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Op-Amp Imperfections in The Linear Range of Operations

Gain and Bandwidth Limitations

Ideal op amps have infinite open-loop gain magnitude (AoL is infinite), but the gain of a

real op amp is finite and a function of frequency dc open-circuit differential voltage gain is typically between 104 to 106

The bandwidth is usually limited by the designer to prevent oscillations from

feedbackby a process is called frequency compensation

AOL (f) - open-loop gain as function of frequency

A0OL - dc open-loop gain

fBOL - open-loop break frequency

AOL (f) - constant up to fBOL then it rolls off at 20

dB/decade

The open loop gain function of an op-amp usually has a single dominant pole and is given as:

2

Gain-Bandwidth Limitations

Assuming infinite input impedance and zero input current

Voltage across resistor R1

Thus,

and

Definition of open-loop gain

Hence from (2.27)

(2.27)Therefore, the closed-loop gain

(2.26)

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In the limit of AOL tending to infinity,

ButFor an ideal op amp

This is the same result as before

Op amp Closed-loop gain is given as,

Putting

We have,

Defining and

we have which is very similar in form to the open loop gain

4

Closed-Loop Bandwidth

But we know that, and

Therefore,

This same formula applies to a non-inverting as well as an inverting amplifier

Substituting,

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Gain Bandwidth Product

Note that you are trading off the high gain of the op-amp for a higher bandwidth

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A0CL A0CL

(dB)

fBCL

1 0.999990 0 4 MHz

0.1 9.9990 20 400 kHz

0.01

99.90 40 40 kHz

Closed-Loop Gain Versus Frequency

Not that at ft the gain becomes 1

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Bandwidths of Inverting and Noninverting Amplifiers

Closed loop bandwidth

Closed loop gain for non-inverting amp

Closed loop gain for inverting amp

Closed loop bandwidth

CL

TBCL A

ff

01

8

Output Voltage Swing

Output Current Limits

Large Signal Operation

Output voltage cannot exceed the maximum supply voltage. It also depends on the type of op-amp design to some extent.

Clipping of the output voltage occurs when either the output voltage or the output current reaches its limit