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EE5602_8_ARFaMT_OSC - Oscillators Oscillation Conditions I...

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Oscillators Oscillation Conditions I Nyquist Criterion Barkhausen Criterion Oscillation Conditions II Concept of negative resistance Use of s-parameters Oscillator Configurations Basic oscillator Matrix conversion Pierce, Colpitts and Clapp family Resonators
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Oscillation Conditions I Feedback theory Oscillation : Nyquist Criterion : Barkhausen Criterion : For oscillation ( 29 ( 29 ( 29 ϖ ϖ ϖ j H j G j G V V i o + = 1 G ( j ) ϖ H ( j ) ϖ V i V o Σ ( 29 ( 29 0 1 = + ϖ ϖ j H j G ( 29 ( 29 1 - = ϖ ϖ j H j G μβ μ - = 1 i o V V 1 = μβ
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Oscillation Conditions II Concept of negative resistance A reflection co-efficient greater than 1 a negative resistance This can be shown by substituting into the following Generally a net loop resistance that is negative will give rise to oscillation Γ - Γ + = + - = Γ 1 1 1 1 z or z z 1 ' 11 s IN = Γ 3 2 1 2 1 1 1 2 : - = - + = Γ - Γ + = = Γ z Example
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Oscillation Conditions II Use of s-parameters From the transducer gain look at the source gain. The locus of |s 11 ’| = 1 was found to be a circle, this boundary separated stability from potential instability. Critical instability, or the point when oscillation just starts is when G S tends to infinity. Conversely it must also be true that, ( 29 IN S S R Z e i s = - = Γ Re . . 1 ' 11 2 ' 11 2 1 1 S S S s G Γ - Γ - = ( 29 OUT L L R Z e i s = - = Γ Re . . 1 ' 22
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Oscillator Configurations : Basic Oscillator An oscillator consists of the following basic elements 2-port active network Feedback network Resonator Load DC bias 2 - p o r t a c t i v e n e t w o r k F e e d b a c k n e t w o r k L o a d D C B i a s R e s o n a t o r Γ L Γ S Γ O U T Γ I N
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Oscillator Configurations : Matrix Conversion 2-port Series feedback requires conversion to z-matrix Parallel feedback requires conversion to y-matrix 3-port Conversion between configuration (CE, CB, CC) requires conversion to indefinite admittance matrix IAM Feedback can also be analyzed using 3-port s-matrices
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