Lecture 3 Oscillator Introduction of Oscillator Linear Oscillator Wien Bridge Oscillator RC Phase-Shift Oscillator LC Oscillator Stability Ref:06103104HKN EE3110 Oscillator

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:06103104HKN EE3110 Oscillator

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:06103104HKN EE3110 Oscillator

Linear Oscillators Wien Bridge Oscillators RC Phase-Shift Oscillators LC Oscillators Stability Ref:06103104HKN EE3110 Oscillator

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:06103104HKN EE3110 Oscillator

Basic Linear Oscillator and If Vs = 0, the only way that Vo can be nonzero is that loop gain A=1 which implies that (Barkhausen Criterion) Ref:06103104HKN EE3110 Oscillator

Wien Bridge Oscillator Frequency Selection Network Let and Therefore, the feedback factor, Ref:06103104HKN EE3110 Oscillator

For Barkhausen Criterion, imaginary part = 0, i.e.,  can be rewritten as: For Barkhausen Criterion, imaginary part = 0, i.e., Supposing, R1=R2=R and XC1= XC2=XC, Ref:06103104HKN EE3110 Oscillator

Example By setting , we get Imaginary part = 0 and Due to Barkhausen Criterion, Loop gain Av=1 where Av : Gain of the amplifier Wien Bridge Oscillator Therefore, Ref:06103104HKN EE3110 Oscillator

RC Phase-Shift Oscillator Using an inverting amplifier The additional 180o phase shift is provided by an RC phase-shift network Ref:06103104HKN EE3110 Oscillator

Applying KVL to the phase-shift network, we have Solve for I3, we get Or Ref:06103104HKN EE3110 Oscillator

Hence the transfer function of the phase-shift network is given by, The output voltage, Hence the transfer function of the phase-shift network is given by, For 180o phase shift, the imaginary part = 0, i.e., Note: The –ve sign mean the phase inversion from the voltage and, Ref:06103104HKN EE3110 Oscillator

LC Oscillators The frequency selection network (Z1, Z2 and Z3) provides a phase shift of 180o The amplifier provides an addition shift of 180o Two well-known Oscillators: Colpitts Oscillator Harley Oscillator Ref:06103104HKN EE3110 Oscillator

For the equivalent circuit from the output Therefore, the amplifier gain is obtained, Ref:06103104HKN EE3110 Oscillator

If the impedance are all pure reactances, i.e., The loop gain, If the impedance are all pure reactances, i.e., The loop gain becomes, The imaginary part = 0 only when X1+ X2+ X3=0 It indicates that at least one reactance must be –ve (capacitor) X1 and X2 must be of same type and X3 must be of opposite type With imaginary part = 0, For Unit Gain & 180o Phase-shift, Ref:06103104HKN EE3110 Oscillator

Hartley Oscillator Colpitts Oscillator Ref:06103104HKN EE3110 Oscillator

Colpitts Oscillator 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:06103104HKN EE3110 Oscillator

Apply KCL at node 1, we have where, Apply KCL at node 1, we have For Oscillator V must not be zero, therefore it enforces, Ref:06103104HKN EE3110 Oscillator

Imaginary part = 0, we have Real part = 0, yields Ref:06103104HKN EE3110 Oscillator

Frequency Stability The frequency stability of an oscillator is defined as Use high stability capacitors, e.g. silver mica, polystyrene, or teflon capacitors and low temperature coefficient inductors for high stable oscillators. Ref:06103104HKN EE3110 Oscillator

Amplitude Stability In order to start the oscillation, the loop gain is usually slightly greater than unity. LC oscillators in general do not require amplitude stabilization circuits because of the selectivity of the LC circuits. In RC oscillators, some non-linear devices, e.g. NTC/PTC resistors, FET or zener diodes can be used to stabilized the amplitude Ref:06103104HKN EE3110 Oscillator

Wien-bridge oscillator with bulb stabilization Ref:06103104HKN EE3110 Oscillator

Wien-bridge oscillator with diode stabilization Ref:06103104HKN EE3110 Oscillator

Twin-T Oscillator Ref:06103104HKN EE3110 Oscillator

Bistable Circuit Ref:06103104HKN EE3110 Oscillator

A Square-wave Oscillator Ref:06103104HKN EE3110 Oscillator