RLC Q Factor Measurement – How to Measure

bandwidthfrequency-measurementpassive-filter

I have a simple parallel RLC circuit (R in series to L and C which are in parallel to each other). I am using a 0.01 micro farad CK05 capacitor a 100k resistor and a 10mH inductor.

I measure a resonance frequency of 17.1kHz which is close to the theoretical resonance frequency of 15.9kHz.

My problem is in the bandwidth. I am measuring a bandwidth of approximately 1.5kHz giving a Q factor of approximately 11.4 while the theoretical value is bigger by an order of magnitude i.e. 10 times larger (using \$ Q=\omega_0RC \$ for parallel RLC circuit I calculated Q=~100).

I measured the bandwidth by varying the frequency and measuring the frequencies where \$V=\frac{\sqrt{2}}{2}V_{max} \$ (using the cursors and measurement options on a digital scope).

What may be the reason for this kind of error?

below I added a picture of the components I used, from left to right:
resistor capacitor and inductor. I used an ohm meter and measured the DC resistance of the inductor to be 66 ohm.
enter image description here

Best Answer

The Q for any tuned LC circuit cannot be higher than the Q for the inductor itself and, if the inductors series resistance is high enough, it dominates the quality factor.

So, given that you have witnessed a Q of 11.9 and that inductive reactance at 16.7 kHz is 1049, the ESR of the inductor must be about 88 ohms.

Now this may not directly translate to the measured DC resistance because of skin effect, proximity effect and possibly core losses but I would expect that the inductor you have chosen is a few tens of ohms in DC resistance.


From wiki, a series RLC tuned circuit has a Q of: -

\$\dfrac{1}{R}\sqrt{\dfrac{L}{C}}\$ and, if you rearrange the formula when the circuit is at resonance you get: -

Q = \$\dfrac{\omega_0L}{R}\$ and this is the same as the Q factor for an inductor.

What is the relevance of this you might ask? It's relevant because if you throw away the 100 k feed resistor you are left with L and C in series with the AC resistance of the coil; in other words, the best Q you can achieve is defined by the Q of a series tuned circuit driven from a perfect voltage source.