Electronic – Understanding what is meant by the magnitude of an Op-Amp’s gain

circuit analysisgainoperational-amplifier

A particular problem I've been given shows two Op-Amps, which can be seen below:

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I'm asked to compute the magnitude of the gain. Not being quite sure what this means, I decided I'd figure out the gain of Op-Amp (a) and then just use that as the "magnitude". Both op-amps supposedly produce an "equal" output signal – I chose A because it has no missing values

Computing the gain

Op-Amp (a) just looks like a simple op-amp to me. I can derive gain as follows:

  1. \$I_{feedback} = \frac{V_{out} – V_{in}}{10000}\$
  2. \$I_{input} = -I_{feedback} = -\frac{V_{out} – V_{in}}{10000}\$
  3. \$\frac{V_{out} – V_{in}}{10000} = -\frac{V_{out} – V_{in}}{10000}\$, \$V_{out} – V_{in} = -V_{out} + V_{in}\$, \$2V_{out} – 2V_{in}\$, \$2V_{out} = 2V_{in}\$, \$\frac{V_{out}}{V_{in}} = 1\$

Magnitude of the gain

Here is where I find myself stuck. The gain isn't apparently the magnitude, and the correct answer has units Ohms. What could magnitude mean in this respect?

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Why is this the case? Is their some special meaning to magnitude in this respect?


I'm adding a sensor mentioned before which may have been needed (I didn't think it was relevant to the question originally)

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Best Answer

The gain is defined as the output signal divided by the input signal.

The amplifier has a voltage output.

It's a virtual ground input configuration, the input will stay at 0v by feedback action. The input is therefore not a voltage signal, but a current signal.

The gain therefore has dimensions volts/amps, otherwise written as ohms. This configuration is usually called a transimpedance amplifier.

The magnitude of the gain is 10k, the same as the feedback resistor, as for a 1mA input, the output will have to be 10V to get a cancelling current flowing back through the resistor, to maintain zero current at the inverting input.

The main feature of a transimpedance amplifier is its (ideally) zero input impedance. This provides isolation between channels when used as a summing amplifier, for instance in audio mixers. It also short-circuits stray capacitance on the input, when used with current output devices like photo-diodes, making them able to operate much faster than with a finite resistive load.