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
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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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