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How
to Measure Mutual Inductance Mutual inductance is a mysterious quantity that we learn about when we study transformer models, but how to measure it is rarely discussed in the literature.
L_{T}= L_{1}+L_{2}, (separate inductors)
L_{T}= L_{1}+L_{2}+2M, (Transformer) This presents us with a simple way to measure the mutual inductance. We can measure the inductance of each coil separately with the other coil left open. Then measure the inductance of the coils in series, and then using the following formula calculate the mutual inductance: M= (L_{T}(L_{1}+L_{2}))/2
Using Step Response to Measure Mutual InductanceThis is the easies measurement to make, but requires some complex math. We'll go through the math first. Let's write the voltage loop equations for each of the two coils of a transformer in the time domain: V_{1}= R_{1}i_{1}+L_{1}(di_{1}/dt) + M(di_{2}/dt), and V_{2}= R_{2}i_{2}+L_{2}(di_{2}/dt) + M(di_{1}/dt) If the second coil is open and at t=0 we apply a voltage a step voltage, then i_{2}= 0, and V_{1}= R_{1}i_{1}+L_{1}(di_{1}/dt) , and V_{2}= M(di_{1}/dt) With calculus we can solve for i_{1} by integrating and we get a decaying exponential curve as follows: i_{1} = V_{1}/R_{1}(1exp(t*R_{1}/L_{1})) It follows that: V_{2}= M*V_{1}/L_{1}*exp(t*R_{1}/L_{1}) At t=0 we get: V_{2}= M*V_{1}/L_{1} and, M= V_{2}L_{1}/V_{1} This gives us an extremely easy way of computing the mutual inductance. Merely, hook the inductor to a battery of voltage V_{1 }and switch in series, and put a scope on the output of the secondary. Flip the switch so current flows, and measure the peak voltage at t=0, on the scope. Using the equation, above the mutual inductance is easily calculated.
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