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2 13. Oscillators

3 Contents Sinusoidal Oscillators RC Oscillators –RC Phase Shift Oscillator –Wein Bridge Oscillator LC Oscillators –Colpitts Oscillator –Hartley Oscillator

4 Sinusoidal Oscillators

5 Introduction An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, such as a sine wave or a square wave. Most of the oscillators produce sinusoidal waveforms. A sinusoidal oscillator consists of an amplifier and a feedback network. In a sinusoidal oscillator circuit, –Active device such as transistor or op-amp is used as an amplifier –Passive components such as R-C or L-C components are used in the feedback network

6 Working Principle of Oscillator As shown in the diagram, a sinusoidal oscillator consists of an amplifier having gain of A, and a positive feedback circuit with gain of . No external input signal is required in the oscillator circuit. Barkhausen conditions for oscillation: the loop gain must equal to unity and the phase shift must be 0  or 360 , i.e. A  = 1+j0 = 1  0  or 1  360  A vovo vfvf vovo

7 Classification of Sinusoidal Oscillators RC Oscillators –Use a resistance-capacitance network to determine the oscillator frequency –Suitable for low (audio range) and moderate frequency applications (5Hz to 1MHz) –Examples: Phase shift oscillator, Wien bridge oscillator LC Oscillators –Use a inductance-capacitance network to determine the oscillator frequency –Suitable for radio frequency (1 to 500MHz) applications –Examples: Colpitts, Hartley Crystal Oscillators –Use piezoelectric crystal (or quartz) which has very high degree of stability and accuracy –Suitable for radio frequency applications

8 RC Oscillators

9 1. Phase Shift Oscillator The frequency dependent network is obtained with a combination of resistors and capacitors. The inverting amplifier provides 180  phase shift and the feedback circuit must has 180  phase shift to achieve total 360  phase shift. + vovo vfvf vovo RfRf RSRS RRR CCC

10 Derivation of the Oscillation Freq (1) For real part: Referring to previous diagram: (180  phase shift) (oscillation conditions)

11 Derivation of the Oscillation Freq (2) For imaginary part:

12 Example Design a RC phase shift oscillator with f o = 1.0 kHz. If C = 0.1µF is used, what resistor value must be used in the RC network? Solution:

13 2. Wein Bridge Oscillator + vovo vfvf vovo RfRf RSRS R1 R2 C1 C2 Fundamental part of the oscillator is a lead-lag network. R1 and C1 form the lag portion, while R2 and C2 form the lead network. Rf and Rs form the feedback network.

14 Derivation of the Oscillation Freq (1) + vovo vfvf vovo RfRf RSRS R R C C z1 z2

15 Derivation of the Oscillation Freq (2) Gain for non-inverting amplifier: For real part: For imaginary part:

16 Design a RC element of a Wein Bridge Oscillator for operation at f o = 10kHz. Solution: Select R = 100 k . Since We can select R F = 200 k  and R S = 100 k  Example

17 RC Oscillators: 1) Phase Shift Oscillator 2) Wien Bridge Oscillator Summary + vovo vfvf vovo RfRf RSRS RRR CCC + vovo vfvf vovo RfRf RSRS R1R1 R2R2 C1C1 C2C2

18 LC Oscillators

19 1. Colpitts Oscillator Consists of an inverting amplifier and a resonant LC feedback network. At resonance, total inductive reactance is equal to total capacitive reactance. X L = X C1 + X C2 vovo vfvf vovo RfRf RSRS L C2C2 C1C1

20 Derivation of the Oscillation Freq (1)

21 Derivation of the Oscillation Freq (2)

22 A 1 mH inductor is used in a Colpitts Oscillator. Select the capacitor values so that f o = 1 MHz and β = -4. Solution: From previous slide: Solve both equations: Example

23 2. Hartley Oscillator Consists of an inverting amplifier and a resonant LC feedback network. At resonance, total capacitive reactance is equal to total inductive reactance. X C = X L1 + X L2 vovo vfvf vovo RfRf RSRS C L2L2 L1L1

24 Derivation of the Oscillation Freq (1)

25 Derivation of the Oscillation Freq (2)

26 A 1pF is used in a Hartley Oscillator. Select the inductor values so that f o = 1 MHz and β = 5. Solution: From previous slide: Solve both equation: Example

27 LC Oscillators: 1) Colpitts Oscillator 2) Hartley Oscillator Summary vovo vfvf vovo RfRf RSRS L C2C2 C1C1 vovo vfvf vovo RfRf RSRS C L2L2 L1L1