MathCad (PDF too) PLL worksheets & my phase noise prediction article from Applied Microwave and Wireless

These worksheets are something I've been working on for many years. They represent a compilation of useful analysis/design equations from a variety of sources. Some of the work is original, but the majority of it has just been collected and assembled into one big working document. Major pieces came from application notes (National Semiconductor, and specifically Dean Banerjee), as well as a variety of magazine articles. See to get a copy of Dean's PLL book.

The worksheets were used in the article I published "Accurate Phase Noise Prediction in PLL synthesizers", Part I, April 2000 and Part II, May 2000 of Applied Microwave & Wireless (for PDF's, click on the following links - Part I and Part II). This article reviews standard phase noise sources/analysis while adding a strong emphasis to the contribution of resistors and op-amps to total synthesizer phase noise. The second part of the article shows the comparison between predicted and measured phase noise for two different loop filters in a synthesized PLL source, showing the difference in performance that can occur with minor parameter changes. The techniques presented in the article are geared towards the very common "charge pump" based synthesizers, but the techniques could be adapted to a variety of different PLL architectures. At the very least you may find some useful MathCAD bits and pieces.

The worksheets cover the following topics:

Most recent version of the MathCad PLL worksheets

- version 3.8 13-Mar-2002 -


Does anyone actually use the analysis that involves the op-amp case in these worksheets? I've never built a PLL this way and I don't intend to at this point in time. Further, I think most people use the op-amp integrator configuration if they use an op-amp at all. I'll probably remove the analysis in the future if nobody complains -- it's really not worth the hassle. Please contact me if you have an opinion either way....

What else is available to help me solve my PLL problems?

If you find these worksheets confusing or you want something more, there are commercial software packages that may be of interest. You may say "why should I buy one when I can get all this for free"? Well, Let me give you some cases where it will be worth your money (time=$):

The only package I've used is SimPLL from Applied Radio Labs. There are a variety of application notes at the Applied Radio Labs website as well as demo versions of the software.

I have not used all of the features but those that I have used I am quite comfortable with. It is easy to use and I am confident in the results. A transient analysis problem that we had recently at our workplace was overlooked because we used a simplistic transient analysis that is contained within my MathCad worksheets above. Within about one minute of firing up SimPLL, I had duplicated what we were seeing in the lab. In this case the engineer working on it was pretty sharp and had figured out what was going on, but the bottom line is that you should always be aware of how complete your analysis is. This was a case where commercial software such as SimPLL could help, because it solved the basic simulation needs as well as accurately handling the transient response. (Disclaimer: this transient case was somewhat peculiar. The (transient) analysis in the worksheets I've created is taken from work by Dean Banerjee and it's quite good for most cases, but there are a few caveats to using it.)

There are also other free and commercial tools for PLL analysis, but as I said, I've not used many of them extensively.