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--- topic:physics:resonators:cheatsheet [2023/12/01 22:52] – created samuel
+++ topic:physics:resonators:cheatsheet [2023/12/01 23:05] (current) – [Loss in resonators] samuel
@@ Line 1: / Line 1: @@
 ====== Cheatsheet - Resonator ======
-| Resonance frequency |  $f$  | [Hz] |
+^ Resonance frequency |  $f$                | [Hz] |
-|Angular frequency    |  $\omega$  | [rad/s] |
+^ Angular frequency   |  $\omega$           | [rad/s] |
-| ::: | $\omega = 2\pi f$ ||
+|  |  $\omega = 2\pi f$  ||
+===== Loss in resonators =====
+^ Quality factor      |  $Q$                                   | unitless |
+Possible definition  $Q = 2\pi \frac{\text{energy in resonator}}{\text{energy lost per cycle}}$
+^ Total loss rate | $\kappa $ | [rad/s] |
+|                 | $\kappa = \kappa_i  + \kappa_e $ ||
+^ Intrinsic losses | $\kappa_i $ | [rad/s] |
+^ Extrinsic losses | $\kappa_e $ | [rad/s] |
+|                  |  $Q = \frac{\omega}{\kappa}$                ||
+Loss rate often given in [Hz] as $\kappa/2\pi$.
+Other common symbols for losses are:
+^ Damping rate  | $\Gamma$ | [rad/s] |

Kollektanee - Samuel Gyger