MULTISTAGE DIFFERENTIAL AMPLIFIERS 
Franclim F. Ferreira, Pedro Guedes de Oliveira, Vítor G. Tavares 
The output resistance of a V_{BE} multiplier 
We want to evaluate the output resistance of the montage represented on the left hand side of the figure below. The equivalent circuit is represented on the right. (cf. fig. 53) 
Using the
circuit transformations method and changing variables, first v_{p} = ( R_{2} // r_{p} ) i and then
i = v / ( R_{1} + R_{2} // r_{p} ) we will successively
obtain: 
we can then write:

The evaluation of the output resistance of the V_{BE} multiplier can also be seen as the computation of the output resistance of the amplifier represented on the right.
It is a feedback amplifier in a shuntshunt configuration, the output resistance of which, according to the
feedback theory, is equal to the open loop output resistance divided by the amount of feedback, i.e.,
R_{of} = R_{o} / (1 + b A). 
The following sequence shows the way to evaluate the equivalent circuit to the feedback block, using the equivalent twoport network technique, in the framework of the method for analysing a feedback amplifier. 

Replacing this in the previous circuit, we get the new circuit as depicted in the figure on the right, from where, the open loop gain (b = 0) is easily obtained:

as R_{o} = R_{1} we have that may be rewritten as This value is slightly different from the exact value obtained above, due to the small error inherent to the method for analysing a feedback amplifier. It is easy to see that the error is really small: taking the values of exercise 7, 1/R_{1} is 36.8 smaller than g_{m}, which induces an error of 2.6% in the evaluation of the output resistance. 