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# Cavity Sensitivity Estimates

## Position Cavity

The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 617 and R/Q from simulation in several codes, of which CST and GdfidL use a hexahedral mesh while Ace3p uses a tetrahedral mesh:

Code R/Q /Ω Sensitivity/V nC-1 mm-1
GdfidL 0.85 8.7
Ace3p 0.77 8.3
CST 0.77 8.3

## Reference Cavity

The measured external quality factor of the reference cavity is 203.

Code R/Q /Ω Sensitivity/V nC-1
GdfidL 28.2 87
Ace3p 9.8 52
CST 10 52

## Electronics Chain Propagation

 Electronics gain/dB 5 -2.6 6 20

Position signal (offset=1mm, charge=1nC) Reference signal (Charge=1nC)
Location Volts dBm Volts dBm
Cavity out 8.3 31.4 52.0 47.3
Electronics in 4.2 25.4 5.2 27.3
Electronics out 7.4 30.4 9.2 32.3
Digitiser in 5.5 27.8 6.9 29.7

• Position scale factor: 1.25 mm

## Correction, June 2013

The mode R/Qs were now calculated by integrating over the full geometry instead of just the cavity length:. The results for the position cavity are:

Code R/Q /Ω Sensitivity/V nC-1 mm-1
GdfidL 3.26 17.08
Ace3p 3.27 17.11
CST 4.55 20.2

The results for the reference cavity are:

Code R/Q /Ω Sensitivity/V nC-1
GdfidL 50.3 117
Ace3p 50.7 118

Position signal (offset=1mm, charge=1nC) Reference signal (Charge=1nC)
Location Volts dBm Volts dBm
Cavity out 14.7 36.4 118 54.4
Electronics in 3.37 23.6 5.39 27.6
Electronics out 5.99 9.60 9.2 32.6
Digitiser in 4.44 26.0 7.11 30.0

• Position scale factor: 0.62 mm

## Finite Decay Time

Because the signal decays with a finite decay time, the assumption that the root mean square voltage over one period is the peak voltage divided by is no longer valid. The corresponding value can be found by

where f is the signal frequency, τ is the decay time and T is the time of one period in time t and is equal to 1/f. Evaluating the definite integral gives
This is one case where the signal is given by a sine function. In the opposing case, where a cosine function is used instead, the expression evaluates to
The median of these two cases is
Another effect is the signal decaying before the first peak in the oscillation is seen. The peak time in the case of a

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Topic revision: r16 - 11 Feb 2014 - FrankieCullinan

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