Experiment

1 OpAmp Circuits and Filters

Operational Amplifiers (OpAmps) have been in use for a long time, their initial application being
in the area of analog computation and sophisticated instrumentation. An Integrated-Circuit (IC)
OpAmp is made up of several transistors, resistors, and usually one capacitor connected in a
rather complex circuit for compensation purposes. Here we will consider OpAmp as a building
block and the circuit inside of it will not be discussed. This experiment will review some of
OpAmp terminal characteristics and applications.

1.1 Objectives:

- Study the characteristics and functions of ideal OpAmps.

- Deal with both DC and ac signals in OpAmp circuits.

- Deal with inverting and non-inverting amplifiers.

- Study the characteristics of Active low-pass and high-pass filters by obtaining their
frequency and step response.

1.2 Components and instruments

Software Components

 741 OpAmp: 1
 Multisim
 Resistors: various
 Capacitors: various

1.3 Information

An Op-Amp, in general, has three terminals, i.e. two input terminals and one output. Most
integrated-circuit (IC) Op-Amps require a DC power supply since any active circuit like an
amplifier requires dc power to operate. This is because most of the time we want the output
signal have larger magnitude than the input, and the amplifier increases the signal power. The
DC sources supply the necessary power needed to amplify the input signal. Fig. 1 shows the
symbol we use to represent an Op-Amp, not showing the power inputs.
 V in -
V out
V in +

Fig. 1: Ideal Op-Amp

The output voltage is equal to the difference between the two voltages applied to the Op-Amp
input terminals multiplied by the Op-Amp Open Loop Gain (A), i.e.

V out = A⋅( V in+ −V in− )

1.4 Ideal Op-Amp:

The Ideal Op-Amp draws no input current, i.e. the DC current into both input terminals are zero.
It means that the input impedance of an Ideal Op-Amp is infinite. The Ideal Op-Amp has a very
large voltage gain, ideally infinite. For this reason, in most applications Op-Amp is used in a
feedback configuration.

1.5 The Inverting Configuration:

Fig. 2 shows the inverting configuration. The OPAmp here is shown with its two power inputs,
namely terminals 4 and 7.

R2
DC = 15v
10k
4

R1
V2 -
Vi 6
1k V3 + Vou
DC = 0.5
t
7

DC = 15v 0

Fig. 2: Inverting Amplifier

In this configuration the input signal is connected to negative input terminal through R1 and the
other input terminal is connected to ground.
As mentioned above the gain A is very large (ideally infinite). If we assume that the circuit in
Fig. 2 is working properly and produces a finite output voltage, then the voltage difference
between the Op-Amp input terminals must be very small (ideally zero). In other words here we
have a virtual short circuit between the two input terminals, i.e.

V2 - V3 = 0. Since V3=0, thus V2=0, and the terminal is a virtual ground. Now we apply the
Ohm’s law and find the current I1 through R1 as follows:

V in −V 2 V in
I1= =
R1 R1 (1.2)

This current can’t go into the Op-Amp since the ideal Op-Amp has infinite input impedance, so it
goes through R2. Then we apply the Ohm’s law to R2 to determine Vout:

R2
V out =V 2 −I 1⋅R2 =0−I 1⋅R2 =−
( )⋅V
R1 in
(1.3)

As a result the transfer function, i.e. the amplifier Closed Loop voltage gain, is given by:

V out R2
=−
V in R1 (1.4)

As shown in (1.4), the circuit gain is simply the ratio of the two resistances R2 and R1 and the
negative sign means that the amplifier provides signal inversion, i.e. 180° phase shift.
 1.5.0 The Non-inverting Configuration:

Fig. 3: Non-Inverting Amplifier

In Fig. 3 the input signal Vin is applied directly to the positive input terminal and the other input
terminal is connected to ground through R1. Here is the analysis of the non-inverting
configuration:

V in R
V out =V in +
( )
R1 ( )
⋅R 2=V in⋅ 1+ 1
R2
(1.5)

Thus the transfer function, i.e. the Closed Loop voltage gain is:

V out R1
=1+
V in R2 (1.6)

(1.6) shows that the amplifier gain is positive and always greater than 1.

1.5.1 Integrator/Differentiator:

The basic inverting feedback amplifier can also be used for a variety of other functions, including
buffering, integration, differentiation and exponential functions. A general form of the amplifier is
shown in Fig. 4. This amplifier has a gain of
 vO Z
Av= =− 2
vI Z1 (1.7)

Z 2

Z 1
V in
V out

Fig. 4: General Inverting Amplifier

The first basic use is as an integrator. In this case a resistor is used for Z1 and a capacitor for
Z2.

Z2 1
v O =− v I =− v
Z1 sR1 C 2 I (1.8)

t
−1
vO = ∫ v I (t ' )d t ' + V C (1.9)
R1C2 0

Where V C is the initial value that the capacitor has been charged with prior to the start of
integration time.

Another useful application of an OPAmp is as a differentiator. In this case a capacitor is used for
Z1 and a resistor for Z2.

Z2
v O =− v =−sR 2 C 1 v I
Z1 I (1.10)

dv I (t )
v O =−R2 C 1
dt (1.11)

1.5.2 Active Low-Pass Filter:

Integrators and differentiators in time domain can also be viewed in frequency domain, as filters.
The maximum voltage gain of a passive filter can only be equal to 1 (0 dB) in the best case.
However, to obtain a gain of more than one we can use active filters, which include amplification.
 Z 2

Z 1
V in
V out

Fig. 5: General Inverting Amplifier

To begin with, consider the general inverting configuration of Fig. 5 where R1 and R2 are replaced
by impedances Z1(s) and Z2(s) respectively. The transfer function becomes:

V out Z2 (s )
=−
V in Z1 (s ) (1.12)

Replacing s by jω in (1.8) it provides the transfer function in terms of ω, R1 and C2. Now let’s
consider the circuit shown in Fig. 6 .

DC = 15v C2

1n

10k
R2
4

R1
V2 -

1k
6 Vou
Vin V3 + t

DC = 0.5
7

DC = 15v 0

Fig. 6: Active Low-Pass Filter

Here we have:

1
Z 2 ( s ) =R2||
Z 1 ( s ) =R 1 , and
s⋅C2 (1.13)

thus:
 R2
V out R1
( jω )=−
V in 1+ jω⋅C 2 R 2 (1.14)

R2
−
It is clear that the maximum voltage gain of the low-pass filter is at  = 0 and equals
R1 .

1.5.3 Comparator

A comparator circuit is essentially a very high gain OpAmp having a plus(+) and a minus(-)
input. The output of the comparator is a logic level that provides an indication of when the plus
input voltage is greater/less than the minus input. Fig. 7 shows a 741 OpAmp used as a
comparator. The reference voltage is set by R1 and R2. The output voltage goes to a high state
if Vi goes lower than Vref and it goes to a low state if Vi > Vref .

Fig. 7: Comparator circuit

1.5.4 Summing Amplifier

Fig. 8 shows a summing amplifier. Based on application of Superposition to the inverting

❑
R0 R0
Vo=− (
R1
V 1+ V 2
R2 )
Fig. 8: Summing amplifier
 1.6 Lab Tasks:

Complete the following tasks before coming to the laboratory:

1.6.0 Op Amp Datasheets

- Familiarize yourself with the op amp datasheets for this lab. The chips (741 OpAmp DIP)
used in this lab are common and datasheets are easily found online.

- Answer the following questions:

a. Sketch the pin connections for the device

b. What is the minimum supply voltage for this chip?

c. What is the maximum voltage gain for this OPAmp?

d. What is the maximum frequency of this OPAmp?

1.6.1 Non-Inverting & Inverting Amplifiers

- Design a single op amp circuit that provides a voltage gain |Av| = -20. The input
resistance should be at least 200 kΩ. Show all the hand calculations.

- Use Multisim to verify your design. Include Multisim graphs.

- What input signal would you use to test this circuit, and what corresponding output signal
would you expect from this test?

- How would you test the input resistance of your circuit?

- Apply an AC input signal with 0.5 V peak-to-peak (Vpp) and a frequency of 1 KHz. Show
the graph of the output.

1.6.2 Differentiating Amplifiers

- Design a differentiator using the op amp circuit with a time constant of 1 ms. Show all the
hand calculations.

- Use Multisim to verify your design. Include Multisim graphs.

- What input signal would you use to test the functionality of this circuit, and what
corresponding output signal would you expect from this test?

- Apply a square wave, a sine wave, and a triangular wave input to the circuit with
appropriate amplitude and frequency to observe the functionality of this op amp circuit, in
time domain. Explain the outputs.

- Run an AC analysis (frequency response simulation) on the circuit. On the Magnitude

- Design an active low-pass filter that meets the following requirements: ( Show all the
hand calculations).

a) Maximum gain of 10

b) -3dB frequency of 15 kHz

- Use Multisim to verify your design. Include Multisim graphs.

- Run an AC analysis on the circuit. Sweep the frequency of the input signal to gather
sufficient data to create a plot of the filter frequency magnitude response and phase
response. Observe the response on the oscilloscope for each case and note down the
peak-to-peak output voltage (Vpp) and phase.

- Find the unity gain frequency for this circuit.

- Find the phase at the frequency of unity gain (gain=0dB). The difference between this
phase and -180o is called phase margin.

- Find the gain at the frequency of phase=180o. The difference between this gain and the
unity gain is called gain margin.

1.6.4 Comparator

- Design a comparator to compare the input voltage with 5V to produce a high or low output
according to the comparison result. Show all the hand calculations.

- Use Multisim to verify your design. Include Multisim graphs.

- What input signal would you use to test the functionality of this circuit, and what
corresponding output signal would you expect from this test?

1.6.5 Summing amplifier

- Use Multisim to verify your design. Include Multisim graphs.

- What input signal would you use to test the functionality of this circuit, and what
corresponding output signal would you expect from this test?

- Connect V1 to 2V DC and V2 to 3V DC. Verify that your circuit meets the design
specifications described in your prelab.
 - Connect V1 to a 10KHz, 0.5VPP sinusoidal input and V2 to a 1KHz, 5V PPsquare wave input.
Explain the output shape and verify the result.

1.7 What should be in the report?

Introduction:

- One short paragraph explaining the purpose of the experiment

Results:

- Discussions, derivations, calculations, and simulations all in the order that is given in the
lab Task.

- Graphs and tables if needed

- Snapshot of circuits created

- Answers to all questions on this manual

Conclusion:

- One short paragraph explaining what you learnt about this experiment