Introduction
Transformers are indispensable components in AC circuits, serving to transform AC voltage and
current between different power levels and various other applications. This lab experiment is
designed to provide a deeper insight of transformer principles and their effects on AC voltages
and currents through physical building a transformer and putting it into use. Before delving
deeper into transformer operation, it is important to understand the theory behind inductors. An
inductor, typically a coil of wire wound around a ferromagnetic core, responds to an alternating
current input by generating an alternating magnetic field. This relationship is described by
Faraday’s Law of Electromagnetic Induction: ε=−dt/dΦ. Where ε is the induced electromotive
force, Φ is the magnetic flux through the coil, and dt/dΦ represents the rate of change of
magnetic flux with respect to time. Now, considering the operation of a transformer, when a
second coil is wound around the same ferromagnetic core as the first, mutual induction occurs,
which leads to the transfer of energy from the primary coil to the secondary coil without direct
electrical connection. The basic equation governing transformer operation is the ideal
transformer equation: Vs/Vp=Ns/Np, Where: Vpand Vs are the voltages across the primary and
secondary coils, respectively, Np and Ns represent the number of turns in the primary and
secondary coils, respectively. The efficiency (η) of a transformer is defined as the ratio of the
power output to the power input. In an ideal transformer with no losses, efficiency is 100%.
However, real transformers experience losses, leading to lower efficiency. The efficiency (η) can
be expressed as: η=Pin/Pout. And the power of the transformer can be calculated by using the
equation P = V*I.
Experiment
In this experiment, we will construct a center-tapped 1:1 transformer with primary and secondary
windings. The primary winding consists of 50 turns, while the secondary winding also has 50
turns but is center-tapped at 25 turns. The key part of the winding process is making sure that
the direction of the winding stays consistent. Once the winding process is complete, solder the
winding ends to the respective binding posts to ensure secure connections. It is essential to
strip off the insulation from the magnet wire at the soldering points to establish good electrical
contact. This set up enables the characterization of step-up, step-down, and unity transformers
by changing the sides in which we measure the voltage output through either the primary or
secondary side. For a Step-Down Transformer, apply a sinusoidal signal to the primary side and
measure the lower voltage output across the secondary windings, demonstrating voltage
reduction. For a Step-Up Transformer, apply the signal to a secondary side and measure a
higher voltage output across the primary winding, illustrating voltage increase. In the 1:1
Transformer setup, apply the signal to the primary side and measure equal voltage outputs
across both secondary windings, indicating no voltage transformation.
Results
Figure 1. Output of the transformer
Figure 2. Output of the transformer
Figure 3. Output of the transformer
Figure 4. Set up of the transformer measuement
Figure 5. Sample calculation of the efficiency and the power
Experimental results are recorded and presented above, including voltage measurements and
calculations. A sinusoidal signal with a frequency of 1 kHz is applied to the primary side of the
transformer, and the resulting output voltages across the secondary windings are measured for
different transformer configurations. The output for step up transformer was measured to be
6.7+/-0.02V, and the step down transformer had an output of 3.5+/-0.02V. The 1:1 transformer
had a measurement of 6.65+/-0.02V. The efficiency of the transformer was calculated by taking
the peak to peak voltage output across the 220 Ohm resistor over the resistance which would get
us the current. We can then calculate the current the power by multiplying the current with Vs
and Vp to calculate for Ps and Pv, which came out to be 1.6293+-0.01W and 0.826812+-0.01W
respectively. And the efficiency is around 50%.
Discussion
During this lab, the concept of a transformer was studied by building a physical version of a
transformer. To be more specific, we learned how to wind the copper wires to further
differentiate and characterize step up, step down, and 1-1 transformer. We were able to gain
hands-on experience in measuing voltage and current from different posts of the device, and
observe the frequency response of the transformer, and evaluate the power effiency of power
transfer. The efficiency only came out to be about 50% which might seem like a large
discrepancy, however, the theoretical value assumed the transformer is going to be 100%
efficient, so discrepancy due to the value of the resistor as well as winding is undoubtedly going
to happen. The voltage phase relationship between the primary and secondary windings, as well
as between the two secondary windings, is determined by the direction of the winding and the
polarity of the applied voltage. If the windings are wound in the same direction, the induced
voltage in the secondary winding will have the same polarity as the primary voltage, resulting in
a phase relationship where both voltages reach their peak values at the same time. Conversely, if
the windings are wound in opposite directions, the induced voltage in the secondary winding will
have the opposite polarity to the primary voltage, leading to a phase relationship where the
voltages are 180 degrees out of phase with each other.
