Ref: HKNEE3110 Oscillator1 Lecture 3 Oscillator Introduction of Oscillator Linear Oscillator –Wien Bridge Oscillator –RC Phase-Shift Oscillator –LC Oscillator Stability

Ref: HKNEE3110 Oscillator2 Oscillators Oscillation: an effect that repeatedly and regularly fluctuates about the mean value Oscillator: circuit that produces oscillation Characteristics: wave-shape, frequency, amplitude, distortion, stability

Ref: HKNEE3110 Oscillator3 Application of Oscillators Oscillators are used to generate signals, e.g. –Used as a local oscillator to transform the RF signals to IF signals in a receiver; –Used to generate RF carrier in a transmitter –Used to generate clocks in digital systems; –Used as sweep circuits in TV sets and CRO.

Ref: HKNEE3110 Oscillator4 Linear Oscillators 1.Wien Bridge Oscillators 2.RC Phase-Shift Oscillators 3.LC Oscillators 4.Stability

Ref: HKNEE3110 Oscillator5 Integrant of Linear Oscillators For sinusoidal input is connected “Linear” because the output is approximately sinusoidal A linear oscillator contains: - a frequency selection feedback network - an amplifier to maintain the loop gain at unity

Ref: HKNEE3110 Oscillator6 Basic Linear Oscillator and If V s = 0, the only way that V o can be nonzero is that loop gain A  =1 which implies that (Barkhausen Criterion)

Ref: HKNEE3110 Oscillator7 Wien Bridge Oscillator Frequency Selection Network Let and Therefore, the feedback factor,

Ref: HKNEE3110 Oscillator8  can be rewritten as: For Barkhausen Criterion, imaginary part = 0, i.e., Supposing, R 1 =R 2 =R and X C1 = X C2 =X C,

Ref: HKNEE3110 Oscillator9 Example By setting, we get Imaginary part = 0 and Due to Barkhausen Criterion, Loop gain A v  =1 where A v : Gain of the amplifier Therefore, Wien Bridge Oscillator

Ref: HKNEE3110 Oscillator10 RC Phase-Shift Oscillator  Using an inverting amplifier  The additional 180 o phase shift is provided by an RC phase-shift network

Ref: HKNEE3110 Oscillator11 Applying KVL to the phase-shift network, we have Solve for I 3, we get Or

Ref: HKNEE3110 Oscillator12 The output voltage, Hence the transfer function of the phase-shift network is given by, For 180 o phase shift, the imaginary part = 0, i.e., and, Note: The –ve sign mean the phase inversion from the voltage

Ref: HKNEE3110 Oscillator13 LC Oscillators  The frequency selection network (Z 1, Z 2 and Z 3 ) provides a phase shift of 180 o  The amplifier provides an addition shift of 180 o Two well-known Oscillators: Colpitts Oscillator Harley Oscillator

Ref: HKNEE3110 Oscillator14 For the equivalent circuit from the output Therefore, the amplifier gain is obtained,

Ref: HKNEE3110 Oscillator15 The loop gain, If the impedance are all pure reactances, i.e., The loop gain becomes, The imaginary part = 0 only when X 1 + X 2 + X 3 =0  It indicates that at least one reactance must be –ve (capacitor)  X 1 and X 2 must be of same type and X 3 must be of opposite type With imaginary part = 0, For Unit Gain & 180 o Phase-shift,

Ref: HKNEE3110 Oscillator16 Hartley OscillatorColpitts Oscillator

Ref: HKNEE3110 Oscillator17 Colpitts Oscillator Equivalent circuit In the equivalent circuit, it is assumed that:  Linear small signal model of transistor is used  The transistor capacitances are neglected  Input resistance of the transistor is large enough

Ref: HKNEE3110 Oscillator18 At node 1, where, Apply KCL at node 1, we have For Oscillator V  must not be zero, therefore it enforces,

Ref: HKNEE3110 Oscillator19 Imaginary part = 0, we have Real part = 0, yields

Ref: HKNEE3110 Oscillator20 Wien-bridge oscillator with diode stabilization