Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series -...
Transcript of Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series -...
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Feedback
CHAPTER 8
1
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Outline
2
1. General Consideration
2. Feedback Topologies
3. Effect of Loading
4. Effect of Feedback on Noise
![Page 3: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/3.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
General Consideration
• H(s) : Feedforward network (Represents an amplifier)
• G(s) : Feedback network (β, feedback factor, freq. independent)
• X(s) – G(s)Y(s) : The input to H(s), also called feedback error
• H(s) : open loop transfer function
• Y(s)/X(s) : closed loop transfer function
3
( ) ( )( ) ( )[ ( ) ( ) ( )],
( ) 1 ( ) ( )
Y s H sY s H s X s G s Y s
X s G s H s
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
General Consideration
• In a well designed negative feedback system, the error term is minimized, making the output G(s) an accurate copy of the input.
• Input of H(s) as “virtual ground”.
• Four elements in the feedback system – The feedforward amplifier.
– A means of sensing the output.
– The feedback network.
– A means of generating the feedback error.
4
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Properties of Feedback Circuits
• Gain Degeneration
• Terminal Impedance Modification
• Bandwidth Modification
• Nonlinearity Reduction
5
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh 6
1. Desensitize the gain : • make gain less sensitive to variations.
2. Reduce nonlinear distortion : • make gain independent of signal level.
3. Reduce effect of noise : • minimize unwanted signal contribution to output.
4. Control the input and output impedance : • use feedback to control impedance.
5. Extend bandwidth of the amplifier.
Negative Feedback properties :
The basic idea of negative feedback is to trade off gain for other desirable properties, like increased input impedance, extended bandwidth… etc.
Properties of Feedback Circuits
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Terminologies
7
Signal-flow diagram
1. Open-loop Gain : 2. Feedback Factor : 3. Loop Gain : 4. Amount of Feedback : 5. Closed-Loop Gain :
A
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1. Af is almost determined by β and independent of A, that is, the process variation. 2. β can be implemented by passive component and accurate, predictable, stable. 3. xi : negative feedback reduces the input signal of the basic Amp by (1+Aβ )
Comparison circuit (Mixer)
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Gain Desensitization
• Gain desensitization
Compared to gm1 ro1, this gain can be controlled with much higher accuracy
because it is given by the ratio of two capacitors – gain desensitization.
8
Poor definition of the gain : both gm1 and ro1 vary with process and temperature.
For the CS amplifier with feedback (C1 & C2)
The overall voltage gain of the circuit at low freq. such that C2 does not load the output node
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Gain Desensitization
• In a feedback system, the closed-loop gain is much less sensitive to device parameters than the open-loop gain is.
• The closed loop gain varies by a small percentage even if the open loop gain A varies a lot if the loop gain (βA) >> 1.
• The higher the loop gain (βA), the less sensitive Y/X will be to variations in A. – We begin with a high-gain amplifier and apply feedback to obtain a low, but
less sensitive closed-loop gain.
9
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loop Gain
• Calculation of loop gain – Set the main input to zero.
– Break the loop at some point.
– Inject a test signal in the right direction.
– Obtain the value that returns to the break point.
10
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
• The input resistance without feedback
• Consider the input resistance with feedback, as
• The Loop gain
Input Impedance Modification
• Common gate circuit with feedback (capacitive voltage divider).
11
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loop Gain
• The feedforward amplifier : M1 and RD (A= )
• Output sensed by C1 and C2.
• The feedback network : C1, C2 and M2 (β= )
• The subtraction occurs in the current domain at the input terminal.
• Loop gain =
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Output Impedance Modification
• Common source stage with feedback.
• Common source stage: M1, RS and RD.
• Feedback network sense the Vout, returning a current equal to
• To find the output resistance at relatively low frequencies
13
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Bandwidth Modification
• Suppose the feedforward amplifier has a one-pole transfer function
• The transfer function of the closed loop system is
• The -3dB bandwidth has increased by a factor , albeit at the cost of a proportional reduction in the gain.
• If A is large, the closed loop gain remains approximately equal to
14
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Bandwidth Modification Example
• Suppose we need to amplify a 20-MHz square wave by a factor of 100 and maximum bandwidth but we have only a single-pole amplifier with an open loop gain of 100 and -3 dB bandwidth of 10 MHz.
(a) With open-loop amplifier, the risetime and falltime is long:
(b) Placing two of the amplifiers with feedback in cascade to achieve the same gain. The power dissipation is doubled.
15
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Types of Amplifiers • Circuits sensing a voltage must exhibit a high Zin (as a voltmeter),
circuits sensing a current must provide a low Zin ( as a current meter).
• Circuits generating a voltage must exhibit a low Zout (as a voltage source), circuits generating a current must provide a high Zout (as a current source).
16
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Amplifiers with Improved Performance
• The basic circuits may not provide adequate performance in many applications.
• Use modified circuits to alter the output impedance or increase the gain.
17
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Sense and Return Mechanisms
• Four type of feedback : voltage-voltage (series-shunt), voltage-current (shunt-shunt), current-current (shunt-series), and current voltage (series-series).
• The first entry in each case denotes the quantity sensed at the output and the second the type of signal returned to the input.
• To sense a current, a current meter is inserted in series with the signal.
• The addition of the feedback signal and the input signal can be performed in the voltage domain or current domain.
18
Sensing a voltage by a voltmeter
Sensing a current by a current meter
Sensing a current by a small resistor
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Return Mechanisms
• To add two quantities, we place them in series if they are voltages and in parallel if they are current.
• The feedback network in reality introduces loading effects that must be taken into account.
19
Voltage mode addition
Current mode addition
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Practical Examples
• Voltage can be sensed by a resistive / capacitive divider in parallel with the port.
• A current can be sensed by placing a resistor in series with the wire and sensing the voltage across it.
• To subtract two voltages, a differential pair or a single transistor can be used.
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Sense and Return Mechanism
• Subtraction of currents can be accomplished as follows.
• In summary
– For voltage subtraction, the input and feedback signals are applied to two distinct nodes.
– For current subtraction, they are applied to a single node.
– It help to identify the type of feedback
21
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Outline
22
1. General Consideration
2. Feedback Topologies
3. Effect of Loading
4. Effect of Feedback on Noise
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Voltage-Voltage (V-V) Feedback
• Voltage-voltage feedback (series - shunt)
– samples the output voltage and returns the feedback signal as a voltage.
• The feedback network is connected in parallel with the output and in series with the input port.
• An ideal feedback network in this case exhibits infinite input impedance and zero output impedance.
23
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Effect of V-V Feedback on Rout
• If the amplifier is loaded by a resistor RL
– Consider a voltage amplifier without feedback (open-loop configuration), the output would drop in proportional to
– Consider a feedback amplifier, if loop gain remains much greater than unity
– The circuit stabilizes the output voltage amplitude despite load variations, it behaves as a voltage source, thus exhibiting a low output impedance.
24
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Effect of V-V Feedback on Rin
• For the open loop Amp, the Rin of the FF Amp sustains the entire Vin.
• For the closed loop Amp, the Rin of the FF Amp sustains only a fraction of Vin .
• The I(Rin) in the FB topology is less than that in the open-loop system.
• Returning a voltage quantity to the input increases the input impedance.
25
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Current-Voltage (I-V) Feedback
• Sense the output current to perform feedback. (series – series)
• The current is usually sensed by placing a small resistor in series with the output and using the voltage across the resistor as the feedback information.
• The feedback factor β (RF) .
• An ideal FB network in this case exhibits zero input and output impedance .
• The loop gain = Gm RF.
26
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Rin/Rout of I-V Feedback Amplifier
• Output resistance of a current-voltage feedback amplifier
• Input resistance of a current-voltage feedback amplifier
27
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Voltage-Current (V-I) Feedback
• The output voltage is sensed and a proportional current is returned to the summing point at the input. (shunt – shunt)
• The feedforward path incorporates a transimpedance amplifier with gain R0 .
• The feedback factor has a dimension of conductance.
• The feedback network ideally exhibiting infinite input and output impedance.
• The Loop gain : gmFR0
28
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Rin/Rout of V-I Feedback Amplifier • Rin of a voltage-current feedback amplifier.
• The Rin of R0 is placed in series because an ideal transimpedance amplifier exhibits a zero input impedance.
• Output impedance of a voltage-current feedback amplifier.
29
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Current-Current (I-I) Feedback
• The feedforward amplifier is characterized by a current gain AI . (shunt – series)
• The feedback network by a current ratio β.
• The closed loop current gain is
• The input resistance is
• The output resistance is
30
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Outline
31
1. General Consideration
2. Feedback Topologies
3. Effect of Loading
4. Effect of Feedback on Noise
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Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Two-Port Network Models
32
For voltage-voltage feedback (G)
For voltage-current feedback (Y) For current-voltage feedback (Z)
For current-current feedback (H)
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![Page 33: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/33.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loading in V-V Feedback
• If A0 is large, the signal amplified by A0 is much greater than the contribution of G12I2.
33
1 0211
11
1
11
22
1
11
1
11
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0
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G G
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![Page 34: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/34.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loading in a V-V Feedback Circuit
• If we define the open-loop gain in the presence of loading as
34
• The finite input and output impedances of the feedback network reduces the output voltage and the voltages seen by the input of the main amplifier.
01
11
1
11
22
, AZG
G
GZ
ZA
outin
inopenv
• G11 is obtained by leaving the output of the feedback network open.
• G22 is calculated by shorting the input of the feedback network.
• Consider the loading effect
2
111
1 0I
IG
V
1 21,
,
GA
A
V
V
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222
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I
![Page 35: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/35.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Example of V-V Feedback
35
2
111
1 0I
IG
V
1
222
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VG
I
1
222
2 0
||S F
V
VG R R
I
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1
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,
,
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v open
v closed
v open
AA
G A
![Page 36: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/36.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loading in I-V Feedback
• Replacing the feedback network by a Z model, and neglect the source Z12I2
• The loaded open loop gain is equal to
36
out
out
outm
in
inoutin I
ZZ
ZG
ZZ
ZIZV
1122
21
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out
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Z
ZZ
ZG
![Page 37: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/37.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loading in V-I Feedback
• Replacing the feedback network by a Y model, and neglect the source Y12V2
• The loaded open loop gain is equal to
37
211
11
1
1101
22
1
22
1
11
1
1101
22
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22
1 YZY
YR
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V
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ZY
Y
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outin
open
![Page 38: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/38.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Example of V-I Feedabck
38
1
222
2 0
1/ ,F
V
IY R
V
2
111
1 0
1/ ,F
V
IY R
V
2
221
1 0
1/ ,F
V
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V
0, ( || ) ( || ) outopen S F m F D
N open
VR R R g R R
I
0,
0,
21 0,
( || ) ( || )
1 1 ( || ) / ( )
open S F m F Dclosed
open m F D S S F
R R R g R RR
Y R g R R R R R
0, ( || ) ( || ) 1 1
1 ( || ) / ( )
closedout out S F m F D
in N S S S m F D S S F
RV V R R g R R
V I R R R g R R R R R
![Page 39: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/39.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Loading in I-I Feedback
• Replacing feedback network by an H model. Neglecting the effect of H12 V2
• The loaded open loop gain is equal to
39
out
out
outI
in
outin IZH
ZA
ZH
HIHI
11
1
22
1
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11
1
22
1
22
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22
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ZA
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ZA
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I
out
outI
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out
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in
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in
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ZA
ZH
HA
11
1
22
1
22,
![Page 40: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/40.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Summary of Loading Effects • The analysis is carried out in three steps
– Open the loop with proper loading and calculate the open-loop gain AOL, and the open-loop input and output impedances.
– Determine the feedback ratio β and hence the loop gain βAOL.
– Calculate the closed-loop gain and input and output impedances by scaling the open loop values by a factor of 1+ βAOL
40
![Page 41: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/41.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Outline
41
1. General Consideration
2. Feedback Topologies
3. Effect of Loading
4. Effect of Feedback on Noise
![Page 42: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/42.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Effect of Feedback on Noise
• Feedback does not improve the noise performance of circuits.
• Assume the open-loop voltage amplifier A1 is characterized by only an input-referred noise voltage and the feedback network is noiseless.
• In practice, the feedback network itself may contain resistors or transistors, degrading the overall noise performance.
42
1
11
1
A
AVVVVAVVV ninoutoutnoutin
![Page 43: Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •](https://reader030.fdocuments.in/reader030/viewer/2022040121/5ebb64efd0ab6c2bf45db1a9/html5/thumbnails/43.jpg)
Analog IC Analysis and Design 8- Chih-Cheng Hsieh
Effect of Feedback on Noise
• As
43
1 , , , , ,, whereas 0Sn in closed n RD n in open
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