CHEM*3440 Operational Amplifiers These integrated circuits form the backbone of modern instrumental methods. Understanding their operation will help you to understand your techniques and be more able to trouble-shoot difficulties.

Circuit Diagram of 741 Op Amp Thanks to Tony van Roon in the Electronics Shop for the use of this picture.

Schematic of Op Amp Only three critical connections: Inverting Input (–) Non-inverting Input (+) Output + – output

Important Fundamentals Important basic properties of an Op Amp High input impedance Low output impedance Large gain (10 4 to 10 6 ) Wide unity gain bandwidth Negligible output when inputs are equal Ideal Op Amp ∞ 0 ∞ 0 Basic operating principles 1.It draws negligible current into its inputs. 2.It will do whatever it can to make the difference between the inputs 0. 3.It is an active device which drives its output from its power supply. Its response is limited by what its power supply can deliver.

The Inputs The notation on the inputs has nothing to do with the polarity of the signal but instead indicates the phase relationship an input signal has with an output signal. + – + – time V

Open Loop Configuration + – V–V– V+V+ V output V output =  (V + – V – ) Gain  = 10 6 When input difference is 15 µV, the output is 15 V, the power supply maximum. +15 –15 15 µV Open Loop Configuration is not useful.

Frequency Response of Op Amp Thanks again to Tony van Roon for the figure. Note how the extremely high gain is applicable only at very low frequencies. The gain decreases as the frequency increases.

Closed Loop Configuration Op Amps are employed usefully when the output signal is fed back into one of the inputs through some passive electronic device. + – V–V– V+V+ V output wire capacitor diode resistor

Voltage Follower + – V–V– V+V+ V output This configuration uses negative feedback : the output is connected to the inverting input.  (V + –V – )=V o but V o = V – so  (V + –V o )=V o  V + =V o +  V o  V + =(1 +  V o But  is huge (10 6 )  (1 +   V + =V o Purpose: A voltage follower buffers a delicate investigation system from a demanding measurement system. Op amp draws negligible input current (not disturbing the investigation system) while being able to deliver significant output current (to meet the demands of the measurement system) in such a way that the output voltage is the same as the input voltage.

Current Amplifier + – I in VoVo R feedback This configuration will convert a small input current into an output voltage that can be easily measured. i in i feed i–i– i in = i – + i feed but i –  0  i in = i feed and since V – = V + = 0 V o = -i f R f = - i in R f If i in = 1 µA and R f = 100 k , then V o = 0.1 V = 100 mV

Voltage Amplifier + – V in VoVo RfRf R in Perhaps the most widely used op amp configuration is that of a voltage amplifier. V in produces an I in to flow through R in. By the same analysis as for the current amplifier, we find that V in / R in = – V o / R f or V o = – [R f /R in ] V in The output voltage is scaled to the input voltage by the ratio of the two resistors. The gain of the circuit is now controlled by the resistor values and not the inherent op amp open loop gain. If R f is larger than R in, we have an amplifier; if R f is less than R in, we have an attenuator.

Integrator + – V in VoVo CfCf R in Reset switch The input current demands a matching feedback current which is delivered by the op amp by changing the output voltage. The reset switch discharges the capacitor and prepares the circuit for another charging cycle.

Differentiator + – V in VoVo C in RfRf By switching the capacitor and resistor in the integrator circuit, we obtain a differential response for the output voltage. V o (t) = – R f C in dV in (t)/dt The output voltage is large when the rate of change of the input voltage is large. This circuit can be used for detecting “spikes” in a signal that need to be identified or guarded against or eliminated.

Logarithmic Amplifier + – V in VoVo diode f R in Many chemical properties have an exponential response (think pH, for example). This circuit can nicely linearize such a response. V o  – log(V in /R in ) By switching the diode and resistor, we can make an antilogarithmic (exponential) amplifier. Circuits are more commonly made using a transistor instead of a diode.

Comparator A useful circuit that answers the question “Is the input voltage greater than or less than a given reference voltage?” + –V in VoVo V ref Because of the huge open loop gain of the op amp, the output voltage is driven to the power supply limits (±15 V) whenever the input exceeds or remains below the reference voltage. When V in is on the inverting input, V o assumes the reverse sign; a non-inverting comparator can be formed by switching the input and reference. This circuit turns a sine wave into a square wave. Often finds use as a trigger circuit. Charge a capacitor and feed it back to the reference input – “remembers” peak value.

Summing Amplifier + – V1V1 VoVo RfRf R1R1 V2V2 R2R2 V3V3 R3R3 We can run several voltages in parallel to produce a summing effect at the output. If R 1 = R 2 = R 3 = R then V o = – [R f /R] (V 1 + V 2 + V 3 ) If R 1 = R 2 = R 3 = R f then V o = – (V 1 + V 2 + V 3 ) If R 1 = R 2 = R 3 = 3R f then V o = – [1/3] (V 1 + V 2 + V 3 )

Multiplying Amplifier By combining a summing circuit with logarithmic and antilogarithmic circuits, we can multiply two voltages together. log amp antilog amp log amp + – R R R A B log A log B log A + log B AB

Difference Amplifier + – V1V1 VoVo RfRf R1R1 V2V2 R2R2 R3R3 With this, we can determine the difference between two voltages. R 1 = R 2 and R f = R 3, then V o = [R f /R 1 ] (V 2 - V 1 ) R 1 = R 2 = R f = R 3, then V o = (V 2 - V 1 )

Dividing Amplifier + – R R R R Combining a difference amplifier with log/antilog circuits allows us to divide to voltages. antilog amp log amp A B B/A

Instrumentation Amplifier This is a high precision, very stable difference amplifier which is at the core of most modern instrumental measurements. Very high CMRR Fixed, precision, internal gain Always used as difference amp V1V1 VoVo R7R7 R1R1 + – V2V2 R2R2 R3R3 + – + – R6R6 R5R5 R4R4

Example: A Spectrometer A simple spectrometer can be built around an op amp. A photodiode can be used as a transducer; its resistance changes when light impinges on it. Resistance is inversely proportional to the power of the impinging light source. + – V source VoVo R ref R sample Sample solution Reference solution (blank) V o = -(R ref /R sample ) V source V o = k (P sample /P ref )

Example: Conductance Cell This is a commonly used detector in devices such as HPLC and ion chromatography and some titrations. In this instrument, note the presence of a standard resistor to regularly calibrate the instrument. The variable resistor can change the gain to cover a larger range of possible cell conductances. + – R variable rectifier meter R standard R cell

Example: Thermocouple Thermocouples are used in pairs; the voltage difference is related to the temperature. A difference amplifier is perfect for this job. + – VoVo R in RfRf RfRf Standard temperature 0 ˚C Test temperature ? VsVs VtVt V o = [R f /R in ] (V t - V s )  T(V o ) copper constantan