Q Factors of a Transmission Line Cavity

On investigating the properties of a transmission line cavity, new expressions for the
Q
factor and logarithmic decrement
\delta
were derived, and were compared with the expressions for a single shunt or series LCR circuit. It was expected that the expressions for
Q
and
{\pi}/{\delta}
would be very similar, if not the same, as is the case with LCR circuits. That this expectation was not realized was attributed to the finite velocity of wave propagation. The two expressions are the same only so long as the transfer of influence is assumed instantaneous or the losses are uniformly distributed. It is possible to define a
Q
of steady-state oscillations ("wavemeter
Q
") and a
Q
of decaying oscillations ("echobox
Q
"). The expressions for these two
Q
factors are the same in the case of an LCR circuit, but for a transmission line cavity the two formulas contain different transcendental functions of the circuit parameters, and tend towards equality only for large
Q
, or no external loading.