Lect15_VCOs III

Lect15_VCOs III - ECE 894 RF and mmWave Front-end Circuit...

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Unformatted text preview: ECE 894 RF and mmWave Front-end Circuit Design Lecture 15 VCOs III Prof. Waleed Khalil 1 Reactive Oscillators- Another Perspective Rp Tank Loss vbias 1/gm Ibias L C vout Rp L C vout 1/gm N2 vbias Impedance Transformation vin 1/gm Ibias vin=Nvout Loop Gain = g m ( R p 1 g m ) CG configuration achieve positive feedback but loop gain is < 1 1 gm Loop Gain = Ng m R p N2 Use impedance transformation to reduce impact of 1/gm loading on tank Q Simple transformers can be used but require large area 2 Colpitts Oscillator (1/2) Use cap transformer to reduce loading Assume cap impedance is much lower than 1/gm at resonance frequency vin ≈ C2 vout = Nvout C1 + C2 Rp L vout C2 N= C1 + C2 Calculating equivalent output resistance using power conservation 2 vout (1 g m ) 2 N2 vbias vin Ibias C2 C1 Impedance Transformation 2 2 vout vin == 2 Req 2 (1 g m ) = ⇒ Req (1 g m= ), Loop Gain N 2 1 gm Ng m R p N2 vout Req C2 C1 Optimum cap transformation ratio N ~ 1/5 vin 1/gm “Analysis of MOS Transformer-Coupled Oscillators ”, JSSC, Dec 1987 3 Colpitts Oscillator (2/2) MOS operating region depends output voltage swing Dictated by Ibias and tank loss, Rp vDD Rp L vout vbias Io vin Ibias C2 C1 Output current consists of narrow square wave pulse of average Ibias Fundamental component of output current is selectively filtered by tank impedance and appears as sinusoidal output Io fund ≈ 2 I bias cos(ωres t ) vout = 2 I bias R p cos(ωres t ) vout vDD 0 Io Ibias t t “Exact Calculation of Oscillation Amplitude and Predicting Power Consumption for CMOS Colpitts Oscillators ”, Int. Symp. on Circuits and Systems, Jun 1997 4 Oscillator Optimization (1/2) Oscillator amplitude and thus its phase noise is dependant on two modes of operation Current limited: Amplitude increases linearly with current Voltage limited: Amplitude is bounded by supply voltage vout Current Limited Voltage Limited Vmax Current Limited vout α I bias Noise α 4kT Ibias γ gm ⇒ Noise α α 3 I bias − Noise 2 Phase Noise = α I bias Psig Voltage Limited Phase Noise 2 2 Psig α vout ⇒ Psig α I bias Current Limited Voltage Limited vout Vmax ⇒ Psig is fixed = Phase Noise α I bias 5 Optimum Ibias Ibias Oscillator Optimization (2/2) Inductor optimization assuming fixed Q and Ibias Current Limited Voltage Limited vout α R p vout = Vmax 2 vout = ⇒ Psig α R p Psig Rp 2 Vmax 1 = ⇒ Psig α Psig Rp Rp Phase Noise α 1 1 ⇒ Phase Noise α Psig Rp Phase Noise α 1 ⇒ Phase Noise α R p Psig Q is fixed ⇒ R p α L : Phase Noise α L Phase Noise 1 : Phase Noise α L Current Limited Voltage Limited Optimum L 6 L Negative Resistance Oscillator Rp L vout C Rp L C Rp L vout vin C vin Ibias Ibias Ibias − jω g m Lp vout = vin ω2 ω1 1− 2 + j ωo Q ωtan k Loop Gain = − (ω g 2 2 m Lp ) 2 ω ω 1 ω2 1 − 2 + 2 j 1 − 2 ωo Q ωtan k ωtan k ω2 1 − 2 ωtan k Q 2 = Loop Gain res ω g L Q) (= ( g 2 o m p m Rp ) 2 7 ...
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Lect15_VCOs III - ECE 894 RF and mmWave Front-end Circuit...

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