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

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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 (104 to 106)

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.

+

–

+

–

timeV

Open Loop Configuration

+

–V–

V+

Voutput

Voutput = (V+ – V–)

Gain = 106

When input difference is 15 µV, the output is 15 V, the power supply maximum.

+15

–15

15 µV

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+

Voutput

wirecapacitor

diode

resistor

Voltage Follower

+

–V–

V+

Voutput

This configuration uses negative feedback : the output is connected to the inverting input.

(V+–V– )=Vo

but Vo = V–

so (V+–Vo )=Vo

V+=Vo + Vo

V+=(1 + Vo

But is huge (106)

(1 +

V+=Vo

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

+

–IinVo

Rfeedback

This configuration will convert a small input current into an output voltage that can be easily measured.

iin

ifeed

i–

iin = i– + ifeed

but i– 0

iin = ifeed

and since V– = V+ = 0

Vo = -if Rf = - iin Rf

If iin = 1 µA and Rf = 100 k, then Vo = 0.1 V = 100 mV

Voltage Amplifier

+

–Vin Vo

Rf

Rin

Perhaps the most widely used op amp configuration is that of a voltage amplifier.

Vin produces an Iin to flow through Rin. By the same analysis as for the current amplifier, we find that

Vin / Rin = – Vo / Rf

or

Vo = – [Rf/Rin] Vin

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 Rf is larger than Rin, we have an amplifier; if Rf is less than Rin, we have an attenuator.

Integrator

+

–Vin Vo

Cf

RinReset 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.

dqdt

=iin=–CfdV0dt

VinRin

=–CfdV0dt

dV0 =–Vin

RinCfdt

dV00

V0 f

∫ =–1

RinCfVin t( )dt

0

t

∫

Differentiator

+

–Vin Vo

Cin

Rf

By switching the capacitor and resistor in the integrator circuit, we obtain a differential response for the output voltage.

Vo(t) = – Rf Cin dVin(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

+

–Vin Vo

diodef

Rin

Many chemical properties have an exponential response (think pH, for example). This circuit can nicely linearize such a response.

Vo – log(Vin/Rin)

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?”

+

–VinVo

Vref

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 Vin is on the inverting input, Vo 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

+

–

V1

Vo

RfR1

V2

R2

V3

R3

We can run several voltages in parallel to produce a summing effect at the output.

If R1 = R2 = R3 = R then

Vo = – [Rf/R] (V1 + V2 + V3)

If R1 = R2 = R3 = Rf then

Vo = – (V1 + V2 + V3)

If R1 = R2 = R3 = 3Rf then

Vo = – [1/3] (V1 + V2 + V3)

V0 =–RfV1R1

+V2R2

+V3R3

⎡

⎣ ⎢

⎤

⎦ ⎥

Multiplying Amplifier

By combining a summing circuit with logarithmic and antilogarithmic circuits, we can multiply two voltages together.

log amp

antilog amplog

amp +

–

RR

R

A

B

log A

log Blog A + log B

AB

Difference Amplifier

+

–V1Vo

Rf

R1

V2R2

R3

With this, we can determine the difference between two voltages.

R1 = R2 and Rf = R3, then

Vo = [Rf/R1] (V2 - V1)

R1 = R2 = Rf = R3, then

Vo = (V2 - V1)

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

log amp

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

V1

Vo

R7

R1 +

–

V2

R2

R3

+

–

+

–

R6

R5

R4

V0 =R6R4

R1+2R2R1

⎡

⎣ ⎢

⎤

⎦ ⎥

⎛

⎝ ⎜

⎞

⎠ ⎟ V2 −V1( )

when R2 =R3 ; R4 =R5 ;R6 =R7

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.

+

–Vsource

Vo

RrefRsample

Samplesolution

Referencesolution (blank)

Vo = -(Rref/Rsample) Vsource

Vo = k (Psample/Pref)

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.

+

–

Rvariable

rectifier

meter

Rstandard

Rcell

Example: Thermocouple

Thermocouples are used in pairs; the voltage difference is related to the temperature. A difference amplifier is perfect for this job.

+

–Vo

Rin

Rin

Rf

Rf

Standard temperature

0 ˚C

Test temperature

?

Vs

Vt

Vo = [Rf/Rin] (Vt - Vs) T(Vo)

copper

copperconstantan