Lect14_VCOs II

Lect14_VCOs II - ECE 894 RF and mmWave Front-end Circuit Design Lecture 14 VCOs II Prof Waleed Khalil 1 Reactance Oscillators(1/5 vout vin = 1 A B

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ECE 894 RF and mmWave Front-end Circuit Design Prof. Waleed Khalil Lecture VCOs II 14 1
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Reactance Oscillators (1/5) Assuming pure reactance feedback elements: 2 B A v out v in ( ) ( ) ( ) ( ) ( ) 1 out in vA v AB ωω ω = g m v in v in + - r o Z 1 Z 3 Z 2 v out A B ( ) ( ) ( ) 2 23 12 3 123 1 in out out mo in o v Z B v ZZ Z v A gr v Z AB g r r Z Z = = +  + = = −  ++  = − + + ( ) ( ) 1 i i o XX Z jX AB g r X j r X = ⇒= + + “CMOS RFIC Design Principles”, R. Caverly, Artech House, 2007
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Reactance Oscillators (2/5) Barkhausen’s oscillation criteria: Angel criteria can be met only if: Feedback circuit contains both capacitive and inductive elements X 2 and X 1 must of same type X 3 is of opposite type 3 B A v out v in g m v in v in + - r o Z 1 Z 3 Z 2 v out A B ( ) ( ) ( ) ( ) 1 & 0 osc osc osc osc AB ωω = ∠= 123 0 XX X ++= 2 1 mo X AB g r X = ( ) 3 12 X = −+
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Reactance Oscillators (3/5) 4 ( ) 3 12 tan 2 1 11 1 1 1 res k mo X XX L CC L CC C AB g r C ω ωω = −+  ⇒= +   + = = = = g m v in v in + - r o v out A B L C 1 C 2 v in C 1 C 2 L v out
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Lect14_VCOs II - ECE 894 RF and mmWave Front-end Circuit Design Lecture 14 VCOs II Prof Waleed Khalil 1 Reactance Oscillators(1/5 vout vin = 1 A B

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