Transcript frequency response & compensation

ANALOG ELECTRONICS
II
FREQUENCY RESPONSE
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Frequency Response
 Frequency response refers to how
voltage gain varies as frequency
changes
 AC amplifier – gain decreases
when input frequency too low or
too high
 DC amplifier – gain falls off at
higher frequency
 Usually use dB to describe the
decrease in voltage gain
 Bode plot – to graph the response
of an amplifier
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Frequency Response of DC
amplifier
Aol (dB)
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Open-Loop vs Closed-Loop
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High-frequency op-amp equivalent
circuit
V1
+
Vid
Ro
Ri
Vout
+
V2
-
AVid
C
Figure 1: High-frequency model of an op-amp with
single break frequency
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Frequency Response
 What causes the gain of an op-amp
to roll off after a certain frequency
is reached?
Note: roll off is the rate of decreases in voltage gain
with frequency. For each ten times reduction in
frequency below fc, there is a 20 dB reduction in
voltage gain.
 Ans: Capacitive component
Recall from basic theory:
Read Floyd page 493, effect of
coupling capacitor
1
XC 
2fC
 Reactance varies inversely with frequency
 Reactance decreases  frequency increases
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Frequency Response
 Two major sources are responsible for capacitive
effects:
 Physical characteristics of semiconductor devices
 The internal construction
 These two capacitances effect causes the gain of opamp to decrease as the frequency increases
Internal transistor capacitances
Recall from basic concept:
Read Floyd page 494-495
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Open-loop Frequency response
 Refer to figure 1
Since
Thus,
Vout
 j 1 j
Vout
and
 jX C
 AVid 

Ro  jX C
X C  1 2fC
AVid
1 j 2fC
 AVid  

Ro  1 j 2fC
1  j 2fRo C
Hence the openloop voltage gain is
Vout
Aol ( f ) 
Vid
A
Aol ( f ) 
1  j 2fRo C
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Open-loop Frequency response
Let
f o  1 2RoC
then
A
Aol ( f ) 
1  j  f fo 
Where Aol(f) = open-loop gain as a function of frequency
A = gain of the op-amp at 0 Hz (dc)
f = operating frequency (Hz)
fo = break frequency of the op-amp (Hz)
Aol ( f ) 
A
1   f fo 
2
 f 
 ( f )   tan  
 fo 
Open-loop gain magnitude
1
Phase angle
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Closed-loop frequency response
Frequency bandwidth is
measured
at the
point
where gain falls to 0.707 of
maximum signal – The -3dB
bandwidth
Open loop configurations
are extremely bandwidth
limited
Closed loop configuration
significantly increases an
opamp’s bandwidth
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Circuit stability
 A system is said to be stable if its output
reaches a fixed value in a finite time.
 To test the stability of the systems : Analytical method – Routh-Hurwitz criteria
 Graphical method – Bode plots
How to determine stability?
 Method 1
 Determine the phase angle when the (Aol)(B) is 0 dB
or 1. If the phase angle is > -180º ----- stable
 Method 2
 Determine the (Aol)(B) when the phase angle is
- 180º. If magnitude is –ve dB --- stable
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Closed-loop system
Vin
+

Aol(f)
Vo
-
Vf
B
A typical closed-loop system (noninverting
amplifier)
Vout
Aol
Acl 

Vin 1  Aol B
where
B = gain of a feedback circuit
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