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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.

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chem 3440

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
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
Schematic of Op Amp

Only three critical connections:

• Inverting Input (–)

• Non-inverting Input (+)

• Output

output

+

important fundamentals
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

It draws negligible current into its inputs.

It will do whatever it can to make the difference between the inputs 0.

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 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.

V

time

+

+

open loop configuration
Open Loop Configuration

Voutput = b (V+ – V–)

Gain b = 106

V–

Voutput

+

V+

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

+15

15 µV

Open Loop Configuration is not useful.

15 µV

–15

frequency response of op amp
Frequency Response of Op Amp

Note how the extremely high gain is applicable only at very low frequencies. The gain decreases as the frequency increases.

Thanks again to Tony van Roon for the figure.

closed loop configuration
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.

diode

resistor

capacitor

wire

V–

Voutput

+

V+

voltage follower
Voltage Follower

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

b(V+–V– )=Vo

but Vo = V–

so b(V+–Vo )=Vo

bV+=Vo + bVo

bV+=(1 + b)Vo

But b is huge (106)

b  (1 + b)

 V+=Vo

V–

Voutput

+

V+

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
Current Amplifier

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

  • iin = i– + ifeed
  • but i– 0
  • iin = ifeed

and since V– = V+ = 0

Vo = -if Rf = - iin Rf

Rfeedback

ifeed

iin

i–

Iin

Vo

+

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

voltage amplifier
Voltage Amplifier

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

Rf

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

Rin

Vin

Vo

+

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
Integrator

The input current demands a matching feedback current which is delivered by the op amp by changing the output voltage.

Cf

Rin

Reset switch

Vin

Vo

+

The reset switch discharges the capacitor and prepares the circuit for another charging cycle.

differentiator
Differentiator

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

Rf

Vo(t) = – Rf Cin dVin(t)/dt

Cin

Vin

Vo

+

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
Logarithmic Amplifier

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

diodef

Vo – log(Vin/Rin)

Rin

Vin

Vo

+

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
Comparator

A useful circuit that answers the question “Is the input voltage greater than or less than a given reference voltage?”

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.

Vin

Vo

+

Vref

• 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
Summing Amplifier

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

R1

Rf

V1

R2

V2

Vo

R3

If R1 = R2 = R3 = R then

Vo = – [Rf/R] (V1 + V2 + V3)

+

V3

If R1 = R2 = R3 = Rf then

Vo = – (V1 + V2 + V3)

If R1 = R2 = R3 = 3Rf then

Vo = – [1/3] (V1 + V2 + V3)

multiplying amplifier

log amp

log amp

antilog amp

Multiplying Amplifier

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

R

R

log A

A

R

AB

B

+

log B

log A + log B

difference amplifier
Difference Amplifier

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

Rf

R1 = R2 and Rf = R3, then

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

R1

V1

Vo

+

V2

R2

R1 = R2 = Rf = R3, then

Vo = (V2 - V1)

R3

dividing amplifier

log amp

log amp

antilog amp

Dividing Amplifier

Combining a difference amplifier with log/antilog circuits allows us to divide to voltages.

R

R

A

B/A

+

B

R

R

instrumentation amplifier

+

+

+

Instrumentation Amplifier

This is a high precision, very stable difference amplifier which is at the core of most modern instrumental measurements.

V1

• Very high CMRR

• Fixed, precision, internal gain

• Always used as difference amp

R6

R2

R4

Vo

R1

R3

R5

R7

V2

example a spectrometer
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.

Vo = -(Rref/Rsample) Vsource

Vo = k (Psample/Pref)

Sample

solution

Reference

solution (blank)

Rref

Rsample

Vsource

Vo

+

example conductance cell

+

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

Rcell

rectifier

Rstandard

meter

example thermocouple

Standard temperature 0 ˚C

Test temperature ?

Example: Thermocouple

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

Vo = [Rf/Rin] (Vt - Vs)  T(Vo)

Rf

Rin

Vs

copper

Vo

constantan

copper

+

Vt

Rin

Rf