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1 Charge Pump PLL

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2 Outline Charge Pump PLL –Loop Component Modeling –Loop Filter and Transfer Function Loop Filter Design Loop Calibration

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3 Charge Pump PLL The charge pump PLL is one of the most popular PLL structures since 1980s Featured with a digital phase detector and a charge pump Advantages –Fast lock and tracking –No false lock Phase Detector Charge Pump Loop Filter VCO N-Divider fifi fofo fofo

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4 Phase Detector Gives the phase difference between the input clock signal and VCO output signal Different types –Nonlinear (such as Bang-Bang) –Linear (such as Hogges Phase Detector) Linear PD output a digital signal whose duty ratio is proportional to the phase difference –In Hogges PD, if the phase difference is θ e, the output digital signal duty ratio is C. Hogge, A Self-correcting clock recovery circuit, Dec, 1985

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5 Typical Phase Detector and Waveform Y. Tang, et., al., "Phase detector for PLL-based high-speed data recovery," Nov. 2002 Circuit Structure Output Waveform When locked

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6 Charge Pump Convert a digital signal into current UP DN I up I dn

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7 Loop Filter Low pass filter –1 st order –2 nd order (higher roll-off speed at high frequency) –3 rd order & higher IpIp VCVC C1 R IpIp VCVC R C2

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8 VCO Tuning gain K VCO is the most important parameter Usually coarse tuning and fine tuning

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9 CP PLL loop modeling Phase Detector Charge Pump Loop Filter VCO fifi fofo fofo θiθi θoθo

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10 2 nd Loop Transfer Function Using a 1 st order LPF: Active PI type Open-loop transfer function Closed-loop transfer function

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11 3 rd Loop Transfer Function Using a 2 nd order LPF Let m=C2/C1 Open-loop transfer function Closed-loop transfer function

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12 Comparison When m becomes 0, the 3 rd order loop degenerates into 2 nd order loop 3 rd order loop gives an extra high frequency pole, which increases the high frequency roll-off in jitter transfer 3 rd order loop is widely used and can be treated as 2 nd order loop for simplification Unfortunately, the 3 rd order loop shows different jitter transfer from the 2 nd order loop We focus on 3 rd order loop

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13 Simplification of 3 rd Order Loop Define natural frequency ω n & damping ratio ξ Then totally 3 loop parameters: ω n, ξ &m Simplified transfer function

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14 LPF Design Consideration 3-dB frequency – easy to control Roll-off speed– easy to meet with 2 nd and 3 rd order transfer function Jitter transfer (jitter peaking)

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15 Jitter peaking of 2 nd order loop Jitter peaking can be reduced or eliminated by increasing the damping ratio –Eliminated when damping ratio ξ >1 Large damping ratio leads to slow closed- loop response Usually suggested ξ=5 to meet the jitter peaking spec

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16 Jitter peaking of 3 rd order loop Usually believed to be similar as the 2 nd order loop Actually quite different from the 2 nd order loop case Jitter peaking always exists even with very large ξ Need to be treated carefully

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17 Jitter peaking is dependent on ξ and m m=0 (2nd loop) jitter peaking can be reduced or eliminated by using large ξ m>0 (3rd loop) ξ is quite small, increasing ξ will decrease the jitter peaking; ξ is larger than a threshold value ξ m, increasing ξ will increase the jitter peaking Jitter peaking versus damping ratio and capacitance ratio

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18 How to achieve the minimum jitter peaking For given m, there exists the minimum jitter peaking --the minimum jitter peaking can be viewed as a function of m: JP(m) The minimum jitter peaking under a given m is achieved only by using a proper ξ --ξ should be a function of m: ξ m (m) JP(m) ξm(m)

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19 Sampling effect of phase detector The phase detector has sampling effect, especially when its rate is not much higher than the loop cut-off frequency Approximate TF of phase detector :

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20 Jitter Peaking w/ PD Sampling Effect It causes the jitter peaking worse when ξ is very small, jitter peaking decreases when ξ increases; when ξ becomes larger than ξ m, jitter peaking increases with ξ; when ξ is larger than ξ m2, jitter peaking decreases when ξ is increased further

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21 JP(m) and ξ m (m) with sampling effect JP(m) with sampling effectξ m (m) with sampling effect

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22 Tables of JP(m) and ξ m (m) for practical design

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23 Design procedures of charge pump PLLs for jitter transfer characteristic optimization 1.Decide the maximum tolerated jitter peaking and find capacitance ratio m using JP(m). 2.Use ξ m (m) to find the optimal damping ratio value ξm; 3.Decide ω n according to the application, choose reasonable K VCO, and calculate I p, R, C 1 and C 2 ; 4.Use time domain simulation to verify that the expected jitter transfer performance can be achieved

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24 Design example Target: to design a 2.5GHz CP PLL, meet the jitter specification Design parameters: m=0.005 and ξ=5.0 Simulation result: jitter peaking is only 0.078dB Jitter transfer characteristic of the designed PLL

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25 More Discussion on Loop Transfer Function The above discussion suggests to use very small m to meet the jitter peaking However, if m is too small, the effect of the second capacitor can even be ignored Compromise should be made between jitter peaking and other performance

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26 Charge pump PLL calibration Purpose: make the loop transfer characteristic meet the spec Calibration types: –Component calibration –Loop calibration

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27 Charge Pump Calibration Purpose: minimize the mismatching between UP and DOWN current Method: switch small current sources UP DN I up I dn UP DN I up I dn … I CAL

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28 Charge Pump Calibration Procedure Use the UP or Down current to charge/discharge a capacitor Compare the time difference and calculate the calibration code UP DN I up I dn Vref Comparator Counter Ref CLK R/S

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29 VCO Coarse Tuning Purpose: to speed frequency tracking Method: make use of the coarse tuning functionality of the VCO When extreme high frequency range is desired, double VCOs can be used to help achieve fine frequency tuning resolution

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30 VCO Coarse Tuning Procedure Apply different coarse tuning voltage (output from a low resolution coarse tuning DAC) Measure VCO output frequency respectively –Compare to the reference frequency Write the desired DAC code into register

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31 Time Constant Calibration Purpose: calibrate the loop transfer function time constant so that the 3-dB frequency meets the spec Method: switch small CAL capacitors … C CAL

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32 Time Constant Calibration Procedure Vref Comparator Counter Ref CLK R Vref R C Vx

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33 Loop Gain Calibration Purpose: calibrate the loop transfer gain to the desired value Method: switch different charge pump output current (K VCO is not changeable usually)

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