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Technical Document Reader

**Document**

086-627

**Name**

The Voltech Handbook of Transformer Testing

**Description**

This article covers a wide range of transformer theory and Voltech's testing capability.

## 2.4 LS, LP - Primary Inductance

An ideal transformer, with the secondaries open-circuit, presents an
infinite impedance to an AC voltage applied to the primary, the
transformer acts as though it were an infinite inductor.

In practice the transformer presents a finite inductive impedance to
the applied voltage given by: -

Inductive impedance (X

_{L}) = 2πfL (ohms)Where L is the inductance of the core (Henries) and f is the frequency
of the applied voltage

The primary inductance is therefore a measure of the input impedance of
the transformer. From this equation it can be seen that the smaller the
inductance, the larger will be the current that will flow when the
transformer is energized.

### Measurement Conditions

To measure inductance, the tester applies an ac voltage across the
selected winding; it then measures the voltage across and the current
through the winding using harmonic analysis. The measured voltage is
divided by the current to obtain a complex impedance and the inductance is
calculated.

The test signal can have a frequency in the range 20 Hz to 3 MHz, and
an amplitude from 1 mV to 5 V.

Generally, it is not necessary to measure the inductance at the normal
operating conditions of the transformer, which could involve, for example,
voltage levels of hundreds of volts.

This is because the B-H curve can normally be assumed to be linear in
the operating region, and the inductance measured at a low level
represents the inductance that will appear in use.

Also, it can usually be assumed that the inductance value does not
vary significantly with frequency.

Therefore, although high frequencies are available with the tester,
measurement frequencies above a few hundred kilohertz should be used with
caution.

This is because the errors caused by the stray inductance and
capacitance of your fixture may become much more significant at these
frequencies. Compensation can be used to eliminate these errors.

The following table suggests suitable test conditions for different
values of expected primary inductance:

Inductance range | Preferred test signal | |

Frequency | Voltage | |

100nH → 1uH 1uH → 10uH 10uH → 100uH 100uH → 1mH 1mH → 10mH 10mH → 100mH 100mH → 1H 1H → 10H 10H → 100H 100H → 1KH 1kH → 10KH |
300KHz 100KHz 30KHz 10KHz 1KHz 100Hz 100Hz 50Hz 50Hz 50Hz 20Hz |
10mV 30mV 50mV 100mV 100mV 100mV 300mV 1V 5V 5V 5V |

### The Test Conditions for Inductance Measurement

Wherever possible, this table should be used for all inductance tests. The inductance range should be chosen based on minimum value of inductance expected.

When choosing the test conditions, the following potential problems should be considered:

a) Current levels

The upper voltage limits should be chosen to give a maximum current
level of about 50mA rms. for the lowest inductance expected. In some
cases, this current may cause core saturation, and a lower voltage should
be used. The minimum voltage level must be chosen so that the test current
does not become so low that it cannot be sensibly measured. The lower
voltage limits in the table above always give test currents higher than
3uA rms.

b) Self-Resonant Frequency

At lower frequencies, the capacitance of the windings can normally be
ignored because its impedance is much higher than that of the inductance.
However, at very high frequencies, this is not so, the capacitance
dominates and inductance cannot be measured. The self-resonant frequency
of the transformer is the change-over point between these two regions.
Normally to get a good measurement of inductance, the test frequency
should be less than 20% of the resonant frequency of the transformer. In
general high values of inductance will have a high inter-turn capacitance
and hence a low resonant frequency. Where there is a choice of test
frequencies always use the lower value, to minimise any problems due to
self-resonance.

c) Non-linear inductance

Normally inductance measurements should be used for transformers where
the B-H characteristics are linear.

However, if inductance measurements are attempted for instance with
line frequency transformers where the core material is non-linear even at
low signal levels, the measured results can be highly dependent on the
applied test signal.

This can be a problem when trying to compare measurements made on
commercially available impedance bridges, or component testers, with
measurements made using the AT. The test signal in such bridges is usually
determined within the instrument, and is often at a fixed frequency and at
a voltage level, which is not guaranteed to be constant for all value of
inductance.

Usually, if the actual test conditions of the bridge can be determined,
and the tester is then programmed to deliver the same test conditions
across the inductance the results will then agree. (See also the comments
below on differences caused by the choice of equivalent circuit)

d) Equivalent circuit

Inductance is always measured as part of a complex impedance, the
result being expressed in terms of either a series or parallel equivalent
circuit. Note that, for any given winding, the inductance values for the
two circuits are not necessarily the same. This should be born in mind
when specifying the test limits.