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Topic 1.4.2 – Inverting amplifier
Learning Objectives:
At the end of this topic you will be able to;
 draw and recognise the inverting amplifier circuit;
 design an inverting amplifier using resistive negative feedback to
achieve specified voltage gain;
 select and use the formulae
G
Vout
R
 f .
Vin
R in
 use the approximation that the input impedance is equal to the
resistance of the input resistor.
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Module ET1
Introduction to Analogue and Digital Systems.
Inverting Amplifier.
The first amplifier that we will look at is the inverting amplifier. The circuit
diagram for this type of amplifier is shown below:
Rf
+V
Rin
Note : The power supply
connections are often left off
the diagram of the amplifier to
make the circuit easier to follow.
Vin
+
-V
Vout
0V
The voltage gain of this amplifier is given by the following formulae.
Voltage Gain 
Vout
R
 f
Vin
R in
Important things to remember for this amplifier are as follows:
i.
Voltage gain can be determined either if Vout and Vin are known or if
Rf and Rin are known.
ii.
The ‘-‘ sign in the formula indicates the inverting action of this
amplifier, so for a positive input voltage, the output will be negative,
and vice versa.
iii. The input impedance of this amplifier is equal to the value of Rin.
iv.
If you are designing an amplifier of this type then all resistors
chosen must be greater than 1kΩ.
We will now look at an example:
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Topic 1.4.2 – Inverting amplifier
Example 1: An inverting amplifier is required to act as a preamplifier for a
public address system. The amplifier requires a gain of -20 and
should have an input impedance of 10kΩ.
(a)
Draw the circuit diagram for an inverting amplifier.
Rf
Rin
+
Vin
Vout
0V
(b)
Determine suitable resistors for Rin and Rf.
In the question we are told that the input impedance must be
10kΩ. This means that Rin must be equal to 10kΩ. We are also told
that the gain needs to be -20, so we now apply the gain formula as
shown below;
Gain  
Rf
R in
Rf
10
 R f  20  10
 20  
R f  200k
3
Module ET1
Introduction to Analogue and Digital Systems.
Example 2. The following circuit shows an inverting amplifier connected to a
±10V power supply.
120kΩ
2kΩ
+
Vin
Vout
0V
(a)
(b)
What is the voltage gain of this amplifier ?
Gain  
Rf
R in
Gain  
120
 60
2
If Vin = 100mV, determine the value of Vout.
Gain 
Vout
Vin
Vout
100
 60  100  6000mV  6V
 60 
Vout
(c)
What is the input impedance of this amplifier ?
Input impedance = Rin = 2kΩ
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Topic 1.4.2 – Inverting amplifier
(d)
The graph below shows an alternating signal applied to Vin. On the
axes below sketch the graph of Vout.
Vin/mV
100
75
50
25
0
-25
-50
-75
-100
Vout/V
Peak output voltage = peak input voltage x gain
8
6
4
2
0
-2
-4
-6
-8
Output graph inverted - i.e.
negative becomes positive etc.
Frequency remains the same
Here are a couple of examples for you to do !
5
Module ET1
Introduction to Analogue and Digital Systems.
Exercise 1:
1.
The following circuit shows an inverting amplifier connected to a ±12V
power supply.
390kΩ
13kΩ
Vin
+
Vout
0V
(a)
What is the voltage gain of this amplifier ?
.......................................................................................................................................
.......................................................................................................................................
(b)
If Vin = 300mV, determine the value of Vout.
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
(c)
What is the input impedance of this amplifier ?
Input impedance = ...........................................
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Topic 1.4.2 – Inverting amplifier
(d)
The graph below shows an alternating signal applied to Vin. On the
axes below sketch the graph of Vout. Label the graph of Vout with
suitable values.
Vin/mV
300
225
150
75
0
-75
-150
-225
-300
Vout/V
0
7
Module ET1
Introduction to Analogue and Digital Systems.
2.
An inverting amplifier is required to act as a preamplifier for an electric
guitar pickup. The amplifier requires a gain of -400 and should have an
input impedance of 2kΩ.
(a)
Draw the circuit diagram for an inverting amplifier.
(b)
Determine suitable resistors for Rin and Rf.
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
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Topic 1.4.2 – Inverting amplifier
Solutions to Student Exercises.
Exercise 1:
1.
(a)
Gain  
Rf
R in
Gain  
390
 30
13
(b)
Gain 
Vout
Vin
Vout
300
 30  300  9000mV  9V
 30 
Vout
(c)
Input impedance = Rin = 13kΩ
(d)
Vout/V
12
9
6
3
0
-3
-6
-9
-12
9
Module ET1
Introduction to Analogue and Digital Systems.
2.
(a)
Rf
Rin
+
Vin
Vout
0V
(b)
Rin = 2kΩ, (since input impedance should be 2kΩ.)
Gain  
Rf
R in
Rf
2
 R f  400  2
 400  
R f  800k
No examination questions have been included with this section, as these will
be included in Topic 1.4.5 – Practical voltage amplifiers.
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Topic 1.4.2 – Inverting amplifier
Self Evaluation Review
Learning Objectives
My personal review of these objectives:



draw and recognise the inverting
amplifier circuit;
design an inverting amplifier using
resistive negative feedback to
achieve specified voltage gain;
select and use the formulae
G
Vout
R
 f
Vin
R in
use the approximation that the input
impedance is equal to the resistance
of the input resistor.
Targets:
1.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
2.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
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