Higher Physics – Unit 2
2.4 Analogue Electronics
Op-Amp
An op-amp has two inputs and one output.
The symbol for an op-amp is:
inverting input
V1
V2
non-inverting input
+ VS
Vo
+
- VS
The supply voltage may or may not be included in circuit diagrams.
An op-amp is used to increase the voltage of a
signal.
The frequency of the signal remains
unchanged.
Vgain
An op-amp typically has a gain of about 100,000.
Such a high gain is limited to a narrow range of frequencies.
100,000
voltage gain
0
1
10
100
1k
10k 100 k 1M
frequency /
Hz
Vo

Vi
Ideal Op-Amp
An ideal op-amp has:
• infinite input resistance
• zero current
• no potential difference between inputs (both the same)
Negative Feedback
All applications we study have a feedback resistor.
Rf
- Rf
Vgain 
R1
R1
V1
V2
+
Gain of the amplifier with feedback depends only on the size of
input resistor and feedback resistor.
Vo
An op-amp used with negative feedback, returns some of the
output signal to the inverting input.
This reduces the size of voltage gain, but it remains constant over
a larger range of frequencies.
100,000
voltage gain
0
1
10
100
1k
10k 100 k 1M
frequency /
Hz
Inverting Mode
The positive input (non-inverting input) voltage is connected to 0V
when in the inverting mode.
Circuit
Rf
R1
+
V1
0 V
Vo
Gain Formula
Vo - Rf

V1
R1
The negative sign means that
input signal is inverted
Output
Inverting
Mode
Input Signal
Output Signal
Non-Inverting
Mode
Example
Calculate the output voltage in the circuit shown.
50 kΩ
2 kΩ
400 mV
+
Vo
0 V
V1  400 mV
Rf  50 kΩ
 50  10 3 Ω
R1  2 kΩ
 2  103 Ω
Vo  ?
Vo - Rf

V1
R1
Vo
- 50  103

-3
400  10
2  103

Vo  25  400  10 -3
Vo  10 V

Experiment
10 kΩ
1 kΩ
RV
V1
+
+12V
-12V
Vo
The size of V1 is altered by varying resistor RV.
V1 and Vo are recorded for various values of RV.
Results
V1 (volts)
Vo (volts)
0
0
0.2
-2
0.4
-4
0.6
-6
0.8
-8
1.0
-10
1.2
-12
1.4
-12
1.6
-12
Graph
12
Vo / volts
-1.2
1.2
V1 / volts
-12
Conclusion
Saturation occurs at +12 V and -12 V.
Saturation is where the output voltage reaches the supply voltage VS.
Vo cannot exceed VS.
Saturation
An op-amp cannot produce an output voltage greater than the
supply voltage.
When Vo reaches VS, the op-amp is said to be saturated.
*** It is NOT the voltage that is saturated. ***
In practice, the op-amp becomes saturated at about 85% of the
supply voltage.
Input Signal
Output Signal
+ VS
- VS
This type of output signal
causes distortion of an
audio signal.
It does however produce a
square wave from a sine
wave.
Square Waves
Example 1
An op-amp is connected as shown.
100 kΩ
10 kΩ
1 V
+
+15 V
-15 V
Vo
0 V
(a)
In what mode is the op-amp being used in this circuit?
(b)
Calculate the output voltage Vo.
(c)
The input voltage is increased to 2 V. Calculate the new output
voltage Vo.
(a)
(b)
Inverting Mode.
V1  1 V
Rf  100 kΩ
R1  10 kΩ
Vo  ?
(c)
V1  2 V
Rf  100 kΩ
R1  10 kΩ
Vo  ?
Vo - Rf

V1
R1
Vo - 100

1
10
Vo  10 V
Vo - Rf

V1
R1
Vo - 100

2
10
Vo  10  2
Vo  20 V
greater than VS: op-amp saturated
Vo  12.8 V
(85% of VS)
Purple Book
Page 57
Q1, Q2 (a) + (c), Q5 (b) + (d)
Page 58
Q1, Q2 (a) + (c), Q3 (b) + (d), Q4
Differential Mode
When the op-amp is in differential mode, both inputs are used.
Circuit
Rf
R1
R3 Rf

R2 R1
-
R2
V1
Resistor R3 is usually
chosen so that:
+
V2
R3
0 V
Vo
Formula
The difference between the 2-inputs is amplified.
Voltage gain in differential mode is
Vgain 
The output voltage is calculated by:
Rf
Vo  V2  V1 
R1
Rf
R1
Example
Calculate the output voltage Vo for the circuit shown.
50 kΩ
2 kΩ
+
40 mV
Vo
25 mV
V1  40 mV
 40  10 -3 V
V2  25 mV
 25  10 -3 V
Rf  50 kΩ
R1  2 kΩ
0 V


Vo  25  10 -3  40  10 -3 
 0.01525
Vo  0.375 V
50
2
Questions
1. Calculate Vo for the circuits shown.
(a)
(b)
30 kΩ
2 kΩ
40 mV
15 mV
+
50 kΩ
2 kΩ
35 mV
Vo
80 mV
+
-0.375 V
Vo
+1.125 V
2. Calculate V for the circuits shown.
(a)
(b)
45 kΩ
5 kΩ
30 mV
V
+
60 kΩ
2 kΩ
V
0.4 V
+0.074 V
80 mV
+
0.6 V
+0.06 V
Purple Book
Page 60
Q1, Q2 (a), Q4 and Q6
Op-Amp and Wheatstone Bridge
20 kΩ
+12 V
4 kΩ
3 kΩ
5 kΩ
+
2 kΩ
3 kΩ
0 V
Calculate the output voltage Vo.
+12 V
-12 V
Vo
Step 1
Calculate the size of V1.
V1 
+12 V
4 kΩ

2 kΩ
V1
R1
 VS
R1  R2 
2
 12
2  4 
V1  4 V
0 V
Step 2
Calculate the size of V2.
V2 
+12 V
3 kΩ
3 kΩ
0 V

V2
R2
 VS
R1  R2 
3
 12
3  3
V2  6 V
Step 3
Calculate V0.
Vo  V2  V1 
 6  4 
 2 4
Vo  8 V
Rf
R1
20
5
Question
An op-amp with a gain of 40 is connected to a Wheatstone bridge
circuit as shown.
+12 V
12 kΩ
18 kΩ
5400 Ω
+
+12 V
-12 V
Vo
0 V
(a) What mode is the op-amp connected in the circuit?
differential
(b) Calculate Vo when the resistance of the LDR is 4000 Ω.
(c) The resistance of the LDR is changed to 3000 Ω.
12 v
- TO +
State what happens to the output voltage after this change.
Question
An op-amp connected to a Wheatstone bridge circuit is shown.
100 kΩ
+12 V
75 kΩ
75 kΩ
3000 Ω
20 kΩ
2900 Ω
0 V
Calculate the output voltage of the op-amp.
-
+
+12 V
-12 V
Vo
Transistor Output
+VS
V1
V2
+
0 V
230
V
M
Vo
motor for
cooling
fan
TURD – temperature up, resistance of thermistor goes down.
Voltage across thermistor goes down.
 V1 goes down.
Consider the equation Vo  V2  V1 
When V1 goes down, Vo goes up.
Transistor switches ON.
Relay switches ON.
Cooling motor switches ON.
Rf
.
R1
Purple Book
Page 62 - Q1, Q2
Page 63 – Q1