Single Phase Transformers

Parameter Measurement

It is possible to obtain the approximate equivalent circuit
parameters of a transformer by conducting two tests, an
open-circuit test and a short-circuit test. As the names of
these tests imply they are performed with the secondary
of the transformer connected either in open-circuit or
short-circuit.

Open-circuit test: This enables the magnetising branch
parameters to be evaluated. The secondary of the transformer
is connected in open-circuit; measurements of the primary
voltage, current and power are taken (see figure 6).
The secondary output voltage can also be measured to
determine the turns ratio. The measurements should be
made at the normal primary supply voltage and frequency
(Q: Why?). Alternatively the secondary winding could be
supplied and with the primary winding on open-circuit.

Figure 6. Open-circuit test.

Short-circuit test: From this test the combined winding

resistance and leakage inductance can be found, the

magnetising branch is neglected. The secondary of the

transformer is connected in short-circuit; measurements

of primary voltage, current and power are made (figure 7).

The secondary current may also be measured. These

measurements should be conducted at the rated transformer

current, which will be achieved at a lower voltage than the

rated value. Alternatively the secondary winding could be

supplied and with the primary winding connected in short-circuit.

Figure 7. Short-circuit test.

These tests do not enable the individual primary/secondary

parameters of resistance and leakage reactance to be

calculated, it is usually assumed that they are equal. The

winding resistances could be measured using a dc supply.

Once the equivalent circuit parameters are known standard

circuit analysis can be used to perform load calculations.

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Real Single Phase Transformers

In practice the transformer windings will have resistance they
will not be perfectly coupled, the transformer core will not have
zero reluctance and the alternating flux in the core will result in
core losses. In a real transformer these all need to be included
in the analysis. To take these factors into account the
equivalent circuit of the transformer will be of the form shown in
figure 3. This takes into account differences between the ideal
and the real transformer as follows:

Winding Resistance (R1 and R2)
Leakage Inductance (l1 and l2)
Magnetising Inductance (Lm)
Magnetising Resistance (Rm)
Hysteresis:
Eddy Currents:
Figure 3. Transformer equivalent circuit

Different Kinds of Single-Phase Transformers

The transformer in Fig A has a single input and a single output.
The output will be rated for voltage and current (Ex: 12VAC @ 1A).
Note: 12VAC is the RMS voltage. The peak voltage is 12*1.41 = 17V
and the peak-to-peak voltage is 34V. The input will have a voltage
rating (usually 120V for the US and 240V for Europe). The input
current depends on the output current. Energy is conserved.
Ex: with an output of 12V@1A a 120V input would draw 0.1A.

The transformer in Fig B has a center tap output. The output

voltage is split evenly over each half of the output (Ex: 12VCT

would have 6VAC from the center tap to the top wire and 6VAC

from the center tap to the bottom wire. Center tap transformers

are useful when making symmetrical positive and negative

power supplies (since the center tap can be tied to ground).

The transformer in Fig C can be wired for different input and

output voltages and currents. If the two input coils are wired in

parallel the input voltage will be half what it would be if the

input coils are wired in series (i.e. 110/220V input). Similarly

the output coils can be wired in parallel for more current or

series for more voltage. Note: The dot marks the polarity. In

parallel the wires with the dots are tied together. In series one

wire with a dot is wired to the other coils wire without the dot.

If wired incorrectly the transformer will get hot and possibly

melt the windings.

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