Transcript Op-Amp Imperfections in The Linear Range of Operations Gain and

The Operational Amplifier continued
The voltage follower provides
unity gain, however, the output
impedance is changed according
to the o/p impedance of the opamp, 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.
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Non-inverting amplifier design: Effects of resistance choice
Av = 10 = 1+R2/R1
For v0 = 10 V, output
current is 1A
Most 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?
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Special circuits: Integrator and differentiators
Therefore,
These circuits are useful for automobile ignition and fuel injection
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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 MW
 For IC op amps made of JFETs open-loop input impedance is about 1012 W
 Open loop output impedance is between 1 and 100 W
 Closed loop impedances will be different, and can be chosen by proper
resistors
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Characteristics of two popular Op Amps
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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
feedback, by a process is called frequency compensation
The open loop gain
function of an op-amp
usually has a single
dominant pole and is given
as:
 AOL (f)
 A0OL
 fBOL
 AOL (f)
- open-loop gain as function of frequency
- dc open-loop gain
- open-loop break frequency
- constant up to fBOL then it rolls off at 20
dB/decade
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Gain-Bandwidth Limitations
Assuming infinite input impedance
and zero input current
Voltage across resistor R1
(2.26)
Definition of open-loop gain
Hence from (2.27)
Thus,
Therefore, the closed-loop gain
and
(2.27)
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For an ideal op amp
But
In the limit of AOL tending to infinity,
This is the same result as before
Op amp Closed-loop gain is given as,
Putting
We have,
Defining
we have
and
which is very similar in form to the open loop gain
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Closed-Loop Bandwidth


Substituting,
But we know that
and
Therefore
This same formula applies to a non-inverting as well as an inverting amplifier
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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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Closed-Loop Gain Versus Frequency
b
A0CL
A0CL
(dB)
fBCL
1
0.999990
0
4 MHz
9.9990
20
400 kHz
40
40 kHz
0.1
0.01 99.90
Not that at ft the gain becomes 1
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