Electronic Circuits Operational amplifiers

Prof. Dr. Nizamettin AYDIN • Introduction

naydin@yildiz.edu.tr • An ideal operational amplifier
• Basic operational amplifier circuits
http://www.yildiz.edu.tr/~naydin
• Other useful circuits
• Real operational amplifiers
• Selecting component values
• Effects of feedback on op-amp circuits

1 2

Introduction… …Introduction

• Operational amplifiers • A single package will often contain several op-amps

(op-amps) are among the
most widely used
building blocks in
electronics
– they are integrated
circuits (ICs)
• often DIL or SMT

3 4

Inside the Op-Amp (IC-chip) Ideal Op-Amp

• Most bioelectric signals are small and require amplifications
Op-amp equivalent circuit:

20 transistors
11 resistors The two inputs are υ1 and υ 2. A differential voltage between them causes
current flow through the differential resistance Rd. The differential voltage
1 capacitor is multiplied by A, the gain of the op amp, to generate the output-voltage
source. Any current flowing to the output terminal vo must pass through the
output resistance Ro.
5 6

1
 Ideal Characteristics Two Basic Rules

• A = ∞ (gain is infinity)
• Vo = 0, when v1 = v2 (no offset voltage) • Rule 1
• Rd = ∞ (input impedance is infinity) – When the op-amp output is in its linear range, the two input terminals
are at the same voltage.
• Ro = 0 (output impedance is zero)
• Rule 2
• Bandwidth = ∞ (no frequency response limitations) and no
– No current flows into or out of either input terminal of the op amp.
phase shift
7 8

Basic operational amplifier circuits… …Basic operational amplifier circuits…

• Inverting and non-inverting amplifiers • When looking at feedback we derived the circuit of an
amplifier from ‘first principles’
• Normally we use standard ‘cookbook’ circuits and select
component values to suit our needs
• In analysing these we normally assume the use of ideal op-
amps
– in demanding applications we may need to investigate the
appropriateness of this assumption
– the use of ideal components makes the analysis of these
circuits very straightforward

9 10

…Basic operational amplifier circuits… …Basic operational amplifier circuits…

• A non-inverting amplifier • Example

Analysis Design a non-inverting amplifier with a gain of 25
Since the gain is assumed infinite, if Vo is finite
Vo R1 + R 2
then the input voltage must be zero. Hence From above G= =
Vi R2
V− = V+ = Vi

Since the input resistance of the op-amp is ∞ If G = 25 then

R1 + R 2
R2 = 25
V− = Vo R2
R1 + R2
R1 + R 2 = 25 R 2
and hence, since V– = V+ = Vi R1 = 24 R 2
R2 Vo R1 + R 2
Vi = Vo and G= =
R1 + R 2 Vi R2 Therefore choose R2 = 1 kΩ and R1 = 24 kΩ
(choice of values will be discussed later)

11 12

2
 …Basic operational amplifier circuits… …Basic operational amplifier circuits…

• An inverting amplifier ...Analysis

Analysis... Therefore, since I1 = -I2
Vo V
Since the gain is assumed infinite, if Vo is =− i
R1 R2
finite the input voltage must be zero. Hence
V− = V+ = 0 or, rearranging
Vo R
G= =− 1
Vi R2
Since the input resistance of the op-amp is ∞
its input current must be zero, and hence • Here V– is held at zero volts by the operation of the circuit, hence
I1 = −I 2 the circuit is known as a virtual earth circuit
Vo − V− Vo − 0 Vo Vi − V− Vi − 0 Vi
Now I1 = = = I2 = = =
R1 R1 R1 R2 R2 R2

13 14

…Basic operational amplifier circuits Other useful circuits…

• Example • In addition to simple amplifiers, op-amps can also be used

Design an inverting amplifier with a gain of –25 in a range of other circuit
• The next few slides show a few examples of op-amp
From above Vo R circuits for a range of purposes
G= =− 1
Vi R2
• The analysis of these circuits is similar to that of the non-
R1 inverting and inverting amplifiers but (in most cases) this
If G = –25 then − = −25
R2
is not included here
R1 = 25 R 2

Therefore choose R2 = 1 kΩ and R1 = 25 kΩ • For more details of these circuits see the relevant section
(we will consider the choice of values later) of the course text (as shown on the slides)

15 16

…Other useful circuits… …Other useful circuits…

• A unity gain buffer amplifier

Analysis • A current to voltage converter
This is a special case of the non-inverting
amplifier with R1 = 0 and R2 = ∞
Hence
R1 + R 2 R1 0
G= = +1= +1=1
R2 R2 ∞

Vo = −I i R
Thus the circuit has a gain of unity

• At first sight this might not seem like a very useful circuit,
however, it has a high input resistance and a low output
resistance and is therefore useful as a buffer amplifier

17 18

3
 …Other useful circuits… …Other useful circuits…

• A differential amplifier (or subtractor) • An inverting summing amplifier

R1 R1
Vo = (V1 − V2 ) Vo = −(V1 + V2 )
R2 R2

19 20

…Other useful circuits… …Other useful circuits

• An integrator • A differentiator

1 t d Vi
Vo = −
RC 0∫Vi d t Vo = − RC
dt

21 22

Display Driver Differential Amplifiers

• Differential Gain Gd v3
vo R
Gd = = 4
v4 − v3 R3 v4

• Common Mode Gain Gc

– For ideal op amp if the inputs are equal
then the output = 0, and the Gc = 0. R4
– No differential amplifier perfectly rejects vo = (v4 − v3 )
the common-mode voltage. R3
• Common-mode rejection ratio CMMR
Gd
– Typical values range from 100 to 10,000 CMRR =
Gc

• Disadvantage of one-op-amp differential amplifier is its low

input resistance
23 24

4
 Instrumentation Amplifiers Active Filters
Adding capacitors to op-amp circuits provides external control of the
cutoff frequencies. The op-amp active filter provides controllable cutoff
frequencies and controllable gain.

• Low-pass filter
• High-pass filter
Differential Mode Gain • Bandpass filter
v3 − v4 = i ( R2 + R1 + R2 ) • Bandstop filter

v1 − v2 = iR1
v3 − v4 2 R2 + R1 The filter transfer function T(s) ≡ Vo(s)/Vi(s).
Gd = =
v1 − v2 R1
Advantages: High input impedance, High CMRR, Variable gain

25 26

Ideal transmission characteristics Specification of the transmission

characteristics of a low-pass filter

27 28

Specification of the transmission Low-Pass Filter—First-Order

characteristics of a bandpass filter

The upper cutoff frequency

and voltage gain are given by:
1 Rf
f OH = Av = 1+
2 πR 1 C 1 R1

29 30

5
 Low-Pass Filter—Second-Order High-Pass Filter

The cutoff frequency is determined by:

The roll-off can be made steeper by adding more RC networks. 1
f OL =
2 π R 1C 1

31 32

Bandpass Filter Multiple-Stage Gains…

There are two cutoff

frequencies: upper and
The total gain (3-stages) is given by:
lower. They can be
calculated using the same
low-pass cutoff and high- A = A1A 2 A 3
pass cutoff frequency
or
formulas in the appropriate
sections.  R  R  R 
A =  1 + f  − f  − f 
 R 1  R2  R3 

33 34

…Multiple-Stage Gains Real operational amplifiers…

• So far we have assumed the use of ideal op-amps

– these have Av = ∞, Ri = ∞ and Ro = 0
• Real components do not have these ideal characteristics
(though in many cases they approximate to them)
• In this section we will look at the characteristics of typical
V R + R2 V R A3 =
Vo R
=− 1 devices
A1 = o = 1 A2 = o = − 1 Vi R2
Vi R2 Vi R2
– perhaps the most widely used general purpose op-amp is
the 741
R1 + R2  R1   R1  R13 + R12 × R2
A = A1 × A1 × A1 = ×  −  ×  −  =
R2  R2   R2  R23

35 36

6
 …Real operational amplifiers… …Real operational amplifiers…

• Voltage gain • Input resistance

– typical gain of an operational amplifier might be – typical input resistance of a 741 is 2 MΩ
100 – 140 dB (voltage gain of 105 – 106) – very variable, for a 741 it can be as low as 300 kΩ
– 741 has a typical gain of 106 dB (2 × 105)
– high gain devices might have a gain of 160 dB (108) – the above value is typical for devices based on
– while not infinite, the gain of most op-amps is bipolar transistors
‘high-enough’ – op-amps based on field-effect transistors generally have a
– however, gain varies between devices and with temperature much higher input resistance – perhaps 1012 Ω

– we will discuss bipolar and field-effect transistors later

37 38

…Real operational amplifiers… …Real operational amplifiers…

• Output resistance • Supply voltage range

– typical output resistance of a 741 is 75 Ω – a typical arrangement would use supply voltages of +15 V
– again very variable and – 15 V, but a wide range of supply voltages is usually
possible
– often of more importance, is the maximum output current – the 741 can use voltages in the range ±5 to ±18 V
– the 741 will supply 20 mA – some devices allow voltages up to ±30 V or more
– others, designed for low voltages, may use ±1.5 V
– high-power devices may supply 1 amper or more
– many op-amps permit single voltage supply operation,
typically in the range 4 to 30 V

39 40

…Real operational amplifiers… …Real operational amplifiers

• Common-mode rejection ratio • Frequency response

– an ideal op-amp would not respond to common-mode – typical 741 frequency
signals. response is shown here
– real amplifiers do respond to some extent – upper cut-off frequency is a
few hertz
– the common-mode rejection ratio (CMRR) is the ratio of
– frequency range generally
the response produced by a differential-mode signal to that described by the
produced by a common-mode signal unity-gain bandwidth
– typical values for CMRR might be in the range 80 to 120 – high-speed devices may
dB operate up to several
• 741 has a CMRR of about 90 dB gigahertz

41 42

7
 Selecting component values Effects of feedback on op-amp circuits…

• Our analysis assumed the use of an ideal op-amp • Effects of feedback on the Gain
• When using real components we need to ensure that our – negative feedback reduces gain from A to A/(1 + AB)
assumptions are valid – in return for this loss of gain we get consistency, provided
• In general this will be true if we: that the open-loop gain is much greater than the closed-loop
– limit the gain of our circuit to much less than the gain (that is, A >> 1/B)
open-loop gain of our op-amp – using negative feedback, standard cookbook circuits can be
– choose external resistors that are small compared with the used – greatly simplifying the design
input resistance of the op-amp – these can be analysed without a detailed knowledge of the
– choose external resistors that are large compared with the op-amp itself
output resistance of the op-amp.
• Generally we use resistors in the range 1 to 100 kΩ
43 44

…Effects of feedback on op-amp circuits… …Effects of feedback on op-amp circuits…

• Effects of feedback on frequency response

• Effects of feedback on input and output resistance
– as the gain is reduced the
bandwidth is increased – input/output resistance can be increased or decreased
– gain × bandwidth ≈ constant depending on how feedback is used.
• since gain is reduced by (1 + AB) • we looked at this in an earlier lecture
bandwidth is increased by (1 + AB) • in each case the resistance is changed by a factor of (1 + AB)
Example
– for a 741, – if an op-amp with a gain of 2 × 105 is used to produce an amplifier with a
gain × bandwidth ≈ 106 gain of 100 then:
• if gain = 1000 BW ≈ 1000 Hz A = 2 × 105
• if gain = 100 BW ≈ 10,000 Hz B = 1/G = 0.01
(1 + AB) = (1 + 2000) ≈ 2000

45 46

…Effects of feedback on op-amp circuits… …Effects of feedback on op-amp circuits

• Example • Example
– determine the input and output resistance of the following – determine the input and output resistance of the following
circuit assuming op-amp is a 741 circuit assuming op-amp is a 741
Open-loop gain (A) of a 741 is 2 × 105 Open-loop gain (A) of a 741 is 2 × 105
Closed-loop gain (1/B) is 20, B = 1/20 = 0.05 Closed-loop gain (1/B) is 20, B = 1/20 = 0.05
(1 + AB) = (1 + 2 × 105 × 0.05) = 104 (1 + AB) = (1 + 2 × 105 × 0.05) = 104
Feedback senses output voltage therefore it Feedback senses output voltage therefore, it
reduces output resistance of op-amp (75 Ω) by reduces output resistance of op-amp (75 Ω) by
104 to give 7.5 mΩ 104 to give 7.5 mΩ
Feedback subtracts a voltage from the input, Feedback subtracts a current from the input,
therefore it increases the input resistance of therefore it decreases the input resistance. In
the op-amp (2 MΩ) by 104 to give 20 GΩ this case the input sees R2 to a virtual earth,
therefore the input resistance is 1 kΩ
47 48

8
 Key points

• Operational amplifiers are among the most widely used building

blocks in electronic circuits
• An ideal operational amplifier would have infinite voltage gain,
infinite input resistance and zero output resistance
• Designers often make use of cookbook circuits
• Real op-amps have several non-ideal characteristics However, if we
choose components appropriately this
should not affect the operation of our circuits
• Feedback allows us to increase bandwidth by trading gain against
bandwidth
• Feedback also allows us to alter other circuit characteristics

49