1-GHz and 2.8-GHz CMOS Injection-locked Ring Oscillator Prescalers

Transcription

1 1-GHz and 2.8-GHz CMOS Injection-locked Ring Oscillator Prescalers Rafael J. Betancourt-Zamora, Shwetabh Verma and Thomas H. Lee Department of Electrical Engineering Stanford University

2 Outline Introduction Injection Locking Theory Circuit Implementation Measured Results Conclusion

3 Goals Understand the Injection-locking mechanism Grasp the limitations of Injectionlocked Frequency Dividers Design Injection-locked Frequency Divider using a Ring Oscillator

4 Motivation: Low-power Frequency Synthesis F REF F OUT PFD N 2µA UP DN 240µA VCO CP & LF MHz CMOS PLL [V.Kaenel 96] 10µA 800µA 50µA 500µA LNA 300µA VCO 100µA Q I 8 150µA 300µA 400µA 900 MHz CMOS RECEIVER [Darabi 00] Frequency synthesizers are implemented using PLLs. Q I Major sources of power dissipation are the VCO and Frequency Divider.

5 Frequency Divider Power Trade-off POWER INCREASES WITH DIVISION RATIO 900 MHz 450 MHz 225 MHz µA 100µA 100µA TOTAL POWER 200µA 300µA 400µA MHz [Darabi 00] We propose a technique in which power decreases with division ratio.

6 Outline Introduction Injection Locking Theory Circuit Implementation Measured Results Conclusion

7 Ring Oscillator Model V O BARKHAUSEN CRITERIA Necessary conditions for oscillation GAIN CONDITION Hjω ( O ) 1 R L PHASE CONDITION Hjω ( O ) = 180 I TAIL C L Neglect feedforward zero SMALL-SIGNAL MODEL H O H S ( jω) = jω ω P ω 1 P = R L C L

8 Ring Oscillator Model (II) V O GAIN CONDITION π H O 1 tan -- n 2 + PHASE CONDITION N-STAGE MODEL n H Hjω ( ) = O 1 j----- ω π -- + tan ω o n n ω P = ω π tan -- n n > 2 ω 0 is free-running oscillator frequency. Each stage contributes π/n to the phase.

9 Ring Oscillator Model (III) V O EXAMPLE Hjω ( ) = n H O 1 j----- ω π -- + tan ω o n n n H 0 ω p ω ω ω 0 DC gain Η 0 decreases with number of stages. Poles ω p coincide with ω 0 only for n=4.

10 Injection-locked Ring Oscillator EXAMPLE: 3-stage, Divide by 4 ω = ω RF 4 R L ω RF C L V BIAS ω RF An oscillator can be injection-locked to a harmonic of the free-running oscillation frequency.

11 Regenerative Divider [Miller 1939] EXAMPLE: Divide by 4 ω RF 3 ω RF ± ---- ωrf 4 H(jω) ω = ω RF 4 FREQ. MULT. 3 Commonly used where the frequency of operation is very high, beyond what can be achieved with flip-flop based circuits. Frequency multiplier can represent non-linearities present in the circuit. Used a model similar to Miller s, since the locking mechanisms are identical.

12 Model for Injection-locked Frequency Divider DC + ω RF RF Port Mixer n-stage LPF H(jω) -1 ω ω RF - (M+1)ω ω RF - (M-1)ω LO+ LO- ω, 3ω, 5ω... ω RF I TAIL Differential Pair s Non-linearity LO Port ω = ω RF /M MIXER Differential-pair single-balanced mixer Injected ω RF into the tail device FILTER Suppress products > ω V O is sinusoidal (small n).

13 Model for Injection-locked Frequency Divider (II) EXAMPLE: 3-stage, Divide by 4 Mixer 3-stage LPF DC + ω H(jω) RF ω -1 ω RF - 5ω RF Port ω RF - 3ω LO+ ω RF LO- I TAIL LO Port ω, 3ω, 5ω... Differential Pair s Non-linearity ω = ω RF /4 With no injection, ω = ω 0.

14 Mixer LO+ I TAIL RF Port LO- Mixer ω, 3ω, 5ω... -V SAT I BIAS I -I BIAS V SAT 2I RF V ω RF I TAIL LO Port V 0 cos(ωt) I TAIL = I RF cos(ω RF t + α) + I BIAS V SAT = ( W L) TAIL ( V W L) ODT DIFF The differential-pair is non-linear with odd symmetry. Non-linearity produces odd harmonics at 3ω, 5ω, etc. I TAIL is modulated by ω and its harmonics.

15 Mixer (II) DEFINE SWING RATIO ρ s = V 0 /V SAT >> 1 (Square Wave) I TAIL Mixer Π() t I TAIL Fourier Coefficients of Mixing Function Π(t) LO Port V 0 cos(ωt) ω, 3ω, 5ω ( 1) ( k 1) 2 C kπ k = odd k 0 otherwise

16 Filter Use Ring Oscillator Model n H Hjω ( ) = O 1 j----- ω π + tan -- ω o n n n-stage LPF H(jω) ω -1 ω RF - 5ω ω RF - 3ω Linearize Phase of H(jω) Hjω ( ) Hjω ( ) π + ω = ω ω O 2π n sin n ω ω 0 π ω Ο dφ/dω ω

17 Describing Function Analysis WRITE PHASE EXPRESSION AROUND THE LOOP η i ( C M 1 C M + 1 ) sinα atan C 1 + η i ( C M 1 + C M + 1 ) cosα MIXER I = Hjω π η RF i = I BIAS FILTER INJECTION EFFICIENCY FIND SOLUTION FOR α (-π, π]. If V O is large, then the injection locking dynamics are determined by the phase relationship around the loop (phaselimited) and therefore we can ignore the amplitude expression.

18 Locking Range of Injection-locked Ring Oscillator WHERE LR 4 k atan π n sin n 2 1 k 1 C k 0 η M 1 C M + 1 C = i k 1 η M 1 + C = M + 1 i C 1 C 1 Function of injection efficiency η i, and the magnitude of the Fourier coefficients C M-1 and C M+1. For small values of injected signal the locking range increases linearly with the injected signal strength.

19 Limited Injection Efficiency and Parasitics INJECTOR NON-IDEALITIES TAIL PARASITICS V SHORT-CHANNEL BIAS I V RF DS = K ( V RF + V ODT ) γ γ = 1-2 V BIAS V RF C PAR η i = V RF γ 2V ODT Limited injection efficiency due to short-channel effects and tail device non-linearity. Shunt path for I RF reducing the injection efficiency at high frequencies.

20 Limited Mixer Gain Normalized Coefficients C /C Swing Ratio, ρ s =V o /V sat C /C 3 1 The assumption that the mixer s switching function is a square wave is very accurate if the swing ratio ρ s >> 1. As ρ s gets smaller, the normalized coefficients C k /C 1 are significantly smaller, thus degrading the locking range.

21 Example: 5-stage, Modulo-8 Ring Oscillator Locking Range (%) a b c V RF /V OD (a)ideal (phase-limited) case (b)compression due to Injector non-linearity (square-law device) (c)effects of Injector non-linearity and tail parasitics (50% loss)

22 Outline Introduction Injection Locking Theory Circuit Implementation Measured Results Conclusion

23 5-stage Injection-locked Ring Oscillator Frequency Divider V CTL Vdd BR B1 B2 B3 B4 B5 BO ω _ + OPAMP V BIAS R BIAS REPLICA BIAS V RF INJECTION-LOCKED RING OSCILLATOR OUT BUFFER Used modified cross-coupled symmetric load buffers. RF signal injected at the tail of the first buffer (single-balanced mixer). The buffer stages behave as the H(jω) filter. V CTL V BIAS V RF

24 Die Micrograph: 5-stage Ring Oscillator Divider RING OSCILLATOR V RF BIAS OUTBUF V OUT Fabricated 3 and 5-stage ring oscillators µm CMOS mm 2 of area

25 Outline Introduction Injection Locking Theory Circuit Implementation Measured Results Conclusion

26 Results Injected Frequency Free-running Frequency Phase Input Locking Range Modulo-2 Modulo-4 Modulo-6 Modulo-8 Power dissipation Vdd Icore Ibias Core power Power efficiency 5-stage ILFD 1.0 GHz 125 MHz -110 dbc/hz 12.7 MHz (-3dBm) 32 MHz (-3dBm) 17 MHz (-3dBm) 20 MHz (-3dBm) 1.5 V 233 µa 108 µa 350 µw 2.86 GHz/mW 3-stage ILFD 2.8 GHz 700 MHz -106 dbc/hz 125 MHz (-3dBm) 56 MHz (-5dBm) no-lock no-lock 3.0 V 331 µa 661 µa 993 µw 2.82 GHz/mW

27 Power Efficiency of Injection-locked Ring Oscillator 3 [ 0] div8 Power Efficiency, GHz/mW [ 0] div4 [ 3] div8 1.5 [13] div128 1 [11] div8 [ 9] div2 0.5 [13] div128 [15] div8 [14] div Frequency, GHz [0] 5-stage (div-8) = 2.86 [0] 3-stage (div-4) = 2.82

28 What We Learned LOCKING RANGE COMPARISON 5-stage 1 GHz 3-stage 2.8 GHz THEORY 9% 34% SIMULATION 5% 17% TEST 2% 2% Large tail device (W/L=10.2/1) caused loss of I RF. Need to lower tail node parasitics to increase the injection efficiency. Resonating tail with an inductor [Wu, ISSCC 01] is not practical at sub-ghz frequencies. Small swing ratio (ρ s 3 4) caused reduction in mixer gain. Need to increase output swing and reduce V SAT.

29 Outline Introduction Injection Locking Theory Circuit Implementation Measured Results Conclusion

30 Conclusion Described the injection locking mechanism and how it applies to CMOS ring oscillators. Showed the design of frequency dividers that can operate up to 2.8-GHz by exploiting injection locking in differential CMOS ring oscillators. Showed measured results for 1-GHz and 2.8-GHz injection-locked frequency dividers fabricated in a 0.24-µm CMOS technology.

31 Acknowledgments National Semiconductor