Part 1

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

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

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

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.

Negative feedback system:

Positive feedback system:

Barkhausen's Criterion:

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

12.3 Types of oscillators: RC oscillators LC oscillators Crystal oscillator

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 180 + 180 = 360°

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

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

AC equivalent circuit of Quartz crystal:

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

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

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

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

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

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)

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

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

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

Step & pulse response of LP circuit:

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

Positive feedback system:

Barkhausen's Criterion:

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

12.3 Types of oscillators: RC oscillators LC oscillators Crystal oscillator

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 180 + 180 = 360°

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

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

AC equivalent circuit of Quartz crystal:

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

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

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

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

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

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)

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

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

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

Step & pulse response of LP circuit:

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

Numerical:

13.3 Basic RC high pass circuit:

13.4 RC high pass circuit as differentiator:

13.5 Basic RL circuit as integrator:

13.5 Basic RL circuit as differentiator:

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

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

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