6.976 High Speed Communication Circuits and Systems Lecture 11 Voltage Controlled Oscillators
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6.976 High Speed Communication Circuits and Systems Lecture 11 Voltage Controlled Oscillators Michael Perrott Massachusetts Institute of Technology Copyright © 2003 by Michael H. Perrott VCO Design for Wireless Systems Zin From Antenna and Bandpass Filter PC board trace Zo RF in Package Interface Mixer 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 blocking and 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 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 wo if Asin(wot) y(t) - Amounts to two conditions: Gain = 1 at frequency wo Phase = n360 degrees (n = 0,1,2,…) at frequency wo 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 Phase equals 360 degrees at frequency of oscillation A 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, though We will focus on LC oscillators in this lecture Some useful info on CMOS ring oscillators - Maneatis et. al., “Precise Delay Generation Using - M.H. Perrott Coupled Oscillators”, JSSC, Dec 1993 (look at pp 127128 for delay cell description) Todd Weigandt’s PhD thesis – http://kabuki.eecs.berkeley.edu/~weigandt/ MIT OCW Example 2: Resonator-Based Oscillator Z(jw) Vout -1 Vx GmVx Rp Cp 0 Lp -1 Vx -Gm Vout Z(jw) Barkhausen Criteria for oscillation at frequency wo: - Assuming G m M.H. Perrott is purely real, Z(jwo) 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 10wo w 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 0 -1 |Vx(w)| 0 Ix Z(jw) Vout A W wo 0 |Ix(w)| Vx -Gm 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 Leveraging Amplifier Nonlinearity as Feedback 0 -1 |Vx(w)| 0 Ix Vout Z(jw) GmA A W wo 0 |Ix(w)| Vx -Gm A GmA Gm wo 2wo 3wo W GmRp=1 A 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 Example – Negative Resistance Oscillator L1 L2 Vout M2 Vs Ibias RL2 L1 L2 Vout M1 C1 RL1 Include loss in inductors and capacitors Vout C2 C1 Vout M1 M2 Vs RC1 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 L1 L2 Vout M2 Vs RC1 Cp1 Lp1 Lp2 Vout Vout M1 C1 Rp1 RL2 C2 RC2 Narrowband parallel RLC model for tank Cp2 Rp2 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 A Cp1 Lp1 Lp2 Vout 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 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 M.H. Perrott MIT OCW bias m1 p1 Calculation of Oscillator Swing Rp1 Cp1 Vout A Lp1 Lp2 I1(t) I2(t) M1 Cp2 Vout Rp2 A M2 Vs Ibias 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 saturation) - We’ll estimate swing as a function of I in next slide Choose transistor size to achieve adequately large g Usually twice as large as 1/R to guarantee startup M.H. Perrott MIT OCW bias m1 p1 Calculation of Oscillator Swing as a Function of Ibias By symmetry, assume I1(t) is a square wave - We are interested in determining fundamental component (DC and harmonics filtered by tank) |I1(f)| I1(t) Ibias/2 1 I π bias W=T/2 Ibias Ibias/2 T T 1 I 3π bias 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 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 Rin= C1 Vout V1 L C2 Vout L N 2 RL C1||C2 1:N Vout RL RL C1||C2 = 1 C 1C 2 C1+C2 N= L C1||C2 N V1=NVout 2 RL C1 C1+C2 Voltage drop across RL is reduced by capacitive voltage divider - Assume that impedances of caps are less than R 1 resonant frequency of tank (simplifies analysis) Ratio of V1 to Vout set by caps and not RL L at Power conservation leads to transformer relationship shown M.H. Perrott MIT OCW Simplified Model of Colpitts L L Include loss in tank Rp vout Vout Vbias id1 M1 C1 1/Gm Ibias M1 V1 C1||C2 Rp|| 1/Gm N2 vout 1/Gm N2 -GmNvout Nvout C 1C 2 C1 N= C1+C2 C1+C2 Purpose of cap transformer - Reduces loading on tank - Reduces swing at source node (important for bipolar version) L v1 C2 C1||C2 = C1||C2 C1||C2 L Rp|| 1/Gm N2 vout -1/Gm N Transformer ratio set to achieve best noise performance M.H. Perrott MIT OCW Design of Colpitts Oscillator L Vout I1(t) Vbias M1 L Req= Rp|| 1/Gm N2 vout -1/Gm N C1 1/Gm Ibias A C1||C2 V1 Gm1 C2 gm1 NGm1Req=1 A Design tank for high Q Choose bias current (Ibias) for large swing (without going far into 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(t) Ibias Ibias |I1(f)| W average = Ibias T T t - Fundamental component is 1 T 1 W f - 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 L Llarge C3 Lp Cp id1 M1 C1 1/Gm Ibias Cp+C1||C2 vout Vout Vbias Rp M1 V1 C1||C2 1/Gm N2 v1 1/Gm N2 vout -GmNvout C 1C 2 C1 N= C1+C2 C1+C2 Cp+C1||C2 Looks similar to Colpitts model - Be careful of parasitic resonances! M.H. Perrott Rp|| Nvout C2 C1||C2 = Lp Lp Rp|| 1/Gm N2 vout -1/Gm N 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 v1 Rp|| 1/Gm N2 vout 1/Gm N2 -GmNvout 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 4 for more info on these Lateral Capacitor Spiral Inductor Bondwire Inductor A A A A B C1 package die 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 - High frequency, but poor accuracy (for resonant frequency) - 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 Voltage Controlled Oscillators (VCO’s) L1 Vout Cvar L L2 Vout Vout M1 M2 Vs Vbias Cvar M1 C1 V1 Vcont Ibias Ibias Cvar Vcont Include a tuning element to adjust oscillation frequency Varactor incorporated by replacing fixed capacitance - Typically use a variable capacitor (varactor) - Note that much fixed capacitance cannot be removed (transistor junctions, interconnect, etc.) Fixed cap lowers frequency tuning range M.H. Perrott MIT OCW Model for Voltage to Frequency Mapping of VCO T=1/Fvco VCO frequency versus Vcont L1 L2 Vout Vout M1 Cvar M2 Vs Vcont Vin Ibias Vbias Fvco Cvar fo Fout slope=Kv Vin Vbias Vcont Model VCO in a small signal manner by looking at deviations in frequency about the bias point - Assume linear relationship between input voltage and output frequency M.H. Perrott MIT OCW Model for Voltage to Phase Mapping of VCO Phase is more convenient than frequency for analysis Intuition of integral relationship between frequency and phase - The two are related through an integral relationship 1/Fvco= α out(t) out(t) 1/Fvco= α+ε M.H. Perrott MIT OCW Frequency Domain Model of VCO Take Laplace Transform of phase relationship - Note that K v is in units of Hz/V T=1/Fvco L1 Vout Cvar Vout M1 M2 Vs Vcont Vin Frequency Domain VCO Model L2 Cvar vin 2πKv s Φout Ibias Vbias M.H. Perrott MIT OCW Varactor Implementation – Diode Version Consists of a reverse biased diode junction - Variable capacitor formed by depletion capacitance - Capacitance drops as roughly the square root of the bias voltage Advantage – can be fully integrated in CMOS Disadvantages – low Q (often < 20), and low tuning range (± 20%) V+ V+ Cvar VP+ V- M.H. Perrott Depletion Region N+ N- n-well P- substrate V+-V- MIT OCW A Recently Popular Approach – The MOS Varactor Consists of a MOS transistor (NMOS or PMOS) with drain and source connected together - Abrupt shift in capacitance as inversion channel forms Advantage – easily integrated in CMOS Disadvantage – Q is relatively low in the transition region - Note that large signal is applied to varactor – transition region will be swept across each VCO cycle V+ V- V+ Cox W/L V- M.H. Perrott Cvar N+ Depletion Region N+ P- Cdep VT V+-V- MIT OCW A Method To Increase Q of MOS Varactor Cvar C 2C 4C W/L 2W/L 4W/L W/L LSB MSB Coarse Control 000 001 010 011 Coarse 100 Control 101 110 111 Overall Capacitance to VCO Vcontrol Fine Control Vcontrol Fine Control High Q metal caps are switched in to provide coarse tuning Low Q MOS varactor used to obtain fine tuning See Hegazi et. al., “A Filtering Technique to Lower LC Oscillator Phase Noise”, JSSC, Dec 2001, pp 1921-1930 M.H. Perrott MIT OCW Supply Pulling and Pushing L1 Vout Cvar L L2 Vout Vout M1 M2 Vs Vbias Cvar M1 C1 V1 Vcont Ibias Ibias Cvar Vcont Supply voltage has an impact on the VCO frequency - Voltage across varactor will vary, thereby causing a shift in its capacitance - Voltage across transistor drain junctions will vary, thereby causing a shift in its depletion capacitance This problem is addressed by building a supply regulator specifically for the VCO M.H. Perrott MIT OCW Injection Locking VCO Vnoise Vin |Vout(w)| |Vnoise(w)| Vout wo W wo -∆w ∆w ∆w Noise close in frequency to VCO resonant frequency can cause VCO frequency to shift when its amplitude becomes high enough |Vout(w)| |Vnoise(w)| wo W wo W -∆w ∆w ∆w |Vout(w)| |Vnoise(w)| wo W wo W -∆w ∆w ∆w |Vout(w)| |Vnoise(w)| wo ∆w M.H. Perrott W W wo W -∆w ∆w MIT OCW Example of Injection Locking For homodyne systems, VCO frequency can be very close to that of interferers Desired RF in(w) Interferer Narrowband Signal 0 wint wo Mixer LNA RF in W LO signal LO frequency Vin - Injection locking can happen if inadequate isolation from mixer RF input to LO port Follow VCO with a buffer stage with high reverse isolation to alleviate this problem M.H. Perrott MIT OCW
