Lecture Electric circuit theory: Two-port networks - Nguyễn Công Phương
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Nguyễn Công Phương
Electric Circuit Theory
Two-port Networks
Contents
I. Basic Elements Of Electrical Circuits
II. Basic Laws
III. Electrical Circuit Analysis
IV. Circuit Theorems
V. Active Circuits
VI. Capacitor And Inductor
VII. First Order Circuits
VIII.Second Order Circuits
IX. Sinusoidal Steady State Analysis
X. AC Power Analysis
XI. Three-phase Circuits
XII. Magnetically Coupled Circuits
XIII.Frequency Response
XIV.The Laplace Transform
XV. Two-port Networks
Two-port Networks - sites.google.com/site/ncpdhbkhn
2
Two-port Network
1.
2.
3.
4.
5.
6.
7.
Introduction
Parameters
Relationships between Parameters
Two-port Network Analysis
Interconnection of Networks
T & П Networks
Equivalent Two-port Networks of Magnetically Coupled
Circuits
8. Input Impedance
9. Transfer Function
Two-port Networks - sites.google.com/site/ncpdhbkhn
3
Introduction
I1
I2
+
+
Linear
Network
–
I1
V2
–
V1
I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
4
Two-port Network
1. Introduction
2. Parameters
a)
b)
c)
d)
e)
f)
3.
4.
5.
6.
7.
8.
9.
Impedance z
Admittance y
Hybrid h
Inverse Hybrid g
Transmission T
Inverse Transmission t
Relationships between Parameters
Two-port Network Analysis
Interconnection of Networks
T & П Networks
Equivalent Two-port Networks of Magnetically Coupled Circuits
Input Impedance
Transfer Function
Two-port Networks - sites.google.com/site/ncpdhbkhn
5
Impedance Parameters (1)
I1
I2
+
+
Linear
Network
V1
–
I1
V2
–
V1 = z11I1 + z12I 2
V2 = z 21I1 + z 22I 2
I2
V1 z11 z12 I1
I1
= [z ]
V = z
2 21 z 22 I 2
I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
6
Impedance Parameters (2)
I1
I2
–
I1
I2
I1
I2 = 0
Linear
Network
I
1
Two-port Networks - sites.google.com/site/ncpdhbkhn
V2
–
V1
–
I2 =0
I2 = 0
–
V2
I1
V2
+
V1
I1
Linear
Network
V1
+
z11 =
V1 = z11I1
→
→
V2 = z 21I1
z =
21
+
+
V1 = z11I1 + z12I 2
V2 = z 21I1 + z 22I 2
I2 = 0
7
Impedance Parameters (3)
I1
I2
Linear
Network
V2
–
V1
–
I1
I2
I1 = 0
I2
+
Linear
Network
–
Two-port Networks - sites.google.com/site/ncpdhbkhn
V2
I2
–
V1
+
V1
z12 =
I 2 I =0
V1 = z12I 2
1
→
→
V2 = z 22I 2
z = V2
22 I
2 I1 =0
+
+
V1 = z11I1 + z12I 2
V2 = z 21I1 + z 22I 2
I1 = 0
8
Impedance Parameters (4)
I1
I2
I2 =0
V2
I1
I2 =0
I1 =0
V2
z 22 =
I 2 I =0
1
–
V1
I1
Linear
Network
V1
I1
V2
–
z11 =
z =
21
+
+
V1 = z11I1 + z12I 2
V2 = z 21I1 + z 22I 2
I2
V1
z12 =
I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
9
Impedance Parameters (5)
Ex.
Find [z]?
I1
10Ω
I2 = 0
30Ω
20Ω
+
30Ω
V2
20Ω
I1
+
+
[z]
V1
V2
–
V1
z11 =
I1
I2
I 2 =0
V1 = (10 + 20)I1 = 30I1
30I1
→ z11 =
= 30 Ω
I1
–
10Ω
–
+
–
V1
I1
I2
V1 = z11I1 + z12 I2
V2 = z 21I1 + z 22I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
10
Impedance Parameters (6)
Ex.
Find [z]?
I1
10Ω
I2 = 0
30Ω
20Ω
+
30Ω
V2
20Ω
I1
+
+
[z]
V1
V2
–
V2
z 21 =
I1
I2
I2 = 0
V2 = VR 2 = 20I1
20I1
→ z 21 =
= 20 Ω
I1
–
10Ω
–
+
–
V1
I1
I2
V1 = z11I1 + z12 I2
V2 = z 21I1 + z 22I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
11
Impedance Parameters (7)
Ex.
Find [z]?
10Ω
I1 = 0
I2
30Ω
20Ω
+
30Ω
20Ω
–
I1
V2
I2
+
+
V2
–
V1
z12 =
I2
[z]
V1
I1 =0
V1 = VR 2 = 20I 2
20I 2
→ z12 =
= 20 Ω
I2
–
10Ω
+
V1
I1
I2
V1 = z11I1 + z12 I2
V2 = z 21I1 + z 22I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
12
–
Impedance Parameters (8)
Ex.
Find [z]?
10Ω
I1 = 0
I2
30Ω
20Ω
+
30Ω
20Ω
–
I1
V2
I2
+
+
V2
–
–
V2
z 22 =
I2
[z]
V1
I1 =0
V2 = (20 + 30)I2 = 50I 2
50I2
→ z 22 =
= 50 Ω
I2
–
10Ω
+
V1
I1
I2
V1 = z11I1 + z12 I2
V2 = z 21I1 + z 22I2
Two-port Networks - sites.google.com/site/ncpdhbkhn
13
Ex.
Impedance Parameters (9)
Find [z]?
10Ω
I1
I2
+
+
[z]
V1
V2
–
–
30 20
z=
20 50
30Ω
20Ω
I1
Two-port Networks - sites.google.com/site/ncpdhbkhn
I2
14
Impedance Parameters (10)
Ex.
Find [z]?
10Ω
V2
V1
I2
+
–
–
–
z=?
+
I2
I1
+
+
[z]
V1
I1
I2
[z]
V2
–
I1
30Ω
20Ω
I1
I2
30 20
z=
20 50
Two-port Networks - sites.google.com/site/ncpdhbkhn
15
Impedance Parameters (11)
I2
I1
Find [z]?
+
+
Method 2
V1
10Ω
30Ω
20Ω
–
V1 = V10 + V20 = 10I1 + 20( I1 + I 2 ) = (10 + 20)I1 + 20I 2
V2 = V30 + V20 = 30I 2 + 20( I1 + I 2 ) = 20I1 + (20 + 30)I 2
+ 20I 2
V1 = (10 + 20)I1
→
20I1 + (20 + 30)I 2
V2 =
V1 = z11I1 + z12I 2
V2 = z 21I1 + z 22 I 2
z11 = 10 + 20 = 30Ω
z = 20 = 20Ω
12
→
z 21 = 20 = 20Ω
z 22 = 20 + 30 = 50Ω
Two-port Networks - sites.google.com/site/ncpdhbkhn
16
V2
–
Ex.
Two-port Network
1. Introduction
2. Parameters
a)
b)
c)
d)
e)
f)
3.
4.
5.
6.
7.
8.
9.
Impedance z
Admittance y
Hybrid h
Inverse Hybrid g
Transmission T
Inverse Transmission t
Relationships between Parameters
Two-port Network Analysis
Interconnection of Networks
T & П Networks
Equivalent Two-port Networks of Magnetically Coupled Circuits
Input Impedance
Transfer Function
Two-port Networks - sites.google.com/site/ncpdhbkhn
17
Admittance Parameters (1)
I1
I2
+
+
Linear
Network
V1
–
I1
I1 y11
I = y
2 21
V2
–
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
I2
y12 V1
V1
= [y]
y 22 V2
V2
Two-port Networks - sites.google.com/site/ncpdhbkhn
18
Admittance Parameters (2)
I1
I2
–
–
V1
V2
–
Two-port Networks
Linear
Network
V1
+
I1
y11 =
V1 V =0
I1 = y11V1
2
→
→
I2
I 2 = y 21V1
y 21 =
V1 V =0
2
+
+
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
V2 = 0
I1
I2
I1
I2
Linear
Network
I1
- sites.google.com/site/ncpdhbkhn
V2 = 0
I2
19
Admittance Parameters (3)
I1
I2
I1
I2
I1
I2
V1 = 0
Linear
Network
I1
- sites.google.com/site/ncpdhbkhn
V2
I2
–
–
V1 =0
V2
–
Two-port Networks
V1 =0
Linear
Network
V1
+
I1
y12 =
V2
I1 = y12 V2
→
→
I2
I 2 = y 22 V2
y 22 =
V2
+
+
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
V1 = 0
20
Admittance Parameters (4)
I1
I2
V2 = 0
I2
V1
V2 = 0
V1 =0
I2
y 22 =
V2 V =0
1
–
I1
V1
Linear
Network
V1
I1
V2
–
y11 =
y =
21
+
+
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
I2
I1
y12 =
V2
Two-port Networks - sites.google.com/site/ncpdhbkhn
21
Admittance Parameters (5)
Find [y]?
I2
1Ω 3Ω
I1
+
Linear
Network
V1
V2 =0
–
1× 2
V1 = (1// 2)I1 =
I1 = 0.67I1
1+ 2
I1
→ y11 =
= 1.5S
0.67I1
I2
+
I1
y11 =
V1
V2 = 0
–
2Ω
–
V1
3Ω
+
+
I1
1Ω
2Ω
I1
V2
–
Ex.
I2
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
Two-port Networks - sites.google.com/site/ncpdhbkhn
22
Admittance Parameters (6)
Find [y]?
I2
1Ω 3Ω
I1
+
Linear
Network
V1
V2 = 0
–
V1 = V1Ω = V2 Ω = −2I 2
I2
→ y 21 =
= −0.5S
−2I 2
I2
+
I2
y 21 =
V1
V2 = 0
–
2Ω
–
V1
3Ω
+
+
I1
1Ω
2Ω
I1
V2
–
Ex.
I2
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
Two-port Networks - sites.google.com/site/ncpdhbkhn
23
Admittance Parameters (7)
Find [y]?
I1
1Ω
V2
I2
I1
–
1Ω 3Ω
3Ω
+
+
I2
+
+
–
I1
y12 =
V2
Linear
Network
V1
V1 = 0
V2 = V3Ω = V2Ω = −2I1
I1
→ y12 =
= −0.5S
−2I1
–
V1 = 0
2Ω
2Ω
I1
V2
–
Ex.
I2
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
Two-port Networks - sites.google.com/site/ncpdhbkhn
24
Admittance Parameters (8)
Find [y]?
I1
1Ω
V2
I2
I1
–
1Ω 3Ω
3Ω
+
+
I2
+
+
–
I2
y 22 =
V2
Linear
Network
V1
V1 =0
2×3
V2 = (2 // 3)I 2 =
V2 = 1.2 V2
2+3
I2
→ y 22 =
= 0.83S
1.2I 2
–
V1 = 0
2Ω
2Ω
I1
V2
–
Ex.
I2
I1 = y11V1 + y12 V2
I 2 = y 21V1 + y 22 V2
Two-port Networks - sites.google.com/site/ncpdhbkhn
25
