Purpose
This experiment is about the characterization of a two-port network by generating a set of coefficients that are defined by the voltages and currents applied and measured on the two ports of the network. The three sets of coefficients computed are as follows: (1) the Z parameters, (2) the Y parameters, and (3) the h parameters. These three sets are discussed in the next section.
Theory
A circuit with any number of components can be replaced by a two-port network with a set of coefficients that define the relationship among the voltages and the currents on the two terminals. Figure 1 shows the diagram of a two-port network.
Figure 1. Two-Port Network
For the purposes of this experiment, the side where V1 and I1 are the voltage and current is called the A side, while the other side where V2 and I2 are the voltage and current is called the B side.
As mentioned in the previous section, the three sets of coefficients are (1) the Z parameters, (2) the Y parameters, and (3) the h parameters. The Z parameters are also the impedance parameters; the Y parameters are also called the admittance parameters; the h parameters are also called the hybrid parameters.
These three sets of coefficients are defined by the following voltages and currents equations:
Z parameter equations
V1=Z11I1+Z12I2
V2=Z21I1+Z22I2
Z11 is the open circuit input impedance. Z22 is the open circuit output impedance. Z12 and Z21 are the open circuit transfer impedances.
Y parameter equations
I1=Y11V1+Y12V2
I1=Y21V1+Y22V2
Y11 is the short circuit input admittance. Y22 is the short circuit output admittance. Y12 and Y21 are the short circuit transfer admittances.
h parameter equations
V1=h11I1+h12V2
I2=h21I1+h22V2
h11 is the short circuit input impedance. h12 is the open circuit reverse voltage gain. h21 is the short circuit forward current gain. h22 is the open circuit output admittance.
Procedure
In this experiment, a T-network comprised of resistors are tested as a two-port network. Figure 2 shows the circuit diagram of the T-network.
Figure 2. T-network
Z parameters
Open circuit the B terminals, and connect the source on A. Then, measure the voltages on both sides and the current on side A. The open circuit input impedance and the open circuit transfer impedance from B to A can be measured.
Z11=V1I1I2=0
Z21=V2I1I2=0
Open circuit the A terminals, and connect the source on B. Then, measure the voltages on both sides and the current on side B. The open circuit output impedance and the open circuit transfer impedance from A to B can be measured.
Z12=V1I2I1=0
Z22=V2I2I1=0
Y parameters
Short the B terminals, and connect the source on A. Measure the currents and the voltage on A side. The short circuit input admittance and the short circuit transfer admittance from B to A are computed.
Y11=I1V1V2=0
Y21=I2V1V2=0
Short the A terminals, and connect the source on B. Measure the currents and the voltage on B side. The short circuit output admittance and the short circuit transfer admittance from A to B are computed.
Y22=I2V2V1=0
Y12=I1V2V1=0
h parameters
Short the B terminals, and connect the source on A. Measure the currents and the voltage on A side. The short circuit input impedance and the short circuit forward current gain are computed.
h11=V1I1V2=0
h21=I2I1V2=0
Open circuit the A terminals, and connect the source on B. Measure the currents and the voltage on B side. The open circuit output admittance and the open circuit reverse voltage gain are computed.
h22=I2V2I1=0
h12=V1V2I1=0
Results
Z Parameters
I2=0, I1=1.17 mA, V1=3.55 V, V2=1.13V
Z11=V1I1I2=0=3.551.17m=3.034 kΩ
Z21=V2I1I2=0=1.131.17m=965.8 Ω
I1=0, I2=0.89 mA, V1=0.9 V, V2=3.58 V
Z12=V1I2I1=0=0.90.89m=1.011 kΩ
Z22=V2I2I1=0=3.580.89m=4.023 kΩ
The Z parameters are:
Z=3.0341.0110.9664.023×103Ω
Y Parameters
V2=0, I1=1.17 mA, I2=0.31 mA, V1=3.55 V
Y11=I1V1V2=0=0.330 m℧
Y21=I2V1V2=0=87.3 μ℧
V1=0, I1=0.32 mA, I2=0.82 mA, V2=3.57 V
Y22=I2V2V1=0=0.82m3.57=0.230 m℧
Y12=I1V2V1=0=0.32m3.57=89.6 μ℧
The Y parameters are:
Y=33089.687.3230×10-6 ℧
h Parameters
V2=0, I1=1.16 mA, I2=0.32 mA, V1=3.56 V
h11=V1I1V2=0=3.561.16m=3.069 kΩ
h21=I2I1V2=0=0.32m1.16m=0.276
I1=0, V1=0.90V, V2=3.58 V, I2=0.89 mA
h22=I2V2I1=0=0.89m3.58=0.249 m℧
h12=V1V2I1=0=0.903.58=0.251
h=3.069 kΩ0.2510.2760.249 m℧
Using the computed parameters, the two-port network can replace the T-network and the behaviour of the currents and voltages on the two terminals will stay the same.
Conclusion
The experiment was able to model the T-network using two-port network models. The impedance, admittance, and hybrid parameters were all successfully and analytically obtained.
