Frequency measurement

   
In truth... The frequency counter more often displayed 7039999.25 Hz or 7040000.5 Hz or etc., but from time to time the Si5351’s output measured dead-on the programmed frequency to the nearest whole cycle at 7040 KHz, as shown in the photo. Moreover, after being powered-on for a short while the clock generator
stayed within a few Hz of the programmed frequency from 3.5 to 30 MHz (80 to 10 meters). The following paragraphs describe the rationale and implementation of a simple and logical Si5351 frequency correction method.

   Popular chip: The Si5351 is ubiquitous. Several ham radio kits and other projects that I have written about have featured this clock generator or the Si5351A (e.g., Hilltopper, QCX, Quadrature VFO, μBITx). The chip is also found in a few familiar manufactured products (e.g., Elecraft KX2, NanoVNA). On reading or skimming articles and web pages about Si5351-based signal generators or VFO’s or other projects, I have been surprised at the number of different ways that frequency control is implemented. In part the diversity of approaches can be understood in relation to the context and period of the project described, or whether an Si5351 library was utilized, or the type of microcontroller that interfaces with the clock generator, etc. It is also curious that Si5351-based projects implement frequency correction in a variety of different ways. 

25 MHz crystal    An article in December 2020 QST magazine1 (the current issue as I write) put in mind to revisit Si5351 frequency programming and correction. The article describes a milliwatts power CW transmitter based on the Si5351. Minimum tuning step is 100 Hz, a workable value for a CW QRP rig. And to correct the generated clock frequency a constant is added-to or subtracted-from the selected (dialed) output frequency before computing Si5351 programming parameters.


    Although adding a correction to the output frequency is common in Si5351 radio projects, the method seems a little off conceptually. It is natural to ask, “What part of frequency determination needs correction?” Output clock frequency is programmed in the Si5351 using parameters that ultimately depend on an external crystal frequency. Every Si5351 generated frequency depends on this reference frequency in more-or-less the same way. VCO frequency is a multiple of the crystal oscillator frequency and this dependency carries through the process of dividing VCO frequency to obtain a desired output.

    At the risk of ‘beating a dead horse’ the crystal that provides a reference frequency for the Si5351 has a marked value (photo left), and under suitable conditions an acceptably stable true value. The discrepancy between marked and true frequency of the crystal oscillator accounts for the error in output frequency. This observation applies to both of the Si5351’s synthesizers, and across the spectrum of frequencies to be generated. An obvious corollary is that if the crystal’s true frequency were specified in place of the marked frequency everywhere that the reference frequency appears in a calculation (generally just one place per clock), then derived frequencies (clock output frequencies) would be correct to within the stability of the circuit. The ‘Correcting Frequency’ section below elaborates this idea, but first...

   Programming frequency: An Internet search yields many helpful examples of programming the Si5351, either with or without the help of Arduino libraries (si5351.h or Adafruit_SI5351.h).
One particularly readable explanation is this page, which presents an easy to follow computational recipe or algorithm for generating clock output frequencies. There is a ‘shortcut’, where the largest allowable denominator (220 - 1) is used in solving for a fraction to represent a decimal computed value. (Si5351 decimal valued parameters must be specified in the form whole number + numerator / denominator.) I have experimented a little with another way of generating good fractions, and also with Silicon Laboratories ClockBuilder Desktop utility. However, one obvious virtue of a fixed denominator is simplicity. No messing around, just solve for the numerator. Using the same denominator in multiple computations is also fast, which could be important, as many Si5351 applications are based on an Arduino Uno or Nano, or other similarly slow MPU platforms—not well suited to computation.

Frequency Error (80 - 10 meters)

   Correcting frequency: Graphs are nice, but in this case not necessary. A single data point suffices to compute the actual ‘crystal oscillator frequency and hence the required correction. For this computation it is not necessary to know how Si5351 parameters were computed or specified, i.e., how the clock output frequency was derived. To illustrate, select a point on the graph that is close to the crystal’s 25 MHz marked frequency. When the Si5351 was programmed to produce an output frequency of 21060 KHz, the measured frequency before correction was 21,059,682.5 Hz or 317.5 Hz below the programmed frequency (4th point from left on graph). Now, 21060000 Hz is 25 MHz multiplied by 0.8424 regardless of the particular Si5351 parameters used to produce this output. Therefore, we can immediately compute the putative reference frequency (i.e., the true frequency of the crystal oscillator) by dividing the measured frequency by 0.8424. This calculation yields 24,999,623 Hz, or 377 Hz below 25 MHz.  Substituting this value for the marked frequency in whatever algorithm is used to setup the PLL and perform the division (or divisions) should cause the clock output frequency to be very nearly exact across the application’s programming range.

    It is a matter of style as to how to implement this simple correction in code. Generally, constant declarations are listed near the top of  a program (or Arduino sketch), and in uppercase. This is convenient when, for example, the value of the constant needs to be revised for a different circuit than the one originally studied.

    How precise is the Si5351 after correction? I have not examined this question over the long term, but for one day of repeated observations, the corrected clock frequency remained within 1 part per million from true (as measured by the GPS-referenced frequency counter) across the range 3.5 to 30 MHz. Again on the following day, measurements remained within the previously observed delta after warmup.


Less than 1 ppm
Less than 1-PPM error at 28 MHz





   


1. The Tuna Tin “S” — A Bare-Bones Synthesized QRPp Transmitter, by Bob Fontana, AK3Y.  QST December 2020, Vol 104, Number 12, pp 30-35.



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