### Operational Amplifiers : A Practical Introduction

Operational amplifiers, or “op-amps” for short are extremely useful for building analog circuits. The term “operational” derives from the fact that these blocks can be wired up to perform mathematical operations such as addition, subtraction, integration and differentiation. In the material that follows I will explain in a non-mathematical way how they are exploited in electrochemical instrumentation.

In a potentiostat, the circuitry surrounding the three electrode electrochemical cell typically consists of a voltage follower, a control amplifier and a trans-impedance or current amplifier. Each of these elements are typically implemented using op-amps.

These two rules are as follows : (i) the op-amp will always try and make the voltage at each of it’s two inputs equal, and (ii) no current flows into either input pin of the op-amp.

_{i. According to rule (i), the (-) pin must be at the same voltage and so the output Vo simply tracks the input. This might seem a rather pointless circuit until it is realized that according to rule (ii), no current will be drawn from the applied external voltage source. In the case of a high impedance input like a Ag|AgCl reference electrode it is essential that the reference’s output be buffered without drawing current otherwise its voltage will drop.}

_{in is applied to the (-) pin of the op-amp, and a feedback resistor Rf is placed between this pin and the op-amp’s output pin. Notice that the non-inverting (+) pin of the op-amp is grounded. Since no current is allowed to flow into the op-amp the input current must flow through the resistor Rf. According to Ohm’s law, this produces a voltage drop IinRf . Since the voltage at the op-amp’s (-) input must be at ground (here this pin is actually described as a “virtual” ground), the output pin will develop a voltage - IinRf. Thus we see that the net effect of this circuit is to generate a voltage from a current with the constant of proportionality being the feedback resistance Rf - hence the term “current amplifier”.}

_{in. Here, a potential is applied with polarity as shown between the junction of the two resistors and the (-) terminal of the op-amp. With the op-amps (+) terminal grounded, the (-) terminal becomes a virtual ground, so that the resistor junction sits at –Ein. Obviously this implies that the op-amp drives a current (–Ein /R) through the resistors. }

_{in is applied at the (-) input to the op-amp through a resistor R and a second resistor R connects from there to the reference electrode. Following similar arguments to those just made one realizes that the potential at the reference electrode will track the input and will at all times be –Vin. Thus the function of the op-amp is to supply current at the counter electrode to maintain the potential of the working electrode at Vin relative to the reference electrode.}