Input resistance of transresistance amplifier

Hi every one,

In Russia, the New Year has come and in this regard, I propose an interesting discussion. This is not a technical issue or a discussion of commercial products.

When designing transimpedance amplifiers or, in other words, current-voltage converters, they tend to get a very low input resistance. At the same time, the input resistance of the op-amp itself is often neglected. Personally, I decided to find out the relationship between the input resistance of the current-voltage converter and the input resistance of the op-amp. I have not seen anything like this in manuals or other free sources.

The feedback network is assumed to be simple resistive, for this reason it is more appropriate to speak here of a transresistive rather than a transimpedance amplifier. I ignored the bias current and the offset voltage. 

The attached file also contains the LTspice circuit, and you can see for yourself how closely the simulation results of the simplest transresistive amplifier and the result obtained by my formula converge.

Input Resistance of

I will be very grateful for your comments and advice.

I hope that it will be useful to someone.