Resonant / tank circuit
Crystal in resonant / tank track to decide frequency

38. 12.16 Voltage controlled oscillator (VCO):
A VCO is an oscillator circuit in which the frequency can be varied by an applied voltage
This is achieved by “varicap”, whose capacitance varies with applied voltage.
Varicap is used in tank circuit, which determines frequency

39. Voltage-controlled Hartley oscillator:
Varicap used as voltage controlled capacitance in resonant / tank circuit
FET used as common-drain amplifier (Av little < 1)
Feedback factor β is large
To avoid noise effect 2 varicaps are used
Fine tuning the frequency is easy with VCO
Feedback path

40. 12.17 Frequency stability:
Oscillators ability to maintain constant frequency, for as long a period as possible
Frequency depends on: (large set of elements)
Circuit components
Stray elements (inter-electrode reactance)
Supply voltages
Active device’s characteristics
But largely frequency depends on RC or LC values (small set of elements)

41. Frequency stability criterion:
θ=phase-shift
Ω=2Πf=frequency
Frequency stability criterion:
A small set of elements (RC / RL) introduces a large change of phase-shift dθ for a given change in frequency dω, then higher the value of dθ
------, dω
more will be the dependence on the these (RC / RL) circuit features

42. When dθ
------ dω
approaches infinity, ω is independent of other circuit features (large set of elements)
More the above ratio more the stability

43. 13.1 Basic RC low pass circuit:
Xc = R 1
XC =
2 Π f C

44. Step & pulse response of LP circuit:

45. 13.2 RC low pass circuit as integrator:
Basics / fundas:
C=Q / V  C= dq / dv ---- in integral form
I=Q / T  i = dq / dt
from 1  dv = dq / C
from 2  = (1/C) i dt 1
v = ∫ i dt C

47. Numerical:

49. 13.3 Basic RC high pass circuit:

51. 13.4 RC high pass circuit as differentiator:

52. 13.5 Basic RL circuit as integrator:

53. 13.5 Basic RL circuit as differentiator:

54. 13.9 Multivibrators:
Multivibrator is a non-sinusoidal oscillator circuit with regenerative feedback with pulsed waveform.
Types:
Bistable
Monostable
Astable

56. Chapter 11: Oscillators
The 555 Timer:
555 is a IC (integrated circuit) that is used to generate –
Accurate time delay (from µS to hours)
Monostable Operation (one stable state)
Rectangular signal
Astable Operation (no stable states)
Both are non-stable states
Non-stable state
Stable state
Here triggered
Need not be triggered
This is Pulse Waveform
This is Rectangular Waveform
Note: 1. Stable state = does not change, unless triggered.
2. Non-stable state = change state after fixed (designed) time. 56

57. Chapter 11: Oscillators Functional Block Diagram: The 555 Timer:
Refer next slide for SR FF
Functional Block Diagram: 57