I hope you don't mind if I continue to post my designs and questions in this thread, since you appear to have abandoned this project.
I've not stopped work on it.
I tested a few piezoelectric transducers designed for audio/alarm applications and noticed how they have various sharp peaks and troughs between 20kHz and 150kHz. I used two units for each test, one as a transmitter and the other as a receiver. I haven't recorded any detailed measurements, simply because I don't have a microphone with any response data over said frequency range. The intention is to use a transducer to test various electret and MEMS microphones to find a suitable candidate.
I've also had a failed attempt a designing a Wein bridge oscillator with AM, for the heterodyne circuit. The oscillator works, but the modulation index sharply declines, as the input frequency increases.
Here's the schematic.
I built it on a solderless breadboard. For simplicity I used the TL071, because it's single channel, so there's no unused op-amp to worry about.
R4 is a small incandescent lamp,
(RS stock code 587-686) I found in a box of old bulbs. I chose this over the J-FET AGC for simplicity's sake. It's run off a +/-6V dual power supply, to avoid the additional complexity of single supply design. It is connected in series with the J113 to 0V. I measured the channel resistance of the F-FET: 54R. This is purely to test the concept, rather than a final design.
The oscillator works perfectly, giving a nice 51.5kHz (very close to the 48.2kHz calculated) sine wave of about 1.2Vpp.
Unfortunately, the amplitude modulation doesn't work properly. 1Vpp (500mVp) of different frequencies were applied to J1's gate. This was low enough to avoid the gate conducting significant current, when forward biased, causing the transistor to work in the enhancement region, yes depletion mode J-FETs can do that.
At very low frequencies, it was enough to saturate the circuit, resulting in a distorted modulation envelope.
128Hz input
This got much better as the input frequency was increased, but note the 45° phase shift and the modulation index decreases drastically, as the frequency is increased.
1.3kHz
5kHz
I tested with 56kHz in and there's hardly any modulation, rendering it useless for the intended application.
The question is: why the steep roll-off? I chose low impedances to avoid the parasitic capacitances of the breadboard being a problem. The output impedance of the signal generator is 50R, connected to 1m of co-axial cable, but I don't see how that's a problem.