This feedback network is seldom used. It's main advantage is the high gain that can be achieved with relatively small resisor values. In case of the standard configuration of an inverting amplifier, you need resitors that differ a factor 1000 in value (say 1Mohm and 1kohm) to get a gain of 1000x. In this configuration, three resistors of equal value (for exa,ple 10k) can be used to get a gain of 1000+ x.
The disadvantage of this circuit is that the input offset voltage is also multiplied by 1000x, so a 1mV offset voltage may show as an offset voltage of 1Volt.
Before we start with the analysis we make the following assumptions; 1) the circuit operates in it's linear region; 2) so the opamp can make the volateg on the inverting and the non-inverting input equal to each other; 3)there is no current flowing into the inpouts of the opamp e.q. the input impedance is infinity.
The output voltage is the sum of the voltage of resistors R_{1} and R_{2}
(1) |
We can rewrite this as function of the input current I and the current through R_{2};
(2) |
The current I_{R2} is equal to;
(3) |
which is equal to:
(4) |
Thus the ouput voltage is equal to:
(5) |
which equals to:
(6) |