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Design Article

# Charge-Pump Phase-Locked Loop—A Tutorial—Part II

## 7/21/2011 1:14 PM EDT

CPLL Tutorial Cont'd.

Example:

Given a charge-pump PLL with α = 4 and loop bandwidth of 1 kHz, the transient response for a step in frequency of 1 kHz is shown in Fig. 5-2. The solid line is exact and corresponds to (5.11), the dashed line is approximate and corresponds to (5.12).

Fig. 5-2  Frequency Step: Δw = 2pi103

The effect of loop bandwidth on acquisition time is demonstrated in the following example.

Example:

Given a charge-pump PLL with a α = 4 and loop bandwidths of 2 kHz and 1 kHz, the transient response for a step in frequency of 1 kHz is shown in Fig. 5-3. Notice that the smaller bandwidth requires longer acquisition time.

Fig 5-3 Frequency step: ƒBW=2 kHz, 1 kHz.

5.2. Noise Bandwidth

The input to the PLL will contain some phase noise. The noise is a random signal and is assumed white, with a power spectral density given by 4, 7

The output noise power spectral density of a random process passed through a linear filter is given by8

Given that the PLL closed-loop response is h(s), then the mean square output noise power is

The noise bandwidth Bn is defined7 such that

Substituting (4.28) into (5.15) and solving for Bn(w) yields

From which the noise bandwidth is

Equation (5.18) indicates the output noise can be minimized by decreasing the loop bandwidth.

6. Reference Suppression

6.1. Jitter Due to Leakage

When the loop is locked, both U and D outputs from the PD would ideally be low, causing no charge-pump current to flow. However, in non- ideal circuits, there will be some leakage current Ik, due mostly to the shunt loading of the VCO3. The leakage current must be nulled out by the loop, since the average current into the filter during steady-state must be zero. The loop therefore, adjusts the phase of the VCO to produce small pulses on either the U or D outputs, depending on the polarity of the leakage. The width of the pulses is such that the average pump current iavg equals the leakage current Ik.

Negative leakage flows into the pump and out of the loop-filter. This decreases the VCO control voltage vC which decreases the frequency. In order to compensate for this negative leakage, the loop must provide pulses on the U input (Fig. 6-1).

Positive leakage flows out of the pump and into the loop-filter. This increases the voltage on vC which increases the VCO frequency. In order to compensate for this positive leakage, the loop provides pulses on the D input (Fig. 6-2).

The average pump current will equal the leakage current.

Therefore, the pulse width of the pump current due to leakage is

For the 2nd-order loop, the pulses required to cancel leakage cause the pump current to drive the loop-filter impedance

Note that the reference frequency is typically many orders of magnitude larger than the loop- bandwidth k.

The reference frequency is typical orders of magnitude larger than the loop bandwidth k so the impedance of the capacitor is negligible. Thus, the reference pulses manifest as instantaneous voltage jumps

The frequency of the VCO follows the voltage steps Δv. The frequency excursion for each pulse is

Where the following constants have been used

The phase excursion (radians) during each cycle is called ripple or jitter denoted by Øj (radians).

Substituting (3.17) into (6.8) yields

6.2. Reference suppression Filter

Many applications may be able to tolerate the reference jitter given by (6.8). However, certain applications (e.g., frequency synthesis) may require a reduction in reference jitter to maintain spectral purity of the clock signal 4. This can be done by adding a reference suppression filter, which is simply a capacitor C2 in parallel with the 1st –order loop-filter as shown in Fig. 6-3 4,7

The addition of C2 adds an additional pole at w2 making the PLL a 3rd-order system. The open and closed-loop gains (straight line approx.) for the 3rd-order PLL are shown in Fig. 6-4 and Fig. 6-5 respectively.

It should be observed that if w2 >>k, then C2 will not appreciably affect the loop transfer function for frequencies near or below the loop bandwidth. This implies that the loop can, for practical purposes, be treated like a 2nd-order loop as described by (4.23) with a rate of closure of -20dB per decade as desired.3,7

As a rule of thumb, to ensure stability with moderate peaking, the following constraints are recommended7.

Jeffrey Pattavina has worked for 30 years in the data and voice communications industry, specializing in: broadband access, high-reliability IP streaming, and TDM carrier-class communication systems. Mr. Pattavina holds a Master of Science degree in electrical engineering from Northeastern University. He has authored four patents and seven technical publications in electronics, reliability, and communication systems.

7. References

1     Bell Labs, Transmission Systems for Communications, 5th, Ed. Bell Telephone Laboratories, Inc., 1982.

2     Calleja, H,, "An Approach to Composite Amplifier Analysis," International Journal of Electrical Engineering Education, vol. 39, pp. 138-147, 2002.

3     Gardner, F., "Charge Pump Phase Locked Loops," IEEE Transactions on Communications, vol. 28, pp. 1849-1858, 1980.

4     Gardner, F., Phaselock Techniques, 2nd ed. New York: John Wiley and Sons, 1979.

5     Jeong, D., et al., "Design of PLL Based Clock Generation Circuits", IEEE Journal of Solid State Circuits, Vol. 2, pp. 255-261, 1987.

6     Jovanovic G. and Stojcev M., "A Method for Improvement Stability of a CMOS Voltage Controlled Ring Oscillator," International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST), vol. 2, Ohrid, 2007.

7     Wolaver, D., Phase Locked Loop Circuit Design, Englewood Cliffs, NJ: Prentice Hall, 1991.

8     Papoulis A., Probability, Random Variables, and Stochastic Processes. New York: McGraw Hill, 1965.

9     Butkov E., Mathematical Physics, Reading: Addison-Wesley, 1968.

10    Millma J. and Halkias C., Integrated Electronics: Analaog and Digital Circuits and Systems, New York” McGraw-Hill, 1972.

ARNAV

7/23/2011 5:27 AM EDT

ptvn

8/15/2011 4:31 PM EDT

The article has some transcribing errors that the editor still needs to fix. I can send you a copy of the original article if you like.

Jeff Pattavina

SYakov

3/14/2012 8:46 PM EDT

Hi Jeff,
Could you please send me a copy of the original article.
Sergei.

WKetel

7/30/2011 8:07 PM EDT

Unfortunately it is difficult to save a copy of this to my HDD.

goranisaev

8/4/2011 6:26 AM EDT

Here is a simple way to save a copy of this article:
1. Mark the text of page 1 of the article and copy it.
2.Paste it in an empty .doc file.
3.Mark, copy and paste page 2 and 3.
4. Save the full document to HDD.

ptvn

8/15/2011 4:32 PM EDT

The article has some transcribing errors that the editor still needs to fix. I can send you a copy of the original article if you like.

Jeff Pattavina

dyos_60

4/4/2012 4:24 AM EDT

Hi Jeff

May I have a copy too?

Tx
Pramod