Two-Port Networks

Abstract

A network is a combination of one or several electric circuits that together perform a specific action. The network might have several inputs that receive excitations and outputs to show the results. A port is a set of two terminals that allows for a source to connect and excite the network or connect a measurement device and record the response. For instance, a voltage source connected to a port of a network may cause currents to flow through the network and voltage drops to appear across the elements. To measure any of these currents or voltages, terminals may be extended to demonstrate some measurment locations, forming an output port. This forms a two-port network. Similarly, two-port networks can be easily expanded to multiple-port networks each showing a parameter in the circuit. Figure 12.1 shows a circuit and the process to consider it as a two-port network.

Problems

• 12.1. Find the impedance parameters of the following circuit.

• 12.2. Find the impedance parameters of the following circuit.

• 12.3. Find the impedance parameters of the following circuit.

• 12.4. Find the impedance parameters of the following circuit.

• 12.5. Find the impedance parameters of the following circuit.

• 12.6. Find the impedance parameters of the following circuit.

• 12.7. Find a two-port network that results in the following Z parameters.

$$ Z=\left[\begin{array}{cc}\frac{3s+1}{s}& \frac{1}{s}\\ {}\frac{1}{s}& \frac{5{s}^2+1}{s}\end{array}\right] $$

$$ Z=\left[\begin{array}{cc}5s+4& 4\\ {}4& 3s+4\end{array}\right] $$

• 12.8. Find admittance parameters in the following circuits.

• 12.9. Find admittance parameters in the following circuits.

• 12.10. Find admittance parameters in the following circuits.

• 12.11. Find a two-port network that results in the following Y parameters.

$$ Y=\left[\begin{array}{cc}\frac{2s+1}{s}& -2\\ {}-2& s+2\end{array}\right] $$

$$ Y=\left[\begin{array}{cc}\frac{s^2+1}{s}& -s\\ {}-s& \frac{s^2+1}{s}\end{array}\right] $$

• 12.12. Find Y and Z.

• 12.13. Find Y and Z.

• 12.14. Find Y and Z.

• 12.15. Find Y and Z.

• 12.16. Find Y and Z.

• 12.17. Find a two-port network that has the following impedance matrix.

$$ Z=\left[\begin{array}{cc}2s+1& 5s+4\\ {}5s+1& s+\frac{1}{s}\end{array}\right] $$

• 12.18. Find a two-port network that has the following admittance matrix.

$$ Y=\left[\begin{array}{cc}\frac{s+1}{s}& s\\ {}-2& 2s+7\end{array}\right] $$

• 12.19. Find transmission matrix of the following two-port network.

• 12.20. Find the impedance and admittance matrix of the circuit in previous problem when ${L}_1=1\ \mathrm{H},\kern0.5em {L}_2=3\ \mathrm{H},\kern0.5em {C}_1=\frac{1}{2}\ \mathrm{F},\kern0.5em {C}_2=\frac{1}{5}\ \mathrm{F},$ and R = 5 Ω.