VoltageControlled Oscillator VCO fosc Desirable characteristics fmax Monotonic

Voltage-Controlled Oscillator (VCO) fosc Desirable characteristics: fmax • Monotonic fosc vs. VC characteristic with adequate frequency range • Well-defined Kvco slope = Kvco fmin VC ^ ^ ^ Noise coupling from VC into PLL output is directly proportional to Kvco. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 1

Oscillator Design loop gain Barkhausen’s Criterion: If a negative-feedback loop satisfies: then the circuit will oscillate at frequency 0. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 2

Inverters with Feedback (1) 1 inverter: V 1 V 2 1 inverter V 2 feedback 1 stable equilibrium point V 1 V 2 2 inverters: V 1 feedback V 2 3 equilibrium points: 2 stable, 1 unstable (latch) 2 inverters V 1 EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 3

Inverters with Feedback (2) 3 inverters forming an oscillator: V 1 V 2 1 unstable equilibrium point due to phase shift from 3 capacitors V 1 Let each inverter have transfer function Loop gain: Applying Barkhausen’s criterion: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 4

Ring Oscillator Operation tp VA tp tp VB VC Total phase shift in loop: Total delay in loop: 3 tp VA VB tp tp VC tp VA EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 5

Variable Delay Inverters (1) Inverter with variable load capacitance: Vin Current-starved inverter: Vout VC Vin Vout VC EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 6

Variable Delay Inverters (2) Interpolating inverter: ISS + VC _ R Vout+ R Vout- Vin+ Vin. RG Ifast RG Islow • tp is varied by selecting weighted sum of fast and slow inverter. • Differential inverter operation and differential control voltage • Voltage swing maintained at ISSR independent of VC. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 7

Differential Ring Oscillator + − VA + − VB VA VC + − VD additional inversion (zero-delay) tp VB VC VD − + VA Total phase shift in loop: Total delay in loop: 4 tp tp Use of 4 inverters makes quadrature signals available. VA EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 8

Resonance in Oscillation Loop 1 r r At dc: Since Hr(0) < 1, latch-up does not occur. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina At resonance: Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 9

LC VCO L Vin C Vout Vin Vout 2 L C C realizes negative resistance EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 10

Variable Capacitance varactor = variable reactance Cj A. Reverse-biased p-n junction + VR – VR B. MOSFET accumulation capacitance Cg p-channel – VBG + n diffusion in n-well accumulation region EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine inversion region VBG 11

LC VCO Variations IS 2 L C C 2 L 2 L C IS 2 L C C C ISS EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 12

Effect of CML Loading 1. 1. ideal capacitor load 1 n. H 3. 8 400 f. F 108 f. F 2. Cg = 108 f. F 1 n. H 400 f. F 3. 8 400 f. F 2. CML buffer load EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 13

CML Buffer Input Admittance (1) where: (note p < z) Substantial parallel loss at high frequencies weakens VCO’s tendency to oscillate EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 14

CML Buffer Input Admittance (2) Yin magnitude/phase: Yin real part/imaginary part: magnitude imaginary phase real Contributes 2 k additional parallel resistance EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 15

CML Buffer Input Admittance (3) 3. CML tuned buffer load Cg = 108 f. F 1 n. H imaginary 3. 8 400 f. F 3. 8 n. H real Contributes negative parallel resistance EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 16

CML Buffer Input Admittance (4) ideal capacitor load Cg = 108 f. F 1 n. H 400 f. F 3. 8 n. H CML buffer load Loading VCO with tuned CML buffer allows negative real part at high frequencies more robust oscillation! EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina CML tuned buffer load Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 17

Differential Control of LC VCO Differential VCO control is preferred to reduce VC noise coupling into PLL output. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 18

Oscillator Type Comparison Ring Oscillator LC Oscillator – slower + faster – low Q more jitter generation + high Q less jitter generation + Control voltage can be applied differentially – Control voltage applied single-ended + Easier to design; behavior more predictable – Inductors & varactors make design more difficult and behavior less predictable + Less chip area – More chip area (inductor) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 19

Random Processes (1) Random variable: A quantity X whose value is not exactly known. Probability distribution function PX(x): The probability that a random variable X is less than or equal to a value x. PX(x) 1 Example 1: Random variable 0. 5 x EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 20

Random Processes (2) Probability of X within a range is straightforward: PX(x) 1 0. 5 x 1 x 2 x If we let x 2 -x 1 become very small … EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 21

Random Processes (3) Probability density function p. X(x): Probability that random variable X lies within the range of x and x+dx. PX(x) p. X(x) 1 0. 5 dx EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina x Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine x 22

Random Processes (4) Expectation value E[X]: Expected (mean) value of random variable X over a large number of samples. Mean square value E[X 2]: Mean value of the square of a random variable X 2 over a large number of samples. Variance: Standard deviation: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 23

Gaussian Function 1. Provides a good model for the probability density functions of many random phenomena. 2. Can be easily characterized mathematically. 3. Combinations of Gaussian random variables are themselves Gaussian. 2 x EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 24

Joint Probability (1) Consider 2 random variables: If X and Y are statistically independent (i. e. , uncorrelated): EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 25

Joint Probability (2) Consider sum of 2 random variables: y dy = dz dx EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina x determined by convolution of p. X and p. Y. Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 26

Joint Probability (3) Example: Consider the sum of 2 non-Gaussian random processes: * EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 27

Joint Probability (4) 3 sources combined: * EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 28

Joint Probability (5) 4 sources combined: * EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 29

Joint Probability (6) Noise sources Central Limit Theorem: Superposition of random variables tends toward normality. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 30

Fourier transform of Gaussians: F Recall: F F -1 Variances of sum of random normal processes add. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 31

Autocorrelation function RX(t 1, t 2): Expected value of the product of 2 samples of a random variable at times t 1 & t 2. For a stationary random process, RX depends only on the time difference for any t Note Power spectral density SX( ): SX( ) given in units of [d. Bm/Hz] EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 32

Relationship between spectral density & autocorrelation function: infinite variance (non-physical) Example 1: white noise EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 33

Example 2: band-limited white noise For parallel RC circuit capacitor voltage noise: x EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 34

Random Jitter (Time Domain) Experiment: CLK data source DATA EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina CDR (DUT) RCK analyzer Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 35

Noise Spectral Density (Frequency Domain) Single-sideband spectral density: Power spectral density of oscillation waveform: Sv( ) 1/ 3 region (-30 d. Bc/Hz/decade) 1/ 2 region (-20 d. Bc/Hz/decade) osc (log scale) osc+ Ltotal( ) given in units of [d. Bc/Hz] Ltotal includes both amplitude and phase noise EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 36

Jitter Accumulation (1) Experiment: Observe N cycles of a free-running VCO on an oscilloscope over a long measurement interval using infinite persistence. NT Free-running oscillator output Histogram plots 1 2 3 4 trigger EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 37

Jitter Accumulation (2) proportional to 2 Observation: As increases, rms jitter increases. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 38

Noise Analysis of LC VCO (1) noise from resistor + C L R -R vc _ C L in. R active circuitry Consider frequencies near resonance: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 39

Noise Analysis of LC VCO (2) + vc _ Noise current from resistor: C L in. R spot noise relative to carrier power Leeson’s formula (taken from measurements): d. Bc/Hz Where F and 1/f 3 are empirical parameters. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 40

Oscillator Phase Disturbance ip(t) Current impulse q/ t ip(t) _ Vosc + t Vosc(t) Vosc jumps by q/C • Effect of electrical noise on oscillator phase noise is time-variant. • Current impulse results in step phase change (i. e. , an integration). current-to-phase transfer function is proportional to 1/s EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 41

Impulse Sensitivity Function (1) The phase response for a particular noise source can be determined at each point over the oscillation waveform. Impulse sensitivity function (ISF): change in phase charge in impulse Example 1: sine wave (normalized to signal amplitude) Example 2: square wave t t Note has same period as Vosc. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 42

Impulse Sensitivity Function (2) Recall from network theory: La. Place transform: Impulse response: time-variant impulse response Recall: ISF convolution integral: can be expressed in terms of Fourier coefficients: from q EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 43

Impulse Sensitivity Function (3) Case 1: Disturbance is sinusoidal: , m = 0, 1, 2, … (Any frequency can be expressed in terms of m and . ) negligible EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine significant only for m=k 44

Impulse Sensitivity Function (4) For Current-to-phase frequency response: I osc osc 2 osc EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 45

Impulse Sensitivity Function (5) Case 2: Disturbance is stochastic: MOSFET current noise: A 2/Hz thermal noise 1/f noise thermal noise osc 2 osc EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 46

Impulse Sensitivity Function (6) Total phase noise: due to thermal noise n osc due to 1/f noise 2 osc EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 47

Impulse Sensitivity Function (7) noise corner frequency n (d. Bc/Hz) 1/( 3 region: − 30 d. Bc/Hz/decade 1/( 2 region: − 20 d. Bc/Hz/decade (log scale) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 48

Impulse Sensitivity Function (8) Example 1: sine wave Example 2: square wave t t is higher will generate more 1/( 2 phase noise Example 3: asymmetric square wave t EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina will generate more 1/( 3 phase noise Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 49

Impulse Sensitivity Function (9) Effect of current source in LC VCO: Due to symmetry, ISF of this noise source contains only even-order coefficients − c 0 and c 2 are dominant. + Vosc EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina _ Noise from current source will contribute to phase noise of differential waveform. Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 50

Impulse Sensitivity Function (10) ID varies over oscillation waveform Same period as oscillation Let Then where We can use EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 51

ISF Example: 3 -Stage Ring Oscillator R 1 A R 1 B M 1 A M 1 B MS 1 R 2 A R 2 B M 2 A M 2 B MS 2 R 3 A R 3 B M 3 A + Vout − M 3 B MS 3 fosc = 1. 08 GHz PD = 11 m. W EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 52

ISF of Diff. Pairs for each diff. pair transistor EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 53

ISF of Resistors for each resistor EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 54

ISF of Current Sources for each current source transistor ISF shows double frequency due to source-coupled node connection. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 55

Phase Noise Calculation Using: Cout = 1. 13 p. F Vout = 601 m. V p-p qmax = 679 f. C = − 112 d. Bc/Hz @ f = 10 MHz EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 56

Phase Noise vs. Amplitude Noise (1) How are the single-sideband noise spectrum Ltotal( ) and phase spectral density S ( ) related? v osct EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina v Spectrum of Vosc would include effects of both amplitude noise v(t) and phase noise (t). Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 57

Phase Noise vs. Amplitude Noise (2) Recall that an input current impulse causes an enduring phase perturbation and a momentary change in amplitude: i(t) t Vc(t) Amplitude impulse response exhibits an exponential decay due to the natural amplitude limiting of an oscillator. . . EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 58

Phase Noise vs. Amplitude Noise (3) + Phase noise dominates at low offset frequencies. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 59

Phase Noise vs. Amplitude Noise (4) Sv( ) phase noiseless oscillation waveform phase noise component amplitude noise component Amplitude limiting will decrease amplitude noise but will not affect phase noise. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine amplitude noise osc Phase & amplitude noise can’t be distinguished in a signal. 60

Sideband Noise/Phase Spectral Density noiseless oscillation waveform EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina phase noise component Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 61

Jitter/Phase Noise Relationship (1) NT 1 2 3 4 autocorrelation functions Recall R and S ( ) are a Fourier transform pair: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 62

Jitter/Phase Noise Relationship (2) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 63

Jitter/Phase Noise Relationship (3) 3 2 Jitter from 1/( noise: ^ Let ^ ^ Consistent with jitter accumulation measurements! EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 64

Jitter/Phase Noise Relationship (4) (d. Bc/Hz) -20 d. Bc/Hz per decade • Let fosc = 10 GHz • Assume phase noise dominated by 1/( )2 -100 Setting f = 2 X 106 and S =10 -10: 2 MHz f Accumulated jitter: Let = 100 ps (cycle-to-cycle jitter): = 0. 02 ps rms (0. 2 m. UI rms) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 65

Jitter/Phase Noise Relationship (5) More generally: (d. Bc/Hz) -20 d. Bc/Hz per decade Nm f Let phase noise increase by 10 d. Bc/Hz: rms jitter increases by a factor of 3. 2 EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 66

Jitter Accumulation (1) in loop filter phase detector fb Kpd VCO vco out Kvco Open-loop characteristic: Closed-loop characteristic: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 67

Jitter Accumulation (2) Recall from Type-2 PLL: -40 d. B/decade (d. Bc/Hz) |1 + G| 1/( 3 region: − 30 d. Bc/Hz/decade |G| z p 1/( 2 region: − 20 d. Bc/Hz/decade 1 As a result, the phase noise at low offset frequencies is determined by input noise. . . 80 d. B/decade EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 68

Jitter Accumulation (3) • fosc = 10 GHz • Assume 1 -pole closed-loop PLL characteristic (d. Bc/Hz) -100 -20 d. Bc/Hz per decade f 0 = 2 MHz EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina f Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 69

Jitter Accumulation (4) f 0 = 2 MHz fosc = 10 GHz (log scale) For small : = 0. 02 ps rms cycle-to-cycle jitter For large : = 1. 4 ps rms Total accumulated jitter EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 70

Jitter Accumulation (5) (log scale) proportional to (due to 1/f noise) proportional to (due to thermal noise) The primary function of a PLL is to place a bound on cumulative jitter: (log scale) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 71

Closed-Loop PLL Phase Noise Measurement L( ) for OC-192 SONET transmitter EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 72

Other Sources of Jitter in PLL • Clock divider • Phase detector Ripple on phase detector output can cause high-frequency jitter. This affects primarily the jitter tolerance of CDR. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 73

Jitter/Bit Error Rate (1) Eye diagram from sampling oscilloscope Histogram showing Gaussian distribution near sampling point L R 1 UI Bit error rate (BER) determined by and UI … EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 74

Jitter/Bit Error Rate (2) 0 T R Probability of sample at t > t 0 from lefthand transition: Probability of sample at t < t 0 from righthand transition: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 75

Jitter/Bit Error Rate (3) Total Bit Error Rate (BER) given by: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 76

Jitter/Bit Error Rate (4) Example: T = 100 ps log(0. 5) log BER t 0 (ps) (64 ps eye opening) (38 ps eye opening) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 77

Bathtub Curves (1) The bit error-rate vs. sampling time can be measured directly using a bit error-rate tester (BERT) at various sampling points. Note: The inherent jitter of the analyzer trigger should be considered. EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 78

Bathtub Curves (2) Bathtub curve can easily be numerically extrapolated to very low BERs (corresponding to random jitter), allowing much lower measurement times. Example: 10 -12 BER with T = 100 ps is equivalent to an average of 1 error per 100 s. To verify this over a sample of 100 errors would require almost 3 hours! t 0 (ps) EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 79

Equivalent Peak-to-Peak Total Jitter BER 10 -10 Areas sum to BER 10 -11 10 -12 10 -13 10 -14 , T determine BER determines effective Total jitter given by: EECS 270 C / Spring 200918 -20 March 2009 Universidad Nacional de Córdoba / Clari. Phy Argentina Prof. M. Green / U. C. Irvine. Prof. Michael Green Univ. of California, Irvine 80