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Op-Amp

Operational Amplifier

Non Inverting Amplifier

Inverting Amplifier

Adder (and Subtractor using an Inverter)

Differential Amplifier

Integrator

Differentiator

Op-Ampname derives from early usage of these elements inperforming mathematical operationsin analog computers.


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Three Ways to Examine Op-Amp Behavior Consider as an Ideal Op-Amp

Component Consider as a Feedback Model and

Examine Behavior

Perform Conventional CircuitAnalysis


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Differential amplifier is a closed loop amplifier

circuit which amplifies the difference between

two signals. Such a circuit is very useful in

instrumentation systems. Differential

amplifiers have high common mode rejection

ratio (CMRR) and high input impedance.

Differential amplifiers can be made using oneopamp or two opamps. Both of these

configurations are explained here.


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The circuit diagram of a differential amplifier using one opamp is shownabove

DIFFERENTIAL AMPLIFIER USING ONE OP-AMP

R1 and R2 are the input resistors

Rf is the feedback resistor

RL is the load resistor.


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Derivation for voltage gain.

When Va is made zero the circuit

becomes a non inverting amplifier. Let

V1 be the voltage at the non inverting

input pin. Relation between Vb and V1

can be expressed using the following

equation.

Output voltage Vob due to Vb alone is

according to the equation


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Let R1 = R2 and R3 =Rf , then

Then overall output voltage is

Therefore overall gain is


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Circuit diagram of a differential amplifier using two opamps is shown below. Main

advantage of differential amplifier with two opamps is that it has increased overall gain.

R1 is the input resistor for IC1

R3 is the input resistor for IC2.

Rf is the feedback resistor

Va and Vb are the two input

voltages applied to the non

inverting inputs of IC2 and IC1

respectively

RL is the load resistor

V+ and V- are the positive and

negative supply voltages.

DIFFERENTIAL AMPLIFIER USING TWO OPAMPS


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DERIVATION OF VOLTAGE GAIN

V1 and Va are the inputs for the second stage

(IC2). Output voltage due to Va alone is.

Output voltage due to Vb alone is

The equation for the output voltage V1 of

the first opamp (IC1) is as follows.


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Overall output voltage Vo = Voa + Vob

Let R1 = R2 and Rf =R1, then we have

Therefore overall voltage gain Av can be

expressed using the equation


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The Summing Amplifier

The Summing Amplifier is a very flexible circuit based upon the standard Inverting

Operational Amplifierconfiguration that can be used for combining multiple inputs.We saw previously in the inverting amplifier tutorial that the inverting amplifier has a

single input voltage, ( Vin ) applied to the inverting input terminal. If we add more

input resistors to the input, each equal in value to the original input resistor, Rin we

end up with another operational amplifier circuit called a Summing Amplifier,

"summing inverter" or even a "voltage adder" circuit as shown below


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The output voltage, ( Vout ) now becomes

proportional to the sum of the input

voltages, V1, V2, V3 etc.

Then we can modify the original equation

for the inverting amplifier to take accountof these new inputs thus:

However, if all the input impedances, ( Rin )

are equal in value, we can simplify the above

equation to give an output voltage of:

Summing Amplifier Equation

We now have an operational amplifier circuit that will amplify each individual input voltage

and produce an output voltage signal that is proportional to the algebraic "SUM" of the

three individual input voltagesV1, V2 and V3. We can also add more inputs if required as

each individual input "see's" their respective resistance, Rin as the only input impedance.

This is because the input signals are effectively isolated from each other by the "virtual

earth" node at the inverting input of the op-amp. A direct voltage addition can also beobtained when all the resistances are of equal value and Ris equal to Rin.


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A Scaling Summing Amplifier can be made if

the individual input resistors are "NOT" equal.

Then the equation would have to be modified

to:

To make the math's a little easier, we can

rearrange the above formula to make the

feedback resistorRF the subject of the equationgiving the output voltage as:

This allows the output voltage to be easily calculated if more input resistors are connectedto the amplifiers inverting input terminal. The input impedance of each individual channel

is the value of their respective input resistors, ie, R1, R2, R3 ... etc.

The Summing Amplifier is a very flexible circuit indeed, enabling us to effectively "Add" or

"Sum" (hence its name) together several individual input signals. If the inputs

resistors, R1, R2, R3 etc, are all equal a unity gain inverting adder can be made. However, if

the input resistors are of different values a "scaling summing amplifier" is produced whichgives a weighted sum of the input signals.


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Summing Amplifier Audio Mixer

Digital to Analogue Converter


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Example No1

Find the output voltage of the

following Summing Amplifiercircuit.

we know that the output voltage is the sum of the two amplified input signals

and is calculated as

we can now substitute the values of the

resistors in the circuit as follows,

Then the output voltage of the Summing

Amplifier circuit above is given as -45 mV and

is negative as its an inverting amplifier.


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the Op-amp Integrator is an operationalamplifier circuit that performs the

mathematical operation ofIntegration


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the voltage on the plates of a capacitor is

equal to the charge on the capacitor divided by

its capacitance giving Q/C. Then the voltage

across the capacitor is output Vouttherefore: -

Vout = Q/C. If the capacitor is charging and

discharging, the rate of charge of voltageacross the capacitor is given as:

But dQ/dt is electric current and since the

node voltage of the integrating op-amp at its

inverting input terminal is zero, X = 0, the input

current I(in) flowing through the input

resistor, Rin is given as:


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The current flowing through the feedback

capacitor C is given as:

Assuming that the input impedance of the op-

amp is infinite (ideal op-amp), no current flows

into the op-amp terminal. Therefore, the nodal

equation at the inverting input terminal is

given as

From which we derive an ideal voltage output

for the OP-amp Integrator as:


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Where = 2and the output voltage Vout is

a constant 1/RC times the integral of the input

voltageVin with respect to time. The minussign ( - ) indicates a 180o phase shift because

the input signal is connected directly to the

inverting input terminal of the op-amp.

simplify the math's a little, this can also be re-

written as


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The Op-amp Differentiator Amplifier

The basic Op-amp Differentiator circuit is the exact opposite to that of

the Integrator operational amplifier circuit that we saw in the previous

tutorial. Here, the position of the capacitor and resistor have been reversedand now the reactance, Xc is connected to the input terminal of the inverting

amplifier while the resistor, Rforms the negative feedback element across the

operational amplifier as normal.

This circuit performs the mathematical operation ofDifferentiation, that is it

"produces a voltage output which is directly proportional to the input voltage's

rate-of-change with respect to time". In other words the faster or larger thechange to the input voltage signal, the greater the input current, the greater

will be the output voltage change in response, becoming more of a "spike" in

shape.

As with the integrator circuit, we have a resistor and capacitor forming an RC

Network across the operational amplifier and the reactance ( Xc ) of the

capacitor plays a major role in the performance of aOp-amp Differentiator.

amplifier summing point X resulting in zero
http://www.electronics-tutorials.ws/opamp/opamp_6.htmlhttp://www.electronics-tutorials.ws/opamp/opamp_6.html


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amplifier summing point, X resulting in zerooutput voltage. The capacitor only allows AC

type input voltage changes to pass through

and whose frequency is dependant on the rate

of change of the input signal.

At low frequencies the reactance of the

capacitor is "High" resulting in a low gain

( R/Xc ) and low output voltage from the op-

amp. At higher frequencies the reactance of

the capacitor is much lower resulting in a

higher gain and higher output voltage from the

differentiator amplifier.

However, at high frequencies an op-amp

differentiator circuit becomes unstable and will

start to oscillate. This is due mainly to the first-

order effect, which determines the frequency

response of the op-amp circuit causing a

second-order response which, at highfrequencies gives an output voltage far higher

than what would be expected. To avoid this

the high frequency gain of the circuit needs to

be reduced by adding an additional small value

capacitor across the feedback resistor R.

Ok, some math's to explain what's going on!.Since the node voltage of the operational


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Ok, some math's to explain what's going on!.

Since the node voltage of the operational

amplifier at its inverting input terminal is zero,

the current, i flowing through the capacitor

will be given as:

The charge on the capacitor equals

Capacitance x Voltage across the capacitor

The rate of change of this charge is

but dQ/dt is the capacitor current i

from which we have an ideal voltage output

for the op-amp differentiator is given as:


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Therefore, the output voltage Vout is a constant -R.C times the derivative of the input

voltage Vin with respect to time. The minus sign indicates a 180o phase shift because the inpu

signal is connected to the inverting input terminal of the operational amplifier.

One final point to mention, the Op-amp Differentiator circuit in its basic form has two main

disadvantages compared to the previous integrator circuit. One is that it suffers from instabilitat high frequencies as mentioned above, and the other is that the capacitive input makes it

very susceptible to random noise signals and any noise or harmonics present in the source

circuit will be amplified more than the input signal itself. This is because the output is

proportional to the slope of the input voltage so some means of limiting the bandwidth in

order to achieve closed-loop stability is required


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