Electronic InstrumentationExperiment 4

* Operational Amplifiers* Op-Amp Circuits* Op-Amp Analysis

Operational Amplifiers Op-Amps are possibly the most versatile linear

integrated circuits used in analog electronics. The Op-Amp is not strictly an element; it contains

elements, such as resistors and transistors. However, it is a basic building block, just like R,

L, and C. We treat this complex circuit as a black box!

• Do we know all about the internal details? No!• Do we know how to use it and interface it with other

electronic components? Yes, we must!

Op-Amp Circuits perform Operations Op-Amps circuits can perform mathematical

operations on input signals:• addition and subtraction• multiplication and division• differentiation and integration

Other common uses include:• Impedance buffering• Active filters• Active controllers• Analog-digital interfacing

The Op-Amp Chip The op-amp is a chip, a small black box with 8

connectors or pins (only 5 are usually used). The pins in any chip are numbered from 1 (starting

at the upper left of the indent or dot) around in a U to the highest pin (in this case 8).

741 Op Amp

Op-Amp Input and Output The op-amp has two inputs, an inverting input (-) and a

non-inverting input (+), and one output. The output goes positive when the non-inverting input (+)

goes more positive than the inverting (-) input, and vice versa.

The symbols + and – do not mean that that you have to keep one positive with respect to the other; they tell you the relative phase of the output. (Vin=V1-V2)

A fraction of a millivolt between the input terminals will

swing the output over its full range.

Powering the Op-Amp Since op-amps are used as amplifiers, they need an

external source of power. The op-amp must be connected to an external

constant DC source in order to function. Typically, this source will supply +15V at +V and -

15V at -V. The op-amp will output a voltage range of of somewhat less because of internal losses.

The power inputs determine the output range

of the op-amp. It can never output more than

you put in. Here the maximum range is about

28 volts.

Amplifiers increase the magnitude of a signal by multiplier called a gain -- “A”.

The internal gain of an op-amp is very high (105-106). The exact gain is often unpredictable. We call this gain the open-loop gain or intrinsic gain.

Op-Amp Intrinsic Gain

5 6outopen loop

in

V A 10 10V

Op-Amp Saturation Note that in spite of the huge gain, the maximum or

minimum output is still limited by the input power. When the op-amp is at the maximum or minimum

extreme, it is said to be saturated. Ideally, the saturation points for an op-amp are

equal to the power voltages, in reality they are 1-2 volts less.

saturationnegativeVVsaturationpositiveVVVVV

out

out

out

Internal Model of a Real Op-amp

• Zin is the input impedance (very large ≈ 2 MΩ)

• Zout is the output impedance (very small ≈ 75 Ω)

• Aol is the open-loop gain

Vout

V2

+V

-V

-+

V1

Vin = V1 - V2Zin

Zout

+

-

AolVin

Real Op-Amp Characteristics dc-coupled: the op amp can be used with ac and dc

input voltages differential voltage amplifier: the op amp has two

inputs (inverting and non-inverting) single-ended low-resistance output: the op amp has

one output whose voltage is measured with respect to ground. The output looks like a voltage source.

very high input resistance: the op-amp input looks like a load circuit to any circuit connected to its input (ideally 0 current; actually < 1nA)

very high voltage gain: the op-amp will saturate either positive or negative depending on the inputs

Problems using op-amps directly as amplifiers The op-amp intrinsic gain, Aol, can be relied upon to be

very large (1 to 5 million V/V ) but cannot be relied upon to be an accurate stable value.

Using op-amps, we can construct circuits whose performance depends mainly on passive components selected to have accurate and stable values.

As long as Aol is large enough, the behavior of our circuits will depend upon the values of the stable components rather than Aol

Feedback is the process of coupling the op-amp output back into one of the inputs. Understanding feedback is fundamental to understanding op-amp circuits.

Types of Feedback

Negative Feedback• As information is fed back, the output becomes more stable. Output

tends to stay in the desired range.• Examples: cruise control, heating/cooling systems

Positive Feedback• As information is fed back, the output destabilizes. The op-amp will

saturate.• Examples: Guitar feedback, stock market crash

Op-Amp Circuits use Negative Feedback Negative feedback couples the output back in such a

way as to cancel some of the input. This lowers the amplifier’s gain, but improves:

• Freedom from distortion and nonlinearity• Flatness of frequency response or conformity to some

desired frequency response• Stability and Predictability• Insensitivity to variation in Aol

Amplifiers with negative feedback depend less and less on the open-loop gain and finally depend only on the properties of the feedback network itself.

Op-Amp Circuits Op-Amp circuits we will do now

• inverting amplifier (multiply signal by negative gain)• non-inverting amplifier (multiply signal by positive gain)• differential amplifier (multiply difference between two

signals by a positive gain) Op-Amp circuits we will do in experiment 8

• weighted adder• integrator• differentiator• buffer (voltage follower)

Inverting Amplifier

in

fin

in

fout R

RAV

RR

V

Non-inverting Amplifier

g

f

ing

fout

RR

A

VRR

V

1

1

Differential (or Difference) Amplifier

in

f

in

fout R

RAVV

RR

V

)( 12

PSpice circuit you will use in exp 4

Op-Amp Analysis

We assume we have an ideal op-amp:• infinite input impedance (no current at inputs)• zero output impedance (no internal voltage losses)• infinite intrinsic gain• instantaneous time response

Golden Rules of Op-Amp Analysis Rule 1: VA = VB

• The output attempts to do whatever is necessary to make the voltage difference between the inputs zero.

• The op-amp “looks” at its input terminals and swings its output terminal around so that the external feedback network brings the input differential to zero.

Rule 2: IA = IB = 0• The inputs draw no current• The inputs are connected to what is essentially an

open circuit

1) Remove the op-amp from the circuit and draw two circuits (one for the + and – input terminals of the op amp).

2) Write equations for the two circuits.3) Simplify the equations using the rules for op amp analysis and

solve for Vout/Vin

How to analyze a circuit with an op-amp

in

f

in

out

f

out

in

inBA

A

f

outB

in

Bin

RR

VV

RV

RVVV

V

RVV

RVV

RVi

0)3

0:

:)2

:

:)1

g

f

in

out

g

gf

in

outout

gf

ginBA

outgf

gB

inA

RR

VV

RRR

VVV

RRR

VVV

VRR

RV

VV

1

)3

:

:)2

::)1

Analysis of Non-inverting Amplifier

Note that step 2 uses a voltage divider to find the voltage at VB relative to

the output voltage.

Analysis of Difference Amplifier(1)

:

:)1

in

fout

outinffoutinf

in

inf

f

fin

fBA

outinf

in

inf

fB

fin

inf

fin

outinf

B

fin

f

out

inBB

fin

fA

f

outB

in

B

RR

VVV

VRVRVRVRR

RVRR

RV

RRR

VV

VRR

RVRR

RV

RRRR

RRVRVR

V

RR

RV

RV

VVforsolve

VRR

RV

RVV

RVVi

12

1212

1

11

2

1

:

11:)3

:

:)2

Analysis of Difference Amplifier(2)

Note that step 2(-) here is very much like step 2(-) for the inverting amplifier

and step 2(+) uses a voltage divider.

What would happen to this analysis if the pairs of resistors were not equal?

Op-Amp Cautions (1) In all op-amp circuits, the “golden rules” will be

obeyed only if the op-amp is in the active region, i.e., inputs and outputs are not saturated at one of the supply voltages.

Typically it can swing only to within 1-2V of the supplies.

There must always be negative feedback in the op-amp circuit. Otherwise, the op-amp is guaranteed to go into saturation.

Do not not mix the inverting and non-inverting inputs.

Op-Amp Cautions (2) Many op-amps have a relatively small maximum

differential input voltage limit. The maximum voltage difference between the inverting and non-inverting inputs might be limited to as little as 5 volts in either polarity. Breaking this rule will cause large currents to flow, with degradation and destruction of the op-amp.

Note that even though op-amps themselves have a high input impedance and a low output impedance, the input and output impedances of the op-amp circuits you will design are not the same as that of the op-amp.