notes on two-port networks
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1
Electronic Circuits 1
Two Port Characterizations
Prof. C.K. Tse: 2-port networks
Contents• Input and output resistances• Two port networks• Models
2Prof. C.K. Tse: 2-port networks
Impedances and loading effectsVoltage amplifiers
+– AvvinRin
Rout
RLOAD
+vo–
+vin–
+–vs
Rs
smaller the better(the best is 0)
larger the better(the best is ∞)
3Prof. C.K. Tse: 2-port networks
Impedances and loading effectsCurrent amplifiers
AiiinRin Rout
larger the better(the best is ∞)
smaller the better(the best is 0)
RLOADioutRsis
iin
4Prof. C.K. Tse: 2-port networks
Impedances and loading effectsTransconductance amplifiers
Gmvin
Rin Rout
larger the better(the best is ∞)
larger the better(the best is ∞)
RLOADiout+–vs
Rs
+vin–
5Prof. C.K. Tse: 2-port networks
Impedances and loading effectsTransresistance amplifiers
Rin
smaller the better(the best is 0)
smaller the better(the best is 0)
RLOAD+– Rmiin
Rout
+vo–
Rsis
iin
6Prof. C.K. Tse: 2-port networks
Finding impedancesInput impedance
Inject a current to the input, find the voltage. The ratio ofthe voltage to current gives the input resistance.
+vx–
ix
Rin
WITH Outputopen-circuit if it issupposed to be a voltageoutput (e.g., voltageamplifiers andtransresistance amplifiers)
short-circuit if it issupposed to be a currentoutput (current amplifiersand transconductanceamplifiers)
7Prof. C.K. Tse: 2-port networks
Finding impedancesOutput impedance
Inject a current at output, find the voltage. The ratio ofthe voltage to current gives the output resistance.
+vx–
ix
Rout
WITH inputshort-circuit if it issupposed to be a voltageinput (e.g., voltageamplifiers andtransconductanceamplifiers)
open-circuit if it issupposed to be a currentinput (current amplifiersand transresistanceamplifiers)
8Prof. C.K. Tse: 2-port networks
Example: CE amplifier with ED
B C
E E
gmvBE~
rπ ro
RE
RB1 || RB2
+vo–
rin
vin
iB
rvi
v vi
vi
vi
rvi
rv
ir R
inin
B
BE E
B
BE
B
E
B
E
B
E
E
E
= =+
= +
= +
= ++
= + +
π
π
π
β
β
/( )
( )
1
1
Input resistance is
9Prof. C.K. Tse: 2-port networks
Example: EF amplifier
B C
E E
gmvBE~
rπ ro
RE
rout
Output resistance is
rvi
vi
vi i g v
v
ivr
g vR r
g
Rg
gR
g
Rg
outm
m
BE
m
BE
E B m BE
E
EE
m EE
m
E
mm
Em
Em
= =−
=−
− −
=
+ +
=
+ +
=
+ +
≈
+
=
π π
β
11 1
11
11
1||
+–
vm
im
10Prof. C.K. Tse: 2-port networks
Quick rule 1
RE
r REπ β+ +( )1
11Prof. C.K. Tse: 2-port networks
Example
RE1r R r RE Eπ πβ β+ + + +( )[ || ( ( ) )]1 11 2
RE2
12Prof. C.K. Tse: 2-port networks
Quick rule 2
11gR
m
B++ β
RB
11gR
Rm
BE+
+
β
RB
RE
13Prof. C.K. Tse: 2-port networks
Example
11g
R RR
m
L BE+
+
+
β
RE
RL
RB
14Prof. C.K. Tse: 2-port networks
General two port characterizations
+v1–
i1
+v2–
i2
1 2
15Prof. C.K. Tse: 2-port networks
Types of characterizations
Immittance parameters- z-parameters- y-parameters
Hybrid parameters- h-parameters- g-parameters
16Prof. C.K. Tse: 2-port networks
z-parameters
vv
z zz z
ii
zvi
zvi
zvi
zvi
i
i
i
i
1
2
11 12
21 22
1
2
111
1 0
121
2 0
212
1 0
222
2 0
2
1
1
2
=
=
=
=
=
=
=
=
=
(open-circuit port 2)
(open-circuit port 1)
(open-circuit port 2)
(open-circuit port 2)
+v1–
i1+v2–
i21 2
17Prof. C.K. Tse: 2-port networks
y-parameters
ii
y yy y
vv
yiv
yiv
yiv
yiv
v
v
v
v
1
2
11 12
21 22
1
2
111
1 0
121
2 0
212
1 0
222
2 0
2
1
1
2
=
=
=
=
=
=
=
=
=
(short-circuit port 2)
(short-circuit port 1)
(short-circuit port 2)
(short-circuit port 2)
+v1–
i1+v2–
i21 2
18Prof. C.K. Tse: 2-port networks
h-parameters
vi
h hh h
iv
hvi
hvv
hii
hiv
v
i
v
i
1
2
11 12
21 22
1
2
111
1 0
121
2 0
212
1 0
222
2 0
2
1
2
1
=
=
=
=
=
=
=
=
=
(short-circuit port 2)
(open-circuit port 1)
(short-circuit port 2)
(open-circuit port 1)
+v1–
i1+v2–
i21 2
h11 = rπ input resistanceh21 = hfe = βh22 = 1/ro Early resistance
BJT model in some books:
19Prof. C.K. Tse: 2-port networks
g-parameters
iv
g gg g
vi
giv
gii
gvv
gvi
i
v
i
v
1
2
11 12
21 22
1
2
111
1 0
121
2 0
212
1 0
222
2 0
2
1
2
1
=
=
=
=
=
=
=
=
=
(open-circuit port 2)
(short-circuit port 1)
(open-circuit port 2)
(short-circuit port 1)
+v1–
i1+v2–
i21 2
20Prof. C.K. Tse: 2-port networks
Example
+v1–
i1+v2–
i2R1
R2
hvi
R RR R
R R
hvv
RR R
hii
RR R
hiv R R
v
i
v
i
111
1 01 2
1 2
1 2
121
2 0
2
1 2
212
1 0
2
1 2
222
2 0 1 2
2
1
2
1
1
= = =+
= =+
= =−
+
= =+
=
=
=
=
||
21Prof. C.K. Tse: 2-port networks
Connecting two-ports — series-series
Z+v1–
i1
+v2–
i2
Z’+v3–
i3
+v4–
i4
Total [Z]T = [Z]+[Z’]
22Prof. C.K. Tse: 2-port networks
Connecting two-ports — shunt-shunt
Y+v1–
i1
+v2–
i2
Y’+v3–
i3
+v4–
i4
Total [Y]T = [Y] + [Y’]
23Prof. C.K. Tse: 2-port networks
Connecting two-ports — shunt-series
G+v1–
i1
+v2–
i2
G’+v3–
i3
+v4–
i4
Total [G]T = [G] + [G’]
24Prof. C.K. Tse: 2-port networks
Connecting two-ports — series-shunt
H+v1–
i1
+v2–
i2
H’+v3–
i3
+v4–
i4
Total [H]T = [H] + [H’]
25Prof. C.K. Tse: 2-port networks
Circuit modelsWe can develop circuit model for each type of two-port descriptions.
Example: h-parameter
vi
h hh h
iv
v h i h vi h i h v
1
2
11 12
21 22
1
2
1 11 1 12 2
2 21 1 22 2
=
⇒= +
= +
+–
h11
h12v2
1/h22
h21i1
i2i1
+v1–
+v2–
26Prof. C.K. Tse: 2-port networks
Example: BJT modelWe can model the BJT as a h-parameter model:
h11 = rπ input resistanceh12 ≈ 0h21 = hfe = βh22 = 1/ro Early resistance
rπro
βi1= gmv1
i2i1
+v1–
+v2–
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