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RFIC_Lecture_Note_No14_p236-p255 _Oscillators1_

RFIC_Lecture_Note_No14_p236-p255 _Oscillators1_ - ECE695F...

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ECE695F RFIC Prof. S. Mohammadi - - 236 Oscillators and Synthesizers Oscillators active device with power gain (amplifier, negative R) frequency setting tank element Why do we need oscillators Æ to provide a stable frequency output * useful for timekeepers * useful for communications mixing with local oscillator (LO) Important attributes of oscillators * long term stability temp. coefficient of oscillation frequency aging and drift Types of active devices used for oscillators * 3-terminal : MOSFET, BJT * 2-terminal : negative resistance diodes (tunnel diode, Gunn, IMPATT, ) L
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ECE695F RFIC Prof. S. Mohammadi - - 237 Types of tank element Q Surface Volume = * Quarter-wave Resonators Distributed elements with high * Lumped LC tank * Xtal * SAW (surface acoustic wave devices) Classification of oscillators * near sinusoidal low phase noise (e.g. high Q LC or Xtal Oscillators) * Relaxation Oscillators poor stability, but can have a very large tunning range (application Æ VCO) (e.g. multivibrator, Ring Oscillator) Approaches to Oscillator Design * negative R 2-terminal active element oscillator used at very high microwave frequencies > 50 GHz * feedback 3-terminal active device We will look at the feedback approach when dealing with MOS oscillators
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ECE695F RFIC Prof. S. Mohammadi - - 238 + A(s) f(s) S out S in ) ( ) ( 1 ) ( s f s A s A S S in out = assuming linear for now DD V out V ' out V Bias V C L R L 1 : n L R high Q tank ckt (very freq. selective impedance) transformer is used for matching O f ) ( f Z AC equivalent i V j C O V O R L R i m V G L C 11 L 1 : n presence of noise starts the oscillation x V source coupled pair 2 gs i C C = 2 m m g G = O O r R = Let s calculate the overall transfer function : ( ) ( ) s V s V i O * Since it is a feedback system 1) find open loop gain with feedback loading ( ) l A T m i O l Z G V V A = = tank ckt impedance
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ECE695F RFIC Prof. S. Mohammadi - - 239 LC s s R L s R R Z T 2 1 1 1 + + = where 11 L L = 2 n C C C i L + = L O R R R = 2) find feedback factor ( ) n s f 1 = ( ) ( ) LC s s n R G R L s L G s V s V m m x O 2 1 1 + + = response of osc. Ckt to an input noise signal V(x) ( ) ( ) ( ) ( ) ( ) ( )( ) 2 1 P s P s s N s D s N s V s V x O = = poles of the transfer function ω j ' 0 ω 0 ω α δ 1 > n R G m poles in RHS unstable condition ( ) ( ) β ω α + = t ke t V t O ' 0 cos depend on initial condition 1 = n R G m 1 < n R G m poles in left-hand side stable condition ( ) t V O t
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ECE695F RFIC Prof. S. Mohammadi - - 240 Oscillator response (Transfer function) LC s s n R G R L s L G V V m m x O 2 1 1 + + = for small signal 2 m m g G = ( ) t V O ( ) ( ) β ω
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