I designed a circuit to have a Q-factor of 15, knowing the inductor value I rearranged the equation \$\omega_o=\frac{1}{\sqrt{LC}}\$ to give me a capacitor value for a certain resonant frequency. When I built the final RCL circuit, the Q factor was found to be way out (using \$\frac{\omega}{\Delta\omega}\$) with a Q factor <7.

I am told this is due to the resistance in say the signal generator, cabling etc and also the inductor. Is it ok to measure the inductor on a bridge using the resistor setting so it gives a value in ohms? Or am I going about this Q factor error the wrong way?

  • \$\begingroup\$ Yes you have to include the 50 ohm gen source impedance for any frequency and coax. capacitance of 100pF/m and probe resistance. time to re-do calculations. You can measure R of an inductor with an DMM which is ok for lower frequency where skin effect is not too significant. Otherwise corrections for skin effects is needed. Good RLC meters apply a CC sine wave and measure voltage amplitude and phase shift to calculate parameters for 120Hz 1kHz up to 1MHz. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Feb 15 '17 at 23:18

Your bridge measurement tends to give unloaded Q. Perhaps you have determined the "R" from your bridge measurement, and used that value in your RCL resonant circuit. Your bridge may measure inductor parameters at a fixed frequency (often 1 kHz) whereas your circuit resonance is at a far different frequency. Be aware that inductor characteristics are often not frequency independent. So that is one caveat. You are probably correct to assume that the capacitors are lossless.
What you've neglected is the coupling from your signal source, and load, which also contributes to "R". So "loaded Q" is always less than raw inductor Q.


simulate this circuit – Schematic created using CircuitLab
The circuit at left has an inductor whose self-resistance yields a Q of 15 at resonance. Yet the resonant voltage across R2 yields a \$ \frac{\omega}{\Delta\omega}\$ loaded Q much less, because total R is now 171 ohms.
The circuit on right has much lower Q to the point where it really cannot be called a resonant circuit. R4 loads the resonator (L2,R5,C2) so much that loaded Q<<1.


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