Applications of OP-AMP

1. Linear Integrated Circuits
(20EC402)
Syllabus - Unit II
Applications of Operational Amplifiers
• Basic Op-amp Applications
– Scale Changer
– Summing Amplifier
– Subtractor
• Instrumentation amplifier
• V-to-I and I-to-V converters
• Precision Rectifier
• Peak detector
• Clipper and Clamper
• Sample and Hold circuit
• Log and Antilog amplifier
• Differentiator
• Integrator
• Comparators
• Schmitt trigger
• Filters:
– Low pass filters
– High pass filters
– Band pass filters
– Butterworth filters.
18-Aug-23 Unit-II: Applications of Op-Amp 1

2. Operational Amplifier Applications
• In linear circuits, the output signal varies with the input signal
in a linear manner.
• Applications:
– Adder,
– Subtractor,
– V to I and I to V Converter,
– Instrumentation Amplifier,…
• In non-liner circuits, the outputs are varying highly non-linear
with the inputs.
• Applications:
– Rectifier,
– Peak Detector,
– Clipper and Clamper,
– SH circuit,
– Log and Antilog amplifier,…
18-Aug-23 Unit-II: Applications of Op-Amp 2

3. Scale Changer/Inverter
18-Aug-23 Unit-II: Applications of Op-Amp 3
• Consider basic inv amplifier
• If
𝑹𝒇
𝑹𝟏
= 𝑲
K is real constant
• Then closed loop gain 𝑨𝑪𝑳 =
− 𝑲
• For 𝑹𝒇 = 𝑹𝟏, 𝑨𝑪𝑳 = −𝟏 → the output is 1800 out of phase.

4. Summing Amplifier
• Op-amp may be used to design a circuit whose output is the sum
of several input signals is called summing amplifier or a
summer.
18-Aug-23 Unit-II: Applications of Op-Amp 4
Inverting Summing Amplifier

5. Inverting Summing Amplifier
18-Aug-23 Unit-II: Applications of Op-Amp 5
Analysis,
• Assume it is an ideal op-amp
(𝑨𝑶𝑳 = ∞, 𝑹𝒊 = ∞ 𝒂𝒏𝒅 𝑰𝑩 = 𝟎) 𝑽𝒅𝒓𝒐𝒑(𝑹𝑪𝒐𝒎𝒑) = 𝟎 ∵ 𝑰𝑩 = 𝟎
• Hence Non-inv input is at ground potential.
• Then, KCL at node ‘a’ is
𝑽𝟏
𝑹𝟏
+
𝑽𝟐
𝑹𝟐
+
𝑽𝟑
𝑹𝟑
+
𝑽𝟎
𝑹𝒇
= 𝟎 ⇒ 𝑽𝟎 = −
𝑹𝒇
𝑹𝟏
𝑽𝟏 +
𝑹𝒇
𝑹𝟐
𝑽𝟐 +
𝑹𝒇
𝑹𝟑
𝑽𝟑
• The output is an inverted, weighted sum of the inputs.
• If, 𝑹𝟏 = 𝑹𝟐 = 𝑹𝟑 = 𝑹𝒇 ⇒ 𝑽𝟎 = − 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑
𝑹𝟏 = 𝑹𝟐 = 𝑹𝟑 = 𝟑𝑹𝒇 ⇒ 𝑽𝟎 = −
𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑
𝟑
• Output is the average of the input signals(inverted).
• To provide input bias current, 𝑹𝑪𝒐𝒎𝒑 can be find by ,
Make 𝑽𝟏 = 𝑽𝟐 = 𝑽𝟑 = 𝟎; Then effective input resistance 𝑹𝒊 = 𝑹𝟏 𝑹𝟐 𝑹𝟑
Then 𝑹𝑪𝒐𝒎𝒑 = 𝑹𝒊 𝑹𝒇 = 𝑹𝟏 𝑹𝟐 𝑹𝟑 𝑹𝒇

6. Non-Inverting Summing Amplifier
• A summer that gives a non-inverted sum
is the non-inverting summing amplifier.
18-Aug-23 Unit-II: Applications of Op-Amp 6
• Let voltage at inv & non-inv input terminal both are Va.
• KCL at nod ‘a’
𝑽𝟏−𝑽𝒂
𝑹𝟏
+
𝑽𝟐−𝑽𝒂
𝑹𝟐
+
𝑽𝟑−𝑽𝒂
𝑹𝟑
= 𝟎
⟹ 𝑽𝒂
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
=
𝑽𝟏
𝑹𝟏
+
𝑽𝟐
𝑹𝟐
+
𝑽𝟑
𝑹𝟑
⟹ 𝑽𝒂 =
𝑽𝟏
𝑹𝟏
+
𝑽𝟐
𝑹𝟐
+
𝑽𝟑
𝑹𝟑
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
• From diagram, 𝑽𝟎 = 𝟏 +
𝑹𝒇
𝑹
𝑽𝒂 = 𝟏 +
𝑹𝒇
𝑹
𝑽𝟏
𝑹𝟏
+
𝑽𝟐
𝑹𝟐
+
𝑽𝟑
𝑹𝟑
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
• Which is a non-inverted weighted sum of inputs.
• Let 𝑹𝟏 = 𝑹𝟐 = 𝑹𝟑 = 𝑹 =
𝑹𝒇
𝟐
⇒ 𝑽𝟎 = 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑

7. Subtractor
• A basic differential amplifier can be used as a
subtractor.
• If all resistors are equal in value, then the
output voltage can be derived by using
superposition principle.
18-Aug-23 Unit-II: Applications of Op-Amp 7
• Output voltage due to V1 alone can be Vo1, make V2=0 then 𝑽𝟏 =
𝑽𝟏
𝟐
∴ 𝑽𝒐𝟏 =
𝑽𝟏
𝟐
𝟏 +
𝑹
𝑹
= 𝑽𝟏 ⇒ 𝑽𝒐𝟏 = 𝑽𝟏
• Similarly,
𝑽𝒐𝟐 = −𝑽𝟐
• Output due to both inputs can be written as
𝑽𝒐 = 𝑽𝒐𝟏 + 𝑽𝒐𝟐 ⇒ 𝑽𝒐 = 𝑽𝟏 − 𝑽𝟐

8. Instrumentation Amplifier
• Measuring and controlling of physical quantity is mandatory in
industry, commercial applications.
• Examples:
– Temperature
– Humidity
– Light Intensity
– Water Flow, etc.,
• Role of instrumentation Amplifier
– Usually measured with transducers, output should be
amplified for display or to drive the system.
18-Aug-23 Unit-II: Applications of Op-Amp 8

9. Instrumentation Amplifier
• Important features of an instrumentation amplifier
– High gain accuracy
– High CMRR
– High gain stability with low temperature coefficient.
– Low DC offset
– Low output impedance.
• Special op-amps designed is μA725
• Monolithic Instrumentation amplifier commercially available
are
– AD521, AD524, AD624,
– LH0036, LH0037,
– INA104, 3626, 3629,…
18-Aug-23 Unit-II: Applications of Op-Amp 9

10. Instrumentation Amplifier
• Consider a differential amplifier as
𝑽𝟎 = −
𝑹𝟐
𝑹𝟏
𝑽𝟐 +
𝟏
𝟏 +
𝑹𝟑
𝑹𝟒
𝑽𝟏 𝟏 +
𝑹𝟐
𝑹𝟏
⟹ 𝑽𝟎 = −
𝑹𝟐
𝑹𝟏
𝑽𝟐 −
𝟏
𝟏 +
𝑹𝟑
𝑹𝟒
𝑽𝟏
𝑹𝟏
𝑹𝟐
+ 𝟏
18-Aug-23 Unit-II: Applications of Op-Amp 10
For
𝑹𝟏
𝑹𝟐
=
𝑹𝟑
𝑹𝟒
⟹ 𝑽𝟎 = −
𝑹𝟐
𝑹𝟏
𝑽𝟐 − 𝑽𝟏
• V1 seems input impedance = R3 + R4 = 101KΩ
• V2 seems input impedance = R1 = 1KΩ
• Low impedance leads the load the signal source heavily

11. • High resistance buffer is used as shown in figure
18-Aug-23 Unit-II: Applications of Op-Amp 11
Instrumentation Amplifier

12. • A, A2 have differential input voltage
• for V1 = V2 , VR=0,
– no current through R, R’
– A1, A2 acts as voltage follower ,
⟹ 𝑽𝟐
′
= 𝑽𝟐, 𝑽𝟏
′
= 𝑽𝟏
18-Aug-23 Unit-II: Applications of Op-Amp 12
Instrumentation Amplifier
• if V1≠ V2 ,
– current flows through R, R’ &
– (V2
’-V1
’)>(V2-V1) has differential gain and more CMRR
• Voltage at positive terminal of op-amp A3 is
𝑹𝟐𝑽𝟏
′
𝑹𝟏+𝑹𝟐
• Using super position theorem
𝑽𝟎 = −
𝑹𝟐
𝑹𝟏
𝑽𝟐
′
+ 𝟏 +
𝑹𝟐
𝑹𝟏
𝑹𝟐𝑽𝟏
′
𝑹𝟏 + 𝑹𝟐
⇒ 𝑽𝟎 =
𝑹𝟐
𝑹𝟏
𝑽𝟏
′
− 𝑽𝟐
′

13. • Since no current flows into op-amp,
Current flow upwards in R, and
passes through R’
𝑰 =
𝑽𝟏 − 𝑽𝟐
𝑹
𝑽𝟏
′
= 𝑹′𝑰 + 𝑽𝟏 = 𝑹′
𝑽𝟏 − 𝑽𝟐
𝑹
+ 𝑽𝟏
18-Aug-23 Unit-II: Applications of Op-Amp 13
Instrumentation Amplifier
𝑽𝟐
′
= −𝑹′
𝑰 + 𝑽𝟐 = −𝑹′
𝑽𝟏 − 𝑽𝟐
𝑹
+ 𝑽𝟐
• We know that,
𝑽𝟎 =
𝑹𝟐
𝑹𝟏
𝑽𝟏
′
− 𝑽𝟐
′
=
𝑹𝟐
𝑹𝟏
𝑹′ 𝑽𝟏−𝑽𝟐
𝑹
+ 𝑽𝟏 + 𝑹′ 𝑽𝟏−𝑽𝟐
𝑹
− 𝑽𝟐
𝑽𝟎 =
𝑹𝟐
𝑹𝟏
𝟐𝑹′
𝑹
𝑽𝟏 − 𝑽𝟐 + 𝑽𝟏 − 𝑽𝟐
𝑽𝟎 =
𝑹𝟐
𝑹𝟏
𝟏 +
𝟐𝑹′
𝑹
𝑽𝟏 − 𝑽𝟐 𝑽𝟎 ∝ 𝑹

14. Instrumentation Amplifier using
Transducer Bridge
• The bridge is initially balanced for Vdc, V1=V2
• When physical quantity changes, RT changes, V1≠V2
• This differential voltage is amplified by 3 op-amp.
18-Aug-23 Unit-II: Applications of Op-Amp 14

15. V to I and I to V converter
V to I Converter (Transconductance Amplifier)
• Op-amp can convert a voltage signal to a proportional output
current. (Types: 1). V-I converter with Floating load, 2). Grounded load)
18-Aug-23 Unit-II: Applications of Op-Amp 15
• Floating load ZL (wkt, Va = Vi),
𝑽𝒊 = 𝒊𝑳𝑹𝟏 ∵ 𝑰𝑩
−
= 𝟎 ⇒ 𝒊𝑳 =
𝑽𝒊
𝑹𝟏
• The input voltage is converted into an output current of
𝑽𝒊
𝑹𝟏

16. 18-Aug-23 Unit-II: Applications of Op-Amp 16
• From diagram (Va = V1)
• By KCL
𝒊𝟏 + 𝒊𝟐 = 𝒊𝑳 ⇒
𝑽𝒊 − 𝑽𝟏
𝑹
+
𝑽𝒐 − 𝑽𝟏
𝑹
= 𝒊𝑳
⇒ 𝑽𝒊 + 𝑽𝒐 − 𝟐𝑽𝟏 = 𝒊𝑳𝑹 ⇒ 𝑽𝟏 =
𝑽𝒊 + 𝑽𝒐 − 𝒊𝑳𝑹
𝟐
V to I Converter (Transconductance Amplifier)
𝒘𝒌𝒕, 𝑨𝑪𝑳 = 𝟏 +
𝑹𝒇
𝑹𝟏
= 𝟏 +
𝑹
𝑹
= 𝟐 ⇒
𝑽𝒐
𝑽𝟏
= 𝟐 ⇒ 𝑽𝒐 = 𝟐𝑽𝟏
𝑽𝟏 =
𝑽𝒊 + 𝑽𝒐 − 𝒊𝑳𝑹
𝟐
⇒ 𝑽𝒐 = 𝟐𝑽𝟏 = 𝑽𝒊 + 𝑽𝒐 − 𝒊𝑳𝑹
⇒ 𝑽𝒊 = 𝒊𝑳𝑹 ⇒ 𝒊𝑳 =
𝑽𝒊
𝑹𝟏
• V to I converter is used for low voltage dc and ac voltmeter, LED
and Zener Diode tester.

17. I to V Converter (Transresistance amplifier)
• Photocell, photodiode and photovoltaic
cell give an output current that is
proportional to an incident radiant
energy or light, these current can be
converted to voltage by using these I to V
converter.
18-Aug-23 Unit-II: Applications of Op-Amp 17
• Here -ve input terminal is virtual grounded,
– no current through Rs and
– Is flows through Rf, then 𝑽𝟎 = −𝑰𝒔𝑹𝑭
• Hence it can detect lower current.
• Sometimes, Rf shunted with a Cf to reduce high frequency noise and
oscillations

18. Op-Amp Circuits using Diodes
• The major limitation of ordinary diode is, it
cannot rectify voltage below 𝑽𝜸 𝟎. 𝟔𝑽 , the
cut-in voltage of the diode.
• When a diode is placed in a feedback loop of
an op-amp it can act as ideal diode.
18-Aug-23 Unit-II: Applications of Op-Amp 18
• 𝑽𝜸 𝟎. 𝟔𝑽 is virtually eliminated due to it is divided by the open loop
gain 𝑨𝑶𝑳 ~𝟏𝟎𝟒
.
• When 𝑽𝒊 >
𝑽𝜸
𝑨𝑶𝑳
𝒊𝒆, .
𝟎.𝟔
𝟏𝟎𝟒 = 𝟔𝟎𝝁𝑽 ⇒ 𝑽𝒐𝑨(ie, when Diode D conducts
when 𝑽𝒐𝑨 > 𝑽𝜸 → Voltage Follower.
• Ie,. Vo follows Vi during +ve half cycle.

19. • When Vi is –ve or 𝑽𝒊 <
𝑽𝜸
𝑨𝑶𝑳
D is off ,
no current is delivered to IL (except
less IBias, ID-Saturation)
• This circuit is called Precision
rectifier.
• Applications:
– Half-wave rectifier
– Full-wave rectifier
– Peak-value detector
– Clipper
– Clamper
18-Aug-23 Unit-II: Applications of Op-Amp 19
Op-Amp Circuits using Diodes

20. Half-Wave Rectifier
18-Aug-23 Unit-II: Applications of Op-Amp 20
• An inv-op-amp can be converted to half-wave
rectifier using two diodes
• When Vi is positive(Vi>0), D1 conducts, VoA is
negative, D2 Reverse Bias, V0 is zero. (Becaues
input current flows through D1 & no current
flows through RF)
• When Vi<0, D2 conducts, D1 is off, VoA is
positive, the circuit acts as inverter for Rf=R1
and V0 is positive.
• Limitaion : Slew rate of the op-amp.
• The circuit provides positive output.
• If both diodes are reversed, then +ve input signal
is transmitted and gets inverted then output is
negative.

21. Full-Wave Rectifier
18-Aug-23 Unit-II: Applications of Op-Amp 21
• Also called absolute value
circuit.
• For Vi>0,
• D1 is on and
• D2 is off.
• Both op-amps A1 and A2 act as
inverter as in equivalent circuit.
• Here V0 = Vi
• For Vi<0,
• D1 is off and
• D2 is on.

22. 18-Aug-23 Unit-II: Applications of Op-Amp 22
Full-Wave Rectifier
• Let output of A1 be V, also differential input at A2=0,
Voltage at inv input is V.
• KCL at node ‘a’ is
𝑽𝒊
𝑹
+
𝑽
𝟐𝑹
+
𝑽
𝑹
= 𝟎 ⇒ 𝑽 = −
𝟐
𝟑
𝑽𝒊
• The equivalent circuit is a non-in amplifier
𝑽𝟎 = 𝟏 +
𝑹
𝟐𝑹
−
𝟐
𝟑
𝑽𝒊 = 𝑽𝒊
• For Vi<0, the output is positive. The input and
output waveforms are as in figure.
• This circuit is also called an absolute value circuit as
output is positive even when input is negative.
• It is possible to obtain negative outputs for either
polarity of input simply reversing the diodes.

23. Peak Detector
18-Aug-23 Unit-II: Applications of Op-Amp 23
• If Vi > VC then diode is forward biased, act as
voltage follower, V0 = Vi
• When Vi < VC, then diode is reverse biased,
capacitor holds the charge till Vi > VC.
• Reset when VC = 0 , made by connecting low
leakage MOSFET switch across the capacitor
• Lowest or negative peak can be detected by reversing
the diode.
• Applications:
• Test,
• Measurement and
instrumentation,
• Amplitude modulation in
communications
• Function is to compute the peak value of input
• The circuit follows
– The voltage peaks of signal and stores the highest value
on a capacitor.
– If highest peak signal value comes, the new value is
stored.
– Highest peak value is stored until capacitor discharges

24. Clipper
18-Aug-23 Unit-II: Applications of Op-Amp 24
• A precision diode may used to clip-
off a certain position of input.
• Clipping level is determined by Vref..
• Vi is given to positive input
• When V0 > Vref then clipped off
– Up to Vi≤ Vref , diode conducts because
opamp will act as voltage follower
(V0 = Vi)
– When Vi > Vref , diode cut-off , opamp is
open loop , V0 = Vref
• If Vref is negative
– V0 above Vref will be clipped off

25. Clipper
18-Aug-23 Unit-II: Applications of Op-Amp 25
• Positive clipper simply converted
to negative clipper by simply
reversing diode D and changing
the polarity of Vref.
• It clips off the negative parts of
input when < Vref
• Negative clipper circuit

26. Clamper
• Also known as dc inserter (or) restorer.
• The circuit used to add desired dc level to V0.
– So output is clamped to desired level.
• In positive clamper,
– clamped dc level is positive
• In negative clamper,
– clamped dc level is negative.
• A variable positive dc voltage is given at
positive input
• This circuit clamps the peaks of input
waveform so called peak clamper.
• Output is the net result of ac and dc input
applied to negative and positive.
18-Aug-23 Unit-II: Applications of Op-Amp 26

27. • If Vref at positive terminal then
– Vref is +ve → V’ is +ve , → diode D is
forward biased, so it acts as voltage
follower, V0 = +Vref.
• Let Vi = Vm sinωt at negative input terminal
– In negative half cycle of Vi , diode D
conducts (FB), C1 charges through D to
Vm (negative peak voltage)
– In positive half cycle of Vi , D is reverse
biased, C1 retains Vm (previous voltage)
• But Vm is in series with ac input signal, then
output = Vi +Vm
• Total output = Vref + Vi + Vm
• Negative peak clamping by reversing diode and
negative reference voltage.
18-Aug-23 Unit-II: Applications of Op-Amp 27
Clamper

28. Sample and Hold Circuit
• Samples, an input signal and holds on to its last sampled value until the
input is sampled again.
• Applications:
– Digital interfacing
– Analog to digital
– Pulse code modulation systems
• The simplest sample and hold circuit is
18-Aug-23 Unit-II: Applications of Op-Amp 28
• MOSFET works as a switch
(controlled by control voltage Vc)
• Capacitor stores the charge.
• Vi to be sampled is applied to drain of
MOSFET and Vc applied to gate.

29. 18-Aug-23 Unit-II: Applications of Op-Amp 29
Sample and Hold Circuit
• When Vc is positive MOSFET turns
on, capacitor charges as Vi.
– Time constant = R0 + rds (ON)
– R0 → output resistance of A1 (voltage follower)
– rds (ON) → resistance of MOSFET when ON.
• Vi appears across C and output of A2
(voltage follower)
• When Vc = 0 → MOSFET is OFF
– But C discharges to A2 , have highest input
impedance, so C holds the voltage across it.
– Ts → sample period (during which VC = Vi)
– TH → Hold period (during which VC =
constant)
• Frequency of VC should be higher , at
least twice the input voltage, to
retrieve the input from output

30. Log Amplifier
18-Aug-23 Unit-II: Applications of Op-Amp 30
• Grounded base transistor is
placed in FB path since collector
is virtual grounded, and base is
also grounded
• Transistor acts as diode
𝑰𝑪 = 𝑰𝑬 = 𝑰𝑺 𝒆
𝒒𝑽𝑬
𝑲𝑻 − 𝟏
Where,
IS → emitter saturation current ≈10-3A
K → Boltzmann’s constant
T → Absolute temperature in (0K) 𝑰𝑪
𝑰𝑺
= 𝒆
𝒒𝑽𝑬
𝑲𝑻 − 𝟏 ⇒ 𝒆
𝒒𝑽𝑬
𝑲𝑻 =
𝑰𝑪
𝑰𝑺
+ 𝟏 ≈
𝑰𝑪
𝑰𝑺
• Taking natural log on both sides
𝒒𝑽𝑬
𝑲𝑻
= 𝒍𝒏
𝑰𝑪
𝑰𝑺
⇒ 𝑽𝑬 =
𝑲𝑻
𝒒
𝒍𝒏
𝑰𝑪
𝑰𝑺

31. Log Amplifier
18-Aug-23 Unit-II: Applications of Op-Amp 31
• From figure
𝑰𝑪 =
𝑽𝒊
𝑹𝟏
, 𝑽𝑬 = −𝑽𝟎, 𝑽𝑬 =
𝑲𝑻
𝒒
𝒍𝒏
𝑰𝑪
𝑰𝑺
𝑽𝟎 = −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒊
𝑹𝟏𝑰𝑺
⇒ 𝑽𝟎 = −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒊
𝑽𝒓𝒆𝒇
Where, 𝑽𝒓𝒆𝒇 = 𝑹𝟏𝑰𝑺
• Output voltage is proportional to
logarithm of input voltage
• We know that, log10X = 0.4343lnX
• Drawback
– IS varies transistor to transistor and with temperature
– Vref cannot be obtained

32. • Drawback This can be eliminated by the circuit as
• Here input applied to one log-amplifier and reference applied to
another log-amplifier
• Integrated in same silicon wafer
• Provides a close match of saturation currents and ensures good
thermal tracking.
18-Aug-23 Unit-II: Applications of Op-Amp 32
Log Amplifier

33. • Assume𝑰𝑺𝟏 = 𝑰𝑺𝟐 = 𝑰𝑺
𝑽𝟏 = −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒊
𝑹𝟏𝑰𝑺
; 𝑽𝟐 = −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒓𝒆𝒇
𝑹𝟏𝑰𝑺
𝑽𝟎 = 𝑽𝟐 − 𝑽𝟏 =
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒊
𝑹𝟏𝑰𝑺
− 𝒍𝒏
𝑽𝒓𝒆𝒇
𝑹𝟏𝑰𝑺
⇒ 𝑽𝟎 =
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒊
𝑽𝒓𝒆𝒇
• Reference can be set by single voltage source but output voltage(V0) is
proportional to T, this can be compensated by the last stage op-amp (A4)
provides non-inverting 𝒈𝒂𝒊𝒏 = 𝟏 +
𝑹𝟐
𝑹𝑻𝑪
𝑽𝟎 𝑪𝒐𝒎𝒑 = 𝟏 +
𝑹𝟐
𝑹𝑻𝑪
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒊
𝑽𝒓𝒆𝒇
– RTC is a temperature sensitive resistance
18-Aug-23 Unit-II: Applications of Op-Amp 33
Log Amplifier

34. Antilog Amplifier
• Input Vi is fed into temperature
compensating voltage divider R2
& RTC , to base of Q2
• V0 is feedback to inverting input
A1 through resistor R1
• The base –Emitter voltage of Q1,
Q2 can be written as
𝑽𝑸𝟏 𝑩−𝑬
= −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝟎
𝑹𝟏𝑰𝑺
𝑽𝑸𝟐 𝑩−𝑬
= −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒓𝒆𝒇
𝑹𝟏𝑰𝑺
18-Aug-23 Unit-II: Applications of Op-Amp 34

35. Antilog Amplifier
• Since the base of Q is tied ground
𝑽𝑨 = −𝑽𝑸𝟏 𝑩−𝑬
= −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝟎
𝑹𝟏𝑰𝑺
• Base voltage VB of Q2 is
𝑽𝑩 =
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝑽𝒊
• Emitter voltage of Q2
𝑽𝑸𝟐𝑬
= 𝑽𝑩 + 𝑽𝑸𝟐 𝑩−𝑬
𝑽𝑸𝟐𝑬
=
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝑽𝒊 −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒓𝒆𝒇
𝑹𝟏𝑰𝑺
• Emitter voltage of Q2=VA = VQ2E
18-Aug-23 Unit-II: Applications of Op-Amp 35
−
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝟎
𝑹𝟏𝑰𝑺
=
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝑽𝒊 −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝒓𝒆𝒇
𝑹𝟏𝑰𝑺
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝑽𝒊 = −
𝑲𝑻
𝒒
𝒍𝒏
𝑽𝟎
𝑹𝟏𝑰𝑺
− 𝒍𝒏
𝑽𝒓𝒆𝒇
𝑹𝟏𝑰𝑺
−
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝒒
𝑲𝑻
𝑽𝒊 = 𝒍𝒏
𝑽𝟎
𝑽𝒓𝒆𝒇

36. Antilog Amplifier
• Change from ln to log10.
−𝟎. 𝟒𝟑𝟒𝟑
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝒒
𝑲𝑻
𝑽𝒊 = 𝟎. 𝟒𝟑𝟒𝟑 𝒍𝒏
𝑽𝟎
𝑽𝒓𝒆𝒇
−𝑲′𝑽𝒊 = 𝒍𝒐𝒈
𝑽𝟎
𝑽𝒓𝒆𝒇
𝑾𝒉𝒆𝒓𝒆, 𝑲′
= 𝟎. 𝟒𝟑𝟒𝟑
𝑹𝑻𝑪
𝑹𝟐 + 𝑹𝑻𝑪
𝒒
𝑲𝑻
⟹
𝑽𝟎
𝑽𝒓𝒆𝒇
= 𝟏𝟎−𝑲′𝑽𝒊
⟹ 𝑽𝟎 = 𝑽𝒓𝒆𝒇 𝟏𝟎−𝑲′𝑽𝒊
18-Aug-23 Unit-II: Applications of Op-Amp 36
• When Input increased by one voltage, output decreased by decade.
• 755 log/antilog amplifier IC chip is available as functional module.

37. Differentiator
• The op-amp circuits that contain capacitor is the differentiating
amplifier or differentiation.
• The output waveform is the derivative of the input waveform.
Analysis
• The node ‘N’ is at virtual ground potential (VN=0), then
𝒊𝑪 = 𝑪𝟏
𝒅
𝒅𝒕
𝑽𝒊 − 𝑽𝑵 = 𝑪𝟏
𝒅𝑽𝒊
𝒅𝒕
• The current through feedback Resistor, 𝒊𝑭 =
𝑽𝒐
𝑹𝑭
& no current into
the op-amp.
18-Aug-23 Unit-II: Applications of Op-Amp 37
• By KCL at node N is
𝑪𝟏
𝒅𝑽𝒊
𝒅𝒕
+
𝑽𝟎
𝑹𝑭
= 𝟎 ⇒ 𝑽𝟎 = −𝑹𝑭𝑪𝟏
𝒅𝑽𝒊
𝒅𝒕
• The minus sign indicates 1800 phase shift of the output wrt to input signal.
• In phasor equivalent 𝑽𝟎 𝒔 = −𝑹𝑭𝑪𝟏𝒔𝑽𝒊 𝒔
• In steady state 𝒔 = 𝒋𝝎.
• The magnitude of gain A is
𝑨 =
𝑽𝟎
𝑽𝒊
= −𝒋𝝎𝑹𝑭𝑪𝟏 = 𝝎𝑹𝑭𝑪𝟏 =
𝒇
𝒇𝒂
Where, 𝒇𝒂 =
𝟏
𝟐𝝅𝑹𝑭𝑪𝟏
• At 𝒇 = 𝒇𝒂, 𝑨 = 𝟏, i.e., 0dB and gain increases at rate of +20 dB/decade.

38. • At high frequency, differentiator become unstable, the input
impedance decreases, this leads sensitive to high frequency
noise.
• Hence,
18-Aug-23 Unit-II: Applications of Op-Amp 38
Differentiator

39. Integrator
• Integrating both the sides,
𝟎
𝒕
𝒅𝑽𝟎 = −
𝟏
𝑹𝟏𝑪𝑭
𝟎
𝒕
𝑽𝒊𝒅𝒕 ⇒ 𝑽𝟎 𝒕 = −
𝟏
𝑹𝟏𝑪𝑭
𝟎
𝒕
𝑽𝒊 𝒕 𝒅𝒕 + 𝑽𝟎 𝟎
• Where, V0(0) is the initial output voltage.
• Due to negative sign in the output it can also known as an inverting integrator.
• Rcomp is connected to minimize the effect of input bias current.
• In phasor notation,
𝑽𝟎 𝒔 = −
𝟏
𝒔𝑹𝟏𝑪𝑭
𝑽𝒊 𝒔
• In steady state 𝒔 = 𝒋𝝎 ⇒ 𝑽𝟎 𝒋𝝎 = −
𝟏
𝒋𝝎𝑹𝟏𝑪𝑭
𝑽𝒊 𝒋𝝎
• The magnitude of gain A is 𝑨 =
𝑽𝟎 𝒋𝝎
𝑽𝒊 𝒋𝝎
= −
𝟏
𝒋𝝎𝑹𝟏𝑪𝑭
=
𝟏
𝝎𝑹𝟏𝑪𝑭
18-Aug-23 Unit-II: Applications of Op-Amp 39
• If the resistor and capacitor of the differentiator is
interchanged, we can obtain the integrator.
• By KCL at node N is
𝑽𝒊
𝑹𝟏
+ 𝑪𝑭
𝒅𝑽𝟎
𝒅𝒕
= 𝟎 ⇒
𝒅𝑽𝟎
𝒅𝒕
= −
𝑽𝒊
𝑹𝟏𝑪𝑭

40. Integrator
18-Aug-23 Unit-II: Applications of Op-Amp 40
• Frequency response (or Bode Plot) of this basic
integrator is,
• At 𝒇 = 𝒇𝒃 𝒇𝒃 =
𝟏
𝟐𝝅𝑹𝟏𝑪𝑭
gain of the integrator is
0dB
• At lower frequency the gain becomes infinite,
hence the feedback capacitor is shunted by a RF
to avoid saturation or infinity.
• The parallel combination of RF and CF, dissipates
power, so it is called ‘Lossy Integrator’

41. Comparator
Introduction
• Op-amp in open loop will act in nonlinear manner.
• Application:
– Comparators
– Detectors
– Limiters
– Digital interfacing devices (converters)
Comparators
• Compares a signal voltage applied at one input with known reference at
another input. i.e., 𝑽𝟎 = ±𝑽𝑺𝒂𝒕(𝒊𝒅𝒆𝒂𝒍 𝒄𝒉𝒂𝒓𝒂𝒄𝒕𝒆𝒓𝒊𝒔𝒕𝒊𝒄𝒔)
• Types:
– Non-inverting comparator
– Inverting comparator
18-Aug-23 Unit-II: Applications of Op-Amp 41

42. Non-Inverting Comparator
• When reference given at negative input and time varying signal(Vi)-input is applied
at positive input.
𝑽𝟎 = −𝑽𝒔𝒂𝒕 𝒇𝒐𝒓 𝑽𝒊 < 𝑽𝒓𝒆𝒇
𝒔𝒊𝒎𝒊𝒍𝒂𝒓𝒍𝒚, 𝑽𝟎 = +𝑽𝒔𝒂𝒕 𝒇𝒐𝒓 𝑽𝒊 > 𝑽𝒓𝒆𝒇
18-Aug-23 Unit-II: Applications of Op-Amp 42

43. • Here reference given at positive input and time varying signal(Vi)-input is at
negative input.
• The practical comparator has the output obtained by zener diode.
• A resistance (limiting the current) and two back to back zener diodes at output.
• The output limiting voltages are 𝑽𝒁𝟏 + 𝑽𝑫 𝒂𝒏𝒅 − 𝑽𝒁𝟐 + 𝑽𝑫
– 𝒘𝒉𝒆𝒓𝒆, 𝑽𝑫 ≅ 𝟎. 𝟕𝑽 𝒊. 𝒆. , 𝒅𝒊𝒐𝒅𝒆 𝒇𝒐𝒓𝒎𝒘𝒂𝒓𝒅 𝒗𝒐𝒍𝒕𝒂𝒈𝒆
18-Aug-23 Unit-II: Applications of Op-Amp 43
Non-Inverting Comparator

44. • Above waveform shown are the instantaneous.
• Practically it takes certain amount of time to switch from one
voltage to another voltage level.
• If 741 internally compensated is used as comparator, primary
limitation is slew rate.
• Uncompensated op-amp make faster comparators than
compensated op-amps.
• Application of comparator:
– Zero Crossing Detector
– Window Detector
– Time Marker Generator
– Phase meter.
18-Aug-23 Unit-II: Applications of Op-Amp 44
Non-Inverting Comparator

45. Zero Crossing Detectors
• Basic comparators can be used as zero crossing detectors.
• Due to input is sine wave, output is square wave it is called as
square wave generator.
18-Aug-23 Unit-II: Applications of Op-Amp 45

46. Window Detector
18-Aug-23 Unit-II: Applications of Op-Amp 46
• Mark the instant at which an
unknown instant is between two
threshold levels is called window
detector.
• Three indicators,
– Yellow (LED-3) for <3V too low
– Green (LED-2) for3-6V for safe input
– Red (LED-1) for>6V high input

47. Time Marker Generator
• Output of zero crossing detector (ZCD) is differentiated by an RC circuit
(RC << T)
– Then V’ is series positive and negative pulses.
– After passing diode D, negative portion clipped off.
• Sinusoidal wave has been converted into train of positive pulses spacing T.
• Used in triggering of Monoshots, SCR, Sweep voltage of CRT etc,.
18-Aug-23 Unit-II: Applications of Op-Amp 47

48. Phase Detector
• Phase angle between two voltages can also be measured using
circuit is called marker generator.
 Both voltages are converted to spikes
 Time interval between pulse spike is measured.
 Time interval depends on phase difference (can measure from (00 to 3600)
18-Aug-23 Unit-II: Applications of Op-Amp 48

49. Regenerative Comparator
(Schmitt Trigger)
• If positive feedback added to comparator then gain is increase
greatly.
• Theoretically, if loop gain (-βAOL) is adjusted to unity, then gain
with feedback(AVF) becomes infinite, but output is extreme.
• Therefore, practical circuits cannot maintain loop gain unity
because of supply voltage and temperature variations, so greater
than unity is chosen.
• Now output is discontinuous
• This phenomenon called hysteresis (or) backlash.
18-Aug-23 Unit-II: Applications of Op-Amp 49

50. 18-Aug-23 Unit-II: Applications of Op-Amp 50
Regenerative Comparator
(Schmitt Trigger)

51. • Regenerative comparator (above) called Schmitt trigger
– Input given to negative terminal
– Feedback given to positive terminal
• The input vi triggers the output V0, when every time exceeds certain voltage
levels
– Then Upper Threshold Voltage VUT
– Lower Threshold Voltage VLT
• The hysteresis width is difference between two threshold VUT - VLT
• Can be calculated as
– When V0 = +VSat , then voltage at positive input terminal will be
𝑽𝒓𝒆𝒇 +
𝑹𝟐
𝑹𝟏 + 𝑹𝟐
𝑽𝒔𝒂𝒕 − 𝑽𝒓𝒆𝒇 = 𝑽𝑼𝑻
• 𝑾𝒉𝒆𝒏 𝑽𝒊 < 𝑽𝑼𝑻 → 𝑽𝟎 = +𝑽𝒔𝒂𝒕
• 𝑾𝒉𝒆𝒏 𝑽𝒊 > 𝑽𝑼𝑻 → 𝑽𝟎 = −𝑽𝒔𝒂𝒕
18-Aug-23 Unit-II: Applications of Op-Amp 51
Regenerative Comparator
(Schmitt Trigger)

52. • Regenerativly switches are remains up to Vi > VUT
– for V0 = -Vsat ,
– voltage at positive terminal is 𝑽𝒓𝒆𝒇 −
𝑹𝟐
𝑹𝟏+𝑹𝟐
𝑽𝒔𝒂𝒕 + 𝑽𝒓𝒆𝒇 = 𝑽𝑳𝑻
• When Vi < VLT (to switch)
V0= -Vsat to +Vsat (regenerative transition take place)
• Usually VLT < VUT
• difference between these two are known as hysteresis (VH)
𝑽𝑯 = 𝑽𝑼𝑻 − 𝑽𝑳𝑻 =
𝟐𝑹𝟐𝑽𝒔𝒂𝒕
𝑹𝟏 + 𝑹𝟐
• Therefore, VH is independent of Vref
• To compensate input bias current 𝑹𝟑 = 𝑹𝟏 𝑹𝟐
• For non-inverting Schmitt trigger Vi, Vref are interchanged
• Important application of Schmitt trigger circuit is to convert very
slowly varying input voltage into square wave output.
18-Aug-23 Unit-II: Applications of Op-Amp 52
Regenerative Comparator (Schmitt Trigger)

53. First and Second Order Active Filter
Electric filters:
• Separation of signals according to their frequencies
• Widely used in communication, signal processing
• Filters can be built from
1). Passive RLC components
2). Crystals (or)
3). Resistors, Capacitors & op-amp (active filters)
RC Active Filters
• In frequency selective circuits the circuit passes signals of specified
band of frequency and attunates the signals outside the band is called
Electric filter
• Type
1). Analog,
2). Digital
• Simplest way is using R,L,C
• Suitable for high frequencies(radio frequency)
18-Aug-23 Unit-II: Applications of Op-Amp 53

54. First and Second Order Active Filter
• Active filters uses op-amp as active element R,C as passive elements
• Op-amp is non-inv mode, offer high input impedance and low output
impedance, provide high load drive capacity.
• Limitations of active filters
– High frequency response is limited by gain BW (GBW) product(X)
and slew rate of op-amp
– High frequency active filters are more expensive.
• Commonly used filters are
– Low Pass Filter (LPF)
– High Pass Filter (HPF)
– Band Pass Filter (BPF)
• Band Reject Filter / Band Stop Filter (BSF)
18-Aug-23 Unit-II: Applications of Op-Amp 54

55. 18-Aug-23 Unit-II: Applications of Op-Amp 55