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For my lab work, I have to design a method to measure the quality factor of an ideal inductor between 1MHz to 5MHz, away from resonance frequency. We know that an ideal inductor has the form (with a series resistor):

schematic

simulate this circuit – Schematic created using CircuitLab

The quality factor is defined as Q = wL/R, but the challenging part is we cannot take measurements between L1 and R1, since it isn't existed in real, I can measure only from node A and node B? I am allowed to use standard values of capacitors and resistors with a digital oscilloscope. Any ideas?

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    \$\begingroup\$ Think about the influence of that series resistor on the impedance between nodes A and B. If I gave you 2 black boxes, one box has L1 and R1 inside, the other box only has L1, (meaning R1 = 0 ) how could you tell which is which ? \$\endgroup\$ Feb 23, 2017 at 21:12
  • \$\begingroup\$ ... and think about the other things you're allowed to use \$\endgroup\$
    – Neil_UK
    Feb 23, 2017 at 21:23
  • \$\begingroup\$ The clue is that the impedance of the pure L varies with frequency. The resistance of the pure R does not vary with frequency. Take several impedance measurements at different frequencies, is one way. Take an impedance measurement, measuring the phase, is another. \$\endgroup\$
    – Neil_UK
    Feb 24, 2017 at 6:47

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After the lab, I have come up with a solution:

As we have an inductor, we have two unknown variables: internal resistance and the inductance.

So, if we connect a series resistor and apply a sinusoidal wave then take a measurement between the inductor and resistor, we will observe and particular output voltage, and also an equation.

Then if we change the resistor value, again we obtain a different voltage value and equation. Since we have two unknowns and two linearly independent equations, we can find L and R by the help of linear algebra.

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