LM13700 gain calculation (open loop circuit)

[tss]

When using the LM13700 in an open look configuration, how can I determine the voltage gain of the circuit? The output of the OTA (before the buffer) is a current source with high impedance, and its max output is the bias current so the voltage output swing is given by the bias current times the load resistor. However this got nothing to do with the input voltage. So, how do you set a certain min and max gain? How do you calculate it?

[merlinb]

When using the LM13700 in an open look configuration, how can I determine the voltage gain of the circuit? The output of the OTA (before the buffer) is a current source with high impedance, and its max output is the bias current so the voltage output swing is given by the bias current times the load resistor. However this got nothing to do with the input voltage. So, how do you set a certain min and max gain? How do you calculate it?

According to the data sheet, the transconductance is 19.2 times the control current. Multiply the transconductance by the load resistor to find the voltage gain. i.e.
Gain = 19.2 * i(abc) * R

[tss]

You are right sir - I somehow missed that!
Is there an advantage is working in open loop or closed loop mode?

[R.G.]

Open loop, the gain is what the gain calcs say it is.

Closed loop, the internal gain is then lowered by the external feedback arrangement.  As in all negative feedback arrangements, negative feedback lowers gain, but reduces distortion and extends frequency response in proportion.

[PRR]

Open-loop, the MAXimum input level is always about 50mV.

(This all goes back to Shockley's Relation, Re is 26 Ohms at 1mA, which goes-around to define Transconductance, and also maximum input level.)

So you could reduce Iabc and load-down the output and get, say, gain-of-4, but the maximum output will be 50mV*4= 200mV.

Note that 50mV input overload is quite small by guitar-stuff standards. Guitars commonly output several times that much. You can pad-down, but you are throwing-away S/N, increasing the gain you must find, and the low input impedance of these chips leads to a low attenuator input impedance, whereas guitar-stuff likes high input impedance.

And while it may not matter here, the open-loop THD is not-small. Perhaps 0.1% to 2% at higher levels, while a 19-cent opamp can do <0.02% at any level short of clipping.

Setting the open-loop gain >>4 and then applying NFB for gain-of-4, the input could be 2V (with +/-15V supplies). Forty times higher. Input overload is whatever you want, and input impedance is much increased by NFB.

Applying NFB around a '3080/13700 is a bit silly. It isn't a great opamp. Better opamps are cheaper. Even at max Iabc it doesn't output the current of a '741 or TL07x. But at max Iabc the input bias current is higher than for-purpose op-amps. And while it may "work" in many applications, AFAIK these OTAs are all out-of-production, yet still valued for their special applications; while TL07x and the other op-amps are still made by the ship-loads.

[tss]

Paul, of course no one would use an OTA instead of a regulator opamp. The reason I am looking at these is because it is easy to implement a current controlled amplifier and that is more tricky to do using a "normal" opamp. The LM13700, for example, is still easier to implement as a VCA than an opamp and JFET. Everything has advantages and disadvantages.