Download - Lecture 27 Two-port Network Hung-yi Lee. Reference Chapter 14.1, 14.2, 14.3 (out of the scope)
Lecture 27Two-port Network
Hung-yi Lee
Reference• Chapter 14.1, 14.2, 14.3 (out of the scope)
Two and Three Terminal Networks
Chapter 4.6 Chapter 2
Two-TerminalNetwork
i
Circuit
i
v
+
-Three-Terminal
Network
Circuit
Four Terminal Network
Input port
i1 = i3
Output port
i2 = i4
4 parameters: i1, v2, i2, v2 (E.g. Filter)
Two-Port Network
Is it a two-port network?
Is it a two-port network?
i1
i1
i2
i2
i11
i12
Note
Two-port network can be expressed by the phasor notation.
A two-port network contains no independent sources, although it may contain controlled sources.
i-v characteristics
2221212
2121111
IIV
IIV
zz
zz
2
1
2
1
II
VV
z
2221
1211
zzzz
z
Z parameters:
Z parameters2221212
2121111
IIV
IIV
zz
zz
Superposition Principle:Any current (or voltage) for an element is the weighted sum of the voltage (or current) of the sources.
Z parameters• How to find the Z parameters?
2221212
2121111
IIV
IIV
zz
zz
Set 0I1 2112 IVz
1111 IVz
2222 IVz
1221 IVz0I2 Set
Z parameters – Example 14.1
2221212
2121111
IIV
IIV
zz
zz
Set 0I1
2112 IVz
2222 IVz sCR 1R||
sCsC
12R1RR
12sCRRsCR 2
21 I
12RR
RV
sC
sC12RR 2
1R2R 2
sCsC
Z parameters – Example 14.1
2221212
2121111
IIV
IIV
zz
zz
Set 0I2
22z 12sCRRsCR 2
21z12z 1R2R 2
sCsC
11z
Find z11 and z21……
symmetric
Equivalent Two Port Network
2221212
2121111
IIV
IIV
zz
zz
Two Impedances, Two controlled sources
Three Impedances, One controlled source
Equivalent Two Port Network• Tee Network
Set 0I1 2112 IVz
1111 IVz
2222 IVz
1221 IVz0I2 Set
2221
1211
zzzz
z
cZ
cZca ZZ
cb ZZ
cbc
cca
ZZZ
zZ
ZZ ReciprocalNetwork
Equivalent Two Port Network• Tee Network
• Reciprocal Network
cbc
cca
ZZZ
zZ
ZZ
22
11
zzzz
zzz 11
z
zz 22
Equivalent Two Port Network
2221212
2121111
IIV
IIV
zz
zz
112212221122
2121111
IIIV
IIV
zzzz
zz
12z
1211 zz 1222 zz
11221 Izz
Other kinds of Parameters
2
1
2
1
II
VV
z
Z parameters:
2
1
2
1
VV
II
y
y parameters:
1 zy
The y parameters does not always exist.
[z] is not always invertible.
6 kinds of Parameters
2
1
2
1
II
VV
z
z parameters:
2
1
2
1
VV
II
y
y parameters:
2
1
2
1
VI
IV
h
h parameters:
2
1
2
1
IV
VI
g
g parameters:
2
2
1
1
IV
IV
T
T parameters:
1
1
2
2
IV
IV
t
t parameters:
42C
Be careful!
T/t Parameters• T/t for transmission
For T Parameters
For t Parameters
2
2
1
1
IV
IV
T
1
1
2
2
IV
IV
t
2I 1I
Connecting the Two-port Networks• Parallel Connection:
• Series Connection:
• Cascade Connection:
Parallel Connection
2
1
2
1
VV
yII
aa
a ay1V
2V
1aI 2aI
2
1
2
1
VV
yII
bb
b by1V
2V
1bI 2bI
Parallel Connection
ay
1V
2V
1aI 2aI
by
1bI 2bI
2
1
2
1
VV
yII
aa
a
2
1
2
1
VV
yII
bb
b
b
b
a
a
II
II
II
2
1
2
1
2
1
bapar yyy
2
1
2
1 VV
yII
par
1I 2I
2
1
VV
yy ba
Parallel Connection - Note
bapar yyy
V10
5V
A0
5.2
5.2
10
5
5.2
Parallel two two-port network can break the port condition
1V
1V
2V
2V
A0
A2 A2
Series Connection
2
1
2
1
II
VV
aa
a z az1aV
2aV
1I 2I
2
1
2
1
II
bb
b zVV bz1bV
2bV
1I 2I
Series Connection
2
1
2
1
II
VV
aa
a z
az1aV
2aV
1I 2I
2
1
2
1
II
bb
b zVV
bz1bV
2bV
1I 2I1V
2V
baser zzz
2
1
II
zz ba
b
b
a
a
VV
VV
VV
2
1
2
1
2
1
Not always true because parallel connection may also break the port condition
Cascade connection
The overall T parameters equals the product of the individual T parameters.
2
2
1
1
IV
TTIV
ba
2
2
1
1
IV
TIV
bb
b
a
aa IV
TIV
2
2
1
1
2
2
IV
T cas
Cascade connection
inV outV
11
1
1
1
V
V
sCR
sC
in
x
22
2
1
1
VsC
R
sCV
x
out
xV
x
out
in
x
in
out
VV
VV
VV
21212
212211 RRR11
V
V
RCCsCRCCsin
out
Cascade connection
inV outV
aT
out
outba
in
in
IV
TTIV
bT
inI 0I out
0DCBA
DCBA outV
out
out
VV
CA
DCBA
out
out
VDCVBA
CACA
CBAAin
out
1VV
21212
212211 RRR11
VV
RCCsCRCCsin
out
Cascade connection
1V
2V
1I 2I
2
2
1
1
IV
IV
T
2
2
IV
DCBA
221
221
IVI
IVV
DC
BA
0I2 2
1
VV
A1
11
11RsCsC
1R11 sC 12
1
VI
C sC
0V2
2
1
IV
B 1R2
1
II
D 1
Cascade connection
inV outV
aT bT
inI 0I out
CBAAin
out
1VV
21212
212211 RRR11
VV
RCCsCRCCsin
out
11R
DCBA
1
111
sCRsC
T a
1
1RDCBA
2
222
sCRsC
T b
This Friday• 練習 2011 的考古題• 記得帶計算機• 每次放一個題目在前面的投影片上• 在限定時間內算出答案 ( 可開書、可討論 )• 隨機點一位同學公布答案
Thank you!
Acknowledgement• 感謝 張桓誠 (b02)• 上課時指出投影片的錯誤
Three Terminal to Two Port