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ECE 205 Laboratory 91
Ideal Transformers
Purpose and Equipment:
In this experiment, you will analyze circuits that utilize Transformers in their design.
You will use phasors to determine the amplitude and phase of your circuit parameters,
and will measure some of the circuit parameters of a physical transformer to determine
how they affect the general transformer performance. You will also investigate the ideal
transformer and calculate the power delivered and absorbed.
Introduction:
A transformer is a specific form of a coupled circuit in which the coupling mechanism is
the mutual inductances between two coils. The common magnetic flux path is provided
by an iron core. A transformer can be represented as shown in Figure 1a. A physical
implementation is given in Figure 1b.
N1, N2 are the number of turns at the primary and secondary windings; φ1 is the flux
produced by I1and φ2 is the flux produced by I2. In Figure 1a, it is seen by using the
right-hand rule method that with the currents as shown the magnetic flux produced by the
coils is additive; if the secondary current
1
This Lab is an extension and modification of a Transformer Lab, originally developed at the University of
Pennsylvania by Dr. G. Hunka and Dr. J. Vander Spiegel.
direction is reversed, the flux would be subtractive. When coil 1 is supplied with an
alternating current, the magnetic field is coupled into coil 2 which induces a voltage V2
across the coil. The resultant current in coil 2 creates its own magnetic field which, in
turn, is coupled to coil 1. This mutual coupling results in a term called mutual inductance,
M. The mutual inductance M is related to the self inductances through the coupling
factor k (k ≤ 1): M  k L1L2 where L1 and L2 are the self-inductances of coils 1 and 2,
respectively. The symbol for mutually coupled coils is shown in Figure 2. For sinusoidal
steady-state the relationship between the voltage and currents (phasors) is given below:
The dots shown in the drawing will indicate the sign of M. By convention, if both
currents are leaving the dots or entering the dots, the sign of M is positive (i.e. the fluxes
are additive). A consequence of a subtractive M is a 180 deg phase reversal between the
input and output voltages measured from a reference point.
An equivalent circuit model of a lossless transformer is shown in Figure 3 (T-model).
The equivalent inductances are La, Lb and Lm and have the following expressions.
3. Ideal iron core transformer
In the ideal transformer the core flux φ links both coils (i.e. the leakage flux is zero) so
that the coupling coefficient k=1. We also assume that the winding resistance is zero and
the hysteresis and eddy current losses in the iron core are zero. The symbol for the ideal
transformer is shown in Figure 4. The relations that describe the ideal transformer are
given below. Z1 is the impedance seen at the primary when the load impedance is ZL
(impedance reflection in the primary.)
4. Pre-lab Assignment
4.1 Consider the following circuit with an ideal transformer.
Find:
a. The currents in the primary and secondary loops (I1 and I2).
b. The voltages V1 and V2 over the primary and secondary terminals.
c. Power supplied by the source and power dissipated by the 1KOhm
resistance and the 8.2 Ohm load resistance. Compare the total power
supplied to the total power dissipated.
d. The value of the impedance Z1 seen at the input of the primary coil.
4.2
Equivalent Circuit of the linear transformer.
Prove that the values of La, Lb and Lm in the equivalent circuit of Figure 3
are equal to:
Hint: You can prove this relationship by comparing the expressions (1) of the
mutual inductances with those of the equivalent circuit: find the expressions of V1
and V2 as a function of I1 and I2 for the circuit of Figure 3. These expressions
should be the same as those if Figure 2.
5. Experimental Procedure
A. Parts and instruments:
• Audio transformer (11.5:1): Mouser Electronics, No. 42TM013
• 1x scope probe
• Function generator
• Oscilloscope
• Power supply
• Multimeter
• Components: 8.2 Ohm, 1KOhm resistors, and a 68nF capacitor.
B. Measurements of current and voltages in the transformer circuit
The goal of this experiment is to experimentally verify the operation of the transformer.
a. Build the circuit of Figure 9 (same as the one in the pre-lab). Use as 8.2 Ω load
resistance RL (this is similar to the load of a speaker). For source resistance Rs
use a 1 KΩ resistor. Adjust the output of the function generator for a sinusoid of 5
Vrms and 1kHz (check on the oscilloscope). Measure the actual values of the
resistors.
b. Measure the voltage V1 and V2 (in V rms) over the primary and secondary
coils using the oscilloscope. Calculate the turn ratio n (V2/V1) and 1/n. Observe
the phase of V2 in reference to V1. Place the dots on the transformer of Figure 9.
Compare the measured values of V1 and V2 with those calculated in the pre-lab.
c. Measure the voltage over the 1 KOhm resistor and calculate the corresponding
current I1 in the primary coil. You can use the multimeter for this measurement
(remember that the multimeter gives rms values). Find also the current I2 in the
secondary loop. Calculate the current ratio and compare it to the voltage ratio.
Also compare the measured current values with those calculated in the pre-lab.
[Note: when you use the amp meter to measure the current I2, use the Fluke
Multimeter and use the current range of 200mA [IF WE HAVE ONE IN THE
LAB.]
d. Based on the measurement of V1 and I1 what is the resistance seen at the input
of the primary coil? How does it compare to the one calculated in the pre-lab?
e. Use the measured values of current and voltage to calculate the power delivered
by the function generator and the power absorbed by the two resistors. Compare
the generated and dissipated power. Explain the difference (hint: the transformer
is not ideal).
Note: for the calculations you can use RMS or amplitude values. Be consistent in
your calculations.
Lab Report:
Put all your results in a neat and detailed lab report. Your report should contain sketches
of the circuits, calculations, computer printouts, and sketches of the observed waveforms
data. You should also note any unexpected results or trouble you had in performing the
experiment.