Difference amplifier

[sy]

Would someone help explain to me what "differential mode gain" and "common mode gain" is for a difference amplifier? I am having trouble finding sources online to explain this.

[MarkT]

gain is output / input, so differential gain is (output2 - output1) / (input2 - input1), common mode gain is (output1 + output2) / (input1 + input2).  For common mode there has to be a reference ground to measure against, that may be explicit or implicit (just ground).

Gain can also be quoted for DC or AC (small signal), the latter not being sensitive to DC offsets.

Gain is usually voltage gain, but current gain is also a thing, same principles apply.

If the device is differential input and single-ended output, simply use ground as the output2 in the equations.

If you have current input and voltage output, gain is called "transimpedance", and has units of ohms,
if voltage input and current output, gain is called "transconductance", units of siemens (1/ohm).

[jim_griff]

I'm sure you know what "gain" is - the amplification factor between input and output. Output/Input = Gain factor.

Common Mode Signal:
A signal that is exactly the same on both inputs.

Differential Mode Signal:
A signal that is exactly the opposite ("different") on both inputs. i.e. You could have a sinewave that is inverted on the 2nd input. The sinewave is 100% differential, 0% common.

A common mode amplifier will use addition. Anything that is different will be suppressed through that addition of signals. Anything that is the same will be added together and amplified. If you add +1 to +1 you get 2. If you add -1 with +1 you get 0. Differential mode signals are cancelled out.

A differential amplifier subtracts input signals from one another. If you subtract -1 from +1 you get 2. If you subtract +1 from +1 (common mode), you get 0.

Differential mode signals are very useful for EMI suppression which is common mode by nature. i.e. EMI will usually affect two wires in almost exactly the same way. So if you are to send a +signal (noninverted) and -signal (inverted) together down two wires into a differential receiver, any EMI that's common mode should be suppressed as it gets cancelled out.

Of course, it's a lot more complex than that, and involves a lot of complex impedance calculations.

[golden_labels]

A small correction to MarkT’s post. Common mode is the average of two signals, not their sum. Threfore in the common-mode gain the denominator is: (input₁ + input₂) / 2. (corrected: see explanation)

Word “gain” may sound like something desired in a circuit, it’s not neccessarily the case. Common-mode gain is a good example. For amplifying differential signals we want it to be possibly close to zero. An ideal differential amplifier has a common-mode gain of 0 and the further a real circuit deviates from it, the more error it introduces into the output. Common-mode rejection ratio is what measures the useful (differential) gain compared to the unwanted (common-mode) gain.

[MarkT]

I never said common mode was their sum, just that common mode gain = (output1 + output2) / (input1 + input2), which is valid as the ratio of sums is the same as the ratio of averages.

[golden_labels]

MarkT is right. I corrected my post above and here is a clarification.

The confusion arisen from me missing MarkT uses an equation for a fully differential amplifier.

The input common mode is average of the inputs, as stated in my post: (input₁ + input₂) / 2. This is true in either case.

However, in a fully differential amplifier the output is described in terms of a common mode and deviation from it. The output common mode is: (output₁ + output₂) / 2.

Division by 2 cancels out for both and indeed we have: (output₁ + output₂) / (input₁ + input₂).

[MrAl]

Would someone help explain to me what "differential mode gain" and "common mode gain" is for a difference amplifier? I am having trouble finding sources online to explain this.

These amplifiers have two inputs.  One would be the inverting input and the other the non inverting input.  They are both used in an application in some way and that gives rise to specifications that involve both terminals at the same time.

Differential gain is the normal gain of the stage and comes from the normal difference in signals on the two input terminals.

Common mode gain is the spec that shows how well the amplifier can reject signals that are exactly the same on both inputs.  This is desirable for rejecting noise and other things like crosstalk.  This is so that you amplify your signals correctly but do not amplify the noise or interference that appears on both inputs especially when you have long wires attached to the two inputs. Low common mode gain is desirable for this reason.

The differential gain amplifies your signals, the low common mode gain helps reject unwanted signals from getting amplified and messing up the measurements.  The lower the common mode gain, the better the device rejects these unwanted signals.

[Terry Bites]

Its best that you first undertsand what differential amplifiers are used for and why two gain terms arrise.

One term relates to the gain for differential potentials at the input terminals and the other for potentials common to both input terminals.
In for many applications you'd want the CM gain to be zero. See attached diagram.
The subtraction is never precisely equal to V1-V2 though, its impossible to perfectly match the amplifier components both internal and external to the chip.
Other non-ideal factors are also responsible for this error: input and source impedance magnitudes, mismatches in those, non linearity, stray capacitance and indcutance and poor frequency/ phase response (and more) all add to your woes. We dream of a true untity cm gain amplifier.

There are circumstances where you'd deliberately configure the diff and cm, gains to achieve an offset. ie the slope and intercept in y=(mx+c)
See pdf