# Techniques for Measuring Frequency Off-the-Air

The technique I use for measuring the frequency of signals received over HF frequencies is actually a very old idea that's been moved into the modern age. You simply tune in the unknown signal and at the same time inject a known reference signal that's tuned to a small offset (usually less than one or two kHz, and sometimes much less) from the unknown signal.

The result will be a beat note at the receiver's audio output, and the frequency of that note will be the difference between the two signals at the antenna input. This audio frequency can be measured quite precisely and added or subtracted as appropriate from the signal generator frequency to yield the frequency of the unknown signal.

In the old days, the reference signal was usually a harmonic of a crystal calibrator and the spacing between marker points was quite large -- a simple calibrator might generate markers 100kHz apart, while fancier ones could generate 10kHz or even 5kHz signals. Therefore, the distance between the unknown signal and the nearest marker might be several kiloHertz. The techniques available to measure the audio beat note were limited, with resolution better than 1Hz quite hard to come by in real-world conditions.

Today, things are different. Synthesized signal generators can provide a reference signal with a resolution of 1Hz or less, and DSP techniques let us measure audio frequencies with millihertz resolution using nothing more than a PC's sound card. So, I updated the old technique (what I call the "delta reference" method") to use new technology.

Here's a crude diagram of the equipment setup:

The idea behind the delta reference system is to use the radio receiver merely as a window on the spectrum; the actual frequency the radio is tuned to doesn't matter. Rather than measuring an audio beat note, we tune the reference generator to a very small offset -- as little as 5 or 10Hz -- from the unknown signal and use spectrum analysis software to measure the difference (or delta) between the known and unknown signals.

Although drift in the receiver won't affect the difference between the two frequencies, it will show up as a slope in the spectrum display, so it's helpful for the receiver to be as stable as possible during the measurement period. The receiver should be set to upper sideband mode to simplify the measurement algebra, and if possible, the automatic gain control (AGC) should be turned off.

The signal generator's output is coupled into the receiver's antenna jack through a combiner or coupler of some sort; the method used isn't critical so long as both the off-air and reference signals find their way into the receiver. It's helpful if the signal generator has an easily adjustable wide-range attenuator, as you will want to set its level to nearly match that of the unknown signal. Of course, the signal generator should be locked to an accurate frequency reference; the quality of the reference will limit the quality of the results.

The unknown signal is tuned near the center of the receiver's passband (which should be reasonably narrow; something between 1000 and 250Hz works well, depending on the level of interference). The signal generator is tuned to output a signal as close as possible to the unknown signal while still being able to tell which is which on the spectrum analyzer display, and at about the same strength. It's critical to identify which is the unknown and which is the reference signal on the display; whether you need to add or subtract the delta will depend on whether the reference is higher or lower than the unknown signal.

The audio output is fed from the receiver into a computer sound card, and your favorite spectrum analysis software is used to measure the difference between the audio tones representing the unknown and the reference signals. Assuming the receiver is set for upper sideband, and the reference is injected at a frequency above that of the unknown, the unknown signal's frequency is then the signal generator frequency minus the delta between the two audio notes.

There's a tradeoff between the resolution of the spectrum analyzer display and how quickly you can follow the signals. My method is to use a relatively low resolution real-time display, and record the signal for later processing. I'm repeating myself, but the key thing when tuning during real-time is to know whether the reference signal is above or below the unknown -- if you screw that up, you'll be in error by twice the delta!

The images below show WWV's (the US standard time/frequency station) 10MHz signal with the reference signal set 5Hz above it. Using the highly cool Baudline spectrum analysis software for Linux, it's easy to measure the difference between the two signals to less than 0.01 Hz. (Since making these screenshots, Baudline's author has added a tool to automatically measure either individual peaks or the difference between the two strongest peaks with a resolution of up to 1uHz. While it takes a very clean signal with a high signal-to-noise ratio to accomplish that level of accuracy, with a decent signal it's easy to get solid milliHertz resolution.)

The first image shows the spectrogram display as well as a snapshot of the spectrum analyzer display. Note that the WWV carrier is barely noticeable at this instant, though the spectrogram shows it clearly but weakly.

The second image shows the average signal over the full data collection time; this very clearly shows the signal peaks and is the screen I use to make final frequency measurements.

One challenge of the FMT is that the signal is transmitted for only a couple of minutes, so it's not possible to use long averaging times and deep FFTs to wring out the maximum possible resolution. Some compromise was necessary, but as this screenshot of the averaged W1AW 40M signal and reference frequency shows, you can still do pretty darn well (apologies for the extra width; I wanted to show the whole screen without introducing jaggies from scaling the image). The W1AW signal is at about 9.5Hz on the display, while the reference is the peak at about 19.4Hz.