I think you may be expecting a bit too much from a simple 'heterodyne' bat detector?
The only way to actually 'hear' the bats in any real detail is to record their original ultrasound transmissions as linear 'audio' sampled at - say - 192KHz onto a solid state recorder with sufficient bandwidth. And with a good quality microphone with an ultrasonic capability..
Then this recording can be analysed, by replaying the recorded file at a much lower speed.
There is special equipment available to do this, but it's very expensive. The only 'commercial' solid state recorder I know that could handle this is something like the Korg MR2 .. and I think even that's now been discontinued!
A heterodyne detector can only reproduce the difference (IF) signal between the ultrasound and the LO. These ultrasound 'bursts' do seem to have an FM component, in some species, and that can be heard as what is often described as a 'wet slap' type of sound.
A fixed frequency is just reproduced as a tuned 'click', similar to the simple 'frequency division' type of detector.
In neither case do you really care whether the 'audio' is above or below the LO frequency. A simple low pass filter following the mixer works just fine...
The link to the maths paper in my previous post (here it is again:
https://www.analog.com/library/analogdialogue/archives/43-09/edch 4 rf if.pdf ) describes almost exactly what I did, in figure 4.4 and 4.5.
The actual device I built (based around the mixer circuit in post#42) was used to make the recording of soprano pippistrelles I linked to here:
https://www.jp137.com/las/soppips.mp3
The LO was set to about 55KHz for that recording.
After a while, you get to recognise the characteristics of different species, both from the frequency range, and the type of 'sound'.
Noctules, for example make a sort of loud 'chonk' sound at around 25KHz. Daubentons (usually found near water) sound like a 'crackling' fire at around 50KHz... and so on......
But as these are only 'fake' sounds,there's no point (IMHO) in trying to make the device any more complex.
As you will discover, the microphone - and microphone preamp - are the most important part of the circuit ... they need to be quite sensitive to be able to find these little critters at distance of up to 30 or 40 metres.
Remember, they move fast, erratically, and it's in the dark!.....
