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PowerPoint Presentation Fundamentals of Electric Circuits AC Circuits Chapter 16 Two port networks 16 1 Introduction 16 2 Impedance parameters 16 3 Admittance parameters 16 4 Hybrid parameters 16 5 Tr[.]

Fundamentals of Electric Circuits AC Circuits Chapter 16 Two-port networks 16.1 Introduction 16.2 Impedance parameters 16.3 Admittance parameters 16.4 Hybrid parameters 16.5 Transmission parameters 16.6 Interconnection of networks FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.1 Introduction + Port: A pair of terminals through which a current may enter or leave a network  is an access to the network and consists of a pair of terminals + One-port networks: two-terminal devices or elements (R, L, C) + Two-port networks: four-terminal devices (op amps, transistors, transformers) A two-port network is an electrical network with two separate ports for input and output + Study of two-port networks:  Useful in communications, control systems, power systems,…  Treat circuit as a “black box” when embedded within a larger network FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.2 Impedance parameters + Impedance & admittance parameters are commonly used in the synthesis of filters + A two-port network may be voltage-driven or current driven  the terminal voltage can be related to the terminal currents as:  V1  Z11 I1  Z12 I2    V2  Z 21 I1  Z 22 I V1   Z11   V2   Z 21 Z12   I1   I1      Z     Z 22   I  I  Z: impedance parameters FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.2 Impedance parameters + The value of the parameters: open circuit impedance Open circuit input impedance: Open circuit transfer impedance from port to port 1: Open circuit transfer impedance from port to port 2: Open circuit ouput impedance: V1  Z11  I  I1 V2 Z 21  I1 V1 Z12  I2 V2 Z 22  I I2  I1  I1  FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.2 Impedance parameters + Characteristics of impedance parameters  two-port network is said to be symmetrical when Z11 = Z22  two-port network is said to be reciprocal when Z12 = Z21 (a linear two- port network and no dependent sources  The T-equivalent circuit: FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.2 Impedance parameters R1 + Example 1: Determine the z-parameters for the given circuit V1 Solution R1  Open the output port: I2 = I2   R1  R3 I1  R  R3 I1 V2 Z 21  I1 I2  R3 I1   R3 I I1   R2  R3 I2  I2  R2  R3 Method 2: Using mesh current method V1  R1  R3 I1  R3 I2    V2  R3 I1  R2  R3 I V1 Z12  I2 I1  R3 I2   R3 I R2 R3 R1  Open the intput port: I1 = V2 Z 22  I2 R3 I1 Method 1: Using definition equation V1 Z11  I1 R2 R2 R3 I V2 FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.3 Admittance parameters + There are some cases (i.e ideal transformer) that the impedance parameters may not exist for a two-port network  need an alternative means of describing + Express the terminal currents in terms of the terminal voltages  admittance parameters  I1  Y11V1  Y12V2     I  Y21V1  Y22V2  I1  Y11 Y12  V1  V1          Y      I  Y21 Y22  V2  V2  Y: admittance parameters FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.3 Admittance parameters + The value of the parameters: short circuit admittance Short circuit input admittance: Short circuit transfer admittance from port to port 1: I1 Y11  V1 I2 Y21  V V2  V2  Short circuit transfer admittance from port to port 2: Short circuit ouput admittance : I1 Y12  V2 I2 Y22  V V1  V1  FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.3 Admittance parameters + Characteristics of admittance parameters  two-port network is said to be symmetrical when Y11 = Y22  two-port network is said to be reciprocal when Y12 = Y21 (a linear two- port network and no dependent sources  The Π-equivalent circuit: FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.3 Admittance parameters g3 I1 + Example 2: Determine the Y-parameters for the given circuit Solution g1 V1 I1 Y11  V1 V2   g1  g V1  g g3 V1  g3 I2 Y21  V1 V2   g 3V1    g3  V1  Shorten the intput port: V1 = I2 Y22  V2 V1    g  g V2 I   g  g Y12  V2 V2 Method 2: Using node voltage method  I1   g1  g V1  g 3V2     I   g 3V1   g  g V2 V1   g 3V2    g3  V2 g2 g1 g3 g1 I2 g2 Method 1: Using definition equation  Shorten the output port: V2 = g2 V2 FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.3 Admittance parameters + Example 3: Obtain the Y parameters for the given circuit Solution Shorten the output port V1  V0 V0 V0 V1  V0 V0 V0  At node 1:  I1       V1  5V0 8      I  V1  V0   5V0  V0  0.75V  Y  I1  0.15S 11 8 V1 At node 2:  1.25V V1  I  I1  I2   I2  1.25V0  Y21    0.25S   V1  5V0 FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.3 Admittance parameters + Example 3: Obtain the Y parameters for the given circuit Solution Shorten the input port  V0 V0 V0  V2  V0 V0 V0  V2  At node 1:  I1   2    V2  2.5V0 8 I1  V0 Y12    0.05S   V2 2.5V0 At node 2:   V0  V2 625 V I  I1  I2   I2  0.625V0  Y22    0.25S   V2 2.5V0  network is not reciprocal FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.4 Hybrid parameters + Input voltage and output current as function of input current and output voltage of a two-port network V1   H11      I   H 21 H12   I1   I1      H     H 22  V2  V2  + Value of the parameters: V1 Short circuit input impedance H11  I1 I2 Short circuit forward current gain H 21  I V2  V2  I2 H 22  Open circuit output admittance V2 V1 Open circuit reverse voltage gain H 12  V2 I1  I1  FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.4 Hybrid parameters + Input current and output voltage of a two-port network as function of input voltage and output current  G parameters  I1  G11 G12  V1  V1        G     V2  G21 G22   I  I  + Value of the parameters: I1 Open circuit input admittance G11  V1 V2 Open circuit forward voltage gain G21  V I2  I2  V2 Short circuit output impedance G22  I2 I1 Short circuit reverse current gain G12  V1 V1  V1  FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.5 Transmission parameters + Transmission parameters:  relates the variables at the input port to those at the output port + Transimission parameters  useful in the analysis of transmission lines (cable, fiber) and in the design of telephone system, microwave network,… + A - parameters: V1   A11    I1   A21 + Value of the A parameters: Open circuit voltage ratio A12  V2  V2      A     A22   I  I2  V1 A11  V2 I2  I1 Open circuit transfer admittance A21  V2 I2  V1 Short circuit transfer impedance A12  I2 I1 Short circuit current ratio A22  I V2 0 V2  FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.5 Transmission parameters + Inverse transmission parameters  express the variables at the output port in term of the variables at the input port + B - parameters: V2   B11    I   B21 + Value of the B - parameters: Open circuit voltage gain B12  V1  V1      B     B22   I1   I1  V2 B11  V1 I1  I2 Open circuit transfer admittance B21  V1 + Reciprocal network: A11 A22  A12 A21  B11 B22  B12 B21  I1  V2 Short circuit transfer impedance B12  I1 I2 Short circuit current gain B22  I V1 0 V1  FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.5 Transmission parameters + Example 4: Find the transmission parameters for the given circuit Solution  Open the output port: I2 = V1  10  20 I1  30 I1 V  20 I  3I  17 I 1 V1 A11  V2 I1 A21  V 30   1.765 I2  17 I1   0.059 I2   17 I  Shorten the output port: V2 = At node A: V1 13I1 V1  Va Va   15.29   I  A12   V2 0    17 / 20I1 I2 10 20 Va  3I1 I1 I1 A22    1.176 V2         13I1  3I1 3I1 I2 I  V1  Va  10 20 10 FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.6 Interconnection of networks + Large, complex network  divided into sub-networks (2 port network) for the purposes of analysis and design + Two-port networks - as building blocks - that can be interconnected (in series, in parallel, or in cascade) to form a complex network + The value of parameters of the complex network:  calculated from the value of each parameters of each building block FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.6 Interconnection of networks Series connection [Z] = [Za] + [Zb] Cascade connection [T] = [Ta][Tb] Parallel connection [Y] = [Ya] + [Yb] FUNDAMENTALS OF ELECTRIC CIRCUITS – AC Circuits 16.6 Interconnection of networks Zd + Example 5: Find the transmission parameters of the given Pi circuit Zn1    Zd I1 I2 V1   I1 I2  V1 Zn1  V2  V2   V    V     Z d             I1   I2     V        I   Z n1 0     V        I2  Tn1 Zn2 Td Tn2 T  Tn1.Td Tn2  T  Tn1 Td Tn   Z  n1 0    Zd   1       Zn2  Zd 1  Zn2 T    Zd     Z n1 Z n Z n1 Z n2     Zd 1  Z n1  Zd 0   