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UNIT –2 / Lecture 01
OPERATIONAL AMPLIFIER
Input offset voltage
The input offset voltage (
) is a parameter defining the differential DC voltage required
between the inputs of an amplifier, especially an operational amplifier(op-amp), to make
the output zero (for voltage amplifiers, 0 volts with respect to ground or between
differential outputs, depending on the output type).[1]
An ideal op-amp amplifies the differential input; if this input is 0 volts (i.e. both inputs are
at the same voltage with respect to ground), the output should be zero. However, due to
manufacturing process, the differential input transistors of real op-amps may not be
exactly matched. This causes the output to be zero at a non-zero value of differential
input, called the input offset voltage.
Typical values for
are around 1 to 10mV for cheap commercial-grade opamp integrated circuits (IC). This can be reduced to several microvolts if nulled using the
IC's offset null pins or using higher-quality or laser-trimmed devices. However, the input
offset voltage value may drift with temperature or age. Chopper amplifiers actively
measure and compensate for the input offset voltage, and may be used when very low
offset voltages are required.
Input bias current and input offset current also affect the net offset voltage seen for a
given amplifier. The voltage offset due to these currents are separate from the input
offset voltage parameter and is related to the impedance of the signal source and of the
feedback and input impedance networks. such as the two resistors used in the basic
inverting and non-inverting amplifier configurations. FET-input op-amps tend to have
lower input bias currents than bipolar-input op-amps, and hence incur less offset of this
type.
Op Amp Input Bias Current
CIRCUIT
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One of the golden rules of op amp analysis says this: no current flows into either input
terminal. This concept is key for analyzing an amplifier's signal gain. However, in reality, a
small current flows into both inputs to bias the input transistors. Unfortunately, this bias
current gets converted into a voltage by the circuit's local resistors and amplified right
along with the signal. The result is an output error in your circuit. What can you do about
it? A clever choice of resistor values can help you cancel most of the output error. The
remaining error can be adjusted to zero if necessary.
INPUT BIAS CURRENT
Depending on the type of input transistor, the bias current can flow in or out of the input
terminals. The input current is modeled as current sources, Ib+ and Ib-, in parallel with
the positive and negative input terminals. How big is this current? The magnitudes can
range fromμA down to pA. Generally speaking, JFET or CMOS op amps have smaller bias
currents than BJT types. Although Ib+ and Ib- are similar in magnitude, there not exactly
the same. This difference, called the input offset current, is described by Iboff = Ib+ - Ib- .
Input offset current
It means a voltage ± 6 mV is required to one of the input to reduce the
output offsetvoltage to zero. The smaller the input offsetvoltage the better the
differential amplifier, because its transistors are more closely matched.
Output offset current
in case of an operational amplifier, a sort of leakage current produced at the output by an
operational amplifier when no input is applied to it.
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UNIT –2 / Lecture 02
Thermal drift
Real op-amps also create noise in the circuit, have an offset voltage,thermal drift and
finite bandwidth. means that there exists a voltage vdwhen both inputs are grounded. This
offset is called an input offset because the voltage vd is offset from its ideal value of zero
volts.
Common mode rejection ratio
The common-mode rejection ratio (CMRR) of a differential amplifier (or other device)
measures the ability of the device to reject common-mode signals, those that appear
simultaneously and in-phase on both amplifier inputs. An ideal differential amplifier
would have infinite CMRR; this is not achievable in practice. A high CMRR is required when
a differential signal must be amplified in the presence of a possibly large common-mode
input. An example is audio transmission overbalanced lines.
Ideally, a differential amplifier takes the voltages,
produces an output voltage
and
, where
on its two inputs and
is the differential gain.
However, the output of a real differential amplifier is better described as
where
is the common-mode gain, which is typically much smaller than
the differential gain.
The CMRR is defined as the ratio of the powers of the differential gain over the
common-mode gain, measured in positive decibels (thus using the 20 log rule):
As differential gain should exceed common-mode gain, this will be a positive
number, and the higher the better.
The CMRR is a very important specification, as it indicates how much of
the common-mode signal will appear in your measurement. The value of the
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CMRR often depends on signal frequency as well, and must be specified as
a function thereof.
It is often important in reducing noise on transmission lines.[citation needed] For
example, when measuring the resistance of a thermocouple in a noisy
environment, thenoise from the environment appears as an offset on both input
leads, making it a common-mode voltage signal. The CMRR of the measurement
instrument determines the attenuation applied to the offset or noise.
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UNIT –2 / Lecture 03
Slew rate
In electronics, slew rate is defined as the maximum rate of change of output voltage per
unit of time and is expressed as volts per second. Limitations in slew rate capability can
give rise to non-linear effects in electronic amplifiers. For a sinusoidal waveform not to be
subject to slew rate limitation, the slew rate capability (in volts per second) at all points in
an amplifie rmust satisfy the following condition:
where f is the operating frequency, and
is the peak amplitude of the waveform.
The slew rate of an electronic circuit is defined as the maximum rate of change of the
output voltage. Slew rate is usually expressed in units of V/µs.
where
is the output produced by the amplifier as a function of time t.
The slew rate can be measured using a function generator (usually square wave) and
an oscilloscope. The slew rate is the same, regardless of whether feedback is
considered.
There are slight differences between different amplifier designs in how the slewing
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phenomenon occurs. However, the general principles are the same as in this illustration.
The input stage of modern amplifiers is usually a differential amplifier with
a transconductance characteristic. This means the input stage takes a differential input
voltage and produces an output current into the second stage.
The transconductance is typically very high — this is where the large open loop gain of the
amplifier is generated. This also means that a fairly small input voltage can cause the
input stage to saturate. In saturation, the stage produces a nearly constant output
current.
The second stage of modern power amplifiers is, among other things, where frequency
compensation is accomplished. The low pass characteristic of this stage approximates
an integrator. A constant current input will therefore produce a linearly increasing output.
If the second stage has an effective input capacitance
and voltage gain
, then slew
rate in this example can be expressed as:
where
is the output current of the first stage in saturation.
Slew rate helps us identify the maximum input frequency and amplitude applicable to
the amplifier such that the output is not significantly distorted. Thus it becomes
imperative to check the datasheet for the device's slew rate before using it for highfrequency applications.
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UNIT –2 / Lecture 04
Power Supply Rejection Ratio
In electronics, power supply rejection ratio or PSRR is a term widely used in the electronic
amplifier (especially operational amplifier) or voltage regulatordatasheets; used to
describe the amount of noise from a power supply that a particular device can reject.
The PSRR is defined as the ratio of the change in supply voltage in the op-amp to the
equivalent (differential) output voltage it produces often expressed indecibels. An ideal
op-amp would have infinite PSRR. The output voltage will depend on the feedback circuit,
as is the case of regular input offset voltages. But testing is not confined to DC (zero
frequency); often an operational amplifier will also have its PSRR given at various
frequencies (in which case the ratio is one of RMS amplitudes of sine waves present at a
power supply compared with the output, with gain taken into account).
Unwanted oscillation, including motor boating, can occur when an amplifying stage is too
sensitive to signals fed via the power supply from a later power amplifier stage.
Some manufacturers specify PSRR in terms of the offset voltage it causes at the amplifiers
inputs; others specify it in terms of the output; there is no industry standard for this
issue. The
following
formula
assumes
it
is
specified
in
terms
of
output:
For example: an amplifier with a PSRR of 100 dB in a circuit to give 40 dB closedloop gain would allow about 1 milli volt of power supply ripple to be superimposed on the
output for every 1 volt of ripple in the supply. This is because
.
And since that's 60 dB of rejection, the sign is negative so:
Note:

The PSRR doesn't necessarily have the same poles as A(s), the open-loop gain of the
op-amp, but generally tends to also worsen with increasing frequency
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
For amplifiers with both positive and negative power supplies (with respect to earth,
as op-amps often have), the PSRR for each supply voltage may be separately specified
(sometimes written: PSRR+ and PSRR-), but normally the PSRR is tested with opposite
polarity signals applied to both supply rails at the same time (otherwise the commonmode rejection ratio (CMRR) will affect the measurement of the PSRR).

For voltage regulators the PSRR is occasionally quoted (confusingly; to refer
to output voltage change ratios), but often the concept is transferred to other terms
relating changes in output voltage to input: Ripple rejection (RR) for low frequencies,
line transient response for high frequencies, and line regulation for DC.

Sometimes kSVR (or simply SVR) is used to denote the power supply rejection ratio.
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UNIT –2 / Lecture 05
Gain Bandwidth product
Adding negative feedback limits the amplification but improves frequency response of the
amplifier.
The gain–bandwidth product (designated as GBWP, GBW, GBP or GB) for an amplifier is
the product of the amplifier's bandwidth and the gain at which the bandwidth is
measured.
For devices such as operational amplifiers that are designed to have a simple onepole frequency response, the gain–bandwidth product is nearly independent of the gain
at which it is measured; in such devices the gain–bandwidth product will also be equal to
the unity-gain bandwidth of the amplifier (the bandwidth within which the amplifier gain
is at least 1.For an amplifier in which negative feedback reduces the gain to below
the open-loop gain, the gain–bandwidth product of the closed-loop amplifier will be
approximately equal to that of the open-loop amplifier,"The parameter characterizing the
frequency dependence of the operational amplifier gain is the finite gain–bandwidth
product (GB)
If the GBWP of an operational amplifier is 1 MHz, it means that the gain of the device falls
to unity at 1 MHz. Hence, when the device is wired for unity gain, it will work up to 1 MHz
(GBWP = gain × bandwidth, therefore if BW = 1 MHz, then gain = 1) without excessively
distorting the signal. The same device when wired for a gain of 10 will work only up to
100 kHz, in accordance with the GBW product formula. Further, if the minimum
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frequency of operation is 1 Hz, then the maximum gain that can be extracted from the
device is 1×106.
We can also analytically show that for
Let
be a first-order transfer function given by:
We will show that:
Proof:
Example for
GBWP is constant.
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UNIT –2 / Lecture 06
Op amp frequency compensation
Most op amp chips have frequency compensation added to them. It is introduced to
ensure they remain stable and do not produce unwanted high frequency spurious
oscillations.
It is required because stray capacitances in the chip can cause unwanted phase shifts at
high frequencies, e.g. 1 MHz and more. While the stray capacitance levels may not be
significant at low frequencies, they can cause significant problems at higher frequencies,
and they are almost impossible to eliminate in the chip.
Most op amp IC manufacturers solve this problem by intentionally reducing the open-loop
gain at high frequencies. This is called compensation and it is normally implemented by
bypassing one of the internal amplifier stages with a high-pass filter. The aim is to reduce
the gain to less than unity at frequencies where there could be a possibility of oscillation.
Very early op amps did not have this frequency compensation built into the chip and
external compensation components were required on the pins provided - the 709 was a
prime example of this. Later chips such as the 741 had internal compensation making the
chips much easier to use. However they also had a low open loop break point. In the case
of the 741 it was just 10 Hz. This compensation is now standard in all general purpose op
amp chips. Modern chips continue to have it built in a standard.
Op amp frequency response with and without frequency compensation
Frequency compensation is the major reason why op-amps are not very fast devices - the
higher frequency components of the signals are intentionally attenuated. The frequency
at which the Op amp open loop gain falls to unity, is called fT - as for bipolar transistors.
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This frequency gives a good indication of the speed of the op-amp.
However, comparators, do not use negative feedback and as a result they are designed
without compensation and their speed of operation is typically much faster than that of
op amps.
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UNIT –2 / Lecture 07
a transient response or natural response is the response of a system to a change from
equilibrium. The transient response is not necessarily tied to "on/off" events but to any
event that affects the equilibrium of the system. The impulse response and step
response are transient responses to a specific input (an impulse and a step, respectively).
Damping
The response can be classified as one of three types of damping that describes the output
in relation to the steady-state response.
An underdamped response is one that oscillates within a decaying envelope. The more
underdamped the system, the more oscillations and longer it takes to reach steady-state.
Here damping ratio is always <1.
A critically damped response is the response that reaches the steady-state value the
fastest without being underdamped. It is related to critical points in the sense that it
straddles the boundary of underdamped and overdamped responses. Here, damping ratio
is always equal to one. There should be no oscillation about the steady state value in the
ideal case.
An overdamped response is the response that does not oscillate about the steady-state
value but takes longer to reach than the critically damped case. Here damping ratio is >1
it is the response of a system with respect to the input as a function of time
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Rise time
Rise time refers to the time required for a signal to change from a specified low value to a
specified high value. Typically, these values are 10% and 90% of the step height.
Overshoot
Overshoot is when a signal or function exceeds its target. It is often associated
with ringing.
Settling time
Settling time is the time elapsed from the application of an ideal instantaneous step input
to the time at which the output has entered and remained within a specified error band.
Delay-time
The delay time is the time required for the response to reach half the final value the very
first time
Peak time
The peak time is the time required for the response to reach the first peak of the
overshoot
Steady-state error
the steady-state error of a system as "the difference between the desired final output and
the actual one" when the system reaches a steady state, when its behavior may be
expected to continue if the system is undisturbed
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UNIT –2 / Lecture 08
TL 082 General Description
These devices are low cost, high speed, dual JFET input
operational amplifiers with an internally trimmed input offset
voltage (BI-FET II™ technology). They require low supply
current yet maintain a large gain bandwidth product and fast
slew rate. In addition, well matched high voltage JFET input
devices provide very low input bias and offset currents.
The TL082 is pin compatible with the standard LM1558
allowing designers to immediately upgrade the overall
performance of existing LM1558 and most LM358 designs.
TL082 Features
– Internally trimmed offset voltage: 15 mV
– Low input bias current: 50 pA
– Low input noise voltage: 16nV/ÖHz
– Low input noise current: 0.01 pA/ÖHz
– Wide gain bandwidth: 4 MHz
– High slew rate: 13 V/μs
– Low supply current: 3.6 mA
– High input impedance: 1012W
– Low total harmonic distortion: £0.02%
– Low 1/f noise corner: 50 Hz
– Fast settling time to 0.01%: 2 μs