2. An application of the admittance parameters
2221212
2121111
VyVyI
VyVyI
212
211
6
5
2
1
2
1
2
3
VVI
VVI
221 4,2 IVAI
The model plus the conditions at the
ports are sufficient to determine the
other variables.
22
4
1
VI
Determine the current through the
4 Ohm resistor
6. LEARNING EXTENSION
5
A10
OI
Use the admittance (Y) parameters to find the current Io
Conditions at I/O ports
AI 101
2
22
5
1
II
VI
o
1I
1V
2I
2V 2221212
2121111
VyVyI
VyVyI
][
21
1
][
14
1
21
11
Sy
Sy
][
21
1
][
7
1
12
22
Sy
Sy
Replace in model
)5(
7
1
21
1
)5(
21
1
14
1
10
1
1
oo
o
IVI
IV
Solve for variable of interest ][
98
420
AIo
7. IMPEDANCE PARAMETERS
The network contains NO independent sources
2221212
2121111
IzIzV
IzIzV
The ‘z parameters’ can be derived in a manner similar to the Y parameters
01
2
21
01
1
11
22
II
I
V
z
I
V
z
02
2
22
02
1
12
11
II
I
V
z
I
V
z
z11 is called open circuit input impedance, z22=open circuit output impedance
Z21 and z12 is called open circuit transfer impedance
8. LEARNING EXAMPLE Find the Z parameters
Write the loop equations
)(42
)(42
1222
2111
IIjIjV
IIjIV
24
442
2221
1211
jzjz
jzjz
212
211
24
4)42(
IjIjV
IjIjV
rearranging
01
2
21
01
1
11
22
II
I
V
z
I
V
z
02
2
22
02
1
12
11
II
I
V
z
I
V
z
2221212
2121111
IzIzV
IzIzV
9. LEARNING EXAMPLE Use the Z parameters to find the current through the 4 Ohm
resistor
2221212
2121111
IzIzV
IzIzV
Output port constraint
22 4IV
Input port constraint
11 )1(012 IV
212
211
24
4)42(
IjIjV
IjIjV
21 )24(40 IjIj
21 4)43(12 IjIj
)43( j
4j
2))43)(24(16(48 Ijjj 73.13761.12I
10. LEARNING EXTENSION Find the Z parameters.
Find the current on a 4 Ohm load with a 24V input source
1I
1V
2I
2V
)(63
)(612
2122
2111
IIIV
IIIV
9,6
6,18
2221
1211
zz
zz
4
V24
212
211
96
618
IIV
IIV
1I
1V
2I
2V
22 4IV :constraintportoutput
][241 VV :constraintportinput
21
21
1360
61824
II
II
)3(
2)639(24 I
][
33
24
2 AI