A to Synth: UPDATE: Flawed - LM13700 simulations, 12/15V supplies

UPDATE: A lot of the values in this post are wrong, as the 5V CV in the 12V circuit made it flatline after about 4.5V CV. I will do a new post with a corrected circut but keep this to be able to see what I originally thought.

I_abc

V_out

Before converting the JP6 filter to 12V, I wanted to know a bit more about what happens when changing the supply of the LM13700 from 15V to 12V. (For simplicity, throughout this text I will say 15V and 12V when I actually mean a +/-15V and +/-12V supply voltage).

As a first model I used the Xonik VCA.

Xonik VCA

I first calibrated the circuit for unity output at 5VCV, 12V supply:

I then tried the same circuit with a 15V supply without changing anything else:

Slight offset of output when 15V supply, slightly reduced gain (surprisingly)

Finally I tweaked the resistors to get a centered output with 15V:

Centred output, 15V supply

Centred output, 15V supply - circuit

EDIT: After completing all measurements I went down the rabbit hole that is reading the datasheet. I discovered that (not that surprisingly really), the gain (transconductance) of the circuit is strongly dependent of the diode bias current. In my 12V version of the circuit this is set to 11.3V/12kOhm = 0.942mA (11.3V is one diode drop short of the positive supply voltage 12V, as anode of the diodes are 0.7V above 0), so when changing to 15V we need to replace the 12k resistor with a 15.19k one. This does not affect the control current generation but it DOES affect the gain, see the last line in the signal voltages table.

Measurements around the LM13700 on the Xonik VCA

CV inputs

CV	Supply	Icv (=-I emm)	I base	Iabc	Vabc	V coll	V base
0V	12V	0V	0V	-11.29pA	-11.289V	-11.289V	33nV
0V	15V	0V	0V	-14.27pA	-14.266V	-14.266mV	33nV
5V	12V	-1.515mA	-271uA	-1.244mA	-10.25V	-49.9mV	-788.7mV
5V	15V	-1.515mA	-15uA	-1.500mA	-13.24V	-942.33mV	-784.7mV

These stay the same even if the diode bias current changes.

Signal voltages

input is -5 to 5V.
CV is 5V
+in is connected to input through a 27k resistor and has a 510R to gnd
bias input is connected to 12/15V through 12k resistor
Output is to gnd via 24.3k resistor, buffered.

Supply	+in	-in	bias	I out (to gnd)	V out
12V	175mV to 275mV (191.7uA to -175uA in 27k, 343uA to 539uA in 510R)	184.5mV to 265mV (373uA to 536uA)	1.03 to 1.12V (-914.5uA to -907uA)	-205 to 206.7uA	V out: -5.02 to +4.98
15V	235.7mV to 234mV [THIS MUST BE WRONG, PROBABLY to 324mV) (193.9uA to -172.8uA in 27k, 462uA to 654uA in 510R)	243mV to 325mV (495uA to 662uA)	1.09 to 1.118V (-1.1589mA to -1.1515mA)	-201.3 to 201.3uA	V out: -4.89 to +4.89
15V*	175.6mV to 278mV (191.7 to -175uA in 27k, 344.3 to 540.8uA in 510R)	184.9mV to 265.5mV (376.8uA to 541uA)	1.03V to 1.12V (-920uA to -914.2uA)	246.8uA to -245.4uA	V out: -6.0V to 5.96V

*with changed diode bias using 15.19k resistor instead of 12k.

Something interesting happened when I changed the diode bias resistor. All signal currents and voltages are suddenly the same as for 12V. The control currents/voltages are still different from 12V but they have not changed from the original 15V. The only thing that is different is I_abc. Let's see what happens when we change that to match the 12V input.

Changing the CV to 4.1465 changes I_abc to -1.244mA. Now the output is back at -5 to +5V! Hooray, this means that we have the exact same I_abc to gain tracking for 12 and 15V. In other words, I_abc tracking is the same as long as we use the correct diode bias.