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1、Design of CMOS analog Integrated Circuits,Oscillators,2019/6/26,2,Outline,1. General Considerations 2. Ring Oscillators 3. LC Oscillators 4. Voltage-Controlled Oscillators 5. Mathematical Model of VCOs,2019/6/26,3,1 . General Considerations,How can a circuit oscillate?,For negative feedback system,B
2、arkhausen criteria,2019/6/26,4,2 . Ring Oscillators,How does the ring oscillator begin to oscillate?,Single pole system, phase shift: max 270 ,Two-pole system, phase shift: 360,Three-pole,Loop gain:,A02,2019/6/26,5,Amplitude Limiting,Closed-loop gain of the three-stage ring,The denominator can be ex
3、panded as,2019/6/26,6,Amplitude Limiting (cont.),Poles of three stage ring oscillator for various A0,不起振,振荡,振荡，实际上电路经历非线性，最终达到“饱和”,For A02,2019/6/26,7,Ring oscillator using CMOS inverters,For large signal,X跳变,Y跳变,Z跳变,1个TD,1个TD,1个TD,For 3-stage ring oscillator, 振荡周期2NTD6TD,2019/6/26,8,3. LC Oscillato
4、rs,3.1 LC tanks,Ideal (lossless) LC tanks,Realistic (loss) LC tanks,Quality factor,Equivalent impedance,2019/6/26,9,3.1 LC tanks (cont.),Serial parallel,For a narrow frequency range, ZSZP,We get,Resonant frequency,2019/6/26,10,3.2 “Tuned” gain stage,LC tank as load,At resonance,接成反馈形式，谐振时，总相移等于180，所
5、以不能振荡,2019/6/26,11,3.3 Crossed-Coupled Oscillator,At resonance, total phase shift is 0,Oscillation conditions:,2019/6/26,12,4. Voltage-Controlled Oscillators,Definition,Center Frequency,Tuning Range 2 1,Tuning Linearity,Output Amplitude,Power Dissipation,Supply and Common-Mode Rejection,Output Signa
6、l Purity 信号抖动（Jitter）;相位噪声(Phase noise),2019/6/26,13,4.1 Tuning in Ring Oscillators,Change load,In every stage, M3M4 all in triode region, controlled by Vcout,Drawback: the output swing of the circuit varies considerably across the tuning range,Change current source,固定负载管的VDS，保证输出摆幅（ISSRon）：M5工作在线性区
7、，通过A1反馈固定VDS，M3和M4跟随M5的导通电阻。,Adjust ISS by Vcont,2019/6/26,14,4.1 Tuning in Ring Oscillators (cont.),Delay Variation by Positive Feedback,-2/gm,Half circuit equivalent: I1|-1/gm3,4| （ -1/gm3,4）|R1,2=R/(1-gm3,4R) fosc ,Issue: as I1 varies, so does the currents steered by M3 and M4 to R1 and R2. Thus,
8、 the output swing is not constant across the tuning range,半边等效,2019/6/26,15,4.1 Tuning in Ring Oscillators (cont.),Delay Variation by Positive Feedback (cont.),Using differential pairs, let IT=ISS+I1 and give a differential swing of 2R1,2IT,To avoid no current carried through M1M2, a small current s
9、ource IH connected from node P, ensuring M1 and M2 always remain on.,Drawback: the additional voltage headroom that it consumes,2019/6/26,16,4.1 Tuning in Ring Oscillators (cont.),Delay Variation by Positive Feedback (cont.),To fix the headroom overhead, using fold structure.,2019/6/26,17,4.1 Tuning
10、 in Ring Oscillators (cont.),Delay Variation by Interpolation,Fast path on, slow path off, maximum oscillation frequency; Fast path off, slow path on, minimum oscillation frequency; Vcont lies between the two extremes, each path is partially on and the total delay is a weighted sum of their delays.,
11、2019/6/26,18,4.1 Tuning in Ring Oscillators (cont.),Delay Variation by Interpolation (cont.),2019/6/26,19,4.2 Tuning in LC Oscillators,Varactors (Varicap): A reverse-biased pn junction can serve as a varactor,保证变容二极管反偏或正偏较弱,2019/6/26,20,4.2 Tuning in LC Oscillators (cont.),Varactors,N阱与衬底的电容,Parallel to decrease the series resistance,2019/6/26,21,4.2 Tuning in LC Oscillators (cont.),To eliminate the parasitic N-well capacitances from tank,The cross-coupled pair incorporates PMOS devies.,2019/6/26,22,Mathematical Model of VCOs,Phase and Frequency,2019/6/26,23,VCO,剩余相位,积分器的传输函数,
