**Lecture 3 Oscillator** • Introduction of Oscillator • Linear Oscillator • Wien Bridge Oscillator • RC Phase-Shift Oscillator • LC Oscillator • Stability 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 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. EE3110 Oscillator

**Linear Oscillators** • Wien Bridge Oscillators • RC Phase-Shift Oscillators • LC Oscillators • Stability 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 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) EE3110 Oscillator

**Wien Bridge Oscillator** Frequency Selection Network Let and Therefore, the feedback factor, EE3110 Oscillator

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

**RC Phase-Shift Oscillator** • Using an inverting amplifier • The additional 180o phase shift is provided by an RC phase-shift network EE3110 Oscillator

**Applying KVL to the phase-shift network, we have** Solve for I3, we get Or EE3110 Oscillator

**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, 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 EE3110 Oscillator

**For the equivalent circuit from the output ** Therefore, the amplifier gain is obtained, EE3110 Oscillator

**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, EE3110 Oscillator

**Hartley Oscillator** Colpitts Oscillator EE3110 Oscillator

**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 EE3110 Oscillator

**At node 1,** where, Apply KCL at node 1, we have For Oscillator V must not be zero, therefore it enforces, EE3110 Oscillator

**Imaginary part = 0, we have** Real part = 0, yields 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. 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 EE3110 Oscillator

**Wien-bridge oscillator with bulb stabilization** EE3110 Oscillator

**Wien-bridge oscillator with diode stabilization** EE3110 Oscillator

**Twin-T Oscillator** EE3110 Oscillator

**Bistable Circuit** EE3110 Oscillator

**A Square-wave Oscillator** EE3110 Oscillator