Hello all,
I'm trying to make sense of two tutorials on another website, the first concerning mutual inductance and the second, two coupled inductors connected in parallel-aiding
and parallel-opposing
configurations. Individually the tutorials are fine but, together, they make no sense at all - at least not to me. I have written the author for clarification but he has not responded.
Firstly we have two mutually-coupled inductors, L1 and L2, whose coupling is 100%. In this case the mutual inductance is calculated as
M = sqrt(L1*L2) .
Next we have two coupled inductors connected in parallel-aiding configuration. The net inductance for parallel-aiding is calculated as
L = (L1*L2 - M^2) / (L1 + L2 - 2M)
and for parallel-opposing as
L = (L1*L2 - M^2) / (L1 + L2 + 2M) ,
but notice that if the two inductors in both configurations are perfectly coupled, the numerator reduces to zero in every case. Yet, in the tutorial text the author claims (without explaining how he arrived at his conclusion) that if the inductances are equal then the net inductance is L = L1 = L2 = M in the first case and, in the second, L = 0.
In the second tutorial's examples, perfect coupling is never assumed and the author never addresses the case where the coupling is 100%. In these examples the mutual inductance is simply a 'given' and always less than 100%.
I am hoping someone here can shed some light on this apparent conundrum.
Thanks!
I'm trying to make sense of two tutorials on another website, the first concerning mutual inductance and the second, two coupled inductors connected in parallel-aiding
and parallel-opposing
configurations. Individually the tutorials are fine but, together, they make no sense at all - at least not to me. I have written the author for clarification but he has not responded.
Firstly we have two mutually-coupled inductors, L1 and L2, whose coupling is 100%. In this case the mutual inductance is calculated as
M = sqrt(L1*L2) .
Next we have two coupled inductors connected in parallel-aiding configuration. The net inductance for parallel-aiding is calculated as
L = (L1*L2 - M^2) / (L1 + L2 - 2M)
and for parallel-opposing as
L = (L1*L2 - M^2) / (L1 + L2 + 2M) ,
but notice that if the two inductors in both configurations are perfectly coupled, the numerator reduces to zero in every case. Yet, in the tutorial text the author claims (without explaining how he arrived at his conclusion) that if the inductances are equal then the net inductance is L = L1 = L2 = M in the first case and, in the second, L = 0.
In the second tutorial's examples, perfect coupling is never assumed and the author never addresses the case where the coupling is 100%. In these examples the mutual inductance is simply a 'given' and always less than 100%.
I am hoping someone here can shed some light on this apparent conundrum.
Thanks!
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