Two port electrical network explanation and examples

1. TWO-PORT NETWORKS
PART III
(Topics)
Hybrid Parameters
Transmission Parameters

2. HYBRID PARAMETERS
The network contains NO independent sources
2221212
2121111
VhIhI
VhIhV


admittanceoutputcircuit-open
gaincurrentforwardcircuit-short
gainvoltagereversecircuit-open
impedanceinputcircuit-short




22
21
12
11
h
h
h
h
These parameters are very common in modeling transistors
01
2
21
01
1
11
22 

VV
I
I
h
I
V
h
02
2
22
02
1
12
11 

II
V
I
h
V
V
h

3. LEARNING EXTENSION Find the hybrid parameters for the network
1I


1V
2I


2V
2221212
2121111
VhIhI
VhIhV


1I


1V
2I
02 V
 14))3||6(12( 1111 hIV
3
2
63
6
2112 

 hII


1V
2I


2V
01 I
3
2
63
6
1221 

 hVV
][
9
1
9
22
2
2 Sh
V
I 

4. LEARNING EXAMPLE Find the hybrid parameters for this circuit
Non-inverting amplifier Equivalent linear circuit
2221212
2121111
VhIhI
VhIhV


21
21
111211 )||(
RR
RR
RhIRRRV ii


2RI
DSI
o
i
DSR
R
IAR
I
RR
R
III 1
1
21
1
22 










21
1
21
RR
R
R
AR
h
o
i
21
1
122
21
1
1
RR
R
hV
RR
R
V




)(||
0
21
2
2
RRR
V
IV
o
i


)( 21
21
22
RRR
RRR
h
o
o




5. LEARNING EXTENSION
4
Determine the input impedance of the two-port
2221212
2121111
VhIhI
VhIhV

1I


1V
2I


2V
22 4IV :constraintportoutput
1
1
I
V
Rin 
)4(
)4(
2221212
2121111
IhIhI
IhIhV


1
22
21
2
41
I
h
h
I


1
22
2112
111
41
4
I
h
hh
hV 






][
9
1
3
2
3
2
,14
2221
1211
Shh
hh





 23.15
13
16
14
)9/1(41
)3/2)(3/2(4
14inR
Verification

13
42
127||612inR

6. TRANSMISSION PARAMETERS
The network contains NO independent sources
221
221
DICVI
BIAVV


02
1
02
1
22 

II
V
I
C
V
V
A
02
1
02
1
22 

VV
I
I
D
I
V
B
ratiocurrentcircuit-shortnegativeD
admittancetransfercircuit-openC
impedancetransfercircuit-shortnegativeB
ratiovoltagecircuitopenA




ABCD parameters

7. LEARNING EXAMPLE Determine the transmission parameters
221
221
DICVI
BIAVV


02
1
02
1
22 

II
V
I
C
V
V
A
02
1
02
1
22 

VV
I
I
D
I
V
B



jAV
j
j
V 

 1
1
1
1
12


j
V
I
I
j
V 
2
1
12
1
02 Iwhen
02 Vwhen
112
1
1
1
1
1
I
j
I
j
j
I






 jD  1
  211 )1(
1
2
)
1
||1(1 Ij
j
j
I
j
V 


















jB  2

8. LEARNING EXTENSION Determine the transmission parameters
221
221
DICVI
BIAVV


02
1
02
1
22 

II
V
I
C
V
V
A
02
1
02
1
22 

VV
I
I
D
I
V
B
1I


1V
2I


2V
02 Iwhen
3
215.10
5.10
12 

 AVV
3I
][
7
1
5.102142
42
2
12
13 S
V
I
C
V
II 


02 VWhen
2
3
2142
42
12 

 DII
)
2
3
(1414)21||42( 2111 IIIV 
 21B

9. Thanks