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 Wireless.national.com 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:
- Loop filter design, based on a National application note.
- Loop simulation (open and closed loop gain, phase).
- Phase noise simulation
- Due to reference oscillator, phase detector, VCO noise sources
- Due to resistors and op-amps in the loop
- Combined effect of phase noise from two synthesizers (uses file I/O)
- Estimation of SNR for QAM (assumes 2nd order carrier recovery loop which you specify the bandwidth of). Total integrated noise is computed as well as RMS phase error.
- Estimation of SNR for FM/FSK systems based on residual FM deviation.
- Estimation of adjacent channel rejection due to phase noise.
- Estimation of the effects of an ideal frequency multiplier/divider after the PLL.
- Provides "guesses" for optimum loop bandwidth for minimizing integrated noise.
- Lock time /transient simulation (note, assumes no saturation occurs, also... the op-amp case may invalidate the transient analysis and other tidbits, it was mainly included as a method to quantify the phase noise degradations when noisy op-amps are thrown in the loop).
- "dual point" modulation analysis (for modulating reference and VCO for flat frequency response)
Most recent version of the RFdude.com MathCad PLL worksheets
- version 3.8 13-Mar-2002 -
- "amplifier" configuration error fixed based on user feedback, units bug that may only affect mathcad2001i file writes
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=$):
- Transient Analysis (true simulation of charge-pump saturation and similar effects)
- Lock Detect Simulation
- Simulation with topologies other than the simple charge-pump based PLL with a passive loop filter (without some work by the user that's all that my analysis will do well).
- If you're new to PLL's or just don't do PLL's that often, the software guides you through specifying the components. With things like the MathCad analysis I have above, you have to pay attention to which parameters you need to change in the document to get your analysis right. It's not that tough, but for some it might be a bother.
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.