OPERATIONAL AMPLIFIER

The ideal OP AMP Characteristics:

• Infinite voltage gain Ad
• Infinite input resistance Ri, so that almost any signal source can drive it and
there is no loading of the input source.
• Zero output resistance RO, so that output can drive an infinite number of other
devices.
• Zero output voltage when input voltage is zero.
• Infinite bandwidth so that any frequency signal from 0 to infinite Hz can be
amplified without attenuation.
• Infinite common mode rejection ratio so that the output common mode noise
voltage is zero.
• Infinite slew rate, so that output voltage changes occur simultaneously with
input voltage changes.
There are practical OPAMPs that can be made to approximate some of these
characters using a negative feedback arrangement.
 Equivalent Circuit of an OPAMP:
• This equivalent circuit is
useful in analyzing the basic
operating principles of
OPAMP and in observing the
effects of standard feedback
arrangements.

vO = Ad (v1 – v2) = Ad vd

• Ri is the input impedance of OPAMP.

• AdVd is an equivalent Thevenin voltage
source.
• RO is the Thevenin equivalent impedance
looking back into the terminal of an
OPAMP.
Open loop OPAMP Configuration:

• In the case of amplifiers the term open loop indicates that no connection,
exists between input and output terminals of any type.
• That is, the output signal is not fedback in any form as part of the input
signal.
• In open loop configuration, The OPAMP functions as a high gain amplifier.

There are three open loop OPAMP configurations.

➢The Differential Amplifier

➢The Inverting Amplifier
➢The Non-inverting Amplifier
 Differential Amplifier
• The OPAMP amplifies the difference the between the two input signals, hence this configuration is called the
differential amplifier.
• The OPAMP amplifies both ac and dc input signals.
• The source resistance Rin1 and Rin2 are normally negligible compared to the input resistance Ri.
• Therefore voltage drop across these resistances can be assumed to be zero.

Therefore

V1 = vin1 and v2 = vin2

vo = Ad (vin1 – vin2 )

where, Ad is the open loop gain.

 Inverting Amplifier
• If the input is applied to only inverting
terminal and non-inverting terminal is
grounded then it is called inverting amplifier.
• v1= 0, v2 = vin.

• vo = -Ad vin
• The negative sign indicates that the output
voltage is out of phase with respect to input
180 ° or is of opposite polarity. Thus the input
signal is amplified and inverted also.
 Non-inverting amplifier
• The input voltage is applied to non-
inverting terminals and inverting
terminal is ground.
• v1 = +vin v2 = 0

• vo = +Ad vin

• This means that the input voltage is

amplified by Ad and there is no phase
reversal at the output.
• In all the configurations any input signal slightly greater than zero
drive the output to saturation level.

• This is because of very high gain.

• Thus when operated in open-loop, the output of the OPAMP is either

negative or positive saturation or switches between positive and
negative saturation levels.

• Therefore open loop op-amp is not used in linear applications.

 Closed Loop Amplifier:
• The gain of the OPAMP can be controlled if feedback is introduced in the circuit.
• That is, an output signal is fedback to the input either directly or via another
network.
• If the signal fedback is of opposite or out phase by 180° with respect to the input
signal, the feedback is called negative fedback. (An amplifier with negative
feedback has a self-correcting ability of change in output voltage caused by changes
in environmental conditions. It is also known as degenerative feedback because it
reduces the output voltage and, in turn, reduces the voltage gain.)
• If the signal is fedback in phase with the input signal, the feedback is called positive
feedback. (In positive feedback the feedback signal aids the input signal. It is also
known as regenerative feedback. Positive feedback is necessary in oscillator
circuits.)
• The negative fedback stabilizes the gain, increases the bandwidth and changes the
input and output resistances. Other benefits are reduced distortion and reduced
offset output voltage. It also reduces the effect of temperature and supply voltage
variation on the output of an op-amp.
Types of feedback
• Voltage – series feedback
• Voltage – shunt feedback
• Current – series feedback
• Current – shunt feedback
Negative feedback
• Reduce the gain, circuit becomes controllable.
• Reduction in distortion.
• Increase in band width.
• Increase in input resistance.
• Decrease in output resistance.
• Reduction in output offset voltage.
• Reduction in temperature and supply voltage variation effects.
 Voltage series feedback:
• It is also called non-inverting voltage
feedback circuit.
• With this type of feedback, the input
signal drives the non-inverting input
of an amplifier; a fraction of the
output voltage is then fed back to the
inverting input.
• The op-amp is represented by its
symbol including its large signal
voltage gain Ad or A, and the feedback
circuit is composed of two resistors
R1 and Rf.
 Voltage series feedback:

• The feedback voltage always opposes

the input voltage, (or is out of phase
by 180° with respect to input voltage),
hence the feedback is said to be
negative.
The closed loop voltage gain is given by
Also called as Non-Inverting Amplifier

The product A and B is called loop gain. The gain loop gain is very large such that AB >> 1

It means that closed loop gain is no longer dependent on the gain of the op-amp, but depends on the feedback of
the voltage divider.
 Voltage shunt Feedback:
• The input voltage drives the inverting terminal, and the amplified as well as
inverted output signal is also applied to the inverting input via the
feedback resistor Rf.
• This arrangement forms a negative feedback because any increase in the
output signal results in a feedback signal into the inverting input signal
causing a decrease in the output signal.
• The non-inverting terminal is grounded. Resistor R1 is connected in series
with the source.
Voltage shunt Feedback:

The negative sign in equation indicates that the input and output signals are out of
phase by 180. Therefore it is called inverting amplifier.
The gain can be selected by selecting Rf and R1 .
Input Resistance with Feedback:
 Input Resistance with Feedback:
• To find the input resistance Miller equivalent of the
feedback resistor Rf, is obtained, i.e. Rf is splitted
into its two Miller components as shown in figure.
• Therefore, input resistance with feedback Rif is then
 Path 1 = Ia (=I0) Ro (small)
Path 2 = Ib (almost 0) (R1+Rf)||Rin (big)
V0 – I0R0 – Avd = 0

• The output resistance with feedback Rof is the resistance

measured at the output terminal of the feedback
amplifier.
• The output resistance can be obtained using Thevenin's
equivalent circuit.
i O = ia + ib
Since RO is very small as compared to Rf +(R1 || R2 )
Therefore,i.e. iO= ia
vO = RO iO + A vd.
vd= vi – v2 = 0 - B vO

I0 = V0(1+AB)/R0
V0/I0 =R0/(1+AB)= R0f

Output Resistance with Feedback: Similarly, the bandwidth increases by (1+ AB) and total output offset voltage reduces by (1+AB).
Thank you
Miller theorem establishes that in a linear circuit, if there exists a branch with impedance Z, connecting two nodes with
nodal voltages V1 and V2, we can replace this branch by two branches connecting the corresponding nodes to ground by
impedances respectively Z/(1 − K) and KZ/(K − 1), where K = V2/V1.