Transcript Slide 1
TWO-PORT NETWORKS
TWO-PORT NETWORK- Definition A port : an access to a network and consists of two terminals
One-port network
I + V I
Linear network
- One pair of terminal - Current entering the port = current leaving the port
Input port
TWO-PORT NETWORK- Definition
Two-port network
+ V 1 I 1 I 1
Linear network
I 2 I 2 + V 2
Output port
- Two pairs of terminal : two-port - Current entering a port = current leaving a port - V 1 ,V 2 , I 1 and I 2 are related using two-port network
parameters
- In SEE 1023 we will study on four sets of these parameters
Impedance parameters Hybrid parameters Admittance parameters Transmission parameters
TWO-PORT NETWORK
Why ?
Typically found in communications, control systems, electronics - used in modeling, designing and analysis Know how to model two-port network will help in the analysis of larger network - two port network treated as ‘black box’
TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 V V 2 1 z 11 z 21 z 12 z 22 I I 2 1 Parameters can be determined by calculations or measurement
V 1 z 11 and z 21 I 1 TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 I 2 + V 2 Output port : open I 2 = 0 Input port : Apply voltage source V V 1 2 z 11 I 1 z 21 I 1 z 11 V 1 I 1 I 2 0 z 21 V 2 I 1 I 2 0
z 12 and z 22 V 1 I 1 =0 + V 1 TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 I 2 V 2 Input port : opened I 1 = 0 Output port : Apply voltage source V V 1 2 z 12 I 2 z 22 I 2 z 12 V 1 I 2 I 1 0 z 22 V 2 I 2 I 1 0
TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 Equivalent circuit based on these equations: I 1 + V 1 z I 11 2 z 12 + + z 22 I 1 z 21 I 2 + V 1
V TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 Linear network with NO dependent sources:
RECIPROCAL
• Voltage source and ideal ammeter connected to the ports are interchangeable
ammeter
Reciprocal network A I I A Reciprocal network V
TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 Linear network with NO dependent sources:
RECIPROCAL
• • • Voltage source and ideal ammeter connected to the ports are interchangeable z 12 = z 21 Can be replaced with T-equivalent circuit: Z 11 -z 12 Z 22 -z 12 + V 1 Z 12 + V 2
TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 Linear network with NO dependent sources:
RECIPROCAL
Network with mirror-like symmetry:
SYMMETRICAL
z 11 = z 22
TWO-PORT NETWORK
Impedance parameters (z parameters)
V 1 z 11 I 1 z 12 I 2 V 2 z 21 I 1 z 22 I 2 Linear network with NO dependent sources:
RECIPROCAL
Network with mirror-like symmetry:
SYMMETRICAL
If the two-port network is reciprocal and symmetrical, only 2 parameters need to be determined
TWO-PORT NETWORK
Admittance parameters (y parameters)
I 1 y 11 V 1 y 12 V 2 I 2 y 21 V 1 y 22 V 2 I I 2 1 y y 11 21 y 12 y 22 V V 2 1 Parameters can be determined by calculations or measurement
y 11 and y 21 I 1 + V 1 TWO-PORT NETWORK
Admittance parameters (y parameters)
I 1 y 11 V 1 y 12 V 2 I 2 y 21 V 1 y 22 V 2 I 2 + V 2 = 0 Output port : shorted V 2 = 0 Input port : Apply current source I I 1 2 y 11 V 1 y 21 V 1 y 11 I 1 V 1 V 2 0 y 21 I 2 V 1 V 2 0
y 12 and y 22 I 1 + V 1 =0 TWO-PORT NETWORK
Admittance parameters (y parameters)
I 1 y 11 V 1 y 12 V 2 I 2 y 21 V 1 y 22 V 2 I 2 + V 2 Input port : shorted V 1 = 0 Output port : Apply current source I I 1 2 y 12 V 2 y 22 V 2 y 12 I 1 V 2 V 1 0 y 22 I 2 V 2 V 1 0
TWO-PORT NETWORK
Admittance parameters (y parameters)
I 1 y 11 V 1 y 12 V 2 I 2 y 21 V 1 y 22 V 2 Equivalent circuit based on these equations: I 1 + V 1 y 11 y 12 V 2 y 21 V 1 y 22 + I 2 V 2
TWO-PORT NETWORK
Admittance parameters (y parameters)
I 1 y 11 V 1 y 12 V 2 I 2 y 21 V 1 y 22 V 2 Linear network with NO dependent sources:
RECIPROCAL
• • • Current source and ideal voltmeter connected to the ports are interchangeable
y 12
Can be replaced with -equivalent circuit: + V 1
= y 21
y 11 + y 12 -y 12 y 22 + y 12 + V 2
TWO-PORT NETWORK
Admittance parameters (y parameters)
I 1 y 11 V 1 y 12 V 2 I 2 y 21 V 1 y 22 V 2 Network with mirror-like symmetry:
SYMMETRICAL : y 11 = y 22
TWO-PORT NETWORK
Hybrid parameters (h parameters)
V 1 h 11 I 1 h 12 V 2 I 2 h 21 I 1 h 22 V 2 I V 1 2 h 11 h 21 h 12 h 22 I 1 V 2 Some two port network cannot be expressed in terms z or y parameters but can be expressed in terms of
h
parameters Parameters can be determined by calculations or measurement
h 11 and h 21 I 1 + V 1 TWO-PORT NETWORK
Hybrid parameters (h parameters)
V 1 h 11 I 1 h 12 V 2 I 2 h 21 I 1 h 22 V 2 I 2 + V 2 = 0 Output port : shorted V 2 = 0 Input port : Apply current source V I 2 1 h 11 I 1 h 21 I 1 h 11 V 1 I 1 V 2 0 ( ) h 21 I 2 I 1 V 2 0
h 12 and h 22 I 1 =0 + V 1 TWO-PORT NETWORK
Hybrid parameters (h parameters)
V 1 h 11 I 1 h 12 V 2 I 2 h 21 I 1 h 22 V 2 I 2 V 2 Input port : opened I 1 = 0 Output port : Apply voltage source V I 2 1 h 12 V 2 h 22 V 2 h 12 V 1 V 2 I 1 0 h 22 I 2 V 2 I 1 0 (S)
TWO-PORT NETWORK
Hybrid parameters (h parameters)
V 1 h 11 I 1 h 12 V 2 I 2 h 21 I 1 h 22 V 2 Equivalent circuit based on these equations: + I 1 h 11 V 1 h 11 V 2 + h 21 I 1 h 22 I 2 + V 2
TWO-PORT NETWORK
Hybrid parameters (h parameters)
V 1 h 11 I 1 h 12 V 2 I 2 h 21 I 1 h 22 V 2 Linear network with NO dependent sources:
RECIPROCAL
• • Current source and ideal voltmeter connected to the ports are interchangeable
h 12 = -h 21
TWO-PORT NETWORK
Hybrid parameters (h parameters)
V 1 h 11 I 1 h 12 V 2 I 2 h 21 I 1 h 22 V 2 Network with mirror-like symmetry:
SYMMETRICAL : h 11 h 22 – h 12 h 21 = 1
TWO-PORT NETWORK
Transmission parameters (t parameters)
V 1 AV 2 BI 2 I 1 CV 2 DI 2 V 1 I 1 A C B D V I 2 2 Used to express the
sending
end voltage an current in terms of
receiving
end voltage and current I 1 -I 2
sending end
+ V 1
Linear network
+ V 2
receiving end
I 1 I 2
TWO-PORT NETWORK
Transmission parameters (h parameters)
V 1 AV 2 BI 2 I 1 CV 2 DI 2 V 1 Output port : opened I 2 = 0 AV 2 A V 1 V 2 I 2 0 I 1 CV 2 C I 1 V 2 I 2 0 V 1 Output port : shorted V 2 = 0 BI 2 B V 1 I 2 V 2 0 I 1 DI 2 For
RECIPROCAL
network, AD – BC = 1 D I I 2 1 V 2 0 For
SYMMETRICAL
network, A = D
TWO-PORT NETWORK
Relationships between parameters
If a two-port network can be presented by different set of parameters, then there exists relationships between parameters.
e.g. relationships between z and y parameters: V V 2 1 z z 11 21 z 12 z 22 I I 2 1 I I 2 1 z z 11 21 z 12 z 22 1 V V 2 1 We know that Therefore I I 2 1 y y 11 21 y 11 y 21 y 12 y 22 y 12 y 22 V V 2 1 z 11 z 21 z 12 z 22 1
TWO-PORT NETWORK
Relationships between parameters
Therefore, y 11 z 22 z z z 22 21 z z z 11 12 y 12 z 12 z where z z 11 z 22 z 12 z 21 y 21 z 21 z y 22 z 11 z The conversion formulae can be obtained from the conversion table e.g. on page 869 of Alexander/Sadiku z z 11 21 z 12 z 22 1
TWO-PORT NETWORK
Relationships between parameters
TWO-PORT NETWORK
Interconnection of networks
Complex large network can be modeled with interconnected two-port networks • Simplify the analysis /synthesis • Simplify the design Parameters of interconnected two-port networks can be obtained easily: depending on the type of parameters and type of connections: • Series: z parameters • Parallel: y parameters • Cascade: transmission parameters
+ I 1a + V 1a V 1 I 1b + V 1b z a z b TWO-PORT NETWORK
Interconnection of networks
Series: z parameters I 2a + V 2a + V 2 I 2b + V 2b I 1 + V 1 z + V 2 I 2 [z] = [z a ] + [z b ]
I 1 + V 1 I 1a + V 1a I 1b + V 1b y a y b TWO-PORT NETWORK
Interconnection of networks
Parallel: y parameters I 2a + V 2a I 2b + V 2b I 2 + V 2 I 1 + V 1 y + V 2 I 2 [y] = [y a ] + [y b ]
I 1 + V 1 I 1a + V 1a TWO-PORT NETWORK
Interconnection of networks
t a Cascade: t parameters -I 2a + V 2a I 1b + V 1b t b -I 2b + V 2b -I + V 2 2 I 1 + V 1 t [t] = [t a ][t b ] -I 2 + V 2