Question 1.23: Given five identical inductors whose value is 45 nH, determi...
Given five identical inductors whose value is 45 nH, determine the parallel equivalent inductor of all five 45 nH inductors in parallel. Assume that the magnetic field produced by each inductor does not couple with the magnetic field produced by any of the other inductors.
From Equation (1.130) we have that
\frac{1}{L_{parallel-equivalent}} =\frac{1}{L_{1}}+\frac{1}{L_{2}}+\frac{1}{L_{3}}+…+\frac{1}{L_{n}}. (1.130)
1/L_{parallel-equivalent} =1/L_{1}+1/L_{2}+1/L_{3}+1/L_{4}+1/L_{5}. (1.132)
But since
L_{1}=L_{2}=L_{3}=L_{4}=L_{5}=45 nH, (1.133)
1/L_{parallel-equivalent}=(1/45 nH+1/45 nH +1/45 nH +1/45 nH +1/45 nH ), (1.134)
from where it is immediate to find that
L_{parallel-equivalent}=45 nH/5 = 9 nH (1.135)