Lecture 2

Op-Amp Building Blocks and Applications

• Instrumentation Amplifiers

• Filters

• Integrators

• Differentiators

• Frequency-Gain Relation

• Non-Linear Op-Amp Applications

• DC Imperfections

1 ELG4139

Check List for Selecting Op-Amps

• Power Supply

• Gain Bandwidth

• Cost

• Voltage Offset

• Stability

• Output Current

• Noise

• Special Functions

2 ELG4139

Types of Op-Amps

• Precision Amplifiers:

– Low noise

– Low Offset Voltage

– Low Input Bias Current.

• Low Power/Low Bandwidth

• Video Amplifiers

• Audio Amplifiers

• High Voltage/High Current

• Differential/Instrumentation Amplifiers

3 ELG4139

Instrumentation Amplifier (IA) Applications

• Used in Environments with High Noise.

• Offers high Input Impedance.

• Low Bias Currents.

• Gain Determined by One Resistor.

• Commercial IA is based on Standard 3-OP Amps.

• Requires Several Matched Resistors.

4 ELG4139

Instrumentation Amplifier

Combines 2 non-inverting amplifiers

with the difference amplifier to

provide higher gain and higher input

resistance.

)b

va(v

3

4v R

R

o

bv

2i)

1i(2

2iav RRR

12

2v

1v

iR

)2

v1

(v

1

21

3

4v

R

R

R

R

o

Ideal input resistance is infinite

because input current to both op

amps is zero. The CMRR is

determined only by Op-Amp 3.

NOTE

ELG4139 5

6

Figure

8.14,

8.15

Instrumentation Amplifier Input (a) output (b)

Stages of IA

1

2

21

21

R

R

R

R

vv

vA Fout

V

ELG4139

Instrumentation Amplifier: Example

• Problem: Determine Vo

• Given Data: R1 = 15 kW, R2 = 150 kW, R3 = 15 kW, R4 = 30 kW V1 = 2.5 V,

V2 = 2.25 V

• Assumptions: Ideal op amp. Hence, v-= v+ and i-= i+= 0.

• Analysis: Using dc values,

Adm

R

4R

3

1R

2R1

30kW

15kW1

150kW

15kW

22

Vo Adm

(V1

V2

)22(2.52.25)5.50V

ELG4139 7

8

Figure

8.20

Op-amp Circuits Employing Complex Impedances

S

F

S

out

S

F

S

out

Z

Zj

V

V

Z

Zj

V

V

1)(

)(

ELG4139

9

Figure 8.21,

8.23

Active Low-Pass Filter

Normalized Response of Active Low-Pass Filter

ELG4139

The Active Low-Pass Filter

Use a phasor approach to gain analysis of

this inverting amplifier. Let s = j.

Av ˜ v o

( j)

˜ v ( j)

Z2

( j )

Z1( j )

Z1

j R1

Z2( j)

R2

1

jC

R2

1

jC

R

2jCR

21

Av R

2R1

1

(1 jCR2

)

R2

R1

ej

(1j

c

)

c 2fc 1R

2C

fc 12R

2C

fc is called the high frequency “cutoff” of

the low-pass filter. ELG4139 10

Active Low-Pass Filter

• At frequencies below fc (fH in the figure), the amplifier is an inverting amplifier with gain set by the ratio of resistors R2 and R1.

• At frequencies above fc, the amplifier response “rolls off” at -20dB/decade.

• Notice that cutoff frequency and gain can be independently set.

Av R

2R1

ej

(1j

c

)

R

2

R1

12

c

2

ej

ejtan1( /

c)

R

2

R1

1

c

2e

j[ tan1( /c

)]

magnitude phase

ELG4139 11

Active Low-Pass Filter: Example

• Problem: Design an active low-pass filter

• Given Data: Av= 40 dB, Rin= 5 kW, fH = 2 kHz

• Assumptions: Ideal op amp, specified gain represents the desired low-frequency gain.

• Analysis:

Input resistance is controlled by R1 and voltage gain is set by R2 / R1.

The cutoff frequency is then set by C.

The closest standard capacitor value of 160 pF lowers cutoff frequency to 1.99 kHz.

100dB20/dB4010 vA

W k51 in

RR

Av

R

2R1

R2

100R1

500kW

C 12f

HR

2

12(2kHz)(500kW)

159pF

and

ELG4139 12

13

Figure

8.24,

8.25

Active High-Pass Filter

Normalized Response of Active High-Pass Filter

ELG4139

14

Figure

8.26,

8.27

Active Band-Pass Filter

Normalized Amplitude Response of Active Band-Pass Filter

ELG4139

Cascaded Amplifiers

• Connecting several amplifiers in cascade (output of one stage connected to the input of the next) can meet design specifications not met by a single amplifier.

• Each amplifer stage is built using an op amp with parameters A, Rid, Ro, called open loop parameters, that describe the op amp with no external elements.

• Av, Rin, Rout are closed loop parameters that can be used to describe each closed-loop op amp stage with its feedback network, as well as the overall composite (cascaded) amplifier.

ELG4139 15

Two-Port Model for a 3-Stage Cascade Amplifier

• Each amplifier in the 3-stage cascaded amplifier is replaced by its 2-port

model.

vo AvA

vs

RinB

RoutA

RinB

AvB

RinC

RoutB

RinC

AvC

vCA

vBA

vAAvA

svov

Since Rout= 0

Rin= RinA and Rout= RoutC = 0

ELG4139 16

Figure

8.30

Op-Amp Integrator

t

S

FS

out dttvCR

tv )(1

)(

ELG4139 17

Inverting Integrator

Now replace resistors Ra and Rf by complex

components Za and Zf, respectively, therefore

Supposing

(i) The feedback component is a capacitor C,

i.e.,

(ii) The input component is a resistor R, Za = R

Therefore, the closed-loop gain (Vo/Vin) become:

where

What happens if Za = 1/jC whereas, Zf = R?

Inverting differentiator

in

a

f

o VZ

ZV

CjZ

f

1

dttvRC

tv io )(1

)(

tj

ii eVtv )(

+

~

Zf

Za

Vin

Vo

+

~

R

Vin

Vo

C

ELG4139 18

Op-Amp Integrator

Example:

(a) Determine the rate of change

of the output voltage.

(b) Draw the output waveform.

Solution:

(a) Rate of change of the output voltage

smV/

F k

V

50

)01.0)(10(

5

W

RC

V

t

V io

(b) In 100 s, the voltage decrease

VμssmV/ 5)100)(50( oV

ELG4139 19

Figure 8.35

Op-Amp Differentiator

dt

tdvCRtv S

SFout

)()(

+

R

C

VoVi

0to t1 t2

0

to t1 t2ELG4139 20

Frequency-Gain Relation

• Ideally, signals are amplified

from DC to the highest AC

frequency

• Practically, bandwidth is limited

• 741 family op-amp have an limit

bandwidth of few KHz.

• Unity Gain frequency f1: the

gain at unity

• Cutoff frequency fc: the gain

drop by 3dB from dc gain Gd

(Voltage Gain)

(frequency)

f1

Gd

0.707Gd

fc0

1

GB Product : f1 = Gd fc

20log(0.707)=3dB

ELG4139 21

Building Filters: Gain and Bandwidth Gain Bandwidth Product = Gain x Bandwidth

ELG4139 22

ELG4139 23

Gain-Bandwidth Product

Example: Determine the cutoff frequency of an op-amp having a

unit gain frequency f1 = 10 MHz and voltage differential gain Gd

= 20V/mV

Sol:

Since f1 = 10 MHz

By using GB production equation

f1 = Gd fc

fc = f1 / Gd = 10 MHz / 20 V/mV

= 10 106 / 20 103

= 500 Hz

(Voltage Gain)

(frequency)

f1

Gd

0.707Gd

fc0

1

10MHz

? Hz

ELG4139 24

Ideal Versus Practical Op-Amp

Ideal Actual

Open Loop gain A 105

Bandwidth BW 10-100Hz

Input Impedance Zin >1MW

Output Impedance Zout 0 W 10-100 W

Output Voltage Vout Depends only

on Vd = (V+V)

Differential

mode signal

Depends slightly

on average input

Vc = (V++V)/2

Common-Mode

signal

CMRR 10-100dB

ELG4139 25

Analysis

Ideal Op-Amp Main Properties:

(1) The voltage between V+ and V is zero V+ = V

(2) The current into both V+ and V termainals is zero

For ideal Op-Amp circuit:

(1) Write the kirchhoff node equation at the noninverting terminal V+

(2) Write the kirchhoff node eqaution at the inverting terminal V

(3) Set V+ = V and solve for the desired closed-loop gain

ELG4139 26

+

vi

Ra

vov-

v+

Rf

+

vi

Ra

vov-

v+

Rf

R2R1

+

vi

vov-

v+

Rf

+

vi

vov-

v+

Rf

R2R1

Noninverting amplifier Noninverting input with voltage divider

i

a

f

o vRR

R

R

Rv ))(1(

21

2

Voltage follower

io vv

i

a

f

o vR

Rv )1(

Less than unity gain

io vRR

Rv

21

2

ELG4139 27

Non-Linear Op-Amp Applications

• Applications using saturation

– Comparators

– Comparator with hysteresis (Schmitt Trigger)

– Oscillators.

• Applications using active feedback components

– Log, antilog, squaring etc. amplifiers

– Precision rectifier

ELG4139 28

Comparators A comparator is a device that compares the magnitude of two inputs and

gives an output that indicates which of the two is larger!

VOUT

VIN

Ideal response VOUT = A0VIN

Practical response (clipped)

If A0 is large, practical response can be approximated as :

VIN > 0 V+ > V- VOUT = +VSAT

VIN < 0 V+ < V- VOUT = -VSAT

ELG4139 29

Hysteresis

• A comparator with hysteresis has a ‘safety margin’.

• One of two thresholds is used depending on the current

output state.

V

time

Upper threshold

Lower threshold

ELG4139 30

Schmitt Trigger

• The Schmitt trigger is an op-amp comparator circuit

featuring hysteresis.

• The inverting variety is the most commonly used.

21

1

RR

RVVVV OUTIN

Switching occurs when:

But,

21

1

RR

RVV

VV

SATTHRESH

SATOUT

ELG4139 31

Schmitt Trigger Op-amp Circuit

• The open-loop comparator from the previous two slides

is very susceptible to noise on the input

– Noise may cause it to jump erratically from + rail to –

rail voltages

• The Schmitt Trigger circuit (see at the left) solves this

problem by using positive feedback

– It is a comparator circuit in which the reference voltage is

derived from a divided fraction of the output voltage, and

fed back as positive feedback.

– The output is forced to either VPOS or VNEG when the

input exceeds the magnitude of the reference voltage

– The circuit will remember its state even if the input

comes back to zero (has memory)

• The transfer characteristic of the Schmitt Trigger is

shown at the left

– Note that the circuit functions as an inverter with

hysteresis

– Switches from + to – rail when vIN > VPOS(R1/(R1 + R2))

– Switches from – to + rail when vIN< VNEG(R1/(R1 + R2))

ELG4139 32

Asymmetrical Thresholds

• We do not need always

want the threshold levels to

be symmetrical around 0 V.

• More general configuration

features an arbitrary

reference level.

Using Kirchoff’s current law:

012

R

VV

R

VV REFOUT

21

21

1212 RR

RRV

R

V

R

V

R

V

R

V REFOUT

21

2

21

1

RR

RV

RR

RVV REFOUT

ELG4139 33

Realising VREF

21

2

21

1

RR

RV

RR

RVV REFSATTHRESH

211 || rrR 21

2

rr

rVV SREF

Providing and

But,

ELG4139 34

DC Imperfections Three DC Imperfections of Real Op-Amps

Input Bias Current; Input Offset Current; and Input Offset Voltage (output voltage

may not be zero for zero input voltage)

𝐼𝐵 =𝐼𝐵++𝐼𝐵_

2

𝐼𝑜𝑓𝑓 = 𝐼𝐵+ − 𝐼𝐵−

Bias Current

Offset Current

Bias Current: All op-amps draw a small constant DC bias currents at their inputs.

Typical value for a 741 is around 100 nA. This is only notable when very high

impedance sources are used. In such cases, an alternative op-amp with lower bias

current should be used.

ELG4139 35

Offset Voltage

• When both input voltages are equal, the output should be zero. Actually it probably won’t be due to an offset voltage between the inputs. Typically, this is around 2 mV.

• Offset voltage is automatically compensated by a negative feedback network. It can be a problem for precision comparator applications.

• Both the offset voltage and bias current are DC. A.C.

operation is not affected by them (they just add an offset)

Negative feedback reduces the effect of both. Steps can be

taken to reduce them (further reading)

ELG4139 36

Example: Find the worst-Case DC Output Voltage of an

Inverting Amplifier assuming vin = 0. The maximum bias

current of the Op-Amp is 100 nA. The maximum offset

current is 40 nA, and the maximum offset voltage is 2 mV.

ELG4139

37

First, Consider the Offset Voltage

𝑉0,𝑣𝑜𝑓𝑓 = − 1 +𝑅2

𝑅1𝑉𝑜𝑓𝑓

𝑉0,𝑜𝑓𝑓 = −11𝑉𝑜𝑓𝑓

𝑉0,𝑜𝑓𝑓 = −22 and + 22mV ELG4139

38

Second, Bias Current Sources

• 𝑉0,𝑏𝑖𝑎𝑠 = −𝑅2𝐼2 − 𝑅1𝐼1

• 𝐼1 = 0

• 𝐼2 = −𝐼𝐵

• 𝑉0,𝑏𝑖𝑎𝑠 = 𝑅2𝐼𝐵

ELG4139

39

Third, Offset Current Source

• 𝑉0,𝑖𝑜𝑓𝑓 = 𝑅2𝐼𝑜𝑓𝑓

2= -2 and 2 mV

• 𝑉0 = 𝑉0,𝑣𝑜𝑓𝑓 + 𝑉𝑜,𝑏𝑖𝑎𝑠 + 𝑉𝑜,𝑖𝑜𝑓𝑓

• 𝑉0 = 22 + 10 +2=34mV

• 𝑉0 = −22 + 0 −2=-24mV

ELG4139

40