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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.
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Op-amps are analog circuit elements that have two inputs, one inverting (-), and one non-inverting (+) as well as one output, as shown by the standard symbol at left. By applying just two simple rules the operation of an op-amp can be easily understood.

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.
Take the voltage follower configuration shown opposite. Here the op-amp’s (+) pin is connected to an external voltage Vi. 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.
The same two rules can be used to analyze the classic circuit for a current amplifier, shown at left. Here the current being measured Iin 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”.
Let us examine one more op-amp configuration as shown here. This is known as a control amplifier and its function is to make the op-amp drive current through the two resistors to keep the potential at their junction at –Ein. 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.
A very similar arrangement is employed in the potentiostat shown at left. The three electrode cell now sits in the position previously occupied by the two resistors. A control voltage Vin 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.
Putting it all together, a schematic for a typical electrochemical measurement system is shown below, where OA1 is the potentiostat’s control amplifier, OA2 is a voltage follower and OA3 is a current amplifier. Although our instrument uses a slightly different configuration to the one just described, exactly the same principles can be used to understand its operation, as we shortly see.