1. Phase Locked Loops Continued
VCO
Ref LO
fLO=fref*N/M
1/M
PFD
Loop Filter
Phase-Locked Loop
1/N
Basic blocks
Phase frequency detector (PFD)
Loop filter (including charge pump)
Voltage controlled oscillator
Frequency divider

2. Phase Locked Loops Continued
Key specs
hold range: the frequency range over which phase tracking can be statically maintained
pull-in range: the frequency range over which PLL can become locked
pull-out range: dynamic limit of frequency range for stable operation
lock range: frequency range within which a PLL locks within one single-beat note between reference frequency and output frequency

3. Illustration of Static Ranges
Very slowly vary input frequency

4. Phase Frequency Detector
Generates phase difference between the input signal and VCO output signal
Distinguish if VCO is faster or slower
Different types
Analog vs digital
Linear vs nonlinear

5. Analog phase detector: multiplier
Linear multiplier
Functions the same way as a mixer
But converting to DC (same frequencies)
Same mixer circuits can be used

6. Simple BJT 2-Quadrant Multiplier

7. Gilbert cell

8. Waveforms

9. CMOS versions

10. 2V, High-Frequency CMOS Multiplier
K-K Kan, D. Ma, K-C Mak and H.C. Luong, “Design Theory and Performance of a 1-GHz CMOS Downconversion and Upconversion Mixers,” Analog Integrated Circuit and Signal Processing, Vol. 24, No. 2, pp , July 2000.
Based on the Gilbert cell
Can operate at a lower supply voltage because the mixer does not use stacking
• Source followers give better linearity
• Has a smaller mixer gain because sharing the bias currents with the followers
reduces gm

11. A Quarter-Square CMOS Multiplier
J.S. Pen˜a-Finol and J.A. Connelly, “A MOS Four-Quadrant Analog Multiplier Using the Quarter-Square Technique,” J. of Solid-State Circuits, vol. SC-22, No. 6, pp , Dec

12. CMOS Four-Quadrant Multiplier
Babanezhad and Temes - JSSC, Dec

13. Digital phase-frequency detector
Compares edges of reference and divided clocks.
If reference clock leads the divided clock, the UP signal is asserted.
If the divided clock leads the reference clock , the DWN signal is asserted.
In an ideal PFD no pulses are present at the output in the locked state.
Duty cycle of inputs is not relevant to the circuit operation.
The width of the UP/DWN pulses is proportional to the phase difference between the clock inputs.

14. Digital Xor phase detector

15. Digital phase-frequency detector
Conceptual diagram

16. Conventional Digital PFD

17. Delay in the Conventional PFD

18. Output of PFD for locked state
In locked state, narrow pulses are generated in both UP/DWN outputs.
The width of these pulses determines the amount of noise introduced to the VCO output by the charge-pump.
Timing mismatch between the UP/DWN pulses is a source of spurious tones.

19. The Charge-Pump converts the phase error information provided by the PFD into a voltage that controls the VCO frequency.
If UP is high, top switch is closed and charge is injected into capacitor, increasing voltage Vout
If DWN is high, bottom switch is closed and charge is extracted from capacitor,decreasing voltage Vout

20. State diagram
Up=0;
Dn=0;
Up=0;
Dn=1;
Up=1;
Dn=0;

21. Non-idealities
In practical PFD the delay of the gates creates non-idealities in the phase input/output characteristic.
The PFD can no longer resolve very small phase errors, and a dead zone is created.
To solve this problem, extra delay is introduced in the feedback path of reset signal.

22. Dead zone problem

23. Non-ideal effects of charge pumps
Current mismatch
Mismatch between source and sink currents in the charge pump introduces a finite phase error.
Current leakage
When the source/sink currents are off, leakage currents can flow and modify the VCO control voltage of the VCO by charging/discharging the loop filter. Spurs are introduced.
Charge sharing
Parasitic capacitances from the switches share charge with the loop filter when the nodes they are connected to have a large change in their voltage.
Charge injection
Occurs when switches are turned off and the charge in their channels is injected/extracted to the loop filter. Spurs are introduced

24. Precharge PFD
S. Kim, et. al., “A 960-Mb/s/pin Interface for Skew-Tolerant Bus Using Low Jitter PLL, IEEE J. of Solid-State Circuits, Vol. 32, No. 5, may 1997, pp

25. Modified Precharge PFD
H. O. Johansson, “A Simple Precharged CMOS Phase Fequency Detector,” IEEE J. of Solid-State Circuits, Vol. 33, No. 2, Feb. 1998, pp