Principle of Inductance and Impedance Test
Principle of Inductance and Impedance Test
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 Time of issue:20210902 14:54
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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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