# Difference: Ctf3Sensitivity (1 vs. 16)

#### Revision 1611 Feb 2014 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 66 to 66

## 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a finite decay time, the assumption that the root mean square voltage over one period is the peak voltage divided by is no longer valid.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

Added:
>
>
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
%BEGINLATEX%
Deleted:
<
<
\begin{equation*} \frac{V_{rms}(\tau)}{\hat{V}}=\int_0^T e^{-\frac{2t}{\tau}}\sin^2 (\omega t) dt = \frac{1}{2}\int_0^T e^{-\frac{2t}{\tau}}(1-\cos (2 \omega t) dt \end{equation*} %ENDLATEX% where ω is the angular frequency, τ is the decay time and T is the time of one period in time t. Evaluating the 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 %BEGINLATEX{}%
Latex rendering error!! dvi file was not created.
\begin{displaymath}
Changed:
<
<
\frac{V_{rms}(\tau)}{\hat{V}}=\frac{\tau}{4}\left(1+\frac{1}{1+\omega^2\tau^2}\right)\left(1-e^{-\frac{T}{\tau}}\right)\, .
>
>
\left(\frac{V_{rms}(\tau)}{\hat{V}}\right)^2=\frac{\tau}{4T}\left(1-\frac{1}{1+(2 \pi f \tau)^2}\right)\left(1-e^{-\frac{2 T}{\tau}}\right)
\end{displaymath} %ENDLATEX%
Added:
>
>
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

Line: 104 to 104

 META FILEATTACHMENT attachment="latexd5e79cee3c33e10c50caf2c7c59c139b.png" attr="h" comment="" date="1392112892" name="latexd5e79cee3c33e10c50caf2c7c59c139b.png" user="pvap079" version="1" attachment="peak.pdf" attr="h" comment="" date="1392113079" name="peak.pdf" path="peak.pdf" size="14135" user="pvap079" version="1" attachment="power.pdf" attr="h" comment="" date="1392113079" name="power.pdf" path="power.pdf" size="21245" user="pvap079" version="1"
Added:
>
>
 META FILEATTACHMENT attachment="latexfa5ca9771b0c8721bc3a056c31644848.png" attr="h" comment="" date="1392118982" name="latexfa5ca9771b0c8721bc3a056c31644848.png" user="pvap079" version="1" attachment="latex971fd647cba55db26bf3980fab976541.png" attr="h" comment="" date="1392118983" name="latex971fd647cba55db26bf3980fab976541.png" user="pvap079" version="1" attachment="latexc2a28d54bc230c4df2ddf10c15af199d.png" attr="h" comment="" date="1392118983" name="latexc2a28d54bc230c4df2ddf10c15af199d.png" user="pvap079" version="1" attachment="latexd9c775860f8cf3f3cb4ac9983f1bb78f.png" attr="h" comment="" date="1392118984" name="latexd9c775860f8cf3f3cb4ac9983f1bb78f.png" user="pvap079" version="1"

#### Revision 1511 Feb 2014 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 62 to 62

 Digitiser in 4.44 26 7.11 30

• Position scale factor: 0.62 mm
Added:
>
>

## 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 ω is the angular frequency, τ is the decay time and T is the time of one period in time t. Evaluating the 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
Another effect is the signal decaying before the first peak in the oscillation is seen. The peak time in the case of a

Latex rendering error!! dvi file was not created.

Added:
>
>

 META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrankieCullinan" version="2" attachment="refsense.png" attr="h" comment="" date="1361106346" name="refsense.png" path="refsense.png" size="86511" stream="refsense.png" user="Public.FrankieCullinan" version="1"
Added:
>
>
 META FILEATTACHMENT attachment="latexd5e79cee3c33e10c50caf2c7c59c139b.png" attr="h" comment="" date="1392112892" name="latexd5e79cee3c33e10c50caf2c7c59c139b.png" user="pvap079" version="1" attachment="peak.pdf" attr="h" comment="" date="1392113079" name="peak.pdf" path="peak.pdf" size="14135" user="pvap079" version="1" attachment="power.pdf" attr="h" comment="" date="1392113079" name="power.pdf" path="power.pdf" size="21245" user="pvap079" version="1"

#### Revision 1408 Aug 2013 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 21 to 21

 Ace3p 9.8 52 CST 10 52
Changed:
<
<
>
>

## Electronics Chain Propagation

Line: 44 to 44
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:

Changed:
<
<
 GdfidL 3.26 14.73 Ace3p 3.27 14.75 CST 4.55 17.4
>
>
 GdfidL 3.26 17.08 Ace3p 3.27 17.11 CST 4.55 20.2
The results for the reference cavity are:

Changed:
<
<
 GdfidL 50.3 118
>
>
 GdfidL 50.3 117

 Ace3p 50.7 118

Position signal (offset=1mm, charge=1nC) Reference signal (Charge=1nC)

#### Revision 1303 Jul 2013 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 54 to 54

 GdfidL 50.3 118 Ace3p 50.7 118
Added:
>
>
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

#### Revision 1203 Jul 2013 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 41 to 41

## Correction, June 2013

Changed:
<
<
The mode R/Qs were now calculated by integrating over the full geometry instead of just the cavity length:
>
>
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 14.73
Ace3p 3.27 14.75
CST 4.55 17.40
Added:
>
>
The results for the reference cavity are:

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

#### Revision 1128 Jun 2013 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 21 to 21

 Ace3p 9.8 52 CST 10 52
Changed:
<
<
>
>

## Electronics Chain Propagation

Line: 41 to 39

• Position scale factor: 1.25 mm
Added:
>
>

## Correction, June 2013

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

Code
<-- -->
R/Q /Ω Sensitivity/V nC-1 mm-1
Ace3p 3.27 14.75
CST 4.55 17.40
GdfidL 3.26 14.73

#### Revision 1012 Apr 2013 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 39 to 39

 Electronics out Digitiser in 7.4 30.4 9.2 32.3 5.5 27.8 6.9 29.7
Changed:
<
<
• Position scale factor: 0.8 mm-1
>
>
• Position scale factor: 1.25 mm

#### Revision 904 Apr 2013 - FrankieCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 39 to 39

 Electronics out Digitiser in 7.4 30.4 9.2 32.3 5.5 27.8 6.9 29.7
Added:
>
>
• Position scale factor: 0.8 mm-1

#### Revision 818 Feb 2013 - webmanip_5foldt2nt_2esh

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 51 to 51

Changed:
<
<
 META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrancisCullinan" version="2" attachment="refsense.png" attr="h" comment="" date="1361106346" name="refsense.png" path="refsense.png" size="86511" stream="refsense.png" user="Public.FrancisCullinan" version="1"
>
>
 META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrankieCullinan" version="2" attachment="refsense.png" attr="h" comment="" date="1361106346" name="refsense.png" path="refsense.png" size="86511" stream="refsense.png" user="Public.FrankieCullinan" version="1"

#### Revision 718 Feb 2013 - FrancisCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

#### Revision 617 Feb 2013 - FrancisCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 21 to 21

 Ace3p 9.8 52 CST 10 52
Added:
>
>

## 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

Added:
>
>

 META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrancisCullinan" version="2" attachment="refsense.png" attr="h" comment="" date="1361106346" name="refsense.png" path="refsense.png" size="86511" stream="refsense.png" user="Public.FrancisCullinan" version="1"

#### Revision 526 Nov 2012 - FrancisCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 8 to 8
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:

Changed:
<
<
>
>
 GdfidL 0.85 8.7

 Ace3p 0.77 8.3 CST 0.77 8.3
Line: 17 to 17
The measured external quality factor of the reference cavity is 203.

Changed:
<
<
 GdfidL 14.1 62
>
>
 GdfidL 28.2 87

 Ace3p 9.8 52 CST 10 52

#### Revision 426 Nov 2012 - FrancisCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 16 to 16
The measured external quality factor of the reference cavity is 203.
Changed:
<
<
>
>

 GdfidL 14.1 62 Ace3p 9.8 52
Changed:
<
<
 CST 9.2 51
>
>
 CST 10 52

#### Revision 326 Nov 2012 - FrancisCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

## Position Cavity

Changed:
<
<
The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 830 and R/Q from simulation in several codes:
>
>
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:

Changed:
<
<
>
>

Changed:
<
<
 Ace3p 0.77 CST 0.77
>
>
 Ace3p 0.77 8.3 CST 0.77 8.3

## Reference Cavity

Changed:
<
<
Code R/Q Sensitivity/VpC-1
GdfidL 14.1
Ace3p 9.8
CST 9.2
>
>
The measured external quality factor of the reference cavity is 203.

Code R/Q Sensitivity/V nC-1
GdfidL 14.1 62
Ace3p 9.8 52
CST 9.2 51

#### Revision 223 Nov 2012 - FrancisCullinan

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

Line: 9 to 9

Code R/Q Sensitivity/VpC-1mm-1
GdfidL
Changed:
<
<
 Ace3p CST
>
>
 Ace3p 0.77 CST 0.77

## Reference Cavity

Code R/Q Sensitivity/VpC-1
Changed:
<
<
 GdfidL Ace3p CST
>
>
 GdfidL 14.1 Ace3p 9.8 CST 9.2

Added:
>
>

<--
Settings just to customise this page
Set STYLESIDEBAR = off
Set ALLOWTOPICVIEW = TWikiGuest, JohnAdamsInstituteGroup
Set MYTITLE = - CTF3 BPM Prototype Overview

-->

#### Revision 123 Nov 2012 - FrancisCullinan

Line: 1 to 1
Added:
>
>
 META TOPICPARENT name="ClicBpm"

# Cavity Sensitivity Estimates

## Position Cavity

The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 830 and R/Q from simulation in several codes:

Code R/Q Sensitivity/VpC-1mm-1
GdfidL
Ace3p
CST

## Reference Cavity

Code R/Q Sensitivity/VpC-1
GdfidL
Ace3p
CST

Copyright © 2008-2022 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding RHUL Physics Department TWiki? Send feedback