Oscillators Feedback amplifier but frequency dependent feedback Positive

Oscillators * Feedback amplifier but frequency dependent feedback * Positive feedback, i. e. βf ( ) A ( ) < 0 * Oscillator gain defined by * Oscillation condition at ω = ωo (Barkhausen’s criterion) Af (ωo) = ECES 352 Winter 2007 Ch 13 Oscillators 1

Wien Bridge Oscillator R 2 R 1 V 0 Vi ZS If ZP ECES 352 Winter 2007 * Based on op amp * Combination of R’s and C’s in feedback loop so feedback factor βf has a frequency dependence. * Analysis assumes op amp is ideal. « Gain A is very large « Input currents are negligibly small (I+ I_ 0). « Input terminals are virtually shorted (V+ V_ ). * Analyze like a normal feedback amplifier. « Determine input and output loading. « Determine feedback factor. « Determine gain with feedback. * Shunt-shunt configuration. Ch 13 Oscillators 2

Wien Bridge Oscillator Define R 1 R 2 V 0 Vi ZS If ZP Output Loading Input Loading ZS Z 1 ZP ECES 352 Winter 2007 V 0 = 0 ZS Vi = 0 Ch 13 Oscillators ZP Z 2 3

Wien Bridge Oscillator I 1 I 2 Amplifier gain including loading effects R 2 R 1 Vi IS IS V 0 IS Z 2 Z 1 Feedback factor If ZP ECES 352 Winter 2007 ZS V 0 Ch 13 Oscillators 4

Wien Bridge Oscillator Oscillation condition Loop Gain ECES 352 Winter 2007 Ch 13 Oscillators 5

Wien Bridge Oscillator - Example Oscillator specifications: o=1 x 106 rad/s ECES 352 Winter 2007 Ch 13 Oscillators 6

Wien Bridge Oscillator Final note: No input signal is needed. Noise at the desired oscillation frequency will likely be present at the input and when picked up by the oscillator when the DC power is turned on, it will start the oscillator and the output will quickly buildup to an acceptable level. ECES 352 Winter 2007 Ch 13 Oscillators 7

Wien Bridge Oscillator * Once oscillations start, a limiting circuit is needed to prevent them from growing too large in amplitude ECES 352 Winter 2007 Ch 13 Oscillators 8

Phase Shift Oscillator IC 3 VX * * * C V 2 IC 2 C R IR 2 V 1 IC 1 C I R R 1 If Rf V 0 Based on op amp using inverting input Combination of R’s and C’s in feedback loop so get additional phase shift. Target 180 o to get oscillation. Analysis assumes op amp is ideal. ECES 352 Winter 2007 Ch 13 Oscillators 9

Phase Shift Oscillator IC 3 VX C R V 2 IC 2 C IR 2 R V 1 IC 1 C IR 1 If Rf V 0 Example Oscillator specifications: o=1 x 106 rad/s Note: We get 180 o phase shift from op amp since input is to inverting terminal and another 180 o from the RC ladder. ECES 352 Winter 2007 Ch 13 Oscillators 10

Colpitts LC-Tuned Oscillator CB V 0 CE Vi V 0 Vi ECES 352 Winter 2007 * Feedback amplifier with inductor L and capacitors C 1 and C 2 in feedback network. « Feedback is frequency dependent. « Aim to adjust components to get positive feedback and oscillation. « Output taken at collector Vo. « No input needed, noise at oscillation frequency o is picked up and amplified. * RB 1 and RB 2 are biasing resistors. * RFC is RF Choke (inductor) to allow dc current flow for transistor biasing, but to block ac current flow to ac ground. * Simplified circuit shown at midband frequencies where large emitter bypass capacitor CE and base capacitor CB are shorts and transistor capacitances (C and C ) are opens. Ch 13 Oscillators 11

Colpitts LC-Tuned Oscillator AC equivalent circuit Voltage across C 2 is just V * Neglecting input current to transistor (I 0), * Then, output voltage Vo is * KCL at output node (C) Assuming oscillations have started, then V ≠ 0 and Vo ≠ 0, so s. C 2 V Iπ ≈ 0 * V 0 s. C 2 V * ECES 352 Winter 2007 Setting s = j Ch 13 Oscillators 12

Colpitts LC-Tuned Oscillator * To get oscillations, both the real and imaginary parts of this equation must be set equal to zero. * From the imaginary part we get the expression for the oscillation frequency * From the real part, we get the condition on the ratio of C 2/C 1 ECES 352 Winter 2007 Ch 13 Oscillators 13

Colpitts LC-Tuned Oscillator Example * Given: « Design oscillator at 150 MHz Transistor gm = 100 m. A/V, R = 0. 5 K * Design: « « ECES 352 Winter 2007 Select L= 50 n. H, then calculate C 2, and then C 1 Ch 13 Oscillators 14

Summary of Oscillator Design Wien Bridge Oscillator * * Phase Shift Oscillator * * Colpitts LC-Tuned Oscillator ECES 352 Winter 2007 * Shown how feedback can be used with reactive components (capacitors) in the feedback path. Can be used to achieve positive feedback. « With appropriate choice of the resistor sizes, can get feedback signal in phase with the input signal. « Resulting circuit can produce large amplitude sinusoidal oscillations. Demonstrated three oscillator circuits: « Wien Bridge oscillator « Phase Shift oscillator « Colpitts LC-Tuned oscillator Derived equations for calculating resistor and capacitor sizes to produce oscillations at the desired oscillator frequency. Key result: Oscillator design depends primarily on components in feedback network, i. e. not on the amplifier’s characteristics. Ch 13 Oscillators 15