Custom Sensor Solutions, Inc.Custom Sensor Solutions, Inc.The operational amplifier (or 'op amp') is a critical component in any apparatus for doing electrochemistry. There are many references to op amps out there, but here, we're going to concentrate only on those features that are important to electrochemical applications.
This is the general schematic for an op amp.
Figure 1. General symbol for an op amp.
There are two input terminals (left side) and one output terminal. By convention, the upper terminal, or (-) is called the inverting input, and the lower terminal, or (+), is the noninverting input (yes, the term is redundant, but that's the convention). The input voltages can be AC or DC, and usually positive or negative.
The output voltage is determined by the following formula:
Where V- is the voltage at the inverting input, V+ is the voltage at the noninverting input, and Vo is the output voltage. Since the 'open loop' gain factor A is very high, usually 100,000 or greater, the unadorned amplifier is not very useful. Usually a feedback network is used to rein in this awesome amplifying power to some reasonable level. The formulas that follow assume that the open loop gain is much higher than the gain of the overall circuit. The reasons for this are beyond the scope of this page, but can be found in the references below.
Op amps are active devices and must be provided with power to operate. Usually, both positive and negative voltages are needed to drive op amps involved in electrochemistry applications. Typical power voltages are +5 to +15 VDC and -5 to -15 VDC.
Op amps come in several packages. A common package for electrochemical construction is the 8-pin DIP package:
The pin connections of nearly all op amps are standard
Here is a simple circuit with a voltage gain of 1 :
The voltage at the output is fed back to the inverting input, so the amplification is controlled by the difference between the Vin and the Vo. To understand this better, imagine what would happen if the Vin increased. The term (V+ - V-) would become positive, which would cause the output voltage to increase until Vo = Vin. If Vin decreased, (V+ - V-) would become negative, which would cause the output to decrease. The only stable point for the circuit occurs when Vo = Vin.
Why would anyone want an amplifier with a gain of only 1 ? Ops amps typically have maximum output currents of several milliamps, whereas the input terminals draw no current (in principal, at least). A high-impedance source, such as a reference electrode, can properly be buffered by a unity-gain amplifier. A reference electrode cannot be depended on to provide a constant voltage if significant current is allowed to pass through it. However, if connected to a unity-gain amp, the RE voltage will be reflected at the output, and there is plenty of drive capacity available to drive subsequent circuits.
The simplest form of 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:
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 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
Current Sept. 8, 2005
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