CNU EE 9.1-1
Microelectronic Circuits II
Ch 9 : Feedback
9.5 The Feedback Transconductance Amplifier (Series-Series ) 9.6 The Feedback Transresistance Amplifier (Shunt-Shunt)
9.7 The Feedback Current Amplifier (Shunt-Series)
Appendix C Two-port Network Parameters
CNU EE 9.1-2 - b circuit samples short-circuit output current Io
& provides a feedback signal Vf à Vi=Vs-Vf - zero resistance to output load à b circuit does
not load the amplifier output
- Ideal voltage source Vf= b Io à b circuit does Not load the amplifier input
- A : transconductance & b : transresistance à Loop gain Ab = dimensionless quantity - Ideal structure : load and source resistances
are absorbed inside the A circuit, and b circuit does not load the A circuit
- Closed loop gain Af :
- Af =short-circuit transconductance
Feedback Transconductance Amplifier (Series-Series)
§Ideal case
b
A A VA I
s o
f º = +
1
- Stabilize Io/Vs à transconductance amplifier - Unilateral open loop amplifier (A circuit) +
ideal feedback network (b circuit)
- A circuit : input resistance Ri, short-circuit transconductance A=Io/Vi, output resistance Ro
Ideal structure
Equivalent circuit for series-series feedback amplifier
CNU EE 9.1-3 - Negative feedback increases the output resistance in the current (series) sampling
- Negative feedback à Io is constant in spite of changes in output voltage à increase in output resistance - While voltage (shunt) sampling reduces the output resistance, current (series) sampling increases it.
- Series-series feedback topology increases the input and output resistance
§ Output Resistance Rof of feedback transconductance amplifier (Series-Series)
x x
of I
R º V
- Vs à 0 & breaks the output loop (at OO/) to apply a test current Ix
- Output resistance Rof :
x o
f
i V I I
V = - = -
b
= -b
(
x i)
o(
x x)
ox I AV R I A I R
V = - = + b
( )
oof A R
R = +
b
\ 1
Feedback Transconductance Amplifier (Series-Series)
( A b )
R R
if=
i+
\ 1
Equivalent circuit for series-series feedback amplifier
§Input resistance with feedback
Series mixing always increases the input resistance by a factor equal to the amount of feedback
CNU EE 9.1-4 - Feedback network is not an ideal current
controlled voltage source
à resistive and hence, load the basic amplifier
à affect A, Ri & Ro
- Rs & RL affect A, Ri & Ro
- Simple method for finding A circuit & b circuit from a given series-series feedback amplifier
•Practical series-series feedback amplifier
- Source and load resistances should be lumped with the basic amplifier - Two-port feedback network is
represented in terms of z parameters - z parameter : a series circuit at the input and a series circuit at the output
Feedback Transconductance Amplifier (Series-Series)
Ideal structure
Practical case
Ri & Ro vs. Rin & Rout vs. Rif & Rof
CNU EE 9.1-5
§ Derivation of A Circuit & β Circuit
use of z parameters (appendix C)
ú û ù ê ë é ú û ù ê ë
= é ú û ù ê ë é
2 1 22
21
12 11
2 1
I I z
z
z z
V V
Feedback Circuit Input Impedance (w/ Output open)
Feedback Circuit Output Impedance (w/ input open) negligible
β Feedback network is represented by a series network at port 1 and a series network at port 2
Feedback Transconductance Amplifier (Series-Series)
Ri & Ro vs. Rin & Routvs. Rif & Rof
CNU EE 9.1-6 à Dispense with the voltage source z21I1
- Forward transmission through the feedback network is negligible in comparison to that through the basic amplifier
- A circuit is composed of the basic amplifier augmented at the input with Rs and z11 and augmented at the output with RL and z22.
- z11 & z22 : impedance looking into ports 1 & 2 of the feedback network while the other port is open- circuited or short-circuited so as to destroy the feedback(open if series & short if shunt)
- b is measured with port 1 open
- Feedback network samples the output current [I2 = Io) & provides a voltage [Vf = V1] that is mixed in series with the input source
§ Derivation of A Circuit & β Circuit
2 0 1 12
1=
º
=
I
Iz V b
amplifier basic network
feedback
z
z
21<<
21network feedback amplifier
basic
z
z
12<<
12- Includes z11 and z22 with the basic amplifier - If basic amplifier is unilateral,
Feedback Transconductance Amplifier (Series-Series)
CNU EE 9.1-7
§ Summary of the rules for finding A and β Circuit
- Ri & Ro : input & output resistance of the A circuit - Rif & Rof : input & output resistance of the feedback amplifier, including Rs & RL - Actual input & output resistance of the feedback amplifier usually exclude Rs
& RLà Rin & Rout I2=0 I1=0
I1=0
Feedback Transconductance Amplifier (Series-Series)
L of
out
s if
in
R R
R
R R
R
-
=
-
=
Ro by breaking the output loop at YY/ & measuring the resistance between Y & Y/
CNU EE 9.1-8 - b circuit samples open-circuit output voltage Vo
& provides a feedback signal If à Ii=Is-If
- infinite resistance to amplifier output àb circuit does not load the amplifier output
- Ideal current source If= bVo à b circuit does not load the amplifier input
- A : transresistance & b : transconductance à Loop gain Ab = dimensionless quantity - Ideal structure : load and source resistances
are absorbed inside the A circuit, and b circuit does not load the A circuit
- Closed loop gain Af :
- Af : open-circuit transresistance
Feedback Transresistance Amplifier (Shunt-Shunt)
§Ideal case
b
A A IA V
s o
f º = +
1
- Stabilize Vo/Isà transressitance amplifier - Unilateral open loop amplifier (A circuit) +
ideal feedback network (b circuit)
- A circuit : input resistance Ri, open-circuit transresistance A=Vo/Ii, output resistance Ro
Ideal structure
Equivalent circuit for shunt-shunt feedback amplifier
CNU EE 9.1-9 - Shunt connection in the input à a reduced current
Ii into the A circuit : Ii = Is – If
- Shunt mixing reduces the input current by the amount of feedback (Vi/Ii = Ri)
- Shunt connection at the input lowers the input resistance by a factor equal to the amount of feedback
§ Output Resistance Rof of feedback tranresistacne amplifier (Shunt-Shunt)
Shunt connection at the output lowers the output resistance by a factor equal to the amount of feedback à The output voltage will change less as we draw current from the amplifier output
- Shunt feedback connection, whether at the input or at the output, always reduces the corresponding resistance
( b )
Ab
R I
A V I
R V i
i i s
i
if = +
= +
º 1 1
Equivalent circuit for series-series feedback amplifier
§Input resistance with feedback
Feedback Transresistance Amplifier (Shunt-Shunt)
b b
b
AI I AI
V
If o i i s
= +
=
= > 1
b
A Rof Ro= + 1
CNU EE 9.1-10 - Simple method for finding A & b circuit - Assume the basic amplifier is unilateral &
the feedforward transmission through the feedback network is negligibly small - A circuit includes Rs across the input
terminals of the amplifier & RL across its output terminal
- Loading effect of the feedback network on the amplifier input à R11 is obtained by looking into port 1 of the feedback network while port2 is shorted (shunt connected output) - Loading effect at the output à R22 is found
by looking into port 2 while port 1 is shorted (shunt connected input)
- Since the feedback network senses Vo & is fed by Vo; delivers a current If that is mixed in shunt at the input, its port 1 is short-circuited àb is found as If/Vo, where If flows through
the short circuit
ú û ù ê ë é ú û ù ê ë
= é ú û ù ê ë é
2 1 22 21
12 11
2 1
V V y
y
y y
I
y parameter
I
Ri & Ro vs. Rin & Rout vs. Rif & Rof
Feedback Transresistance Amplifier (Shunt-Shunt)
Ideal structure
Practical case
CNU EE 9.1-11
§Summary of the rules for finding A and β Circuit
÷÷ ø ö çç
è
æ -
=
s if
in R R
R 1 1
/ 1
÷÷ ø ö çç
è
æ -
=
L of
out R R
R 1 1
/ 1
network feedback amplifier
basic
y
y
12<<
12amplifier basic network
feedback
y
y
21<<
21Condition for Reverse y parameter of the basic amplifier & feedback network
Condition for Forward y parameter
Actual input & output resistance of the feedback amplifier usually exclude Rs
& RL V2=0 V1=0
V1=0
Feedback Transresistance Amplifier (Shunt-Shunt)
CNU EE 9.1-12 - b circuit samples short-circuit output current Io
& provides a feedback current If à Ii=Is-If - zero resistance to the output loop à b circuit
does not load the amplifier output
- Ideal current source If= bIo à b circuit does not load the amplifier input
- A & b : current gain
à Loop gain Ab = dimensionless quantity - Ideal structure : load and source resistances
are absorbed inside the A circuit, and b circuit does not load the A circuit
- Closed loop gain Af :
- Af : closed-loop current gain
§Ideal case
b
A A IA I
s o
f º = +
1
- Stabilize Io/Isà current amplifier
- Unilateral open loop amplifier (A circuit) + ideal feedback network (b circuit)
- A circuit : input resistance Ri, short-circuit current gain A=Io/Ii, output resistance Ro
Ideal structure
Equivalent circuit for shunt-shunt feedback amplifier
Feedback Current Amplifier (Shunt-Series )
CNU EE 9.1-13 - Shunt mixing reduces the input current by the
amount of feedback (Vi/Ii = Ri)
- Shunt connection at the input lowers the input resistance by a factor equal to the amount of feedback
§ Output Resistance Rof of feedback current amplifier (Shunt-Series)
- By setting Is = 0, breaking the short-circuit output loop, at say OO/, and measuring the resistance between the two terminals à Output Resistance Rof
- Series connection at the output always raises the output resistance by a factor equal to the amount of feedback
b
A Rif Ri= + 1
Equivalent circuit for shunt-series feedback amplifier
§Input resistance with feedback
( )
oof A R
R = 1+
b
Feedback Current Amplifier (Shunt-Series )
CNU EE 9.1-14 - Simple method for finding A & b circuit - Assume the basic amplifier is unilateral &
the feedforward transmission through the feedback network is negligibly small - A circuit includes Rs across the input
terminals of the amplifier & RL in series with its output terminal
- Loading effect of the feedback network on the amplifier input à R11 is obtained by looking into port 1 of the feedback network while port2 is open (series connected output) - Loading effect at the output à R22 is found
by looking into port 2 while port 1 is shorted (shunt connected input)
- Since the feedback network senses Io & is fed by Io; delivers a current If that is mixed in shunt at the input, its port 1 is short-circuited à b is found as If/Io, where If flows through
the short circuit Ri & Ro vs. Rin & Rout vs. Rif & Rof
Ideal structure
Practical case
Feedback Current Amplifier (Shunt-Series )
ú û ù ê ë é ú û ù ê ë
= é ú û ù ê ë é
2 1 22 21
12 11
2 1
I V g
g
g g
V
g parameter
I
(inverse hybrid)
CNU EE 9.1-15
§ Summary of the rules for finding A and β Circuit
÷÷ ø ö çç
è
æ -
=
s if
in R R
R 1 1
/ 1
L of
out R R
R = -
amplifier basic network
feedback
g g
21<<
21network feedback amplifier
basic
g
g
12<<
12Most of the forward
transmission occurs in the basic amplifier
Most of the reverse
transmission takes place in the feedback network
Actual input & output resistance of the feedback amplifier usually exclude Rs
& RL I2=0 V1=0
V1=0
Feedback Current Amplifier (Shunt-Series )
Ro by breaking the output loop at YY/ & measuring the resistance between Y & Y/
CNU EE 9.1-16
Summary for four Feedback-Amplifier Topologies
h
g
z
y
CNU EE 9.1-17
Summary of the Feedback Analysis Method
1. Always begin the analysis by determining an approximate value for the closed-loop gain Af, assuming that the loop gain Ab is large and thus
Af ~ 1/b : the approximate value depends on how large Ab is compared to unity
2. The shunt connection at input or output always results in reducing the corresponding resistance (input or output). The series connection at input or output always results in increasing the corresponding resistance (input or output).
3. In utilizing negative feedback to improve the properties of an amplifier under design, the starting point in the design is the selection of the feedback topology appropriate for the application at hand.
Then the required amount of negative feedback (1+ Ab) can be ascertained utilizing the fact that it is this quantity that determines the magnitude of improvement in the various amplifier parameters.
Also, the feedback factor b can be determined from b ~ 1/ Af
CNU EE 9.1-18
Two-port Network Parameters
§ Characterization of Linear two-port networks
2 22 1
21 2
2 12 1
11 1
V y V
y I
V y V
y I
+
=
+
=
§ Four port variables of two-port network - V1, I1, V2, I2
§ Linear two-port network
- two of the variables à excitation variables - the other two à response variables
§ Example : excited by V1 & V2, responded by I1 & I2 - V1, V2 : independent variables
- I1, I2 : dependent variables
- network operation is described by the two equations
§ y11, y12, y21, y22 : admittances à completely characterized the linear two-port network
§ Depending on which two of the four port variables are used to represent the network excitation, a different set of equations (and a correspondingly different set of parameters) is obtained for characterizing the network
§ Four parameters sets commonly used in electronics
§ Independent Variable : Shunt à V, Series à I
§ Dependent Variable : Shunt à I, Series à V
CNU EE 9.1-19
y Parameters
2 22 1
21 2
2 12 1
11 1
V y
V y I
V y V
y I
+
=
+
=
§ Excitation by V1 & V2
§ Short-circuit admittance (or y-parameter) characterization
(b) y11 : input admittance at port 1 with port 2 short- circuited
1 0 1 11
2=
º V V
y I
2 0 1 12
1=
º V V
y I (c) y12 : transmission from port 2 to port 1, internal feedback
1 0 2 21
2=
º V V
y I
(d) y21 : transmission from port 1 to port 2, forward gain or transmission
2 0 2 22
1=
º V V
y I
(e) y22 : admittance looking into port 2 with port 1 short-circuited, output short-circuit admittance
CNU EE 9.1-20
z Parameters
2 22 1
21 2
2 12 1
11 1
I z I
z V
I z I
z V
+
=
+
=
§ Excitation by I1 & I2
§ Open-circuit impedance (or z-parameter) characterization
- Duality between the z- and y- parameters characterization
CNU EE 9.1-21
h Parameters
2 22 1
21 2
2 12 1
11 1
V h I
h I
V h I
h V
+
=
+
=
§ Excitation by I1 & V2
§ Hybrid (or h-parameter) characterization
(b) h11 : input impedance at port 1 with port 2 short- circuited
1 0 1 11
2=
º I V
h V
2 0 1 12
1=
º V I
h V
(c) h12 : reverse or feedback voltage ratio with input port open-circuited
1 0 2 21
2=
º I V
h I
(d) h21 : current gain with output port short-circuited, short-circuit current gain
2 0 2 22
1=
º V I
h I
(e) h22 : output port admittance with input port open-circuited
CNU EE 9.1-22
g Parameters
2 22 1
21 2
2 12 1
11 1
I g V
g V
I g V
g I
+
=
+
=
§ Excitation by V1 & I2
§ Inverse-hybrid (or g-parameter) characterization
- Duality between the g- and h- parameters characterization
CNU EE 9.1-23
Equivalent-circuit representation
§ Four possible equivalent circuits
