# Accurate Measurement of Radio Frequencies

I have long been fascinated by the various methods of accurately measuring the frequencies of HF radio signals.  I suppose it all started when I was in high school and my first shortwave radio had a dial that was accurate only to the nearest ten or twenty kilocycles per second (now kilohertz, kHz).

To make a very long story short, the method I now use involves these four things :

1. a frequency standard that I can keep close to the UTC frequency scale,
2. a 1 kHz harmonic generator derived from the frequency standard,
3. a radio receiver that I can use as a tunable RF filter,
4. some FFT spectrum analyzer software that will run from my computer's soundcard with audio from the radio receiver as input.

## New (Old) Frequency Standard and Marker Generator

In late 2010 I was forced to replace my old frequency standard (a Sulzer model 5A crystal-controlled laboratory-grade frequency standard) with a Spectracom model 8164 disciplined crystal oscillator.  The 8164 includes a receiver for the LF standard frequency signal from Station WWVB (60 kHz) for making a phase comparison between the WWVB signal and the 8164's internal crystal oscillator and then adjusting the frequency of its internal oscillator.  The crystal oscillator provides good short-term stability while the WWVB signal provides good long-term stability (except for occasional propagation disturbances).  Besides other outputs, the 8164 provides a 1 MHz TTL signal which is fed to my decade frequency divider and harmonic generator.  A block diagram of the frequency divider appears below.

And here is a circuit diagram of the decade frequency divider and harmonic generator that provide the necessary calibrator signal for making on-air frequency measurements.

So with a 1 kHz marker spacing, there will always be some harmonic of the calibrator signal within 500 hertz of the unknown signal.  The trick then is to measure precisely that frequency difference.  An example of a 40 m situation with a "380 Hz beat note" between an unknown signal and the nearest 1 kHz marker is shown below.

## Measuring the Frequency Difference

I use a modern but ordinary radio receiver (usually a Yaesu FT-990) to tune in the unknown signal and the nearest marker or reference signal.  I usually set the receiver to USB mode to make the arithmetic a little easier.  The radio receiver tells me the approximate frequency of the unknown signal to better than one kilohertz of accuracy.  Then the computer with audio spectrum analyzer software is used to measure the difference frequency between the unknown and the nearest marker to less than one hertz of accuracy, depending on which software is used.

In this way, the radio receiver itself has little to do with the precision measurement, acting only as a tunable RF filter to bring in the unknown signal and the nearest harmonic of the calibrator.  The real work is done by the Spectran 8164 frequency standard, the 1 kHz harmonic generator, and the FFT spectrum analyzer software that is used to measure the frequency difference.

In the spectrogram above, produced by SpectrumLab FFT software by Wolfgang Buescher, DL4YHF,, you can see a Morse signal as a complex vertical line in the middle portion of the waterfall display and a two clean spectral lines from the harmonic (marker) generator in the top and bottom portions of the display.  In a waterfall display time usually flows down the display and frequency increases to the right.  For this example the receiver, in USB mode, was tuned to 3581.0 kHz.  According to the spectrum display, the audio Morse signal is on approximately 504.35 hertz, and the marker is on approximately 1002.10 hertz.  (Unfortunately in the illustration above you can not see the cursor which was used to find these frequencies.)  We know the markers are at multiples of exactly 1 kHz so we can subtract 1000 hertz from the measured marker frequency and use the remaining 2.10 hertz to correct the measured tone of the Morse signal.  Doing the arithmetic, we find the Morse signal on (504.35 hertz) - (2.10 hertz) = 502.25 hertz.  Now we add the approximate RF frequency from our receiver (remember, it's only a tunable RF filter) and we have (3581 kHz) + (502.25 hertz) = 3581.50225 kHz or 3581,502.25 hertz.  Remember that this only works if the receiver is in USB mode; if it is in LSB mode you will have to deal with a mirror image of this spectrum and subtract instead of adding, and vice versa.

As a single measurement, this is probably not very accurate.  More accurate results can be obtained by manually averaging a number of readings, both of the unknown signal and of the marker, or by using the automatic logging feature in SpectrumLab for recording a series of frequency measurements which you can process after the fact by hand or in a spread-sheet.  (I set up a QuattroPro spread-sheet to do my statistics for each measurement in a test.)  You can access the automatic logging feature in SpectrumLab by clicking on Text file export -> FFT (spectrum) export.  It is also advisable to measure the frequency of the marker signal both before and after you measure the unknown, and then average the two readings in order to compensate for any drift in your receiver.

## Learning More

SpectrumLab is powerful and sophisticated software and involves a fair learning curve.  I strongly recommend studying the tutorial about SpectrumLab by Jacques Audet, VE2AZX.  Jacques has a lot of useful information about precision frequency-measuring techniques and equipment on his Web site.

Also see the famous "FMT" website by Connie Marshall, K5CM, for information about his frequency measuring tests (FMTs) where participants often have errors of just a few millihertz, and some of the methods they use to do it.  Connie also sponsors and moderates a welcoming and helpful discussion group on Yahoo called FMT-nuts where frequency-measuring enthusiasts discuss their equipment, methods and results, as well as related frequency and time matters.

## Practical Results

In the ARRL Frequency Measuring Tests (FMT) I have almost always achieved average absolute errors of 2 hertz or less, and often less than 1 hertz with an average of several measurements, sometimes achieving accuracies of a few tens of millihertz (mHz).  Indeed, some Amateurs do this routinely, for example, N8UR and VE2IQ  At this level of precision, Doppler shifting of the signal by relative motion in the ionosphere can be a real problem and is often the limiting factor in anyone's practical results.

At right is the equipment I am now using at VE3OAT to make precision frequency measurements.  At the bottom is the Spectracom 8164 WWVB-disciplined crystal frequency standard.  The home-brew decade frequency divider and 1 kHz harmonic generator is mounted just above the 8164.  These two, plus my FT-990 transceiver (not shown), are the heart of my frequency measuring setup.  As for the other equipment in the rack, at top is a simple 6-channel HF receiver for WWV and CHU time signals.  Just below that is a dual-preset counter that I use for precision baud-rate measurements and other timing experiments, and below that is a General Radio 1123-A digital clock that I use as my station clock.  All of the commercial equipment was purchased used at Amateur Radio flea markets and other electronic surplus sales; none of it was very expensive.

## The Old Way (Even Cheaper)

If you don't have a good quality frequency standard or any spectrum analyzer software, you can still make accurate frequency measurements similar to what I did many years ago with very simple equipment.  My "frequency standard" was a simple 10 MHz crystal oscillator with an inch or so of styrofoam insulation all around the crystal to improve temperature stability (or so I hoped) and a chain of TTL 7490 decade dividers to produce the required 1 kHz marker outputs.  I simply connected the marker output to my receiver antenna input through a potentiometer to allow adjustment of the marker signal amplitude and then listened to the beat note between the nearest marker and the carrier of the unknown signal.  (The beat note is clearest when the marker and unknown signal amplitudes are nearly the same.)  Note that to do this successfully the receiver must be in AM mode with a suitably narrow IF bandwidth.  At the time this was easy using my Drake R-4C receiver.  Then I tuned a cheap audio oscillator to the same beat note and measured the frequency of the audio oscillator with an inexpensive frequency counter which told me the difference between the unknown and the nearest 1 kHz marker.  The receiver's dial and a little arithmetic would then tell me the frequency of the unknown carrier signal to an accuracy of a few tens of hertz if I was both careful and lucky.  The only problem with this setup was that I had to re-zero the frequency standard to Station WWV at least every hour and hope that propagation conditions weren't causing a lot of Doppler frequency shift in the WWV signal that I was receiving.  With a cheap set up one can't expect perfection; however, I used this method successfully when I first entered ARRL's Frequency Measuring Test (FMT) in 1981 and achieved an average error of only 2 hertz.  I was very pleased of course but I'm sure that Lady Luck had a lot to do with it.

Tuning the audio oscillator to the same pitch as the beat note was often tricky so I simply fed the audio oscillator signal to the X-amplifier of an old audio-grade X-Y oscilloscope and the receiver's audio output (containing, in this case, the audio beat note between the unknown signal and the marker) to the Y-amplifier.  The result is what is referred to in classical electronics literature as a Lissajous figure, a geometric representation of the frequency ratio between two sine waves.  In our case, we want a ratio of 1:1 which will appear as something between a circle at one extreme and a diagonal, straight line at the other extreme.  The beauty of this method is that you can use "visual integration" to average out the effects of noise, interference, signal fading, and propagation-induced phase changes.  A somewhat noisy Lissajous figure showing the audio oscillator at the same pitch as the beat note appears at left.

If you have an older computer with an ISA sound card (instead of the newer PCI types) and you still want to use spectrum analyser software, I recommend AF9Y's "FFTDSP" program which is powerful yet very easy to use and which requires minimal setup to make frequency measurements and frequency difference measurements.  I used it happily for a number of years while working as a volunteer monitor for the IARU Intruder Watch monitoring service.

I hope that some of these ideas will be useful to you.  Please contact me to discuss any of the ideas here or possibly other ideas you might have or have seen somewhere else.

## Bibiography of Magazine Articles

Over the years I have compiled a bibliography of magazine articles about easily-built Amateur frequency standards and calibrators and applicable measurement techniques.  If you are interested and have trouble finding any of these articles, I can provide single copies of most of them for your personal, non-commercial use.