It's possible to
measure the self inductance of a circuit using a transient technique. This technique
uses the exponential current transient to determine the time constant and hence
inductance of the coil. While this method can readily provide inductance information
about a circuit it does require the use of a digital storage oscilloscope or graphical
multimeter. Some of the more advanced multimeters have an inductance measuring
facility but if you are serious about investigating and designing coilguns then
a good quality DSO should be a high priority on your shopping list. This article
describes how to determine the coil's inductance from a trace of its current transient.
In order to accurately
determine the inductance it is necessary to know the circuit resistance
to a reasonable accuracy of say +/- 5%. This is not necessarily
easy since the total circuit resistance is usually around 1
or less. Most multimeters only have a resolution of 0.1
and a dedicated ohmmeter is an expensive piece of kit. It is possible
to get around this problem by introducing a much larger series resistance
into the circuit. For a circuit with an estimated resistance of
the additional resistance can be say 100.
This resistance then becomes the dominant resistance and we can
ignore the resistance of the rest of the circuit. Since the coil
is by far the largest inductive component we can solve for this
inductance using the following method.
Fig 1 shows the
main parameters of this inductive circuit. The transient response to a step voltage
is governed by the time constant of the circuit and follows an exponential growth
according to the function:
time constant is
L and R are the circuit inductance and resistance respectively.
important feature of this type of exponential growth is that there are almost
exactly 5 time constant periods from the application of the step voltage until
the current stablises. What we are interested in is the period of the time constant.
This is best determined over the initial part of the exponential curve since it
yields a more accurate result. In fact we are only going to consider the very
first time constant period. If we solve the exponential current equation above
for the first time constant period (t /=
1) then we find that i = 63.2% of maximum. Therefore to find all
we need to do is find the time value corresponding to the current at 63.2% of
maximum. The trace below is from Test Coil A using a 100
series resistor and a step voltage of 10V.
that the voltage markers (horizontal dotted lines) are set to a
dV of 6.38V which is 63.8% of the applied 10V. This is the closest
value which could be set. The timebase markers (vertical dotted
lines) are set to intersect the transient at the points where the
voltage markers cut the curve. The resulting dt gives us the time
constant for the circuit, in this case it's 19.38us. I typically
work with 3 significant figures unless the calculations or experiments
demand more. So now we have R=100
therefore the inductance of the circuit is 1.94mH. Since the coil
inductance is the dominant inductance then we can say that the coil
has an inductance of 1.94mH. It should be remembered that the coil
inductance is frequency dependent, so different series resistor
values will yield different results. An alternative method of calculating
the coil inductance using FEMM is presented here.