# One-Port Networks. One-Port. Network

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1 TwoPort s Definitions Impedance Parameters dmittance Parameters Hybrid Parameters Transmission Parameters Cascaded TwoPort s Examples pplications OnePort s v i' 1 OnePort pair of terminals at which a signal (voltage or current) may enter or leave is called a port network having only one such pair of terminals is called a oneport network No connections may be made to any other nodes internal to the network y KCL, we therefore have i 1 We discussed in ECE 221 how oneport networks may be modeled by their Thévenin or Norton equivalents J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver TwoPort s: Definitions & Requirements TwoPort s: Defining Equations TwoPort i' 1 i' 2 TwoPort Twoport networks are used to describe the relationship between a pair of terminals The analysis methods we will discuss require the following conditions be met 1. Linearity 2. No independent sources inside the network 3. No stored energy inside the network (zero initial conditions) 4. i 1 and i 2 If the network contains dependent sources, one or more of the equivalent resistors may be negative Generally, the network is analyzed in the s domain Each twoport has exactly two governing equations that can be written in terms of any pair of network variables Like Thévenin and Norton equivalents of oneports, once we know a set of governing equations we no longer need to know what is inside the box J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

2 Impedance Parameters Impedance Parameter Measurements TwoPort TwoPort z 11 z 12 z 21 z 22 z11 z 12 z 21 z 22 Suppose the currents and voltages can be measured lternatively, if the circuit in the box is known, and can be calculated based on circuit analysis Relationship can be written in terms of the impedance parameters We can also calculate the impedance parameters after making two sets of measurements z 11 z 12 z 21 z 22 If the right port is an open circuit ( 0), then we can easily solve for two of the impedance parameters: z 11 z 21 I2 0 I2 0 J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Impedance Parameter Measurements Continued Impedance Parameter Measurements Summarized TwoPort TwoPort z 11 z 12 z 21 z 22 If the left port is an open circuit ( 0), then we can easily solve for the other two impedance parameters: z 12 z z 11 z 21 I2 0 I2 0 z 12 z J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

3 Impedance Parameter Equivalent Example 1: Impedance Parameters 200 Ω 40 Ω z 11 z 22 z 12 z Ω 500 Ω 1kΩ z 11 z 12 z 21 z 22 Find the z parameters of the circuit. Once we know what the impedance parameters are, we can model the behavior of the twoport with an equivalent circuit. Notice the similarity to Thévenin and Norton equivalents J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Example 1: Workspace Example 2: Parameter Conversion TwoPort z 11 z 12 z 21 z 22 In general, the two defining equations can be written in terms of any pair of variables. For example, rewrite the defining equations in terms of the voltages and. J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

4 Example 2: Workspace Example 2: Workspace Continued J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Impedance & dmittance Parameters Hybrid Parameters TwoPort TwoPort Impedance Parameters z 11 z 12 z 21 z 22 z11 z 12 z 21 z 22 Hybrid Parameters h 11 h 12 h 21 h 22 h11 h 12 h 21 h 22 dmittance Parameters y 11 y 12 y 21 y 22 y11 y 12 y 21 y 22 Inverse Hybrid Parameters g 11 g 12 g 21 g 22 g11 g 12 g 21 g 22 J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

5 Transmission Parameters Transmission Parameter Conversion TwoPort TwoPort Transmission Parameters a 11 a 12 a 21 a 22 a11 b 12 V2 V2 a 21 a 22 Inverse Transmission Parameters b 11 b 12 V2 b11 b 12 b 21 b 22 b 21 b 22 V2 ltogether there are 6 sets of parameters Each set completely describes the twoport network ny set of parameters can be converted to any other set We have seen one example of a conversion complete table of conversions is listed in the text (Pg. 933) You should have a copy of this in your notes for the final J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Example 3: TwoPort Measurements The following measurements were taken from a twoport network. Find the transmission parameters. Port 2 Open Example 3: Workspace 150 cos(4000t) V applied 25 cos(4000t 45 ) measured 1000 cos(4000t 15 ) V measured Port 2 Shorted 30 cos(4000t) V applied 1.5 cos(4000t 30 ) measured 0.25 cos(4000t 150 ) measured J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

6 Example 4: TwoPort nalysis Example 4: Workspace 800 Ω 800 Ω 40 Ω 160 Ω 40 Ω 160 Ω v Ω 16.2 v 3 v Ω 16.2 v 3 Find the hybrid parameters for the circuit shown above. J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Example 4: Workspace Continued Example 5: TwoPort Measurements The following measurements were taken from a twoport network. Find the transmission parameters. Port 1 Open Port 1 Shorted 1 mv 0.5 µ 10 V 80 µ 200 µ 5 V Hint: b b 11 b 22 b 12 b 21, a 11 b 22 b, a 12 b 12 b, a 21 b 21 b, and a 22 b 11 b. J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

7 Example 5: Workspace Example 6: TwoPort nalysis R 1 R 3 v R 4 C 1 v R 2 C 2 Find an expression for the transfer function, h 11, z 11, g 12, g 22, a 11, and y 21. J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Example 6: Workspace R 1 R 3 v R 4 Example 6: Workspace Continued (1) R 1 R 3 v R 4 C 1 v R 2 C 1 v R 2 C 2 C 2 J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

8 Example 6: Workspace Continued (2) Cascaded TwoPort s R 1 R 3 v R 4 C 1 v R 2 C 2 Two networks are cascaded when the output of one is the input of the other Note that and The transmission parameters take advantage of these properties J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver Cascaded TwoPort s Cascaded TwoPort s Continued a11 a 12 a 21 a 22 V2 a11 a 12 a 21 a 22 V2 The inverse transmission parameters are also convenient for cascaded networks. V2 a11 a 12 a 21 a 22 a11 a 12 a 21 a 22 V2 V2 b11 b 12 b 21 b 22 V2 b11 b 12 b 21 b 22 V2 V2 b11 b 12 b 21 b 22 b11 b 12 b 21 b 22 J. McNames Portland State University ECE 222 TwoPort s Ver J. McNames Portland State University ECE 222 TwoPort s Ver

9 Cascaded Systems: TwoPort s versus H Twoports and transfer functions H are closely related H only relates the input signal to the output signal Twoports relate both voltages and currents at each port You cannot cascade H unless the circuits are active Twoport networks have no such restriction Twoports are used to design passive filters However, twoports are more complicated than H J. McNames Portland State University ECE 222 TwoPort s Ver

### Circuit Theorems Overview Linearity Superposition Source Transformation Thévenin and Norton Equivalents Maximum Power Transfer

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