# What makes transconductance negative?

Quote...

"transconductance is -1 amps/volt"

Refer to this link for the source of my question...

This reference lacks the negation of A/V while this reference includes it? I'm confused...to say the least.

• It makes perfect sense. Commented Jul 17, 2021 at 9:42

Quoting from the same answer, next sentence: "It's minus only to avoid messy looking wire crossings in the image."

• @Chet Micro-Cap didn't allow to flip only the output terminals of the current controlled voltage source. To avoid harmfully crossing wires I typed negative transconductance. The minus reverses the current direction when compared what + and - signs in the drawing symbol claim. As you have already seen the same trick is used often. Most common case: The output current is drawn from left to right, no matter a component or circuit actually sinks the current from right to left. Minus makes it mathematically sound and the image looks nice when output current is pushed from left to right.
– user136077
Commented Jul 17, 2021 at 16:34

More properly, the transconductance gain is -1 A/V.

A transconductance amplifier has a high-impedance input, and it responds to a voltage on that input, while using minimal* current. It has a high-impedance output, and it forces a current on that output without significantly* changing its output current.

The gain of -1 A/V means that -- assuming it's within the range of the amplifier -- changing the input by +1V changes the output by -1A. Changing the input by -0.1V changes the output by +0.1A. Basically, the input/output relationship is $$\\Delta i_{out} = \left ( -1 \mathrm{\frac{V}{A}} \right ) \Delta v_{in}\$$. With luck, there's no significant** offset, and for all intents and purposes, $$\i_{out} = \left ( -1 \mathrm{\frac{V}{A}} \right ) v_{in}\$$.

* It's usually poor engineering practice to use words like "minimal" and "significantly", without specifying what you mean. In this case those qualities really are in the eyes of the designer -- a transconductance amplifier that would win prizes in 1948 might be pretty mediocre today, and a transconductance amplifier operating no higher than 60Hz should be orders of magnitude better in these regards than one operating at 60kHz.

** There's that word again

Transconductance is not, in general, negative. The transconductance of the specific amplifier in the question you link is negative, but in general transconductance can be either positive or negative. Or zero, for that matter.