Improved determination of Q-factor and resonant frequency by a quadratic curve-fitting method

The Q-factor and peak frequency of resonant phenomena give useful information about the propagation and storage of energy in an electronic system and therefore its electromagnetic compatibility performance. However, the calculation of Q by linear interpolation of a discrete frequency response to obtain the half-power bandwidth can give inaccurate results, particularly if the data are noisy or the frequency resolution is low. We describe a more accurate method that makes use of the Lorentzian shape of the resonant peaks and involves fitting a second-order polynomial to the reciprocal power plotted against angular frequency. We demonstrate that this new method requires less than one quarter the number of frequency points as the linear method to give comparable accuracy in Q. The new method also gives comparable accuracy for signal-to-noise ratios that are approximately 8 dB greater. It is also more accurate for determination of peak frequency. Examples are given both from measured frequency responses and from simulated data obtained by the transmission line matrix method.