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OP-AMPS Characteristics Analysis

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1 Faculty of Computing, Engineering and Technology Assignment 1 Assignment title: Bandwidth, Slew Rate and offset Module: Analogue and RF (CE00051-6) Student : Forhadul Islam Submitted to: Prof. Noel Shammas 09006169 Page 1
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Faculty of Computing, Engineering and Technology

Assignment 1

Assignment title: Bandwidth, Slew Rate and offset

Module: Analogue and RF (CE00051-6)

Student: Forhadul Islam

Submitted to: Prof. Noel Shammas

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Abstract

Operational amplifiers are the fundamentals building blocks of analogue electronics .Op-amps

are high gain components and used to use in analogue computers for linear, non-linear and

various frequency dependants’ applications. And now a day’s op-amps are widely used in Signal

processing, communications and audio engineering. This Assignment focuses on 741 operational

amplifier. Throughout the report experiments results of various characteristics of op-amps has

been outlined with the comparison of manufacturer given data for this particular 741.

Contents

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1 Introduction..............................................................................................................................................6

2 Literature Review.....................................................................................................................................6

2.1 Op-Amps and 741:.............................................................................................................................6

2.2 Input and output resistance................................................................................................................7

2.3 Open loop Gain..................................................................................................................................8

2.4 Bandwidth.........................................................................................................................................8

2.5 Gain bandwidth product....................................................................................................................8

2.6 Slew rate............................................................................................................................................9

2.7 Input offset voltage..........................................................................................................................11

2.8 Input bias current.............................................................................................................................11

3 741- Op-amps Specifications..............................................................................................................12

4 Specification analysis.............................................................................................................................12

4.1 Objectives:.......................................................................................................................................12

4.2 Equipment List:...............................................................................................................................12

5 Procedures:.............................................................................................................................................13

5.1 Procedure 1: Voltage Follower........................................................................................................14

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5.2 Procedure 2.....................................................................................................................................15

5.3 Procedure 3& 4................................................................................................................................16

5.4 Procedure 5, 6 & 7...........................................................................................................................19

5.5 Procedure 8&9.................................................................................................................................23

5.6 Procedure 10...................................................................................................................................23

5.7 Procedure 11&12.............................................................................................................................24

6 Discussion and analysis...........................................................................................................................25

7 Conclusion..............................................................................................................................................26

8 References..............................................................................................................................................26

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Table of Figures:

Figure 1: Ideal Op-amps model....................................................................................................................6

Figure 2:LM741 connections diagram (datasheet)......................................................................................7

Figure 3:open loop gain response curve of an op-amp (electronic tutorial)...............................................8

Figure 4:: input vs output signal of an op-amps........................................................................................11

Figure 5: Frequency -gain relation of an op-amps.....................................................................................13

Figure 6: Voltage Follower.........................................................................................................................14

Figure 7: Input and Output Signal of the Voltage follower........................................................................14

Figure 8: Input and output Signal where Vo decreases to 0.707 times its value at 100Hz........................15

Figure 9: Non-inverting amplifier Circuit...................................................................................................16

Figure 10: Input vs output waveform with 47k feedback resistor.............................................................17

Figure 11: Determining Fc frequency with 47k feedback resistor............................................................17

Figure 12:Input and output waveform with 100k feedback resistor.........................................................18

Figure 13:Determining Fc with 100k feedback resistor............................................................................18

Figure 14:741 op-amp circuit configurations to demonstrate slew rate...................................................19

Figure 15:Showing gain of figure 4.1 ........................................................................................................20

Figure 16:Changing edge of the output Vo according to the change in time............................................20

Figure 17: Effects of exceeding maximum frequency that slew rate imposed..........................................22

Figure 18: Circuit configuration to measure total output voltage.............................................................23

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Figure 19: 741 offset null circuit................................................................................................................24

Figure 20: internal schematic of 741(datasheet).......................................................................................24

1 Introduction

Operational amplifier is the fundamentals building blocks and extremely efficient device of an electronics

circuit. At the beginning op-amps were made of vacuum tubes which used to occupied lots of spaces and

of course energy. The “Operational Amplifiers” term is used to describe the mathematical operations

capability of an Amplifier. And it can perform addition, subtraction, average, integration and

differentiation when appropriate feedback components are used. Operational amplifiers originated from

analogue computers where there had performed linear, non-linear and many frequency dependants

applications. These are relatively cheap and being used in industrial, academic, consumers and scientific

applications.

2 Literature Review

2.1 Op-Amps and 741:

Op-amps normally have one input ports and one output port and basically gives an output

according to their two inputs difference and this difference is then multiply by the amplifiers

gain.

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Figure 1: Ideal Op-amps model

The basic form of an op-amp is a high gain dc-amplifier with a differential input port and a single output port. A differential input has two terminals, which are both independent of ground or common. The signal between these two terminals is the input signal, which will be amplified.

The terminals are called non-inverting input and inverting input.

For this assignment a general purpose µA741 amplifier from Fairchild were used.

Figure 2: µA741 connections diagram (data sheet)

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Parameter that describes the basic characteristics of ideal Op-Amps is outlined below.

2.2 Input and output resistance

Input resistance at two input pins of op-amps is infinite assuming that op-amp has ideal characteristics.

When input resistance is infinite, op-amps basically does no draw any current. 741 op-amp has a input

resistance of 2Mohms.Output resistance of an op-amps is ideally zero.

2.3 Open loop Gain

The main purpose of an op-amps is to amplify the input signal and if the open loop gain of the amplifier is

greater, the amplification will be even better, The open loop gain of an ideal amplifier is the gain without

any feedback and it is infinite for an ideal op-amps.(electronics tutorial,2011).but in practical it is finite.

2.4 Bandwidth

Ideally Op-amps have infinite bandwidth because of infinite frequency response but in practical

bandwidth are maintained by gain-bandwidth product and the bandwidth will be the same as the

frequency where op-amps gain is unity.

2.5 Gain bandwidth product

Gain –Bandwidth product is the multiplication of open loop gain if the op-amps and bandwidth between

the 3dB point .Gain bandwidth of 1 MHz of an amplifier is only achievable at unity gain.

Gain Bandwidth Product ,GBP = Open loop gain x Bandwidth

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Figure 3: open loop gain response curve of an op-amp (electronic tutorial,2011)

The open loop gain and cutoff frequency is normally known from the manufacturer and for 741 op-amps

Open loop gain = 105 and cutoff frequency is 10 Hz at the -3dB point ,

so the Gain-bandwidth product of 741 op-amps is,

GBP = 105 x 101 = 106 Hz = 1MHz

The Gain-Bandwith product for a closed loop gain amplifier’s ,

GBP = Lower frequency gain x Frequency at the -3dB point.

Gain bandwidth product of an op-amps is constant . If gain icreases , bandwidth will have be decreased

to maintain GBP constant. for a higher bandwidth , there will be lower gain. If any application requires

large gain and large bandwith then 741 op-amps will be unsuitable.(Prof. ShammasAssignment

1Handout)

The closed loop gain and gain bandwith product is releted in the following equation,

BW CL=f c=f T x β = fT / GCL

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BWCL = Closed loop bandwith , fT = Unity gain frequency ,β = Feedback ratio and GCL= Cloosed loop

gain.

2.6 Slew rate

The maximum rate of change of output voltage of an op-amp to follow the input voltage is called Slew

Rate and it defines how fast the output of op-amps can follow the input. Slew rate happens because of

compensated capacitor of an op-amps has limited current available to charge and discharge.(National

Semiconductor,1972). When the input signal is very big, op-amps give up all the currents to its

compensated capacitor. And it’s charging capabilities can be expressed as ,

V= Iomax . ∆ TC

So, Slew Rate=∆ V out

∆ t=

I omax

C , and expressed (unit) as

Vµ s

A sinusoidal output will discontinue being a small signal when its maximum rate of change is equal to the

slew rate limit of the op-amps.

The maximum rate of change occurs at the zero crossing and expressed as follows,

V out=V pk sin 2π ft

So,d V out

dt=2 πf cos2 πft

d V out

dt=2 πf V pk W h en t=0

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Sr=2 π f max V pk

Where Vout = output Voltage

Vpk = Output Peak voltage

Sr = maximum d V out

dt

The maximum frequency of an input sine wave for op-amps with known slew rate will remain same

without making the output to take a triangular shape and this can be expressed as the function of peak

amplitude of the output and given below ,( National Semiconductor,1972)

f max=Sr

2 π Ppk

Figure 4:: input vs output signal of an op-amps

In the above graph, Output signal of an op-amps slews when it is trying to follow the applied input

signal.

Slew rate limitations make op-amps unsuitable for applications that require fast rising pulses.

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2.7 Input offset voltage

When two applied input signal difference is zero of an op-amps, the output should be ideally zero.. In real

world, due to the manufacturing techniques, when there is no signal applied to the input terminals of an

op-amp, there will be little voltage present at the terminals. This input signal variations can only be

around of 1 mV(Gerardo M.1993 page 195), but this will be unacceptable because of op-amps high

implication characteristics. And the input Voltage that eliminates the output signal to zero is called the

input offset voltage.(Prof.shammas handout on op-amps)

2.8 Input bias current

Ideally the input current of an op-amp is to be zero but the amplifier will not work if there are no current

flows into the input terminals. This input current is called input bias current .and for a 741 – this is

typically in the range of 0.1µA.( Gerardo M.1993 page 195).

3 µA741- Op-amps Specifications

Typical specification of 741-op-amps is given in the following table from Fairchild datasheet.

Input Resistance 2 MΩ

Output Resistance 75Ω

Input offset Voltage 1 mV

Input offset Current 20 nA

Input Bias current 80 nA

Slew Rate 0.5 V/µs

Gain Bandwidth product 1 MHz

Offset Voltage adjustment range ±15 mV

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4 Specification analysis

4.1 Objectives:

To investigate the bandwidth of an operational amplifier as a function of gain. To determine the slew rate of an operational amplifier. To investigate the output offset voltage at the output of an operational amplifier

4.2 Equipment List:

741 Operational amplifier or the Equivalent DC power supply(±12V) Analogue signal generator (50Vpk sine, 10Vpk Sine, 1Vpk square wave-all with variable

frequency. Resistor: 2 x 1MΩ,1 x47kΩ , 1x 100kΩ,1x470kΩ, 2x10kΩ. Potentiometer: 1x10kΩ. Dual-trace oscilloscope DVM (Digital Voltmeter)

5 Procedures:

All the equipments were setup as per instructions in the Assignment (LAB) Handout. Experiment was carried out ignoring components tolerances.e.g Resistors (5% tolerance).

Calculating Unity gain frequency:

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(Voltage Gain)

(frequency)f1

Gd

0.707Gd

fc0

1

Figure 5: Frequency -gain relation of op-amps

Unity gain Frequency f1, the gain at unity. Cut-off frequency fc where gain decreased by 0.707 times from DC gain Gd Gain-bandwidth product : f1 = Gd x fc.

Gain bandwidth product of an op-amps is constant .And bandwidth of an op-amps is proportional to the op-amps closed loop gain. If bandwidth increases, Gain decreases or vice versa to maintain constant value of gain bandwidth product.

5.1 Procedure 1: Voltage Follower

The first op-amp circuit that will be investigated is a non-inverting Voltage Follower. Output Signal connected to the inverting input. For Voltage follower Vin= Vout. .

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Figure 6: Voltage Follower.

In this case there is no the fedback Resistor Rf between inverting input and output Vo and input

signal that is connected to the non-inverting input will not be inverted which will results output

voltage is equal to the input voltage.

Figure 7: Input and Output Signal of the Voltage follower

Channel 1 is the input signal and Channel 2 is the output.

It Very clear from above waveforms, Vin=Vout. Where Input and output Signal has same amplitude and frequency and with the same phase.

Gain = Vin / Vout =( 50/50 ) m Vpk = 1 .

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For a Voltage follower, Feedback resistor Rf = 0 and Resistor R1 = ∞ , hence gain of the amplifier as follows,

Gain = (Rf + R1) / R1 = (0 + ∞ ) /∞ = 0/∞ + 1 = 1

In theory and in practical simulation, It has been proved that the µA 741 voltage follower has a gain of unity.

5.2 Procedure 2

Unity gain frequency of the amplifier.

Practical Simulation:

Figure 8: Input and output Signal where Vo decreases to 0.707 times its value at 100Hz

Ch1 is input and Ch2 is output Signal and 50mV/DIV. When input Signal frequency is 1.011MHz, Output Vo decreases to 0.707 times its value at 100Hz.

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In this case unity gain frequency 1.011 MHz , where DC gain is 1, Cut-off frequency 1.011MHz. As the feedback ratio is zero(no feedback resistor used) We can say Bandwidth of this amplifier 1.109MHz. This is slightly more than then the manufacturer specified bandwidth 1MHz.

Unity gain frequency f T = DC gain X Cut-off frequency = 1 x 1.011 MHz = 1.011 MHz.

5.3 Procedure 3& 4

Demonstrate Gain Bandwidth product is Constant.

Figure 9: Non-inverting amplifier Circuit

Feedback resistor 47 kΩ

Input frequency 100Hz and Peak value of the input amplitude is 50mV .Output Voltage Vo ,Where Ch1 input and Ch2 output.

Figure 10: Input vs output waveform with 47k feedback resistor.

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From the above graph, Vin= 50mVpk and Vo=150mvVpk.

Vo decreases to 0.707 time of its value at 100HZ, When input Signal frequnecy reaches to 175kHz.

Figure 11: Determining Fc frequency with 47k feedback resistor.

Cutt-off frequency fc = 175KHz.

Feedback ratio,β=R1

R1+Rf

= 1010+47

=0.176

Unity gain frequency or gain bandwidth product , GBP = 175KHz / 0.176 = 994.3 KHz

Feedback resistor 100kΩ

Output Voltage Vo, Where Ch1 output and Ch2 input. And input frequency is 100Hz.

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Figure 12:Input and output waveform with 100k feedback resistor.

At 100 Hz 50mVpk input signal , Vout = 55mV.(in Figure 12)

Figure 13:Determining Fc with 100k feedback resistor

When the input signal frequency is approximately 90KHz, Output signal amplitude reaches to 0.7070 time of its value at 100Hz input.

So the cut-off frequency or -3dB frequency or bandwidth of the op-amps is 90 KHz with 100KΩ non-inverting configuration.

Feedback ratio β=R1

R1+Rf

= 1010+100

=0.091

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And the unity gain frequency or gain bandwidth product GBP=f c

β= 90

0.091=989 KHz

For the 47 K and 100K feedback resistor, gain-bandwidth product is 996 KHz and 989 KHz respectively. From manufacturer datasheet which is attached in the appendices, Gain-bandwidth product is 1 MHz that is slightly higher than experimented value or nearly 1 MHz.

For these 741 op-amps, gain bandwidth product is constant. If gain increases then bandwidth decreases or vice versa and gain bandwidth product remains almost same.

5.4 Procedure 5, 6 & 7

Measuring Slew rate and calculating maximum frequency imposed by the slew rate

Op-amps in the inverting configuration

Linear effect occurs because of bandwidth limitation of operational amplifier that limits the output rise time .howerever, because of the availability of charging current limitation internally; operational amplifiers also exhibit non linearity distortion. And the output changing rate needs to maintain a fixed value, which is slew rate.

Figure 14:741 op-amp circuit configurations to demonstrate slew rate

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Figure 15: Input vs output waveforms of figure 14

.

Figure 16: Changing edge of the output Vo according to the change in time

Rising edge or falling edge of a square wave can be used to calculate Slew rate. Increasing gain eventually decrease bandwidth and amplifier’s ability to outputs a clean square wave will be limited.

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From the above changing edge ,

∆t = 35μs and Vpk =10

Slew Rate, S = ∆V/∆t = 20 V/36μs = 0.550 V/μs

In manufacturer data sheet, slew rate for this amplifier is 0.5V/μs

Now Vs = 10 Vpk sine wave at 1 KHz and Rf = 10 K ohms and op-amps in the inverting configuration gives the following output displayed in the graph in chennel 2.

Output is following input at the same amplitude and opposite phase. The feedback ratio with 10 K ohms Feedback resistor,

β=R1

R1+Rf

= 1010+10

=0.5

And Closed loop gain for the inverting amplifier is = - VoutVin

=−Rf

R1

=−1010

=−1 , the negative

sign here means that the output signal is 1800 out of phase with the respect of input signal.

Now, the peak value of the output, K= 1 x 10 = 10 V

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fs(max)= S/(2пk) where K is peak value of the output voltage (Assignment handout) and f s= maximum frequency imposed by the slew rate.

f s¿¿

Input frequency exceeded the maximum frequency imposed by the slew rate:

Figure 17: Effects of exceeding maximum frequency that slew rate imposed.

When the input signal exceeded the maximum frequency that slew rate imposed, the output signal of an op-amp gets distorted and starts to take triangular shape.

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5.5 Procedure 8&9

Total offset Voltage

When op-amps receive same amount of voltage in the input terminals, the output should be zero

volts but in practice, there will always be some voltage at the output and this is called offset

Voltage.

Figure 18: Circuit configuration to measure total output voltage

DC output voltage, Vo =55.76 mV

5.6 Procedure 10

Non-inverting input of figure 17 was short circuited and grounded . In this step short circuit were replaced by 47 KΩ resistor and then using voltmeter , output voltage was measured.

DC output Voltage Vo= 5.62 mV

And it this process of adding a 47k ohms resistor in the non-inverting input reduced the total output voltage significantly.

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5.7 Procedure 11&12

Figure 19: 741 offset null circuit

When Potentiometer is 0Ω the output offset voltage is .002mV

Figure 20: internal schematic of 741(datasheet)

The offset null pins in µA741 is 1 and 5 which made it possible to reach 1k ohms emmiter

resistor in the input satge of op-amp. And offset null circuit is nothing but 10 K pot

(receommended by the manufacturer) connected to them which gives a easy technique to balance

out the internal.And by varying the external resistance using potentiometer, output offset voltage

goes nearly zero.

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6 Discussion and analysis

Fairchild µA741 operational amplifiers has a gain of unity and when it is used in voltage

follower configuration in out experiment, gain is 1 and its unity gain frequency is 1Mhz(Slightly

variations in the practical result which is ignore in the discussion).And in procedure 3 & 4 we

have proved that gain-bandwidth product of this amplifier is 1 MHz constant. If input frequency

increases, gain decrease and keeps a balance in the gain-bandwidth product.

We have measured the slew rate of this op-amps is 0.55 v/µs where manufacturer defined slew

rate is 0.5 V/µs means the output signal can follow the input signal by 0.55 volts per micro

seconds. And it is clear from the slew rate that if we take a large signal as input signal, 741 op-

amps will not work properly. if the input signal is larger than the calculated maximum input

frequency that is imposed by the slew rate , output signal will be distorted and will start to take

triangular shape.

According to op-amps characteristics, output voltage should be zero, if both input difference are

equal. But in our experiment in procedure 8 to 10, it is clear that the output offset is not zero. It is

in mV. Howe ever, for precision and proper operation, some applications need the output offset

voltage to be zero. And In procedure 11 & 12, we have null the offset voltage using a 10KΩ

potentiometer connected to the op-amp’s pin 1 and 5.

7 Conclusion

It can be summarised that µA741 op-amps is a general purpose small signal amplifier. And there

is a small variation between the experimental results and manufacturer specification due to the

real life compensations. And 741 operational amplifiers are not suitable for fast switching

application due to its slew rate limitation.

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8 References

Printed Source

[1] Gerardo Mesias (1993) 1st edn. Electronics Theory and Practice. Oxford: Newnes

Internet Source

[2] National Semiconductor (1972) Predicting Op Amp Slew Rate Limited Response [online]

available from <http://www.national.com/ms/LB/LB-19.pdf> [27 March 2011]

[3] National Semiconductor (2000) LM741 [online] available from

<http://www.national.com/ds/LM/LM741.pdf > [3 April 2011]

[4] eCircuit Centre (2010) Op Amp Bandwidth [online] available from

<http://www.ecircuitcenter.com/circuits/op_bandwidth1/op_bandwidth1.htm> [28 March 2011]

[5] eCircuit Centre (2009) Slew-Rate Using LIMIT [online] available from

<http://www.ecircuitcenter.com/OpModels/Ilimit_Slew/ILim_Slew.htm> [28 March 2011]

[6] Electronics tutorial (April , 2011) Operational Amplifiers [online] available from

<http://www.electronics-tutorials.ws/opamp/opamp_1.html> [ 4th April 2011]

[7] Peggy Alavi (2003) Op-amps basics [online] available from

<http://www.national.com/onlineseminar/2003/opamps_basics/090303_Opamp_Trivia_Notes.pd

f> [1 April 2011]

[8] National Semiconductor (1972) Predicting Op Amp Slew Rate Limited Response [online]

available from <http://www.national.com/ms/LB/LB-19.pdf> [27 March 2011]

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Data sheet has been attached in the appendices along with the assignment handout-

Appendices

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