1

The Operational Amplifier continued

The voltage follower provides unity gain, however, the output impedance is changed according to the o/p impedance of the op-amp, which is very useful sometimes. Thus the op-amp acts as the buffer stage preventing the o/p load fluctuations to affect the i/p voltage signal.

2

Non-inverting amplifier design: Effects of resistance choice

Av = 10 = 1+R2/R1

For v0 = 10 V, output current is 1AMost op amps cannot handle such large current, so small R’s should be avoided

Very large resistances tend to be unstable, and lead to coupling of unwanted signals especially at higher frequencies. Why?

Special circuits: Integrator and differentiators

3

Therefore,

These circuits are useful for automobile ignition and fuel injection

4

Op-Amp Imperfections in the linear range of operations

• Non-ideal properties in the linear range of operation

• Nonlinear characteristics

• DC offsets

Input and Output Impedances

An Ideal op amp has infinite input impedance and zero output impedance A Real op amp has finite input impedance and nonzero output impedance For IC op amps made of BJTs open-loop input impedance is about 1 M For IC op amps made of JFETs open-loop input impedance is about 1012 Open loop output impedance is between 1 and 100Closed loop impedances will be different, and can be chosen by proper

resistors

5

Characteristics of two popular Op Amps

6

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:

7

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)

8

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

9

Closed-Loop Bandwidth

But we know that and

Therefore

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

Substituting,

10

Gain Bandwidth Product

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

11

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