ABSTRACT
The experiment that have being carry out in the lab is to check and verify the
analysing AC port in a two-port network. In this lab required an oscilloscope to
measure the waveform. The T-network is construct before construct the full circuit.
The objective of this experiment is to prove the calculation, simulation and
measurement is accurate and will not get unexpected error. The calculation is been
made on every component and part so we can get the accurate result.
INTRODUCTION
A two-port network is an electrical network or device with the two port pairs of
terminals to connect to external circuits. Two terminals constitute a port if the currents
applied to them satisfy the essential requirement known as the port condition:
the electric current entering one terminal must equal the current emerging from the
other terminal on the same port. The ports constitute interfaces where the network
connects to other networks, the points where signals are applied or outputs are taken.
In a two-port network, often port 1 is considered the input port and port 2 is
considered the output port. By port we mean a pair of terminals of a circuit in which,
at all times, the instantaneous current flowing into one terminal is equal to the
instantaneous current flowing out the other. For each port, we label one node the
active node and the other one the reference node.
Figure 1: A two port network
The Z-parameters or the “Open Circuit” parameters associated to the output currents
from the ports to their input voltages. It is called as “Open Circuit” because it
calculates for example Z11 we need to do open circuit of the output (I2 = 0).
The two-port network model is used in mathematical circuit analysis techniques to
disengage portions of larger circuits. A two-port network is properties describes by a
matrix of numbers. This grants the response of the network to signals applied to the
ports to be calculated easily without solving for all the internal voltages and currents
in the network. For resistance, transistors are usually regarded as two ports
characterized by their h-parameters which are listed by the manufacturer. Any linear
circuit with four terminals can be viewed as a two-port network provided that it does
not involve an independent source and satisfied the port conditions.
PROCEDURES
Component used in lab were calculated from Task 1, hence the value is determined
and circuit are assembled. But after doing the calculation the results may have a
slightly different measurement. This happen because of few errors during the
experiment. The error can be from the component resonant or while doing calibration
of oscilloscope. In addition, error also occur appeared during the lab when doing
measurement in components and the circuits
Figure 2: Practical Circuit Diagram
1.
Setting and Calibrate the equipment.
• Set the voltage value (Vpp), frequency and measurement on function
generator by using multimeter.
2.
Calibrate the Oscilloscope.
• Setting the function generator and check the voltage and frequency with
the oscilloscope.
3.
Construct the Circuit.
• Construct the circuit with the real components
4.
Take the measurement for Vin, Vout, Vin pk and Vout pk.
RESULTS
Table 1
Parameters
Calculation (Ω)
Measurement (Ω)
Z11
5.9k
5.83k
Z12
2k
1.97k
Z21
2k
1.99k
Z22
5.9k
5.85k
Parameters
Calculation
Measurement
Supply voltage
4V
4.08 Vp-p
Load voltage
331m V
232 mVp-p
Phase angle
17.44◦
11.7◦
Power factor
0.954
0.98
Table 2
EXPERIMENTAL AND SOLUTION
Experimental procedure
Task 1 :
Figure 3: Measurement of Z11 = 5.83k Ω
Figure 4: Measurement of Z12 = 1.97k Ω
Figure 5: Measurement of Z21 = 1.99k Ω
Figure 6: Measurement of Z21 = 5.85k Ω
Task 2 :
Figure 7: Completed circuit being construct
Figure 8: Value of phase angle at channel 2 is 11.7° on oscilloscope.
Simulation
Simulation for task 1
Figure 9: Value simulation of Z11 = 5.9k Ω
Figure 10: Value simulation of Z12 = 2.0k Ω
Figure 11: Value simulation of Z21 = 2.0k Ω
Figure 12: Value simulation of Z22 = 5.9k Ω
Simulation for task 2
Figure 13: Value simulation for angle difference max output and max input is 1.25us
Figure 13: Value simulation for period at positive max output is 20.00us
Analysis and Discussion
Ac power in a two-port network is measured using three methods which were the
calculations, simulation and constructed circuit based on Figure 1 which produced
different results that caused by zero error or components failure. The calculations can
be measured using Mesh Currents Law in order to obtain the value of different Zparameters which are Z 11 , Z 12 , Z 21 and Z 22 for task 1. For task 2, apparent power
(S=Vrms x Irms) and power factor formulas are used to obtain for the supply voltage,
load voltage, phase angle and power factor parameters. After doing for calculations,
the simulation for AC power based on Figure 1 is created and simulated also
measured those parameters using the Multisim software in order to compare the
results after calculations while preparing for circuit construction experimental. Then,
the experiment is continued by constructing circuit of AC power Symmetrical
T-Network type. The circuit is correctly done but the results value came out quite
different as stated above. The parameters for task 1 and task 2 were measured using
an electrical measuring instruments, the Multimeter and an oscilloscope. The results is
measured and recorded into the table given. Theoretically, any Z parameters must be
choosing as an illustration. When I2 = 0, output port is open while I1= 0, input port is
open. When the two-port does not contain any dependent source, then Z 12 = Z 21 . Z 11
& Z 22 are called driving-point impedances. Z 12 & Z 21 are called transfer impedances.
When Z 11 = Z 22 , the two-port circuit is said to be symmetrical. When Z 12 = Z 21 , the
two-port circuit is called a reciprocal circuit which can also be represented by the
T-equivalent circuit. Thus, all the values obtained from different methods stated as
above are compared and power factor values for this AC power can be determined
successfully.
Recommendation for Power Factor Correction
Based on the calculations and experimental, the power factor for ours is 0.98 which is
closed to 1 that is not really necessary to do any power factor correction as the
inductor value, 1.0mH is adequate for this AC power for two port network circuit and
its effectiveness to the power factor improvement. But the power factor that were
obtained from simulation is 0.92 and if we have to do some improvements, we would
suggest to perform few methods of power factor improvement.
Methods of Power Factor Improvement
1. Capacitors: Improving power factor means lowering the phase difference
between voltage and current. Since majority of loads are of inductive nature,
they require some amount of reactive power for them to function. This reactive
power is provided by the capacitor or bank of capacitors installed parallel to the
load. They act as a source of local reactive power and thus less reactive power
flows through the line. Basically, they reduce the phase difference between the
voltage and current.
2. Synchronous condenser: They are 3 phase synchronous motor with no load
attached to its shaft. The synchronous motor has the characteristics of operating
under any power factor leading, lagging or unity depending upon the excitation.
For inductive loads, synchronous condenser is connected towards load side and
is overexcited. This makes it behave like a capacitor. It draws the lagging
current from the supply or supplies the reactive power.
3. Phase advancer: This is an ac exciter mainly used to improve pf of induction
motor. They are mounted on shaft of the motor and is connected in the rotor
circuit of the motor. It improves the power factor by providing the exciting
ampere turns to produce required flux at slip frequency. Further if ampere turns
are increased, it can be made to operate at leading power factor.
Conclusions
As conclusions, the students are able to measure power factor correction using
different methods which are calculations of parameters for Z 11 , Z 12 , Z 21 , Z 22 and
compared it with the theoretical results based on Mesh analysis, simulation from
Multisim and circuit construction experimental measured using the multimeter and
oscilloscope. The results from those methods are obtained successfully, recorded,
compared and analyzed. There is slight difference in values between the
experimental results and theoretical results due to the errors occurred during the
experiment process and calculation, such as systematic error or measuring device
failure as had been discussed. From this experiment, the students can learn and
understand more about this topic by performing AC circuit analysis using two-port
network theory while doing this laboratory experimental. Thus, the power factor value
is 0.98 that is also closer to 1 which is good enough as it is no need to do any power
factor correction for improvement this time, as usually the capacitors are used to
improve the power factor.
References
1. http://fourier.eng.hmc.edu/e84/lectures/ch2/node4.html
2. https://paginas.fe.up.pt/~fff/eBook/MDA/Diporto.html
3. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ca
d=rja&uact=8&ved=0ahUKEwjZ4bKKtsDUAhVGTLwKHWCSAYEQFghA
MAQ&url=http%3A%2F%2Fwww.gatestudy.com%2Fwp-content%2Fupload
s%2F2015%2F01%2FTwo-Poart-Networks.pdf&usg=AFQjCNH3yLeOsA-fU
ZP_5BsTCYmVoZbvbA&sig2=1NjXVuxKLwm4UTeIAAaDxA
4. https://www.scribd.com/document/311006590/Models-of-Two-port-Networks
-Z-Y-H-parameters
5. https://www.gatestudy.com/wp-content/uploads/2015/01/Two-Poart-Networks
.pdf