EE3110 AEC3_Oscillators and Waveform Generation_2007

# EE3110 AEC3_Oscillators and Waveform Generation_2007 - 3...

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Unformatted text preview: 3 Oscillators and Waveform Generation 3.1 Feedback Concept v i v ε v o v fb A(s) Frequency selective network, β (s) ) ( ) ( 1 ) ( ) ( s A s s A s A f β- = Closed loop transfer function ) ( ) ( 1 =- s A s β Condition for oscillation 1 ) ( ) ( = s A s β Barkhausen Criterion λ Total phase shift through the amplifier and feedback network = N × 360 o . λ Magnitude of loop gain must be unity 3.2 Phase Shift Oscillator A 1 v i v 1 v 1 v 2 v 2 v 3 v o A 2 A 3 i v sRC sRC v × + = 1 1 Transfer function of first RC network Assuming all RC networks are identical and A 1 = A 2 = 1, ) ( 1 3 3 s sRC sRC v v i β = + = Feedback transfer function Let A 3 = A(s) = A ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 3 3 3 1 1 ) ( ) ( C R RC j C R RC RC j A sRC sRC A s s A ϖ ϖ ϖ ϖ ϖ β- +- ×- = + × = To satisfy the Barkhausen criterion 1 ) ( ) ( = s s A β , 3 1 2 2 2 =- C R ϖ Giving, RC 3 1 = = ϖ ϖ At this frequency, ( 29 ( 29 ( 29 ( 29 ) 3 / 1 ( 3 3 / 3 / 1 3 / 1 ) ( ) (- + ×- = = j j A s s A β Giving 8- = A 3.3 Wien Bridge Oscillator A v i v o ) ( s Z Z Z v v s p p o i β = + = Feedback transfer function Let A(s) = A ( 29 sRC sRC A Z Z Z A s s A s p p / 1 3 ) ( ) ( + + = + × = β To satisfy the Barkhausen criterion...
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EE3110 AEC3_Oscillators and Waveform Generation_2007 - 3...

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