6.776 High Speed Communication Circuits and Systems Lecture 14 Voltage Controlled Oscillators
advertisement
6.776 High Speed Communication Circuits and Systems Lecture 14 Voltage Controlled Oscillators Massachusetts Institute of Technology March 29, 2005 Copyright © 2005 by Michael H. Perrott VCO Design for Narrowband Wireless Systems Zin From Antenna and Bandpass Filter PC board trace Zo Mixer RF in Package Interface IF out To Filter LNA LO signal VCO Reference Frequency Frequency Synthesizer Design Issues - Tuning Range – need to cover all frequency channels - Noise – impacts receiver sensitivity performance - Power – want low power dissipation - Isolation – want to minimize noise pathways into VCO - Sensitivity to process/temp variations – need to make it manufacturable in high volume M.H. Perrott MIT OCW VCO Design For Broadband High Speed Data Links Zin From Broadband Transmitter PC board trace Zo Data Package Interface In Amp Clock and Data Recovery Clk Data Out Data In Phase Detector Clk Out Loop Filter VCO Design Issues - Same as wireless, but: Required noise performance is often less stringent Tuning range is often narrower M.H. Perrott MIT OCW Popular VCO Structures LC oscillator VCO Amp -Ramp Vout C Vin L Rp Ring oscillator Vout Vin -1 LC Oscillator: low phase noise, large area Ring Oscillator: easy to integrate, higher phase noise M.H. Perrott MIT OCW Barkhausen’s Criteria for Oscillation x=0 e H(jw) y Barkhausen Criteria e(t) Closed loop transfer function Asin(wot) H(jwo) = 1 Self-sustaining oscillation at frequency ωo if Asin(wot) y(t) - Amounts to two conditions: Gain = 1 at frequency ωo Phase = n360 degrees (n = 0,1,2,…) at frequency ωo M.H. Perrott MIT OCW Example 1: Ring Oscillator ∆t (or ∆Φ) A B C A A B C Gain is set to 1 by saturating characteristic of inverters A Odd number of stages to prevent stable DC operating point Phase equals 360 degrees at frequency of oscillation (180 from inversion, another 180 from gate delays) T - Assume N stages each with phase shift ∆Φ - Alternately, N stages with delay ∆t M.H. Perrott MIT OCW Further Info on Ring Oscillators Due to their relatively poor phase noise performance, ring oscillators are rarely used in RF systems - They are used quite often in high speed data links, - We will focus on LC oscillators in this lecture Some useful info on CMOS ring oscillators - Maneatis et. al., “Precise Delay Generation Using - Coupled Oscillators”, JSSC, Dec 1993 (look at pp 127128 for delay cell description) Todd Weigandt’s PhD thesis – http://kabuki.eecs.berkeley.edu/~weigandt/ M.H. Perrott MIT OCW Example 2: Resonator-Based Oscillator Z(jw) Vout -1 Vx GmVx Rp Cp 0 Lp Vx -1 -Gm Vout Z(jw) Barkhausen Criteria for oscillation at frequency ωo: - Assuming G m M.H. Perrott is purely real, Z(jωo) must also be purely real MIT OCW A Closer Look At Resonator-Based Oscillator Rp Gm 0 Z(jw) Vout |Z(jw)| 0 90o 0o Z(jw) -90o wo 10 wo w 10wo For parallel resonator at resonance - Looks like resistor (i.e., purely real) at resonance M.H. Perrott Phase condition is satisfied Magnitude condition achieved by setting GmRp = 1 MIT OCW Impact of Different Gm Values jw S-plane Increasing GmRp Open Loop Resonator Poles and Zero σ Locus of Closed Loop Pole Locations Root locus plot allows us to view closed loop pole locations as a function of open loop poles/zero and open loop gain (GmRp) - As gain (G R ) increases, closed loop poles move into m p right half S-plane M.H. Perrott MIT OCW Impact of Setting Gm too low GmRp < 1 jw S-plane Closed Loop Step Response Open Loop Resonator Poles and Zero σ Locus of Closed Loop Pole Locations Closed loop poles end up in the left half S-plane - Underdamped response occurs Oscillation dies out M.H. Perrott MIT OCW Impact of Setting Gm too High jw S-plane Closed Loop Step Response GmRp > 1 Open Loop Resonator Poles and Zero σ Locus of Closed Loop Pole Locations Closed loop poles end up in the right half S-plane - Unstable response occurs Waveform blows up! M.H. Perrott MIT OCW Setting Gm To Just the Right Value jw S-plane Closed Loop Step Response GmRp = 1 Open Loop Resonator Poles and Zero σ Locus of Closed Loop Pole Locations Closed loop poles end up on jw axis Issue – GmRp needs to exactly equal 1 - Oscillation maintained - How do we achieve this in practice? M.H. Perrott MIT OCW Amplitude Feedback Loop Output Oscillator Adjustment of Gm Peak Detector Desired Peak Value One thought is to detect oscillator amplitude, and then adjust Gm so that it equals a desired value - By using feedback, we can precisely achieve G R m p =1 Issues - Complex, requires power, and adds noise M.H. Perrott MIT OCW Leveraging Amplifier Nonlinearity as Feedback -Gm 0 -1 |Vx(w)| 0 Ix Z(jw) Vout A W wo 0 |Ix(w)| Vx GmA wo 2wo 3wo W Practical transconductance amplifiers have saturating characteristics - Harmonics created, but filtered out by resonator - Our interest is in the relationship between the input and the fundamental of the output M.H. Perrott MIT OCW Amplifier Nonlinearity as Amplitude Control As input amplitude is increased - Effective gain from input to fundamental of output drops - Amplitude feedback occurs! (G R = 1 in steady-state) m M.H. Perrott p MIT OCW One-Port View of Resonator-Based Oscillators Zactive Active Negative Resistance Generator Zres Vout Active Negative Resistance Zactive 1 = -Rp -Gm Resonator Zres Vout Resonator Rp Cp Lp Convenient for intuitive analysis Here we seek to cancel out loss in tank with a negative resistance element - To achieve sustained oscillation, we must have M.H. Perrott MIT OCW One-Port Modeling Requires Parallel RLC Network Since VCO operates over a very narrow band of frequencies, we can always do series to parallel transformations to achieve a parallel network for analysis Cs Ls Rp RsC Cp Lp RsL - Warning – in practice, RLC networks can have secondary (or more) resonant frequencies, which cause undesirable behavior Equivalent parallel network masks this problem in hand analysis Simulation will reveal the problem M.H. Perrott MIT OCW VCO Example – Negative Resistance Oscillator L1 L2 Vout RL1 Include loss in inductors and capacitors RL2 L1 L2 Vout Vout C1 M1 M2 Vs C2 C1 Vout M1 M2 Vs RC1 Ibias C2 RC2 Ibias This type of oscillator structure is quite popular in current CMOS implementations - Advantages Simple topology Differential implementation (good for feeding differential circuits) Good phase noise performance can be achieved M.H. Perrott MIT OCW Analysis of Negative Resistance Oscillator (Step 1) RL1 Rp1 RL2 L1 Cp1 Lp1 Lp2 Rp2 L2 Vout Vout Vout M1 C1 Cp2 M2 Vs RC1 C2 RC2 Narrowband parallel RLC model for tank Vout M1 M2 Vs Ibias Ibias Derive a parallel RLC network that includes the loss of the tank inductor and capacitor - Typically, such loss is dominated by series resistance in the inductor M.H. Perrott MIT OCW Analysis of Negative Resistance Oscillator (Step 2) Rp1 Cp1 Lp1 Rp1 Vout Vout M1 M2 Cp1 Vout Lp1 Rp1 Cp1 Vout -1 M1 Lp1 1 -Gm1 Vs Ibias Split oscillator circuit into half circuits to simplify analysis - Leverages the fact that we can approximate V as being incremental ground (this is not quite true, but close enough) s Recognize that we have a diode connected device with a negative transconductance value - Replace with negative resistor Note: Gm is large signal transconductance value M.H. Perrott MIT OCW Design of Negative Resistance Oscillator Rp1 Cp1 Lp1 Lp2 Vout A Cp2 Vout M1 Rp2 Rp1 Cp1 Vout A M2 Vs Lp1 1 -Gm1 Gm1 gm1 Ibias Gm1Rp1=1 A Design tank components to achieve high Q - Resulting R p value is as large as possible Choose bias current (Ibias) for large swing (without going far into Gm saturation) - We’ll estimate swing as a function of I shortly Choose transistor size to achieve adequately large g - Usually twice as large as 1/R to guarantee startup bias m1 p1 M.H. Perrott MIT OCW Calculation of Oscillator Swing: Max. Sinusoidal Oscillation Rp1 A Cp1 Vout Lp1 Lp2 I1(t) I2(t) M1 Vs Cp2 Vout Rp2 A M2 Ibias If we assume the amplitude is large, Ibias is fully steered to one side at the peak and the bottom of the sinusoid: M.H. Perrott MIT OCW Calculation of Oscillator Swing: Squarewave Oscillation If amplitude is very large, we can assume I1(t) is a square wave - We are interested in determining fundamental component (DC and harmonics filtered by tank) I1(t) |I1(f)| Ibias/2 1 I π bias W=T/2 1 I 3π bias Ibias Ibias/2 T T t - Fundamental component is 1 1 T W f - Resulting oscillator amplitude M.H. Perrott MIT OCW Variations on a Theme Bottom-biased NMOS Top-biased NMOS Top-biased NMOS and PMOS Ibias L1 Vout C1 Ibias L2 M3 Vout M1 M2 L1 C2 Vs Ibias L2 Vout C1 Ld Vout M1 M2 M4 Vout C2 C1 Vout M1 M2 C2 Biasing can come from top or bottom Can use either NMOS, PMOS, or both for transconductor - Use of both NMOS and PMOS for coupled pair would appear to achieve better phase noise at a given power dissipation See Hajimiri et. al, “Design Issues in CMOS Differential LC Oscillators”, JSSC, May 1999 and Feb, 2000 (pp 286-287) M.H. Perrott MIT OCW Colpitts Oscillator L Vout Vbias M1 C1 V1 Ibias C2 Carryover from discrete designs in which single-ended approaches were preferred for simplicity - Achieves negative resistance with only one transistor - Differential structure can also be implemented, though Good phase noise can be achieved, but not apparent there is an advantage of this design over negative resistance design for CMOS applications M.H. Perrott MIT OCW Analysis of Cap Transformer used in Colpitts Voltage drop across RL is reduced by capacitive voltage divider - Assume that impedances of caps are less than R L at resonant frequency of tank (simplifies analysis) Ratio of V1 to Vout set by caps and not RL Power conservation leads to transformer relationship shown (See Lecture 4) M.H. Perrott MIT OCW Simplified Model of Colpitts Purpose of cap transformer Transformer ratio set to achieve best noise performance - Reduces loading on tank - Reduces swing at source node (important for bipolar version) M.H. Perrott MIT OCW Design of Colpitts Oscillator Design tank for high Q Choose bias current (Ibias) for large swing (without going far into Gm saturation) Choose transformer ratio for best noise Choose transistor size to achieve adequately large gm1 - Rule of thumb: choose N = 1/5 according to Tom Lee M.H. Perrott MIT OCW Calculation of Oscillator Swing as a Function of Ibias I1(t) consists of pulses whose shape and width are a function of the transistor behavior and transformer ratio - Approximate as narrow square wave pulses with width W |I1(f)| I1(t) Ibias Ibias W average = Ibias T T t 1 T 1 W f - Fundamental component is - Resulting oscillator amplitude M.H. Perrott MIT OCW Clapp Oscillator L Llarge C3 Vout Vbias M1 C1 1/Gm Ibias V1 C2 Same as Colpitts except that inductor portion of tank is isolated from the drain of the device - Allows inductor voltage to achieve a larger amplitude without exceeded the max allowable voltage at the drain Good for achieving lower phase noise M.H. Perrott MIT OCW Simplified Model of Clapp Oscillator Looks similar to Colpitts model - Be careful of parasitic resonances! M.H. Perrott MIT OCW Hartley Oscillator C Vout Vbias L2 L1 M1 V1 Cbig Ibias Same as Colpitts, but uses a tapped inductor rather than series capacitors to implement the transformer portion of the circuit - Not popular for IC implementations due to the fact that capacitors are easier to realize than inductors M.H. Perrott MIT OCW Simplified Model of Hartley Oscillator C Vout Vbias L2 L1 M1 C V1 Cbig C L1+L2 vout id1 M1 Ibias Rp L1+L2 Rp|| 1/Gm N2 vout 1/Gm N2 -GmNvout v1 Nvout N= L2 L1+L2 C Similar to Colpitts, again be wary of parasitic resonances M.H. Perrott L1+L2 Rp|| 1/Gm N2 vout -1/Gm N MIT OCW Integrated Resonator Structures Inductor and capacitor tank - Lateral caps have high Q (> 50) - Spiral inductors have moderate Q (5 to 10), but completely integrated and have tight tolerance (< ± 10%) - Bondwire inductors have high Q (> 40), but not as “integrated” and have poor tolerance (> ± 20%) - Note: see Lecture 6 for more info on these Lateral Capacitor Spiral Inductor Bondwire Inductor A A A A package die B C1 Lm B B B M.H. Perrott MIT OCW Integrated Resonator Structures Integrated transformer - Leverages self and mutual inductance for resonance to achieve higher Q - See Straayer et. al., “A low-noise transformer-based 1.7 GHz CMOS VCO”, ISSCC 2002, pp 286-287 A B Cpar1 k L1 D A B L2 C M.H. Perrott C Cpar2 D MIT OCW Quarter Wave Resonator λ0/4 Z(λ0/4) x y z z L ZL 0 Impedance calculation (from Lecture 4) - Looks like parallel LC tank! Benefit – very high Q can be achieved with fancy dielectric Negative – relatively large area (external implementation in the past), but getting smaller with higher frequencies! M.H. Perrott MIT OCW Other Types of Resonators Quartz crystal - Very high Q, and very accurate and stable resonant - frequency Confined to low frequencies (< 200 MHz) Non-integrated Used to create low noise, accurate, “reference” oscillators SAW devices MEMS devices - Wide range of frequencies, cheap (see Lecture 9) - Cantilever beams – promise high Q, but non-tunable and haven’t made it to the GHz range, yet, for resonant frequency - FBAR – Q > 1000, but non-tunable and poor accuracy - Other devices are on the way! M.H. Perrott MIT OCW
