Formula Sheets: Two Port Networks | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

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Net w ork Theory: T w o-P ort Net w orks F orm ula Sheet
for Electrical GA TE
T w o-P o rt N et w ork Basics
• Definition : A t w o-p ort net w ork has t w o p orts (input and output) with v oltages (V
1
,
V
2
) and curren ts (I
1
, I
2
).
• Con v en tions : I
1
en ters p ort 1, I
2
lea v es p ort 2 (standard con v en tion for GA TE).
• P arameters : Describ e relationships b et w een V
1
, V
2
, I
1
, and I
2
.
Z-P arameters (Imp edance P arameters)
• Definition : Express v oltages as functions of curren ts.
V
1
=Z
11
I
1
+Z
12
I
2
, V
2
=Z
21
I
1
+Z
22
I
2
• F orm ulas :
Z
11
=
V
1
I
1




I
2
=0
, Z
12
=
V
1
I
2




I
1
=0
Z
21
=
V
2
I
1




I
2
=0
, Z
22
=
V
2
I
2




I
1
=0
• Units : ? .
Y-P arameters (A dmittance P arameters)
• Definition : Express curren ts as functions of v oltages.
I
1
=Y
11
V
1
+Y
12
V
2
, I
2
=Y
21
V
1
+Y
22
V
2
• F orm ulas :
Y
11
=
I
1
V
1




V
2
=0
, Y
12
=
I
1
V
2




V
1
=0
Y
21
=
I
2
V
1




V
2
=0
, Y
22
=
I
2
V
2




V
1
=0
• Units : S .
h-P arameters (Hybrid P arameters)
• Definition : Express V
1
and I
2
in terms of I
1
and V
2
.
V
1
=h
11
I
1
+h
12
V
2
, I
2
=h
21
I
1
+h
22
V
2
1
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Net w ork Theory: T w o-P ort Net w orks F orm ula Sheet
for Electrical GA TE
T w o-P o rt N et w ork Basics
• Definition : A t w o-p ort net w ork has t w o p orts (input and output) with v oltages (V
1
,
V
2
) and curren ts (I
1
, I
2
).
• Con v en tions : I
1
en ters p ort 1, I
2
lea v es p ort 2 (standard con v en tion for GA TE).
• P arameters : Describ e relationships b et w een V
1
, V
2
, I
1
, and I
2
.
Z-P arameters (Imp edance P arameters)
• Definition : Express v oltages as functions of curren ts.
V
1
=Z
11
I
1
+Z
12
I
2
, V
2
=Z
21
I
1
+Z
22
I
2
• F orm ulas :
Z
11
=
V
1
I
1




I
2
=0
, Z
12
=
V
1
I
2




I
1
=0
Z
21
=
V
2
I
1




I
2
=0
, Z
22
=
V
2
I
2




I
1
=0
• Units : ? .
Y-P arameters (A dmittance P arameters)
• Definition : Express curren ts as functions of v oltages.
I
1
=Y
11
V
1
+Y
12
V
2
, I
2
=Y
21
V
1
+Y
22
V
2
• F orm ulas :
Y
11
=
I
1
V
1




V
2
=0
, Y
12
=
I
1
V
2




V
1
=0
Y
21
=
I
2
V
1




V
2
=0
, Y
22
=
I
2
V
2




V
1
=0
• Units : S .
h-P arameters (Hybrid P arameters)
• Definition : Express V
1
and I
2
in terms of I
1
and V
2
.
V
1
=h
11
I
1
+h
12
V
2
, I
2
=h
21
I
1
+h
22
V
2
1
• F orm ulas :
h
11
=
V
1
I
1




V
2
=0
, h
12
=
V
1
V
2




I
1
=0
h
21
=
I
2
I
1




V
2
=0
, h
22
=
I
2
V
2




I
1
=0
• Units : h
11
(? ), h
12
(dimensionless), h
21
(dimensionless), h
22
(S ).
ABCD P arameters (T ransmission P arameters)
• Definition : Express input quan tities in terms of output quan tities.
V
1
=AV
2
-BI
2
, I
1
=CV
2
-DI
2
• F orm ulas :
A =
V
1
V
2




I
2
=0
, B =-
V
1
I
2




V
2
=0
C =
I
1
V
2




I
2
=0
, D =-
I
1
I
2




V
2
=0
• Units : A (dimensionless), B (? ), C (S ), D (dimensionless).
P arameter Con v ersions
• Z to Y P arameters :
[Y] = [Z]
-1
• Z to h P arameters :
h
11
=
det[Z]
Z
22
, h
12
=
Z
12
Z
22
, h
21
=-
Z
21
Z
22
, h
22
=
1
Z
22
• Z to ABCD P arameters :
A =
Z
11
Z
21
, B =
det[Z]
Z
21
, C =
1
Z
21
, D =
Z
22
Z
21
• Recipro cal Net w ork : AD-BC = 1 (for recipro cal t w o-p ort net w orks).
Key Notes
• Use SI units: V oltage (V ), Curren t (A ), Imp edance (? ), A dmittance (S ).
• F or parameter calculations, ensure prop er op en-circuit or short-circuit conditions.
• Chec k for recipro cit y (Z
12
=Z
21
, Y
12
=Y
21
, h
12
=-h
21
, AD-BC = 1 ).
• F or GA TE, fo cus on Z, Y, and h parameters; ABCD parameters are useful for cascaded
net w orks.
• V erify matrix symmetry for passiv e, bilateral net w orks.
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