Topic 1.4.6 – Signal distortion
Learning Objectives:
At the end of this topic you will be able to;
 understand the power supply requirements for an op-amp limit the
output voltage swing;
 recognise clipping distortion, and describe how it can be reduced;
 recognise the distortion that occurs when the slew rate of an op-amp
is exceeded;
 select and use the formula: SR 
Vo
.
t
1
Module ET1
Introduction to Analogue and Digital Systems.
Signal distortion.
Until now we have kind of assumed that as long as we have drawn the correct
circuit diagram for an inverting or non-inverting amplifier that everything will
work no matter what input we provide. In reality there are a couple of
limitations that we have to take into consideration, because they have serious
implications on the ability of the amplifier to produce the correct output.
The first of these is the power supply for the op-amp. The op-amp power
supply is critical in determining the maximum output voltage that can be
obtained from the amplifier. Typically the output voltage maximum is between
1-2V less than that of the power supply. For example if the power supply was
±15V, then the maximum output would be limited to around ±13V. If the same
amplifier was then connected to a ±5V supply, without making any changes to
the ciruit, the maximum output would then be limited to just ±3V. We call this
effect saturation, because the amplifier cannot produce an output voltage
greater than its own power supply, since then it would be creating more
energy that it has been provided which is impossible. In most exam questions
you will be provided with the saturation values. If for any reason these are
not provided or for general design work you can assume that they are 2V
inside the power supply values.
We will now look at the effect of saturation in both the d.c. and a.c. cases.
2
Topic 1.4.6 – Signal distortion
D.C Case.
We will assume we have constructed a non-inverting amplifier with a gain of
+10, connected to a ±15V power supply, with saturation occurring at ±13V. The
following graph shows what happens as VIN is increased from -2.0V to +2.0V
VOUT /V
15
10
Saturation
occurs @ +13V
5
-2.0
-1.5
-1.0
-0.5
0.5
1.0
1.5
VIN /V
2.0
-5
-10
Saturation
occurs @ -13V
-15
The gain of amplifier can be
determined from gradient of
V
5
 10
the line i.e. OUT 
VIN
0.5
If the amplifier was inverting then the graph would look slightly different as
shown below:
VOUT /V
15
10
Saturation
occurs @ +13V
-2.0
-1.5
5
The gain of amplifier can be
determined from gradient of
V
10
 10
the line i.e. OUT 
VIN
1
VIN /V
-1.0
-0.5
0.5
1.0
1.5
2.0
-5
-10
-15
Saturation
occurs @ -13V
3
Module ET1
Introduction to Analogue and Digital Systems.
A.C. Case.
In the a.c. case there will be a constantly changing input signal, however this
can be dealt with in exactly the same way, if the required amplitude of the
output is above the saturation value then the output will be saturated. Look
at the following example.
An amplifier has a gain of +200, and saturates at ±12V, when the following
signal is applied to the input
VIN /mV
100
-100
Required Output
Actual Clipped Output
VOUT /V
15
10
5
-5
-10
-15
The output signal has been clipped at the saturation values of ±12V, when the
required output should be at ±20V. The result is distortion of the waveform.
4
Topic 1.4.6 – Signal distortion
There are two ways in which this type of distortion can be avoided:
i.
increase the power supply voltage range to ±25V for example in
this case. {However this is only possible if the op-amp can operate
at this voltage level.}
ii.
decrease the gain of the amplifier so that the maximum signal
output is limited to ±13V.
The second type of distortion is caused by the slew rate of the amplifier.
Slew rate refers to the ability of the amplifier to respond to a rapidly
changing input voltage. This occurs with high frequency, or step inputs which
are the most difficult signals for an amplifier to deal with. The slew rate is
given for an amplifier in units of V/s i.e. volts per microsecond. This is the
maximum rate at which the output voltage can increase, and is defined by the
formula.
Slew.Rate.(S.R.) 
Vo
t
Where ∆Vo = change required in VOUT and ∆t = time taken for the change.
The following graph shows a typical response of an amplifier to a step input.
VIN
VOUT
Output voltage is ‘slewed’ on both rising
and falling pulses.
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Module ET1
Introduction to Analogue and Digital Systems.
Example : The following graph shows a step input signal applied to the input
VIN, and the corresponding output graph for VOUT.
VIN / V
1.2
0.8
0.4
0
-0.4
1
t/s
2
3
4
5
6
7
8
9
10
11
12
11
12
-0.8
-1.2
VOUT / V
14
12
10
8
6
4
ΔVOUT = 11 – (-11) = 22V
2
0
-2
1
t/s
2
3
4
5
6
7
8
9
-4
-6
-8
-10
-12
Δt = 6 - 2 = 4s
-14
Estimate the slew-rate of the amplifier.
Answer: S.R 
6
VOUT 22V

 5.5V / s
t
4 s
10
Topic 1.4.6 – Signal distortion
If the input signal was a high frequency a.c. signal then the following sort of
output signal will be observed.
VIN / V
1.2
0.8
0.4
0
-0.4
1
t/s
2
3
4
5
6
7
8
9
10
11
12
-0.8
-1.2
Actual Output – does not match
required output because the
amplifier cannot respond to the
rapid changes in input signal.
Required Output
VOUT / V
14
12
10
8
6
4
2
0
-2
1
t/s
2
3
4
5
6
7
8
9
10
11
12
-4
-6
-8
-10
-12
-14
The only way to avoid this type of distortion is to select an op-amp with a
higher slew-rate value.
Now its time to put all of your knowledge together with some examination
questions.
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Module ET1
Introduction to Analogue and Digital Systems.
Examination Style Questions:
1.
(a)
For an IDEAL operational amplifier what are the assumed values of
(i)
the input impedance, …………………………………………
(ii)
the output impedance, ………………………………………..
(iii)
the voltage gain, ………………………………………………
(iv)
the slew rate ? …………………………………………………
[4]
(b)
(i)
Draw a diagram showing how an op-amp and 2 resistors can be used to produce a
non-inverting amplifier with a fixed voltage gain of 10. Give suitable values for the
two resistors.
(ii)
How is the bandwidth of this amplifier related to its gain ?
[1]
………………………………………………………………………………………..
………………………………………………………………………………………..
(iii)
One undesirable effect which can occur in this amplifier is clipping of the output
waveform. Describe one cause of clipping.
[1]
………………………………………………………………………………………..
………………………………………………………………………………………..
8
Topic 1.4.6 – Signal distortion
(c)
The upper graph shows a signal applied to the input of a voltage amplifier. The lower
graph shows the resulting output.
Estimate the slew-rate for the op-amp, giving the appropriate unit.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
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Module ET1
Introduction to Analogue and Digital Systems.
2.
(a)
Give two of the characteristics which an ideal op-amp should have.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
[2]
(b)
The graph shows the voltage characteristics of an audio amplifier.
(i)
Calculate the voltage gain of the amplifier.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
[2]
10
Topic 1.4.6 – Signal distortion
(ii)
Design a suitable circuit for this audio amplifier based on a single op-amp.
Draw your circuit in the space below.
Calculate suitable values for any resistors used.
Add labels to identify the input and output of the amplifier.
[6]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
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Module ET1
Introduction to Analogue and Digital Systems.
3.
The following table gives some data about an op-amp, when used with a ±15V power supply.
Parameter
Open-loop gain
Saturation voltages
Gain bandwidth product
Slew-rate
Value
105
±13V
2 MHz
2 V/µs
The op-amp is used as a voltage amplifier with a gain of +100.
(a)
Calculate the bandwidth of the amplifier.
……………………………………………………………………………………
[1]
(b)
What is the biggest input voltage this amplifier can have without experiencing clipping
distortion at the output?
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
[2]
12
Topic 1.4.6 – Signal distortion
(c)
The signal shown below is applied to the input of the amplifier.
(i)
Calculate the maximum value of the output signal.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
[1]
(ii)
Calculate the time taken for the output to reach this maximum value.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
[2]
(iii)
Use the axes provided to sketch the output signal.
Both graphs have the same scale on the time axes.
[1]
13
Module ET1
Introduction to Analogue and Digital Systems.
4.
This question concerns two voltage amplifiers A and B.
(a)
The graph shows how the output voltage of amplifier A changes as the DC input voltage
increases from -3V to +3V.
(i)
What is the positive saturation voltage for this amplifier?
…………………………………………………………………………………………
[1]
(ii)
What is the voltage gain of this amplifier?
………………………………………………………………………………………....
…………………………………………………………………………………………
[2]
(b)
Amplifier B has a voltage gain of +200 and a bandwidth of 5kHz.
(i)
Sketch a graph to show the frequency response of this amplifier.
[2]
14
Topic 1.4.6 – Signal distortion
(ii)
This amplifier has a slew rate of 10V/µs, and saturates at ±12V.
Draw this amplifier output signal when the signal shown below is applied to its
input.
[3]
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Module ET1
Introduction to Analogue and Digital Systems.
5.
Here is the circuit diagram for a voltage amplifier.
The output of the amplifier saturates at +12V / -12V.
(a)
Calculate the voltage gain of the amplifier.
[2]
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
16
Topic 1.4.6 – Signal distortion
(b)
The variable amplitude signal shown below is applied to the input.
Sketch the output produced by the amplifier.
[3]
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Module ET1
Introduction to Analogue and Digital Systems.
(c)
The bandwidth of the amplifier is 60 kHz.
(i)
Use the axes provided to sketch the frequency response of the amplifier.
[2]
(ii)
The 10k resistor is now replaced by a 20k resistor.
Give the new value of:
the voltage gain ……………………………………………………………..
the bandwidth ……………………………………………………………….
the input impedance …………………………………………………………
[3]
18
Topic 1.4.6 – Signal distortion
6.
(a)
Draw the circuit diagram for a non-inverting voltage amplifier, using an op-amp.
[3]
+
0V
(b)
Calculate suitable resistor values to give the amplifier a voltage gain of 25.
[2]
………………………………………………………………………………………………..
………………………………………………………………………………………………..
………………………………………………………………………………………………..
………………………………………………………………………………………………..
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Module ET1
Introduction to Analogue and Digital Systems.
(c)
The amplifier uses a ±15V power supply.
The table gives data for the op-amp under these conditions.
Characteristic
Open-loop gain
Output saturation voltages
Input impedance
Value
1.0 x 105
±13V
1.0 x 106
The diagrams below show two input signals applied to this amplifier.
In each case, draw the corresponding output signal using the axes provided.
In the first example, the voltage scale for the output signal is provided.
In the second case, you must label the output signal with appropriate voltages.
[5]
(i)
20
Topic 1.4.6 – Signal distortion
(ii)
(d)
What factor determines the input impedance of a voltage amplifier, based on an op-amp
configured as :
(i)
a non-inverting amplifier.
[1]
…………………………………………………………………………………………
…………………………………………………………………………………………
(ii)
an inverting amplifier.
[1]
…………………………………………………………………………………………
…………………………………………………………………………………………
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Module ET1
Introduction to Analogue and Digital Systems.
7.
(a)
The graph shows how the output voltage of a non-inverting amplifier responds to a step
input voltage.
(i)
What is the saturation voltage of this amplifier ?
[1]
…………………………………………………………………………………..
(ii)
Calculate the slew rate of this amplifier.
[1]
…………………………………………………………………………………..
…………………………………………………………………………………..
(b)
This op-amp voltage amplifier is used to produce a gain of +4.8.
[3]
Use the axes provided to sketch the voltage characteristics for this amplifier.
22
Topic 1.4.6 – Signal distortion
8.
The circuit diagram shows part of a temperature control system. The output of the temperature
sensor changes by 5mV for each change of 1°C in the temperature. A non-inverting amplifier
based on an op-amp is then used to process this voltage.
The system is adjusted so that the temperature sensor output VT = 0mV at 0°C.
(a)
What will be the output voltage, VT, of the temperature sensor at 25°C?
[1]
................................................................................................................................................
(b)
(i)
What is the voltage gain of the non-inverting amplifier?
[1]
................................................................................................................................................
................................................................................................................................................
(ii)
Calculate the output voltage, VOUT, of the amplifier at 25°C.
[1]
................................................................................................................................................
(c)
What will be the maximum change in temperature that this system can measure if the
output of the operational amplifier saturates at 12V?
[3]
................................................................................................................................................
................................................................................................................................................
................................................................................................................................................
(d)
Why is it preferable to use a non-inverting amplifier rather than an inverting amplifier for
this application?
[2]
................................................................................................................................................
................................................................................................................................................
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Module ET1
Introduction to Analogue and Digital Systems.
9.
An extract from the data sheet of an op-amp is shown in the following table.
Parameter
Input Impedance
Open loop gain
Output Impedance
Gain bandwidth product
Slew rate
Value
10MΩ
105
100Ω
1.2MHz
6 Vs-1
The circuit diagram shows the op-amp set up as a voltage amplifier . The switch allows the user to
change the gain.
An input voltage of 0.8V is applied to VIN.
The op-amp is powered from a ±15V supply and saturation occurs at ±12V.
(a)
The switch is initially connected to point X.
[6]
(i)
Determine the input impedance of the amplifier.
....................................................................................................................................
(ii)
Calculate the voltage gain of the amplifier.
....................................................................................................................................
....................................................................................................................................
(iii)
Calculate the output voltage when VIN = 0.8V.
....................................................................................................................................
(iv)
Calculate the bandwidth of the amplifier.
....................................................................................................................................
....................................................................................................................................
24
Topic 1.4.6 – Signal distortion
(b)
The switch is moved to position Y. This doubles the voltage gain of the amplifier.
[3]
(i)
Calculate the value of resistor R.
....................................................................................................................................
....................................................................................................................................
(ii)
Determine the output voltage for VIN = 0.8V.
....................................................................................................................................
....................................................................................................................................
(c)
State what change, if any, has occurred to the following after the switch is moved from X
to Y.
[2]
(i)
the input impedance ............................................................................................
(ii)
(d)
the bandwidth ......................................................................................................
Calculate the time it would take for the output voltage to change from -9V to +9V in
response to a large step change in input voltage. Show your working and give the
appropriate unit.
[3]
.................................................................................................................................................
.................................................................................................................................................
.................................................................................................................................................
.................................................................................................................................................
25
Module ET1
Introduction to Analogue and Digital Systems.
10.
The table gives some data about an op-amp.
Parameter
Input Impedance
Open loop gain
Gain bandwidth product
Slew rate
Value
1.0 x 106 Ω
1.0 x 105
3 MHz
2 Vs-1
The graph below shows the characteristics of the op-amp configured as a voltage amplifier.
(a)
Use the graph to determine the voltage gain of this amplifier.
[2]
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
26
Topic 1.4.6 – Signal distortion
The amplifier is modified to give a voltage gain of -20.
(b)
(i)
Complete the circuit diagram for a voltage amplifier based on an op-amp which
will have a gain of -20.
[3]
-
VIN
+
VOUT
N
0V
(ii)
Calculate suitable resistor values to give this gain.
[2]
.................................................................................................................................................
.................................................................................................................................................
.................................................................................................................................................
(c)
State the input impedance of this amplifier.
[1]
.................................................................................................................................................
(d)
Calculate the bandwidth of the amplifier when the voltage gain is -20.
[2]
.................................................................................................................................................
.................................................................................................................................................
(e)
Calculate the time taken for the output to change from 0V to 11V in response to a large
step change in input voltage.
[2]
.................................................................................................................................................
.................................................................................................................................................
.................................................................................................................................................
27
Module ET1
Introduction to Analogue and Digital Systems.
11.
When designing op-amp circuits, careful consideration needs to be given to their different
parameters. The following table is an extract from the data sheet of a typical op-amp.
Supply Voltage /V
Input Impedance / Ω
Open loop gain
Max. output current /mA
Gain bandwidth product / MHz
Slew rate / Vs-1
Saturation voltage / V
(a)
±15
4 x 106
1 x 105
20
6
1.3
±13
Calculate the time for the output to change from +13V to -13V for a large step change in
input voltage.
[2]
……………………………………………………………………………………………..
……………………………………………………………………………………………..
(b)
Resistors are added to produce a non-inverting amplifier of gain 50.
(i)
What is the maximum input voltage that can be applied, for which the output
remains unsaturated?
[2]
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
(ii)
What is the bandwidth of this amplifer.
[2]
……………………………………………………………………………………………..
……………………………………………………………………………………………..
(iii)
If the input voltage is increased to more than that in (b) (i) distortion occurs. What
name is given to this effect?
[1]
……………………………………………………………………………………………..
28
Topic 1.4.6 – Signal distortion
12.
An audio pre-amplifier is shown below.
The amplifer has a voltage gain of 250.
The op-amp is powered from a ±15V supply and saturation occurs at ±12V.
(a)
A test signal of amplitude 8mV is applied to the amplifier input.
(i)
Calculate the amplitude of the output voltage.
[1]
.................................................................................................................................................
.................................................................................................................................................
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Module ET1
Introduction to Analogue and Digital Systems.
(ii)
The test signal is shown on the following graph.
Draw the graph of the amplifier output on the axes below.
Mark on the graph any significant voltage.
[2]
30
Topic 1.4.6 – Signal distortion
(b)
The amplitude of the test signal is increased to 80mV. Use the axes provided to sketch the
resulting output signal. [The time axis has the same scale.]
[2]
(c)
The amplifier (voltage gain 250) has a bandwidth of 25 kHz. Use the axes provided to
sketch the frequency response of this amplifier.
[2]
31
Module ET1
Introduction to Analogue and Digital Systems.
Self Evaluation Review
My personal review of these objectives:
Learning Objectives



understand the power supply
requirements for an op-amp limit the
output voltage swing;
recognise clipping distortion, and
describe how it can be reduced;
recognise the distortion that occurs
when the slew rate of an op-amp is
exceeded;
select and use the formula: SR 
Targets:
1.
Vo
.
t
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
2.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
32