The simplest practical amplifer is the inverting voltage amplifier:

The voltage gain of the circuit is simply the ratio of the feedback resistor to the input resistor, Rf/Ri. Why is this? As with the unity gain amplifier, the operation of the circuit is easier to understand if we look at changes, rather than at the stable circuit.

The circuit is stable when the voltage at V- = 0, or ground. The resistors Rf and Ri form a resistor ladder between Vo and Vin. The voltage at V-, then, is:

Since V- must be 0 for stability, then

(Vo / Vin ) = ( Rf / Ri ).

Or Vo = ( Rf / Ri ).Vin

Now, if Vo goes more positive, then the voltage at V- also goes positive. The term (V+ - V-) becomes negative, and the output voltage decreases until the term (V+ - V-) once more becomes zero.

This circuit is an integral part of many potentiostats. It is exactly like the inverting amplifier, but the input resistor is omitted. This circuit has two important properties:

* The V- input terminal is held at ground, and

* The Vo (volts) is equal to the input current (amps) x feedback resistance (ohms).

Hence, the current delivered from an electrochemical device can be measured exactly, as a simple voltage.

In this case, the input current Iin cannot flow in or out of the input terminal of the op amp. Therefore, it must flow through the feedback resistor Rf.

The terminal V- must be kept at ground potential, since otherwise Vo would rise or fall 'infinitely'. The op amp must provide a voltage that drives a current through Rf that is equal an opposite to the Iin. This would occur when Vo = - Rf .Iin.

If Vo were to go positive, the current through Rf would increase. That is, the flow of electrons to the right would increase, causing Vin to be depleted in electrons. The voltage at V- would go positive, causing the term (V+ - V-) to decrease. This would force the output voltage to fall, returning the current to zero.

There is much more to learn about op amps, but hopefully, this brief explanation should help understand the operation of the potentiostat and other electrochemical circuits.

Walter G. Jung, *IC Op Amp Cookbook, 3rd Edition***.** Actually, any of the editions are very useful, and can often be obtained used. This reference is modest on theory and strong on applications, which, as a practicing chemical engineer or chemist, is probably what you want.

Although this site describes specifically the old and obsolete workhorse type 741 amplifier, the principles apply to all op amps. http://www.uoguelph.ca/~antoon/gadgets/741/741.html

The Wikipedia reference is concise but competent: http://en.wikipedia.org/wiki/Operational_amplifier

A handy reference on op amps, but not a good introduction: http://www.cybermike.net/reference/liec_book/Semi/SEMI_8.html