The Voltech Handbook of Transformer Testing

2.6 QL - Q factor

When a transformer is energized the changing magnetic field in the core causes losses in the core.

Two types of losses occur in the core: - Hysteresis losses and Eddy current losses.

These losses are described in section 1.3 and 1.4

The total of these losses can be represented on the transformer equivalent circuit by a resistance associated with the inductance of the winding.

This resistance may be shown either in series with an inductance or in parallel with an inductance, as shown in the following diagrams:

Either the parallel or series circuit can be used, with equal validity, in the transformer equivalent circuit where: -

R_P = (R_S² + ω²L_S²)/R_S where ω=2πf
L_P = (R_S² + ω²L_S²)/ω²L_s

It is clear from this equation that series and parallel inductance do not necessarily have the same value, so when a value for inductance is specified, it must be specified as series or parallel equivalent circuit.

For a series circuit, the 'quality factor' Q is defined as:-

For a given inductance, the lower the value of the equivalent series resistance, the higher is the value of Q, i.e. the 'better' the coil. Typical value of Q range from about 2 to several hundred

Where Used

The Q factor measurement would normally follow a measurement of the inductance of the primary winding in the test program.

As with an inductance measurement, the Q factor test would normally be used for signal, pulse and switched mode power transformers, where the normal operating conditions require only small excursions of the B-H curve, never extending beyond the linear regions.

A Q factor test is one way of highlighting shorted turns within the transformer.

Measurement Conditions

To measure Q factor, the tester performs exactly the same steps that would be used to measure inductance.

The only difference is in the calculation at the end of the test: the measured voltage is divided by the current to obtain a complex impedance from which the Q factor is calculated.

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

Normally when following an inductance test, you would choose the same test conditions for the QL test. If the QL test does not have an associated inductance test, then choose the test conditions as detailed in the Table on page 23, based on the value of the inductance of the winding under test.