skrf.qfactor.Qfactor.angular_weights

static Qfactor.angular_weights(f, f_L, Q_L)[source]

Diagonal elements W_i of weights matrix.

\[W_i = \frac{1}{\left[ \frac{2 Q_L (f_i - f_L)}{f_L} \right]^2 + 1}\]

The weights are needed when frequencies are equally-spaced (rather than points equally spaced around the Q-circle), and help reducing systematic error [MAT58].

Parameters:
  • f (np.ndarray) – Frequency values array.

  • f_L (float) – Loaded resonant frequency.

  • Q_L (float) – Loaded Q-factor.

Returns:

W_i – Weighting factors in proportion to the rate of change of angle with frequency relative to the centre of the Q-circle.

Return type:

np.ndarray

References

[MAT58]

“Q-factor Measurement by using a Vector Network Analyser”, A. P. Gregory, National Physical Laboratory Report MAT 58 (2021) https://eprintspublications.npl.co.uk/9304/ section 2.4, eqn. (28).