diff amp - Calculate differential amplifier's input impedance

How does one calculate the input impedance of a differential amplifier?

Since the input impedance of an op-amp is very high, the input impedance for V₂ should be R₂ + R_g. But what would be the input impedance for V₁?

Answer

Differential input impedance is the ratio between the change in voltage between V1 and V2 to the change in current.

When the op-amp working, the voltages at the inverting and non-inverting inputs are driven to be the same. The differential input impedance is thus R1 + R2.

If the op-amp was 'railed' (saturated) then the differential input impedance would be higher: R2 + Rg + R1 + Rf.

Here is a circuit that can be simulated, based on the above definition of differential input impedance (values picked to be different). The input current is 333.3uA = 1V/3K.

^{simulate this circuit – Schematic created using CircuitLab}

Edit: To summarize the discussion with Dave Tweed below in comments, there are three impedances we can calculate.

1. 
   

   The differential input impedance is R1 + R2 as stated above.

   
   


2. 
   

   The input impedance looking in from V2 is R2 + Rg.

   
   


3. 
   

   The input impedance looking in from V1 is R1 (assuming the op-amp is functioning and not saturated). That is because the voltage at the inverting input is driven by the op-amp to be the same as the voltage on the non-inverting input, and it does not depend on the value of V1, only on V2.

   
   

The first two impedances have no voltage sources associated with them. The third one has a voltage with respect to ground of \$V2 Rg\over {Rg + R2}\$, so current will flow in or out of the V1 terminal depending on whether V1 is higher or lower than that value.