The Operational Amplifier

Fall 2001 The Op Amp 1

The Operational Amplifier

The integrated circuit operational amplifier (IC op amp) is one of the most widely used and most versatile electronic components. The device is found in many modern electronic systems because of its versatility, ease of use, and cost effectiveness. Various schematic symbols for an op amp are shown below.

•In reality, all three schematic symbols are the same. The symbol on the far left explicitly shows connections to external power, while the two symbols on the right do not show these connections but imply them, nevertheless.

•Op amps are active devices and, therefore, require an source of power (also called bias voltages).

•The two symbols on the right are identical except for their orientation.

op amp schematic symbols


Op amp connections

inverting input

noninverting input

+ vout -output

V++, positive power supply (bias) connection

V--,negative power supply (bias) connection

Often, in order to make circuit diagrams simpler, the power supply connections are not shown. However, as stated earlier, they must always be made in practice.


Op amp model

Ri is the input resistance of the op amp. Ri is very large, several 100M or several thousand M . Ideally, Ri = ( an open circuit). Because Ri is so large, under normal operating conditions the currents into the inputs of the op amp are negligible.

Ro is the output resistance of the op map. Ro is very small, less than 100. Because Ro is so small, under normal operating conditions the output voltage Vo is the same as the voltage at the dependent source (Vo Avocvid) . Avoc is the open-circuit voltage gain. Avoc is very large, typically 100,000 or greater. Ideally, Avoc is infinite. When operating under normal conditions, this large value of Avoc causes the differential input voltage, vid, to be very small; ideally vid = 0.

-vid

+

+Avocvid

-

+vo

-

0 A

0 A


Ideal op amp assumptions;

The input of an ideal op amp acts like both an open circuit (zero current) and a short circuit (zero voltage) simultaneously.

-0v+

0A

0A

Using these two assumptions along with circuit analysis techniques such as Ohm’s law, KVL and KCL, we can derive equations which define the operation of a number of basic and useful op amp circuits.

An op amp is often used to construct an amplifier. An amplifier is a circuit which converts a small input signal into a larger signal at the output. While amplification is not the only reason to use an amplifier, it is one of the primary reasons.


The inverting amplifier

+vin

-

+vo

-

The voltage at the noninverting terminal is zero because the terminal is tied to common.

The voltage at the inverting terminal is zero because there is no voltage drop across the op amp input. The inverting terminal is at virtual ground

0v

By KVL, vin - I1R1 = 0 I1 = vin/R1

I1 0A

I2

By KCL, I2 = I1= vin/R1

By KVL, vo + I2R2 = 0 vo = -I2R2 = -(vin/R1) R2

2

1o

vin

v RA

v R

Note also that vin “sees” R1 ohms of resistance. The input resistance of the inverting amplifier is R1.


The noninverting amplifier The input signal is applied at the noninverting terminal

The voltage at the inverting terminal is also vin since there is no voltage drop across the op amp input. vin

By KVL, vin - I1R1 = 0 I1 = vin/R1

I10A

I2

By KCL, I2 = I1= vin/R1

By KVL, vo - I2R2 - I1R1 = 0 vo = I2(R1 + R2) = (vin/R1) (R1 + R2 )

21

1o

vin

v RA

v R

Note also that vin “sees” an open circuit since the op amp input current is zero.

+vin

-

+vo

-


Op amp circuitsThe inverting amplifier

1R

2R

v

vA

in

ov

+vin

-

+vo

-

Iin

1RR1R

vI in

oin

+vin

-

+vo

-

1R

2R1

v

vA

in

ov

Iin

inin R0I

The noninverting amplifier


The buffer amplifier

+vin

-vin

+vo

-

vo = vin

Q: Since there is no gain (vo = vin gain = 1) is this circuit useful? If so, why?

A: Iin = 0 since the input is tied to the noninverting input of the op amp.

There is no power demanded from the input source. vin sees a very large (ideally infinite) input resistance.

vo is the same value as vin, but any power demanded from vo comes from the op amp (the op amp power supplies) and not the input signal.


+vo

-

I1

I2

If = I1 + I2

0v

1 21 21 2

v vI and I

R R

( 1 2)

1 2

1 2

o f f f

o f

v R I R I I

v vv R

R R

• The output is a weighted sum of the input signals, v1 and v2.• If R1 = R2, vo is proportional to the sum of the inputs.• The circuit is sometimes called an inverting adder, summer, or mixer.

The mixer

Observations:


The difference (differential) amplifier. Vo = K(V2 - V1)

+vo

-

+vX

-

By VDR: 22

1 2X

RV V

R R

vX

Since the voltages at the noninverting and inverting terminals are the same, the voltage at the inverting terminal is also Vx

Writing a nodal equation at the inverting terminal yields:

1 1 1 10

1 2 1 2 1 2

2 1 1

1 2 1 2

2 2 2 1 1

1 2 1 2 1 2

22 1

1

X o oXX

oX

o

o

V V VV V VV

R R R R R R

VR R VV

R R R R

VR V R R V

R R R R R R

RV V V

R

22 1

1o

RV V V

R

The output is proportional to the difference of the two inputs.

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The Operational Amplifier