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

non-inverting input

+

-+ VS

- VS

Vo

V1

V2

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.

i

ogain V

VV

0 100 k1 10

100 1k

10k 1M

voltage gain

frequency / Hz

100,000

An op-amp typically has a gain of about 100,000.

Such a high gain is limited to a narrow range of frequencies.

Ideal Op-Amp

An ideal op-amp has:

• infinite input resistance

• zero current

• no potential difference between inputs (both the same)

All applications we study have a feedback resistor.

+

-R1

Vo

V1

V2

Rf

1

fgain R

R-V

Gain of the amplifier with feedback depends only on the size of input resistor and feedback resistor.

Negative Feedback

0 100 k1 10

100 1k

10k 1M

voltage gain

frequency / Hz

100,000

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.

Inverting Mode

Circuit

+

-R1

Vo

V1

Rf

0 V

The positive input (non-inverting input) voltage is connected to 0V when in the inverting mode.

Gain Formula

1

f

1

o

R

R-

VV

Output

Inverting Mode

Non-Inverting

Mode

Input Signal

Output Signal

The negative sign means that input signal is inverted

mV 400V1

kΩ 50Rf Ω 1050 3

kΩ 2R1 Ω 102 3

?Vo

1

f

1

o

R

R-

VV

3

3

3-o

1021050-

10400V

-3o 1040025V

V 10Vo

Example

Calculate the output voltage in the circuit shown.

+-

Vo

400 mV

50 kΩ

0 V

2 kΩ

Experiment

+-

10 kΩ

1 kΩ +12V

-12V VoV1

The size of V1 is altered by varying resistor RV.

V1 and Vo are recorded for various values of RV.

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

V1 / volts

Vo / volts12

-12

1.2

-1.2

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.

+-

Vo

1 V

100 kΩ

0 V

10 kΩ +15 V

-15 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) Inverting Mode.

(b) V 1V1

kΩ 100Rf

kΩ 10R1

?Vo

1

f

1

o

R

R-

VV

10100-

1Vo

V 10Vo

(c) V 2V1

kΩ 100Rf

kΩ 10R1

?Vo

1

f

1

o

R

R-

VV

10100-

2Vo

V 12.8Vo

210Vo V 20Vo

greater than VS: op-amp saturated (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

+

-R1

Vo

V1

Rf

0 V

R2

R3

V2

Resistor R3 is usually chosen so

that:

1

f

2

3

R

R

RR

Formula

The difference between the 2-inputs is amplified.

Voltage gain in differential mode is

The output voltage is calculated by:

1

fgain R

RV

1

f12o R

R VVV

Example

Calculate the output voltage Vo for the circuit shown.

+

-2 kΩ

Vo

40 mV

50 kΩ

0 V

25 mV

mV 40V1 V 10 40 -3

mV 25V2 V 10 25 -3

kΩ 50Rf

kΩ 2R1

250

1040 1025V 3-3-o

250.015

V 0.375Vo

Questions

1. Calculate Vo for the circuits shown.

15 mV

+-

2 kΩ

Vo

40 mV

30 kΩ

80 mV

+-

2 kΩ

Vo

35 mV

50 kΩ

(a) (b)

2. Calculate V for the circuits shown.

V+-

5 kΩ

0.4 V

30 mV

45 kΩ

80 mV+-

2 kΩ

0.6 V

V

60 kΩ

(a) (b)

-0.375 V +1.125 V

+0.074 V

+0.06 V

Purple Book

Page 60

Q1, Q2 (a), Q4 and Q6

Op-Amp and Wheatstone Bridge

+

-5 kΩ

Vo

20 kΩ

0 V

4 kΩ

2 kΩ

3 kΩ

3 kΩ

+12 V

+12 V

-12 V

Calculate the output voltage Vo.

Step 1

Calculate the size of V1.

0 V

2 kΩ

4 kΩ

+12 V

V1

S21

11 V

RRR

V

1242

2

V 4V1

Step 2

Calculate the size of V2.

0 V

3 kΩ

3 kΩ

+12 V

V2

S21

22 V

RRR

V

1233

3

V 6V2

Step 3

Calculate V0. 1

f12o R

RVVV

5

2046

42

V 8Vo

Question

An op-amp with a gain of 40 is connected to a Wheatstone bridge circuit as shown.

(a) What mode is the op-amp connected in the circuit?

(b) Calculate Vo when the resistance of the LDR is 4000 Ω.

(c) The resistance of the LDR is changed to 3000 Ω.

State what happens to the output voltage after this change.

differential

12 v

- TO +

+

-

Vo

0 V

12 kΩ

18 kΩ 5400 Ω

+12 V

+12 V

-12 V

+

-20 kΩ

Vo

100 kΩ

0 V

75 kΩ

75 kΩ 2900 Ω

+12 V

+12 V

-12 V

Question

An op-amp connected to a Wheatstone bridge circuit is shown.

3000 Ω

Calculate the output voltage of the op-amp.

Transistor Output

TURD – temperature up, resistance of thermistor goes down.

Voltage across thermistor goes down.

V1 goes down.

V1

0 V

+VS

V2 +-

230 V

motor for

cooling fan

M

Vo

Consider the equation . 1

f12o R

RVVV

When V1 goes down, Vo goes up.

Transistor switches ON.

Relay switches ON.

Cooling motor switches ON.

Purple Book

Page 62 - Q1, Q2

Page 63 – Q1