Vector measurements with the rtl-sdr

21.06.2020 11:41

Previously I was writing about some experiments with reflection measurements using an rtl-sdr receiver. I used the rtl-sdr as a simple power meter together with an RF bridge to measure VSWR. This was a scalar measurement. All the phase information from the signal was lost and with it also the angle information about the complex impedance of the load I was measuring. Since I was happy with how the method performed in that experiment I was wondering if I could adapt the setup to measure the phase information as well.

With a vector measurement I need a reference signal to compare the phase of the measured signal to. This is a problem, since the rtl-sdr only has one input and can only sample a single signal at a time. My idea was that perhaps I could multiplex the reference and the measured signal onto the single input. Both time and frequency multiplex seemed doable, but time multiplex seemed by far simpler to implement in hardware. Integrated microwave switches with usable characteristics, such as Renesas F2976, are reasonably cheap these days.

Previously I recorded a 2 second array of digital samples of the measured signal for each scalar measurement point. With the time multiplex setup, I could record similar 2 seconds of input, but that input would now contain both the reference and the measured signal. I could then de-multiplex and process it in software. The new setup would look something like the following. The device under test could again be a bridge, or something else:

Block diagram of the vector measurement setup.

The time multiplex board contains two SPDT switches. In one position, the switches direct the reference signal to the rtl-sdr. In the other position the signal passes through the device under test and then back to the rtl-sdr. The switch frequency I'm thinking about is somewhere around 100 Hz. A complex baseband signal recorded by the rtl-sdr would then look something like this:

Plot of the simulated complex baseband signal.

Most of the complexity in this setup would be in software. The software would need to find out which parts of the recording is the reference and which part is the measured signal. This is similar to clock recovery in a receiver. It would then compare the two signals and do some filtering. This is a rough block diagram of the processing pipeline:

Block diagram of the signal processing setup.

The reality is a bit more complicated though. Especially clock recovery seems tricky. My original intention was to use auto-correlation of the signal but it turned out much too slow. Right now I'm just using simple amplitude thresholding, which works as long as DUT is attenuating the signal enough compared to the reference. There's also some additional processing required to account for the fact that my delay is an integer number of samples, which introduces an additional random phase shift that needs to be accounted for.

So far I've only performed some proof-of-concept simulations of this setup using the performance of the rtl-sdr I've seen in my scalar measurements and the properties of the switches from the datasheet. It does seem feasible. Here are simulated vector measurements of three points on the complex plane. For example, these might be complex reflection coefficient measurements on the Smith chart. The gray dots show the true value and the blue dots show the simulated measurements:

Simulated vector measurements of three points on the complex plane.

There is some angle and amplitude error, but otherwise the principle seems to work fine. These are the histograms of the errors over a large number of simulated measurements of random points on the complex plane, where the measured signal was well above the receiver noise floor:

Histogram of the amplitude measurement errors.

Histogram of the angle measurement errors.

I'm not sure yet what part contributes the most to these errors. I'm simulating several hardware imperfections, such as switch cross-talk, frequency and phase inaccuracies and receiver noise. The most complicated part here is the clock recovery and I suspect that has the largest effect on the accuracy of the output. The problems with clock recovery actually made me think that having a four-state "off-dut-off-ref" cycle instead of a two-state "dut-ref" for the switches would be better since that would gave a much stronger pattern to match against. Another idea would be to lock the multiplex clock to the actual signal. ERASynth Micro does provide a 10 MHz reference clock out, but dividing it down to 100 Hz would need a huge divider.

Anyway, the simulations so far seem encouraging and I probably can't get much further on paper. I'm sure other factors I haven't thought of will become evident in practice. I plan to make the time multiplexing board in the future and try to do some actual experiments with such a setup.

Posted by Tomaž | Categories: Analog

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