linear5 circuit analysis Charateristics of Op-Amp.ppt

LINEAR INTEGRATED CIRCUITS
Subject Code: EE3402
Presented By:
Dr. A. SANTHI MARY ANTONY,
ASSISTANT PROFESSOR,
DEPARTMENT OF EEE,
LOYOLA – ICAM COLLEGE OF ENGINEERING AND TECHNOLOGY (LICET)
LOYOLA – ICAM
COLLEGE OF ENGINEERING AND TECHNOLOGY (LICET)
Loyola Campus, Nungambakkam, Chennai.

UNIT III – APPLICATIONS OF OP-AMP
 INSTRUMENTATION AMPLIFIER AND ITS APPLICATIONS FOR TRANSDUCER BRIDGE
 LOG AND ANTILOG AMPLIFIERS
 ANALOG MULTIPLIER & DIVIDER
 FIRST AND SECOND ORDER ACTIVE FILTERS
 COMPARATORS, MULTI VIBRATORS
 WAVEFORM GENERATORS
 CLIPPERS, CLAMPERS, PEAK DETECTOR, S/H CIRCUIT
 D/A CONVERTER (R- 2R LADDER AND WEIGHTED RESISTOR TYPES)
 A/D CONVERTERS USING OP-AMPS

UNIT III – APPLICATIONS OF OP-AMP – MIND MAP

INSTRUMENTATION AMPLIFIER
• In a number of industrial and consumer applications, the important requirement is
to measure and control physical quantities.
• Some typical examples are measurement and control of temperature, humidity,
light intensity, water flow etc.
• These physical quantities are usually measured with the help of transducers.
• The output of transducer has to be amplified so that it can drive the indicator or
display system.
• This function is performed by an Instrumentation Amplifier.
• Used mainly in Thermo Couple and Acoustic Systems etc.

FEATURES OF INSTRUMENTATION AMPLIFIER
The important features of an instrumentation amplifier are :
1. High gain accuracy
2.High CMRR
3. High gain stability with low temperature coefficient
4.Low DC Offset
5. Low output impedance

What is Op-Amp
INSTRUMENTATION AMPLIFIER
What an Op-Amp looks like to a lay-person
 These are specially designed op-amp such as µa25 to meet the above stated
requirements of a good instrumentation Amplifier.
 Monolithic (Single chip) Instrumentation amplifier are also available commercially
such as AD521, AD524, AD620 by National Semiconductor and INA101, 104, 3626,
3629 b Burr Brown.

Differential Amplifier using Single Op-amp
(CIRCUIT ANALYSIS)
Consider the basic differential amplifier. It can been seen that the output voltage is given by,

Differential Amplifier Analysis

Differential Amplifier Analysis
When Non inverting input alone is given,

When both the inputs are given
simultaneously,
• In this circuit , source V1 sees an input impedance =R3 + R4 (=101Kῼ) and the impedance
seen by source V2 is only 1Kῼ
• This low impedance may load the signal source heavily.
• Therefore, high resistance buffer is used proceeding each input to avoid this loading effect.

IMPROVED INSTRUMENTATION AMPLIFIER
• The op-amps A1 and A2 have differential input voltages as zero.
• For V1 = V2, that is under common mode condition, the voltage across R will be zero.
• As no current flows through R and R’ the non-inverting amplifier A1 acts as voltage follower, so
its output V2’ = V2 .
• Similarly op-amp A2 acts as voltage follower having output V1’ =V1.
• However if V1 ≠ V2, current flows in R and R’, and ( V2’ - V1’) > ( V2 –V1).
• Therefore, this circuit has differential gain and CMRR more compared to the single Op-amp
circuit.

The output voltage can be calculated as follows,
Using super position theorem

IMPROVED INSTRUMENTATION AMPLIFIER

INSTRUMENTATION AMPLIFIER USING TRANSDUCER BRIDGE

INSTRUMENTATION AMPLIFER IC-AD620
• IC-AD620 is a low cost instrumentation amplifier
• It require only one external resistor, RG to set gains from 1 to 1000.
• The relationship between gain and RG as given by the manufacturer is

LOGARITHMIC (LOG) AMPLIFIERS
• Log-amp can be used to compress the dynamic range of a signal.
• The fundamental log-amp circuit is shown in Fig, where a grounded base transistor is placed in the feedback path.
Fig. Log amplifier
• The collector is held at virtual ground and the base is also
grounded, the transistor's voltage-current relationship
becomes that of a diode and is given by,

• The output voltage is thus proportional to the logarithm of input voltage. The circuit gives natural log (In), one can
find log10 by proper scaling

• The circuit however has one problem.
• The emitter saturation current Is, varies from transistor to transistor and with temperature. Thus a
stable reference voltage Vref cannot be obtained.
• This is eliminated by the circuit given in Fig.
• The input is applied to one log-amp, while a reference voltage is applied to another log amp. The two
transistors are integrated close together in the same silicon wafer. It provides a close match of
saturation currents and ensures good thermal tracking.
Fig. Log-amp with saturation current and temperature compensation

• The voltage V0 is still dependent upon temperature and is directly proportional to T.
• This is compensated by the last op-amp stage A4 which provides a non-inverting gain of (1 + R2/RTC). Now, the
output voltage is,
Where, RTC is a temperature-sensitive resistance with a positive coefficient of temperature.
• The slope of the equation becomes constant as the temperature changes.
Fig. Log-amp using two op-amps only

ANTILOG AMPLIFIER
• The circuit is shown in Fig. The input Vi for the antilog-amp is fed into the temperature compensating voltage
divider R2 and RTC and then to the base of Q2.
• The output Vo of the antilog-amp is fed back to the inverting input of A1 through the resistor R1. The base to
emitter voltage of transistors Q1 and Q2 can be written as

OP-AMP USED AS COMPARATORS
• A comparator is a circuit which compares a signal voltage applied at one input of an op-amp with a known
reference voltage at the other input.
• It is basically an open-loop op-amp with output ±Vsat (=Vcc) as shown in the ideal transfer characteristics
Fig. The transfer characteristics (a) ideal comparator. (b) Practical comparator
There are basically two types of comparators: (i) Non-inverting comparator (ii) Inverting comparator

Non-Inverting Comparator
• A fixed reference voltage Vref applied to (-) input and a time varying signal Vi is applied to (+) input.
• The output voltage is at -Vsat for Vi < Vref and Vo goes to + Vsat for Vi > Vref .
• The output waveform for a Sinusoidal input signal applied to the (+) input is shown in Fig. (b and c) for positive and
negative Vref respectively.
Fig. Input and output of a Comparator when
(a) Vref > 0 V (b) Vref < 0V
Fig. Non-Inverting Comparator

• In a practical circuit Vref is obtained by using a 10KΩ potentiometer which forms a voltage divider with the supply
voltages V+ and V- with the wiper connected to (-) input terminal as shown in Fig.
• Vref of desired amplitude and polarity can be obtained by simply adjusting the 10KΩ potentiometer.
Fig. Practical Non-Inverting Comparator

Inverting Comparator
• A practical inverting comparator in which the reference voltage Vref is applied to the (+) input and Vi
is applied to (-) input.
• For a sinusoidal input signal, the output waveform is shown in Fig.(b) and (c) for Vref positive and
negative respectively.
Fig. Practical Inverting Comparator

Fig. Input and output waveforms for (b) Vref Positive (c) Vref negative

• A basic comparator, a feedback is not used the op-amp is used in the open loop mode.
• As open loop gain of op-amp is very large, very small noise voltages also can cause triggering of the comparator, to
change its state. Such a false triggering may cause lot of problems in the applications of comparator as zero-crossing
detector.
• This may give a wrong indication of zero-crossing due to zero-crossing of noise voltage rather than zero crossing of
input wanted signals.
• Such unwanted noise causes the output to jump between high and low states.
• The comparator circuit used to avoid such unwanted triggering is called regenerative comparator or Schmitt trigger,
which basically uses a positive feedback.
• The figure shows the basic Schmitt trigger circuit. As the input is applied to the inverting terminal, it is called
inverting Schmitt trigger circuit.
• The inverting mode produces opposite polarity output. This is fed-back to the non-inverting input which is of same
polarity as that of the output. This ensures a positive feedback.
REGENERATIVE COMPARATOR (SCHMITT TRIGGER)
Figure Schmitt trigger using op amp.(Inverting)

• The values of these voltages can be determined and adjusted by selecting proper values of R1 and R2.
and
• The output voltage remains in a given state until the input voltage exceed the threshold Voltage level either
positive or negative.
• The fig. shows the graph of output voltage against input voltage. This is called transfer characteristics of
Schmitt trigger.
• The graph indicated that once the output changes its state it remains there indefinitely until the input voltage
crosses any of the threshold voltage levels. This is called hysteresis of Schmitt trigger.
• The hysteresis is also called as dead-zone or dead-band.
Fig. Hysteresis of Schmitt trigger.
• The difference between VUT and VLT is called width of
the hysteresis denoted as H,

• The schmitt trigger eliminates the effect of noise voltages less than
the hysteresis H, cannot cause triggering.
• As for positive Vin greater than VUT, the output becomes –Vsat and
for negative Vin less than VLT, the output becomes +Vsat, this is called
Inverting Schmitt Trigger.
• If input applied is purely sinusoidal, the input and output waveforms
for inverting Schmitt trigger can be shown as in fig.
Fig. Input and output waveforms of Schmitt trigger

OP-AMP OSCILLATORS
• In electronics, oscillators are circuits that generate sinusoidal or non-sinusoidal waveforms used as
reference signals in communication engineering.
• The non-sinusoidal waveforms are triangular, ramp, saw-tooth, pulse, TTL, rectangular, spike etc.
• The oscillator has an amplifier with a positive feedback for generating oscillations.
• The basic oscillator circuit with feedback is shown below fig
Fig. Basic Feedback Oscillator

Fig. Feedback Oscillator Output
• For a sustained (continuous and steady) oscillations Barkhausen‟s criteria are to be satisfied.
• The criteria states ,
1. The total gain of the circuit should be equal to or more than one and 2.
2. The overall phase shift in the circuit (amplifier and feedback circuit) should be zero.
• If gain of the amplifier is considered as A and feedback factor is β, then
Criterion 1:
• Modulus of the product of the amplifier gain A and feedback factor of feedback network β should be equal to
or greater than zero.

• As shown in fig, a noise voltage introduced by existing imbalances in the circuit is amplified by the circuit
itself.
• The frequency of noise voltage depends on the design aspects of the circuit and when multiplication factor
of total gain |A β | =1 and when |A β |  1, the amplitude of the generated voltage increases till saturation is
reached.
• The oscillation at the particular frequency is generated and sustained.
• This is done when the phase shift of the circuit is 0° or 360° (0 or radians).
• In the following sections two such sinusoidal oscillators are being explained. They are
(1) RC phase shift oscillator
(2) Wien Bridge oscillator
Criterion 2:  A β = 0° or 360° (0 or radians )
• Phase angle between the amplifier gain A and feedback factor of feedback network β or total phase
shift in the circuit should be equal to or greater than zero. Criterion 1 and 2 are Barkhausen‟s criteria for
sustained oscillations.

RC Phase Shift Oscillators
• RC phase shift oscillator generates sinusoidal output and hence categorized under sinusoidal oscillators.
• In this oscillator the amplifier used is a negative feedback and Inverting Operational amplifier connected to a RC
feedback network
Fig. RC Phase Shift Oscillator

Construction:
• The oscillator comprising of a negative feedback inverting operational amplifier whose input resistor is
R1 and feedback resistor is R2 as shown in the fig.
• An RC network, where one end of the resistor R is connected to the ground, the other end is
connected to a capacitor C and the other end of the capacitor acts as an input terminal.
• The combined end of the capacitor and resistor acts as output terminal.
• Each RC network provides 60° ( /3 radians) phase shift between their input and output terminals.
Thus three networks are connected in series, so as to provide a phase shift of 180° or  radians.
• The feedback RC network shifts the phase this is termed as RC phase shift oscillator.
• The amplifier is an inverting amplifier and 180° or  radians phase shift between input and output.
• Hence second Barkhausen‟s criterion is fulfilled.
• Choosing the value of amplifier voltage gain to be more (nearly 30 or so), we can fulfill first Barkhausen‟s
criterion of having overall gain more than 1.

Working:
• Practically an OP AMP is not perfect and so imbalances are prevailing between their input terminals. This
imbalance generates a minor sinusoidal noise voltages fed between the input terminals.
• This noise voltage is amplified by the amplifier and a sinusoidal output voltage Vo is generated at the output
terminal.
• The RC network provides 180° or 2  radians, where Vo is fed into the feedback RC network and an inverse
voltage of Vf shown in fig.
• We can understand that Vf is 180° (or 2  radians) phase shifted Vo.
•The feedback voltage Vf is fed into the inverting terminal of the operational amplifier through an input resistor R1.
•The voltage is phase inverted of 180° (or 2  radians) by the amplifier and the output Vo is inverse of Vf.
•The circuit fulfills the criteria for sustained oscillations, the circuit continuously generates sinusoidal output.
Fig. RC Phase Shift Oscillator- Feedback network

Derivation of frequency of oscillation of RC Phase shift oscillator

Problem 1 : Solved Problem
• The capacitor value of an RC phase shift oscillator using OP AMP is 0.01μF and the desired frequency of
oscillation is 25 KHz.
• The voltage gain of the amplifier should be 30.
• Thus calculate the value of R of RC feedback network, input resistor R1 and feedback resistor R2 connected
to the amplifier.

Possible questions:
• What is the phase shift introduced by the three RC feedback network and how?
• Explain briefly about construction and working of RC Phase shift oscillator using OP AMP with neat sketches.
• Explain briefly about how RC Phase shift oscillator using OP AMP satisfies Barkhausen‟s criteria.

Wien’s Bridge Oscillators
• Unlike RC phase shift oscillator, Wien bridge oscillator never uses phase-shift concept. It uses balancing
concept of lead-lag network.
Construction:
• Here this oscillator is connected in a bridge fashion.
• The inverting terminal is connected to a junction where resistors R3 and RF are connected.
• The other end of R3 is grounded and RF is connected to output terminal of the amplifier.
• This forms a reference voltage across R3 being fed into inverting terminal as shown in the fig.
Fig a. Wien’s Bridge Oscillator

Fig. Wien’s Bridge Oscillator-Reconstructed
• The non-inverting connected in between two reactance offering components Z1 and Z2 as shown in the fig.
• Z1 comprises of serially connected resistor R1 and capacitor C1 whereas Z2 comprises of parallel connected
resistor R2 and capacitor C2.
• This combination of Z1 and Z2 is termed as lead-lag circuit.

Working:
• The reactive circuits Z1 and Z2 connected to non-inverting terminal at B as shown in the fig.
• A noise voltage is generated between the imbalanced input terminals is amplified by the amplifier and fed
in the bridge circuit.
• For particular low-frequencies, the capacitors act as open circuit and thus the output voltage of lead-lag
circuit shall be zero and for high frequencies the capacitors act as short circuit and thus voltage shall be
zero.
• Only for a particular frequency called resonant frequency, resistance value equals to capacitive reactance
value.
• Maximum current is available at this frequency only. So the output appears only for resonant frequency.
•The other resistor values of R3 and RF of bridge are adjusted to enhance the output to a maximum level.
Thus the oscillation is generated.

Possible question:
• Explain briefly about construction and working of Wien bridge oscillator using OP AMP with neat
sketches.

OP-AMP MULTIVIBRATORS
•Multivibrators are square wave oscillators that produce pulse waveforms with various ON time and OFF time.
•As shown in fig.a, P1, P2 and P3 are ON time of the pulse whose total time period is 10 ms with TON and
TOFF are 3.5 ms and 6.5 ms respectively. TON and TOFF are two states of the pulse.
•The place where TON transits to TOFF or TOFF to TON is termed as state transition.
•The state transition may have slope (with a small time for transition) or infinite slope (No time for transition-
being abrupt).
Fig a. Pulse waveform - model

• There are three types of multivibrators available according to their state transition.
They are (a.) astable, (b.) monostable, and (c). bistable multivibrators.
• Astable multivibrator is one that generates pulses those transits from one state to another without any
external trigger.
• It is done by its free-will controlled by the design aspects. Thus this is called free-running multivibrator.
• So the states are not stable for a long time, the states can be termed as Quasi-stable states.
• Hence this multivibrator generates pulses of no stable states, it is termed as astable multivibrator.
• Monostable multivibrator is one that generates pulses those transits from one state to another with the
help of one external trigger.
• The multivibrator remains in one state (stable state) and when an external pulse is applied then it transits
state from present Stable state to a quasi-stable state.
• It remains at quasi-stable state for a time period of T as it is designed and then returns to a stable state
without any external trigger. Since it changes state from stable to quasi-stable using one external trigger, it is
termed as one-shot multivibrator or monostable multivibrator.

•Bistable multivibrator is one that generates pulses those transits from one state to another with the help of
two external trigger.
•The multivibrator remains in one state (stable state) and when an external pulse is applied then it transits
state from present Stable state to a next stable state.
•It remains at second stable state until another external trigger is applied.
•Thus this multivibrator has stable states only and the transitions happen only when triggers are applied, it
is termed as bistable multivibrators.
Possible questions:
What is a Multivibrator?
Define the terminology of astable, monostable and bistable multivibrators.

Astable Multivibrators
These multivibrators are termed as “Free Running” multivibrators, and they have only quasi stable
states as seen earlier in introduction.
The circuit diagram of astable multivibrator using Operational amplifier is shown below fig.a.
Fig a. Astable Multivibrator – Circuit Diagram

Construction:
• The circuit as simple and resembles like OP AMP Schmitt trigger circuit. One end of a capacitor C and a
resistor R are connected to the inverting terminal.
• The other end of the resistor is connected to the output terminal and that of capacitor is connected to
ground terminal.
• This capacitor C and feedback resistor R decide the period for oscillation of the multivibrator.
• A resistor R1 is connected between the output terminal and non-inverting terminal and another resistor R2
is connected between non-inverting terminal and ground terminals.
• If the output voltage is considered as Vo, then the voltage tapped between R2 shall be a reference voltage
applied to the non-inverting terminal with amplitude of βVo where β is feedback factor for comparison.
Working:
• Considering fig.a and b, the working part of this generator can be explained. At Time 0: At time 0,
assume the output transits from -Vsat to +Vsat. Since the output is +Vsat at time 0, reference voltage +βVo
and capacitor voltage is -βVo.

From Time 0 to Time T1: Since reference is at +βVo, the inverting terminal is also at +βVo due to virtual
ground. Now the capacitor tries to charge till the output voltage +Vo. It reaches +βVo and tries to charge more,
then the inverting terminal go beyond reference voltage +βVo after time constant RC.
At Time T1: At time T1, since the inverting terminal goes little above than reference voltage +βVo, the output
transits from +Vsat to -Vsat. Now capacitor voltage remains at +βVo. The reference voltage at non-inverting
terminal is at -βVo. The time T1 is decided by RC (time constant) factor.
After Time T1: Since reference is at -βVo, the inverting terminal is also at -βVo due to virtual ground. Now the
capacitor tries to charge till the output voltage -Vo. It tries to reach -βVo and tries to charge more, then the
inverting terminal go beyond reference voltage -βVo after time RC (time constant). Now again whatever
happened at time 0 happens again. These 3 steps repeat periodically till power is available for the circuit.
Fig b. Astable Multivibrator – Output Waveforms

Possible question:
Explain construction and working of Astable Multivibrator using OP AMP using neat sketches.

Monostable Multivibrators
• These multivibrators are termed as “one-shot multivibrators” and they have only one stable state and
other is quasi-stable state induced by single external trigger as seen earlier in introduction.
• The circuit diagram of monostable multivibrator using Operational amplifier is shown below fig.a.
Fig a. Monostable Multivibrator Using OP AMP

Construction:
• The circuit as simple and resembles like OP AMP Schmitt trigger circuit.
• One end of a capacitor C and a resistor R are connected to the inverting terminal.
• The other end of the resistor is connected to the output terminal and that of capacitor is connected to
ground terminal. A diode D1 is connected parallel to the capacitor C.
• This capacitor C and feedback resistor R decide the period for T of the multivibrator. A resistor R1 is
connected between the output terminal and non-inverting terminal and another resistor R2 is connected
between non-inverting terminal and ground terminals.
• If the output voltage is considered as Vo, then the voltage tapped between R2 shall be a reference
voltage applied to the non-inverting terminal with amplitude of βVo where β is feedback factor for
comparison.
• A pulse trigger circuit consisting of diode D2 and a differentiator circuit connected to pulse generator of
negative pulse width Tp. The anode of the diode D2 is connected to non-inverting terminal

Fig b. Monostable Multivibrator - Waveforms
Working: Considering fig.a and b, the working part of this generator can be explained.
In fig. b has three waveforms. Waveform a shows the pulse trigger waveform whose trigger pulse width is TP,
waveform b shows voltage output VC across capacitor C and waveform c shows the monostable output Vo of
quasi-stable state of time T.

Before pulse trigger: At time before pulse trigger, assume the output is at +Vsat. Since the output is at
+Vsat, then reference voltage is at +βVo and so capacitor voltage VC tries to charge towards +Vsat.
Due to this the diode D1 gets forward biased when inverting terminal is positive, and the diode D1 starts
conducting beyond 0.7V (Approximate cut-in voltage of Silicon diode).
Thus the diode D1 conducts and provides a short path beyond 0.7V, and hence the capacitor C which is
parallel can charge upto 0.7V only. So now the capacitor voltage VC is 0.7V.
This voltage is shown as VD in the fig.b waveform (b).
At time of pulse trigger: As shown in fig.b waveform (a & b), a negative pulse trigger is applied at non-
inverting terminal and its amplitude being –Vin.
Hence at the non-inverting terminal, pulse voltage –Vin and reference voltage +βVsat exists. The total
voltage is (+βVsat –Vin). The amplitude of this voltage is less than 0.7V due to existence of diode D2 which
is forward biased (ON) due to –ive trigger pulse (Cathode of the diode D2 is negative due to -Vin and
anode is positive due to +βVsat).

Now non-inverting terminal acts as reference terminal of an inverting comparator. At this point
inverting terminal is at 0.7V and non-inverting reference voltage is below 0.7V.
Hence inverting terminal is more than reference voltage at non-inverting terminal and the output
transits from +Vsat to –Vsat as shown in fig. 2.3.2.b waveform (c).
That is output transited from stable high state to low state. The capacitor voltage VC is at 0.7V and
output is at –Vsat.
Hence the capacitor C starts charging towards -Vsat through the resistor R. The non-inverting terminal
reference voltage is less than 0.7V.
At Time AFTER pulse trigger: When pulse trigger ends after time TP, it becomes positive.
So the cathode of diode D2 is at positive voltage and anode is at –βVsat.
Thus the diode D2 is in reverse bias condition (OFF).
Due to this the non-inverting voltage is affected only by reference voltage across resistor R2 which is -
βVsat.

Now reference voltage is at –βVsat and the charging capacitor is charging towards –Vsat. but when capacitor
voltage VC reaches just above –βVsat, output transits from -Vsat to +Vsat (Inverting terminal voltage VC is more
than reference voltage at non-inverting terminal).
This transition happens at time T from start of pulse trigger where T is decided by RC time constant.
That is capacitor C took time period of T for charging from VD to –βVsat which is through resistor R.
The output stays at a quasi-stable state for a time period of T.
After Time T: Now output voltage Vo is at +Vsat and reference voltage at non-inverting terminal is at +βVsat.
The capacitor starts charging from –βVsat to +Vsat.
But when the capacitor voltage VC increases more than VD, diode D1 is forward biased and starts
conducting. Hence the capacitor voltage VC cannot charge beyond VD.
The waveform is shown in fig.b waveform (a).

As seen initially, now the amplitude at inverting terminal is VD due to charge of capacitor, non-inverting
terminal voltage is at +βVsat.
The output is a negative pulse voltage whose time period is T.
This negative pulse was generated due to an external negative trigger (one-shot trigger).
The output transit from a stable high state to a low quasi-stable state time T and then to a stable high
state.
This is a monostable waveform because it has one stable state and a quasi-stable state.
In next section, discussion about derivation of time period T is done.

Possible question:
Explain the construction and working of monostable multivibrator using OP AMP with neat sketches.

OP-AMP RECTIFIERS
PRECISION RECTIFIERS
Rectifiers convert bipolar AC signals into unipolar DC signals. The circuit mainly uses diodes that block
signals when reverse biased and allow signals when forward biased. But when forward biased diode can only
allow signals above 0.7V (cut-in voltage of Silicon diode).
So the rectifier cannot precisely rectify ac signals of peak to peak voltages below 0.7V. For eradicating this
disadvantage of not rectifying signals below 0.7V we use operational amplifiers for rectification. OP AMP
inverting amplifier circuits are added with diodes to function as precision rectifiers to rectify voltages below
0.7V (cut-in voltages).
Precision Half-wave Rectifiers
As discussed this precision rectifier is used for rectifying ac signals below cut-in voltages.
Circuit construction: An inverting amplifier with input resistor R1 and feedback resistor R2 is altered by
adding two diodes D1 and D2 in series as shown in the fig.a.
D1 is connected between output terminal of OP AMP and resistor R2 as shown and diode D2 is connected
between input inverting terminal and anode of the diode D1

Working: An AC signal Vin is applied to the inverting terminal and output Vo is tapped at the cathode of
diode D1 and one end of resistor R2 as shown in the following fig. The analysis of this circuit in both
positive and negative cycle becomes essential.
In positive cycle: The inverting terminal becomes positive in positive input cycle and since it is an
inverting amplifier and output terminal becomes negative. Thus Diode D1 becomes reverse biased and
remains in OFF state but diode D2 becomes forward biased and remains ON. Since Diode D1 is OFF
and diode D2 is ON and D2 provides short circuit between inverting and non-inverting terminals, so the
output Vout is zero.
Fig. a Half-wave precision rectifier

Fig. b Half-wave precision rectifier-waveforms

In negative cycle: The inverting terminal becomes negative in negative input cycle and since it is an
inverting amplifier and output terminal becomes positive.
Thus Diode D1 becomes forward biased and remains in ON state but diode D2 becomes reverse biased
and remains OFF.
Since Diode D1 is ON and diode D2 is OFF and provides high resistance path between inverting and non-
inverting terminals. But resistor R2 provides alternate path between input and output.
Since D1 is ON, it connects Vout with output terminal.
Now the circuit becomes normal inverting amplifier and so output Vout is the input multiplied by scaling
factor (-R2/R1).
Thus the rectifier circuit allows one cycle (negative half cycle of the input) but blocks other cycle (positive
half cycle).
Since the diode doesn‟t directly involve in rectification and OP AMP has high gain factor, this circuit rectifies
even signals less than cut-in voltage. The waveforms are shown in the fig. b.

Precision Full-wave Rectifiers
Circuit construction: Two inverting amplifiers with input resistor R and feedback resistor R is altered by
adding two diodes D1 and D2 in series as shown in the fig. a.
D1 is connected between output terminal of OP AMP and feedback resistor R as shown and diode D2 is
connected between output terminal and other end of the resistor R connected to inverting terminal of the
first OP AMP and also connected to non-inverting terminal of the second OP AMP.
Working: An AC signal Vi is applied to the inverting terminal through the resistor R and output Vo is tapped
at output of second OP AMP as shown in the following fig. The analysis of this circuit in both positive and
negative cycle becomes essential.
Fig.a Full-wave precision rectifier

In positive cycle: The inverting terminal of first OP AMP becomes positive, in positive input cycle and
diode D1 is forward biased.
But diode D2 is reverse biased because output terminal becomes negative. Now D1 is ON and D2 is OFF.
The circuit looks as shown in fig.b.
Thus output voltage Vo is double inverted signal of input voltage Vi. Since gain of both amplifiers is R/R=1,
and Vo = Vi.
Fig. b Full-wave precision rectifier-during positive half cycle

In negative cycle: The inverting terminal of the first OP AMP becomes negative in negative input cycle,
the Diode D1 becomes reverse biased and remains in OFF state but diode D2 becomes forward biased
and remains ON.
Since Diode D1 is OFF and diode D2 is ON as shown in fig. 2.4.2.c. But resistor R provides alternate path
between input and output. In second amplifier, voltage at inverting terminal is V/2R volts and non-inverting
terminal is V/R. thus non-inverting terminal of second amplifier holds two times of voltage than inverting
terminal.
Thus output voltage Vo is ((V/R)-(V/2R)=V/2R) and is adjusted by changing the value of Feedback resistor
R of second amplifier. Hence we get output for negative half-cycle too.
Fig. c . Full-wave precision rectifier-during negative half cycle

This is shown in the fig. of waveforms fig.d. thus this rectifier converts bipolar AC input to unipolar DC output
Fig.d Full-wave precision rectifier waveform
Possible questions:
What is the principle behind precision rectification?
Explain the construction and working of half and full wave precision rectifiers with neat sketches.

WAVE SHAPING CIRCUITS
 Wave shaping circuits are the electronic circuits, which produce
the desired shape at the output from the applied input wave form.
 These circuits perform two functions :
(i) Attenuate the applied wave
(ii) Alter the dc level of the applied wave.
 There are two types of wave shaping circuits:
1. Clippers
2. Clampers

PEAK DETECTOR
A Peak Detector is a circuit that produces an output voltage equal to the positive or
negative peak value of the input voltage. A positive peak detector detects the positive peak
magnitude of the input and a negative peak detector identifies the negative peak magnitude
of the input
The basic blocks required for the peak detector circuit are:
(i) an analog memory such as a capacitor to store the charge proportional to the peak value
(ii)a unidirectional switch such as a diode to charge the capacitor when a new peak arrives
at the input
(iii)a device such as a voltage follower circuit for making the capacitor charge to the input
voltage
(iv)a switch to periodically reinitialise the output to zero

PEAK DETECTOR
Peak Detectors are used in the applications of test and measurement
instrumentation as well as in Amplitude Modulation (AM) Communication.

Sample and Hold Circuit
• A sample and hold circuit samples an input signal and holds on to its last sampled value until the
input is sampled again.
• This type of circuit is very useful in digital interfacing and analog to digital and pulse code modulation
systems.
• One of the simplest practical sample and bold circuit configuration is shown in Fig a
Fig. a Sample and hold circuit

• The n-channel E-MOSFET works as a switch and is controlled by the control voltage Vc and the
capacitor C stores the charge.
• The analog signal Vi to be sampled is applied to the drain of E-MOSFET and the control voltage Vc
is applied to its gate.
• When Vc is positive, the E-MOSFET turns on and the capacitor C charges to the instantaneous
value of input Vi with a time constant [Ro +rDS (on) C]
• Here Ro is the output resistance of the voltage follower A1 and rDS(on) is the resistance of the
MOSFET when on.
• Thus the input voltage vi appears across the capacitor C and then at the output through the
voltage follower A2. The waveforms are as shown in Fig a

Fig. a Input and output waveforms
• The capacitor C is now facing the high input impedance of the
voltage follower A2 and hence cannot discharge. The capacitor
holds the voltage across it.
• The time period TS, the time during which voltage across the
capacitor is equal to input voltage is called sample period.
• The time period TH of vc , during which the voltage across the
capacitor is held constant is called hold period.
• The frequency of the control voltage should be kept higher than
(at least twice) the input so as to retrieve the input from output
waveform.
• During the time when control voltage vc is zero, the E-MOSFET is off.
• A low leakage capacitor such as Polystyrene, Mylar or Teflon should be used to retain the stored charge.

• Specially designed sample and hold lCs of make Harris semiconductor HA2420, National
semiconductor such as LF198, LF398 are also available. A typical connection diagram of the LF398 is
shown in Fig. a. It may be noted that the storage capacitor C is connected externally.
Fig. a. Typical connection diagram

Introduction: D-A and A-D Converters
• Most of the real world physical quantities such as voltage, current, temperature, pressure and time
etc. are available in analog form.
• Even though an analog signal represents a real physical parameter with accuracy, it is difficult to
process, store or transmit the analog signal without introducing considerable error because of the
superimposition of noise as in the case of amplitude modulation.
• Therefore, for processing, transmission and storage purposes, it is often convenient to express these
variables in digital form.
• It gives better accuracy and reduces noise.
• The operation of any digital communication system is based upon analog to digital (A /D) and digital
to analog (D/A) conversion.

Fig a. Circuit showing application of A/D and D/A converter
• Figure a. highlights a typical application within which A /D and D/A conversion is used.
• The analog signal obtained from the transducer is band limited by antialiasing filter.
• The signal is then sampled at a frequency rate more than twice the maximum frequency of
the band limited signal.
• The sampled signal has to be held constant while conversion is taking place in A /D converter.

• This requires that Analog to Digital Convertor (ADC) should be preceded by a sample and hold (S /H)
circuit.
• The ADC output is a sequence in binary digit.
• The micro-computer or digital signal processor performs the numerical calculations of the desired
control algorithm.
• The D/A converter is to convert digital signal into analog and hence the function of Digital to Analog
convertor (DAC) is exactly opposite to that of ADC.
• The D/A converter is usually operated at the same frequency as the ADC. The output of a D/A
converter is commonly a staircase.
• This staircase - like digital output is passed through a smoothing filter to reduce the effect of
quantization noise.
• Both ADC and DAC are also known as data converters and are available in IC form.

Basic Digital to analog converters (DAC) -Techniques
• The schematic of a DAC is shown in Fig. a.
• The input is an n-bit binary word D and is combined with a reference voltage VR to give an analog
output signal.
• The output of a DAC can be either a voltage or current.
Fig. a Schematic of DAC
For a voltage output DAC, the D/A converter is mathematically described as

There are various ways to implement
Here we shall discuss the following resistive techniques only.
Weighted resistor DAC
R-2R ladder

Binary weighted resistor DAC
• One of the simplest circuits shown in the previous figure uses a summing amplifier with a binary
weighted resistor network. It has n-electronic switches d1, d2..., dn controlled by binary input word.
These switches are single pole double throw (SPDT) type.
• If the binary input to a particular switch is 1, it connects the resistance to the reference voltage (- VR).
• If the input bit is 0, the switch connects the resistor to the ground.
From Fig. a, the output current Io for an ideal op-amp can be written as

Fig. a Binary weighted resistor DAC
Comparing Eq. with Eq.,
it can be seen that if Rf = R then K = 1 and VFS= VR
The circuit shown in Fig. a uses a negative reference voltage.
The analog output voltage is therefore positive staircase as shown in Fig. b for a 3 bit weighted resistor DAC.
Fig. b Transfer Characteristics of 3 bit DAC

It may be noted that
• Although the op-amp in Fig. a is connected in inverting mode, it can also be connected in non-
inverting mode.
• (ii) The op-amp is simply working as a current to voltage converter.
• (iii) The polarity of the reference voltage is chosen in accordance with the type of the switch used.
For example, for TIL compatible switches, the reference voltage should be + 5 V and the output will
be negative.
• The accuracy and stability of a DAC depends upon the accuracy of the resistors and the tracking of
each other with temperature.
Disadvantages of binary weighted type DAC
– Wide range of resistor values required.
– The fabrication of such a large resistance in IC is not practical

R-2R Ladder DAC
• Wide ranges of resistors are required in binary weighted resistor type DAC.
• This can be avoided by using R-2R ladder type DAC where only two values of resistors are required.
• It is well suited for integrated circuit realization. The typical value of R ranges from 2.5 KΩ to 10 KΩ.
Fig. (a) R-2R ladder DAC Fig. (b) Equivalent Circuit of (a)
Fig. (c) Equivalent Circuit of (b)

• For simplicity, consider a 3 bit DAC as shown in Fig. (a), where the switch position d1 d2 d3
corresponds to the binary word 100.
• The circuit can be simplified to the equivalent form of Fig. (b) and finally to Fig. (c).
• Then, voltage at node C can be easily calculated by the set procedure of network analysis as

Characteristics of Digital to Analog Converters
• Both D/A and AID converters are available with wide range of specifications.
• The various important specifications of converters generally specified by the manufacturers are
analyzed.
– Resolution
– Linearity
– Accuracy
– Monotonicity
– Settling time
– Stability

Resolution
• The resolution of a converter is the smallest change in voltage which may be produced at the output (or
input) of the converter.
• For example, an 8-bit D/A converter has 28 -1 = 255 equal intervals.
• Hence the smallest change in output voltage is (1/255) of the full scale output range.
• In short, the resolution is the value of the LSB.

Linearity
• The linearity of an AID or D/A converter is an important measure of its accuracy and tells us how
close the converter output is to its ideal transfer characteristics
• In an ideal DAC, equal increment in the digital input should produce equal increment in the analog
output and the transfer curve should be linear.0
• However, in an actual DAC, output voltages do not fall on a straight line because of gain and offset
errors as shown by the solid line curve in Fig. a

• The static performance of a DAC is determined by fitting a straight line through the measured output
points.
• The linearity error measures the deviation of the actual output from the fitted line and is given by
as shown in Fig. a.
• The error is usually expressed as a fraction of LSB increment or percentage of full-scale voltage.
• A good converter exhibits a linearity error of less than ± (1/2) LSB.

Accuracy
• Absolute accuracy is the maximum deviation between the actual converter output and the ideal
converter output.
• Relative accuracy is the maximum deviation after gain and offset errors have been removed.
• Data sheets normally specify relative accuracy rather than absolute accuracy.
• The accuracy of a converter is also specified in terms of LSB increments or percentage of full scale
voltage.
Monotonicity
• A monotonic DAC is the one whose analog output increases for an increase in digital input. Figure b
represents the transfer curve for a non-monotonic DAC, since the output decreases when input code
changes from 001 to 010.
• A monotonic characteristic is essential in control applications, otherwise oscillations can result.

Fig. b A non-monotonic 3-blt DAC
•If a DAC has to be monotonic, the error should be less than ± (1/2) LSB at each output level.
•All the commercially available DACs are monotonic because the linearity error never exceeds ± (1/2)
LSB at each output level

Settling time
• It represents the time it takes for the output to settle within a specified band ± (1/2) LSB of its final
value following a code change at the input (usually a full scale change).
• The most important dynamic parameter is the settling time
• It depends upon the switching time of the logic circuitry due to internal parasitic capacitances and
inductances.
• Settling time ranges from 100 ns to 10 μs depending on word length and type of circuit used.
Stability
• The performance of converter changes with temperature, age and power supply variations.
• So all the relevant parameters such as offset, gain, linearity error and monotonicity must be specified
over the full temperature and power supply ranges.

Analog to Digital Converters
Why do we need A/D conversion?
• Most of the real world physical quantities such as voltage, current, temperature,
pressure and time etc are available in analog form
• Even though an analog signal represents a real physical parameter with accuracy, it is
difficult to process, store or transmit the analog signal without errors because of the
superimposition of noise.
• Therefore for processing, transmission and storage purposes, it is often convenient to
express these variables in digital form it gives better accuracy and reduces noise.
• The operation of any digital communication system is based on A/D conversion or
D/A conversion

Classification of ADC
• Direct Type ADC
• Integrating Type ADC
(i) Direct Type of ADC:
It compare a given analog signal with the internally generated equivalent signal. This group include
1. Flash Type converter
2. Counter type
3. Tracking or Servo converter
4. Successive approximation type converter
(ii) Integrated Type ADC:
It performs conversion in an indirect manner by first changing the analog input signal to a linear function of time
or frequency and then to a digital code. The two most widely used integrating type converters are,
1. Charge balancing ADC
2. Dual slope ADC

Flash AD converters (The Parallel Comparator)

Parallel Comparator( Flash) A/D Converter

INTEGRATING TYPE ADC
The integrating type of ADC do not require S/H circuit at the input.
If the input changes during conversion, the ADC output code will be proportional to the value of the
input averaged over the integration period.
 Charge Balancing ADC
 Dual slope ADC

CHARGE BALANCING ADC
• The principle of charge balancing ADC is to first convert the input signal to a
frequency using a voltage to frequency using a voltage to frequency (V/F)
converter.
• This frequency is then measured by a counter and converted to an output code
proportional to an analog input.
• The main advantage of these converters is that it is possible to transmit frequency
even in noisy environment or in isolated form
• The drawback is that the output of V/F converter depends upon an RC product
whose value cannot be easily maintained with temperature and time.

The circuit consists of a high input impedance bufferA1, precision integratorA2 and
a voltage comparator.
The converter first integrates the analog input signal Va for a fixed duration of 2n
clock periods as shown in figure.
Then it integrates an internal reference voltage VR of opposite polarity until the
integrator output is zero.
The number of clock cycles required to return the integrator to zero is proportional
to the value of Va averaged over the integration period.
Hence N represents the desired output code

FILTERS
• FILTERS are circuits used to select signal components of required frequencies and reject other
unwanted frequency components.
• The selectivity is one of the main criteria for a filter circuit in communication engineering.
• These filters are actually allowing the required frequency bands and attenuate the unwanted frequency
bands but they are not adaptive and precise.
• The allowing band is termed as pass band and attenuating band is termed as stop band.
• The output gain of the filters in pass band is high and in stop band is very low (negligible).
• For ideal filters, pass band gain is infinite and stop band gain is zero.
• The frequency that acts as a barrier between stop and pass band is termed as cut-off frequency.
• The design of a filter is based particularly on this cut-off frequency. It is found that the practical value of
the cut-off frequency is 3dB less than the maximum frequency allowed.

Advantages of active filters over passive filters
• Reduced size and weight
• Increased reliability and improved performance
• Simple design and good voltage gain
• When fabricated in larger quantities, cheaper than passive filters
Disadvantages of Active Filters
• Limited bandwidth only.
• Quality factor is also limited
• Require power supply (passive doesn't require power supply)
• Changes due to environmental factors.
Possible question: What is an active filter? What are its advantages over passive filters?

PASSIVE FILTERS
• Passive filters are considered to be passive, when passive components like resistors, capacitors and
inductors are used in constructing the circuits.
• Passive filters are the basic filters used in communication engineering but they are not adaptive and
precise.
• For a good filter, the slope of frequency response plot from pass band to stop band or vice versa
should be high.
• Passive filters have very low slope for changing input signals and other factors.
• Pass band the gain is not constant but varies. These problems are minimized by using active filters
which are adaptive (manage the gain to be constant throughout the pass band and slope to be very high
for even a major change in input signals).
• Active filters use OP AMP to be adaptive in nature with lager controllable gain value
ACTIVE FILTERS

Order of Butterworth filters
• Butterworth filters were designed by a British engineer Stephen Butterworth as a maximally
flat-response filter.
• This filter minimizes ripples and manages to maintain a flat response in pass band.
• Order of a filter is the magnitude of voltage transfer function of a filter that decreases by -
(20*n) dB/decade as the order, “n‟ increases in stop band and flat in pass band.
• Butterworth filters have flat response in pass bands and decrease in response of -20dB /per decade in
pass bands.
• If order of the filter increases
1. The magnitude of voltage transfer function in stop band is very high and slope decreases by
20 db/decade.
2. The circuit complexity increases.

Types of filters according to the frequency response
Filter Responses of all types

A Sample Butterworth Filter Response - Order wise
• Butterworth filters have flat response in pass bands and decrease in response of -20dB /per decade in pass
bands.

Low Pass Filters
• A low pass filter allows low frequencies up to a corner frequency (cut-off frequency) and attenuates (stops)
high frequencies above cut-off frequency. This is shown in the frequency response figure.
• The circuit is a simple non-inverting amplifier, where a RC low pass filter circuit is connected to the input.
• Capacitor allows low frequencies through it and blocks high frequencies. This characteristic of capacitor is
used in these filters.
Figure Active Low pass filter- First Order

• The resistor R, smoothens the input signal and the capacitor C allows higher frequencies to reach the ground.
• The high frequency signals never reach the input terminal and only low frequency signal reaches the input terminal.
• In the response figure, a frequency is noted where the response curve point meets a -3dB line drawn below the
maximum gain.
• The frequency is considered as corner frequency (fC) above which the filter attenuates the input signal and below which
it allows the signal.
• As shown in the figure response -20 dB/decade slope is obtained. The response analysis shall be analyzed in the
following section.

Figure. Second Order Active Low Pass Filter
• With first order circuit, another RC circuit is added as shown in the figure and the response is shown
in the figure for second order LPF with a slope of -40 dB/ decade.
• This is due to the fact that, each RC network introduces -20dB decrease in stop band response slope
SECOND ORDER LOW PASS FILTER

Second Order Active Low Pass Filter

High Pass Filters
A high pass filter attenuates low frequencies below corner frequency (cut-off frequency) and allows high frequencies
above cut-off frequency. This is shown in the frequency in fig b
The circuit is a simple non-inverting amplifier, where a RC low pass filter circuit is connected to the input.
Fig : First Order Active High Pass Filter

Second Order Active High Pass Filter

HIGHER ORDER HIGH PASS FILTER
THIRD ORDER HIGH PASS BUTTER-WORTH FILTER

Band Pass Filters
A Band pass filter allows a band of frequencies and blocks lower and higher frequencies other than the
allowed band as shown in fig b. As shown in the fig a, high pass and low pass filters are connected in series.
Fig. a. Active Band Pass Filter
Fig b. Response of Active Band Pass Filter
The corner frequency of low pass filter fL is chosen to be lower than that of high pass filter fH. Thus the
difference between fH and fL is considered to be the pass band. In low frequency stop band, the response
increases 20 dB per decade and in high frequency stop band, the response decreases by 20 dB per
decade.

This filter has a maximum gain at the resonant frequency ( fr), which is defined as
(i) Narrow Band Pass Filter – Quality Factor (Q > 10)
(ii) Wide Band Pass Filter – Quality Factor (Q < 10)

NARROW BAND PASS FILTER
The Node Voltage equation at Node A : ViY1 + VoY3 = VA (Y1+Y2+Y3+Y4)
Assuming VB = 0 (Virtual Ground), the node voltage equation at Node B is,

Band Reject Filters (Notch filter)
•A Band pass filter blocks a band of frequencies and allows lower and higher frequencies other than the
blocked band as shown in fig.b.
•As shown in the fig.a, band pass filter is connected to a summer circuit.
•The input and output of the band pass filter is summed up at the inverting summer input.
•The bands are inverted by the inverting summer and so pass band of band pass filter becomes stop band
and stop bands becomes pass bands.
•Thus this filter only allows particular band above lower corner frequency fL and below upper corner
frequency fH.
Fig.a. Active Band Reject Filter

Fig. b. Response of Active Band Reject Filter
Possible questions:
•Write briefly about first and second order Butterworth Low-pass filter with neat sketches.
•Write briefly about first and second order Butterworth high-pass filter with neat sketches.
•Write briefly about first order Butterworth band-pass filter with neat sketches.
•Write briefly about first order Butterworth band-reject filter with neat sketches.
•Write briefly about Notch filter with neat sketches.

BAND REJECT FILTER
WIDE BAND REJECT FILTER

NARROW BAND REJECT FILTER (NOTCH FILTER)

As K approaches unity, Q factor becomes very large and B approaches zero. In fact, mismatches between
resistors and capacitors limit the Q factor and bandwidth (B) to a practically realisable value.
They are also useful for the rejection of a single frequency, such as 50 or 60 Hz power line frequency

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