1. Charge Pump PLL

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

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 fi fo

4. C. Hogge, “A Self-correcting clock recovery circuit”, Dec, 1985
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 Hogge’s Phase Detector)
Linear PD output a digital signal whose duty ratio is proportional to the phase difference
In Hogge’s PD, if the phase difference is θe , the output digital signal duty ratio is
C. Hogge, “A Self-correcting clock recovery circuit”, Dec, 1985

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

6. Charge Pump
Convert a digital signal into current UP
Iup
Idn DN

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

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

9. CP PLL loop modeling fi fo Phase Detector Charge Pump Loop Filter VCO

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

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

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

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

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

15. Jitter peaking of 2nd 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

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

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 ξm, increasing ξ will increase the jitter peaking
Jitter peaking versus damping ratio and capacitance ratio

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: ξm(m)
JP(m)
ξm(m)

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 :

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 ξm, jitter peaking increases with ξ;
when ξ is larger than ξm2, jitter peaking decreases when ξ is increased further

21. JP(m) and ξm(m) with sampling effect
JP(m) with sampling effect
ξm(m) with sampling effect

22. Tables of JP(m) and ξm(m) for practical design

23. Design procedures of charge pump PLLs for jitter transfer characteristic optimization
Decide the maximum tolerated jitter peaking and find capacitance ratio m using JP(m).
Use ξm(m) to find the optimal damping ratio value ξm;
Decide ωn according to the application, choose reasonable KVCO, and calculate Ip, R, C1 and C2;
Use time domain simulation to verify that the expected jitter transfer performance can be achieved

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

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

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

27. Charge Pump Calibration
Purpose: minimize the mismatching between UP and DOWN current
Method: switch small current sources UP UP
Iup
Iup
ICAL
ICAL …
ICAL
ICAL
Idn
Idn DN DN

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
Ref CLK UP
Vref
Counter
Iup
R/S
Comparator
Idn DN

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

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

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
CCAL
CCAL …
CCAL
CCAL

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

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