What Is Leakage Inductance?
Leakage inductance is an inductive component present in a
transformer that results from the imperfect magnetic linking of one
winding to another. Any magnetic flux that does not link the primary
winding to the secondary winding acts as inductive impedance in series
with the primary, therefore this "leakage inductance" is shown on a
schematic diagram as an additional inductance before the primary of an
ideal transformer.
In certain applications, such as switchedmode power
supplies and lighting ballasts, leakage inductance of the transformer may
play a critical function in the product design. For this reason, accurate
measurement of leakage inductance is often an important test function for
transformer manufacturers. In order to avoid confusion with other
transformer characteristics, this technical note will not refer to other
components of loss such as winding resistance or interwinding
capacitance.
Ideal transformer
For a theoretical, ideal transformer, there are no
losses. Voltages are transformed in the direct ratio of the turns;
currents in the inverse ratio of turns (figure 1).
Real transformer
In a real transformer, some of the flux in the primary
may not link the secondary winding. This "leakage" flux takes no part in
the transformer action and can be represented as an additional inductive
impedance that is in series with the primary winding (figure 2).
Real transformer plus an air gap
In certain transformer designs, leakage inductance must
be a greater proportion of the total inductance and is specified within a
tight tolerance. The increased proportion of leakage inductance is usually
achieved by introducing an air gap in the core design, thus reducing the
permeability of the core and therefore the value of primary inductance.
The ratio of flux that does not link the primary winding to the secondary
winding will therefore increase relative to the flux that links both
windings (figure 3).
Why is measurement of leakage inductance important?
Leakage inductance (LL) may be undesirable in a wound
component, in which case it is important to measure the value to show that
it is low or, in some applications, such as electronic lighting ballasts
and resonant power converters, leakage inductance is deliberately
introduced and its value is an integral part of the circuit design.
In these applications, the leakage inductance provides an
energy storage medium that is essential to achieve correct operation of
the finished product.
It is therefore important that the value of leakage
inductance of the transformer is known to be within specified limits.
How is leakage inductance measured?
When an LCR meter is connected to the primary winding of
a transformer with opencircuit secondary terminals (figure 4), the value
of inductance (L) comprises primary inductance (LP) plus leakage
inductance (LL).
Since LL is a function within the transformer, it is
clearly not possible to measure its value directly. A method must
therefore be used to subtract the value of LP from the total measured
inductance. This is achieved by applying a short circuit across the
secondary terminals (figure 5). A perfect short circuit will result in
zero volts on the output terminals (figure 6) and, through transformer
action, zero volts will also appear across the primary inductance. The
measured value of inductance at the primary terminals will therefore be
the true leakage inductance (LL).
Unfortunately, achieving a perfect short circuit on the
secondary of a transformer is difficult in a laboratory and completely
impractical in a production environment. In production, it is common for
the short circuit to be applied manually or via a switchable relay. Under
these conditions, a perfect short circuit cannot be achieved, and it
follows that the secondary voltage will not be truly zero. The voltage
attributable to the imperfect short circuit will then appear across the
primary inductance as a shortcircuit error multiplied by the turns ratio
(figure 7).
Ls/c is reflected in the primary as N^{2}Ls/c
because, in any winding, L is proportional to the number of turns squared
(L α N^{2}). Thus, Ls/c is reflected as a function of:
( Np / Ns ) ^ 2 = ( Lp / Ls )
The measured value of the primary inductance can be
considered vectorially as the sum of the leakage impedance plus the
reflected impedance of the shortcircuit error. This is shown in figure 8.
The traditional solution
In order to obtain the true value of leakage inductance,
engineers will carefully apply a soldered short circuit to the secondary
of the transformer to be tested and measure the value of inductance on the
primary.
This value of inductance will be recorded as the 'true'
leakage inductance (e.g. 150μH).
The inductance will then be measured on the same
transformer after the soldered short circuit has been replaced by either a
shorting clip or a fixture with relayoperated short circuit, depending on
the technique that will be chosen for production.
The measured inductance is again recorded (e.g. 180μH).
This value will, of course, be greater than the original
because it includes the true leakage inductance plus the shortcircuit
error inductance.
The difference between these two values (in our example
30μH) is then used in production testing as a fixed offset that is
programmed into a production LCR meter to obtain an approximation of the
correct value in the presence of an imperfect short circuit.
In practice, it is impossible to achieve a relaybased or
manualbased short circuit that produces exactly the same shortcircuit
error every time.
This nonrepeatability of shortcircuit error is such
that the fixed offset cannot provide a production department with accurate
and repeatable results. This is illustrated in the following table:

True LL

Measured value

Fixed offset

Result

Pass/fail

Measurement #1 
150μH 
180μH 
30μH 
150μH 
✓ 
Measurement #2 
150μH 
200μH 
30μH 
170μH 
X 
Measurement #3 
150μH 
250μH 
30μH 
175μH 
X 
The Voltech solution
Voltech have developed their AT series testers with an
architecture and processing ability to remove the shortcircuit error from
the primary inductance measurement during each and every test.
This technique is shown vectorially below using the
measured values from the preceding table as an example.
From the primary vector diagram, it can be seen that each
measurement is the sum of the voltage attributable to the leakage
inductance plus the error voltage from the secondary short circuit.
Before applying a short circuit, the Voltech AT series testers measure the
primary to secondary turns ratio.
The testers then automatically apply a short circuit, using an internal
relay matrix, and measure the shortcircuit voltage at the transformer
secondary pins.
The vector of this short circuit voltage is automatically multiplied by
the turns ratio, producing an 'error vector' that is equal to the
shortcircuit error voltage reflected into the primary measurement.
The leakage inductance is then computed from the total primary inductance
value less the primary error vector that has been calculated.
This process enables Voltech AT series testers to provide the true leakage
inductance value, irrespective of short circuit variability.

True LL

Measured value

Realtime vector compensation

Result

Pass/fail

Measurement #1 
150μH 
180μH 
✓ 
150μH 
✓ 
Measurement #2 
150μH 
200μH 
✓ 
150μH 
✓ 
Measurement #3 
150μH 
250μH 
✓ 
150μH 
✓ 
Leakage Inductance Conclusion
Leakage inductance is a critical transformer
characteristic that presents a particular measurement challenge to both
design and production test engineers.
By looking at the factors effecting measurement integrity
and developing innovative measurement techniques to overcome these
factors, Voltech provides a unique solution to a problem of measurement
variability that faces almost all transformer manufacturers.
Should you have questions on any of the other test
functions available for the Voltech AT series transformer testers, please
do not hesitate to contact us.