Principle of Inductance and Impedance Test

The resistance of any component can be expressed as R+Xi.

Among them, R is the resistance of the real part and X is the resistance of the imaginary part. The impedance is the modulus of the complex number, Z=√(R+X^2 ).

The characteristic of the real part R is that R does not change with the change of frequency, and is a fixed resistance.

The characteristic of the imaginary part X is that X will change with the change of frequency.

X>0 is called inductive, that is, inductance.

X<0 is called capacitive, that is, capacitance.

Resistance, inductance, and capacitance are defined in the following table:

Resistance	R>>\|X\|, the resistance of the real part is much larger than the imaginary part, indicating that this is a resistance. The smaller X is, the better, if X=0, this is the theoretical resistance
inductance	R≈0, X>0, indicating that this is an inductance. The smaller R is, the better, if R=0, this is the theoretical inductance
capacitance	R≈0, X<0, indicating that this is a capacitor. The smaller R is, the better, if R=0, this is the theoretical capacitance

How to calculate L and Q

According to the above, the expression of inductance is: R+Xi X=2πfL then L=X/(2πf)

f is the frequency, X is directly tested by the LCR bridge. The quality factor Q=X/R, we know that the smaller the R, the better, then the larger the Q value, the better, indicating that the quality of the inductor is better.

Selection of test frequency

Assuming we have a 1nH inductor here, what frequency should be used to test it, let’s look at the following list, the resistance value of the inductor at different frequencies:

frequency	X(Ω)= 2πfL
1kHz	6.28uΩ
10kHz	62.8 uΩ
100kHz	628 uΩ
1MHz	6.28mΩ
10MHz	62.8mΩ
100MHz	628mΩ

For the LCR Meter, the test accuracy will be worse if the impedance is less than 1mΩ. Therefore, it is more appropriate to choose a frequency above 1MHz for testing.

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