Audio Quadrature Shifters
It is often neccesary to shift 2 audio signals so that they are 90 degrees apart in phase, for example, to generate single sideband by phasing method, or to cancel out a sideband given the I and Q outputs of a Tayloe detector. It is difficult to achieve an precise 90 degree shift across a wide frequency range with analog circuits, so usually it’s done by DSP now. Nevertheless, I wanted to build such a circuit, perhaps for later use in a DC reciever.
After so much searching, I was so glad I found a calculator that designs such an all pass filter automatically for you. Very unfortunately, now that I am writing this, I cannot find the website again. I have the executable saved though, which you can download.
You may input the frequency range you wish the filter to operate at, the number of stages the filter has, and what value capacitors you will use. It will return the resistor values needed in the circuit, as well as the phase error and sideband cancellation as a function of frequency. Sweet! See this example with 4 stages, range of 270-3600 Hz, and 10nF capacitors:
So using this calculator I designed a 2 stage shifter with a range of 270-2700 Hz, again with 10nF capacitors. This can be build around one quad opamp. (in the diagram, output from U1 is supposed to be connected directly to R4 and C2. The additional voltage source was just for testing.)
I replicated this design in LTSpice and tested it; it worked perfectly. (You can try simulating it too, I attached my LTSpice file here) Then I soldered the circuit together on a small piece of copper clad board. I used the closest resistor values to those called for (e.g. 33k for 31.2k), or I put two resistors in parallel (e.g. 300k || 220k = 126.9k for 123.1k). The value of feedback resistors are not critical as long as they are equal; I just happened to have 4.42k resistors on hand. I used smd X7R 10nF ceramic caps- these are temperature sensitive and ended up being closer to 9.6nF. The opamp is a TL074 quad opamp.
Time for testing. The circuit was powered by a 9V battery. I connected both inputs together, and connected my signal generator to the input. Then at the 2 outputs I connected my scope probes. Putting the scope on XY mode allows me to visually see a 90 degree phase shift as a perfect circular trace. I then swept the frequency with my function generator. It stays a circle over the specified frequency range, 270-2700Hz. Past that and you can see it becomes elliptical, meaning the phase shift is no longer 90 degrees.
In conclusion, I’m very happy that I now can design and build these quadrature shifters. This was just a proof of concept build, and better results can be achieved with more stages/more accurate components. I look forward to using these in a Tayloe-detector based reciever. Unfortunately I don’t know how to precisely measure the phase shift to the scale of degrees or tenths of a degree since my scope only gives rough estimates of phase measurements. To solve the inaccurate capacitor problem you could order many capacitors then measure and pick out the ones closest to 10nF. Also, I ordered some of these 10nF NP0 caps for this purpose but I haven’t tested them yet.
Hope this helps!