LM13700 as a four-quadrant multiplier

[mckinnonbuilding]

Hey all, I'm delving into analog computers for a hobby project and making a Lorentz attractor circuit to start. Made the circuit in Kicad and simulated it with BSOURCE=X*Y for the multipliers. Now I'm trying to make it for realsies. AM633s are expensive, and I saw a suggestion that the LM13700 be used.

Looking at the datasheet for this, I see
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Great!
Made this circuit in Kicad as a standalone, to unit test it:
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Did some tuning with R4, R10/R11 (instead of a single trimpot), and got the noise floor down pretty low when Vin1=Vin2=0 - a constant output of Vout=-1.2V, which from what I've read is a bias output from the darlington pair (... correct me if I'm wrong?).

afaiu, Vout = K*V1*V2 + (1.2) (in my case)

Tested with some constant nonzero values:
V1   V2   Vout
0     0      -1.2
1     1     -0.83 (at this stage, I calculate K as 0.37)
-1   1       -1.57 (K = 0.37 predicts this nicely)
1     -1     -0.7 (.....welp that's not predicted)

But apparently this is not designed for DC values, it's better for fluctuating signals. So I put in some sine waves:
Vin1 = 1*sin(f=100Hz)
Vin2 = 0.5*sin(f=200Hz)
and
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I did a test with python, what should the product of these two things be (ignoring the K factor), and you get an amplitude of 0.4 with two obvious waves, 100Hz and smaller wiggles at 300Hz. This output, though, is just my 100Hz, it looks like Vin is just getting scaled?

I've tried tuning the various resistors furhter - one source suggested upping R4 to reduce bias from Vcc, and let more Vin2 through, but this failed. Another suggested changing Rm, but this didn't help either. I've been reading through "Nonlinear Circuits Handbook", specifically the multipliers chapter, but this discusses these more as a black box assuming they are already producing multiplying behaviour.

Does anyone know what might be going wrong here/what effects I am missing?

[mckinnonbuilding]

I knwo attachments aren't working, trying to fix it with https://www.eevblog.com/forum/beginners/upload-image/

for now it looks like they are attached to this, in order? Multiplier is first image referenced, schematic is second, sines is third



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[mckinnonbuilding]

Went over more theory, looking at Iabc

Iabc = (Vin2 - (Vee+1.4))/RC
Using my Vee = -9, we get
Iabc = (Vin2 + 7.6)/RC
and then apparently the constant term here dominates because the actual signal provides so little current as it's a voltage source not a current source (I don't follow this one, there's a cosntant resistor and a changing voltage. Any current should therefore be proportional)
Ok, well, to nullify the constant term I added a bias of -7.6 to my Vin2 sine wave, therefore Iabc = Vin2/RC (in theory)
(sorry if attachment didn't work, still getting the hang of this)
Looking at the spice output, the purple output wave certainly has another frequency component (how do I do FFT in kicad spice?), but it's out of phase and very small in amplitude.

Definitely don't understand how I'm getting this output

[TC]

Do you know trigonometry?

Look up what happens when you multiply two sines. Then think what happens if they are the same frequency.

Hints...

Sin(alpha) =sin(2*pi*freq-A + phase-A)
Sin(beta) =sin(2*pi*freq-B + phase-B)

Apply the trig formula for multiplying two sines.

Set freq-A = freq-B ...simplify.

Look at the resulting equation and look at your waveform.

[mckinnonbuilding]

I do know trig, and I did mention initially "I did a test with python, what should the product of these two things be (ignoring the K factor), and you get an amplitude of 0.4 with two obvious waves, 100Hz and smaller wiggles at 300Hz". Perhaps I should have uploaded that image:

My spice waveform does not look like this.

Regardless, assuming educational intent, I don't follow what you're trying to say. My read is "hey check your math again, that's the waveform you should get", but then I must ask: why is the resultant waveform I read from spice using so little of the Vin2 sine wave?
There's clearly a piece of theory I must be missing, and I might need it explained a little clearer rather than hinted at.

I'll ask a different way: is there anything wrong with the circuit/have i made a fundamental error in circuitry and am working from a bad construction?