AFE,signal processing

photohomoeopathAI and Robotics

Nov 24, 2013 (3 years and 8 months ago)

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7/22/02

Ring BPM FDR

1

Ring BPM Electronics

FDR

M. Kesselman

7/22/02

Ring BPM FDR

2

Outline


General information



Configuration



Processing Technique


RF



Base
-
band



Filtering and bandwidth considerations



S/N Estimates





7/22/02

Ring BPM FDR

3

Requirements


Intensity


5E10 to 2E14 ppp


Range


+/
-

pipe radius


Accuracy


1% of half aperture


Resolution


0.5%/1% averaged/turn
-
turn


HEBT, Ring, RTBT position:

HEBT (TOF) (Phase):


Range


+/
-

180 degrees


Accuracy


+/
-

2 degrees


Resolution


0.1 degrees

7/22/02

Ring BPM FDR

4

Quantities


HEBT:


12cm bpm:

31


21cm bpm:

4


TOF systems:

6


Ring: (Floated stripline)


21cm bpm:

28


26cm bpm:

8


30cm bpm:

8


RTBT: (Shorted stripline)


21cm bpm:

15


36cm bpm:

2

Electronics:


LANL



BNL



BNL


Cables:

ORNL


Specs:

BNL


7/22/02

Ring BPM FDR

5

Design Philosophy


Maintain a linear system


Digitize as soon as possible


Process data digitally


Permits choice of processing algorithm


log(ratio)


pk diff over sum


mean
-
square diff over sum


log(mean
-
square ratio)


diff over sum at any sample


etc.


Permits digital filtering if desired to reduce bandwidth and improve
S/N by averaging over many mini
-
pulses


7/22/02

Ring BPM FDR

6

BPM General Block Diagram

ADC

CIRCULAR

BUFFER

INPUT


SIGNAL

CONDITIONING

ADJ. GAIN

DIGITAL

SIGNAL

PROCESSING

7/22/02

Ring BPM FDR

7

System Configuration

PUE

A
F
E

40 MHz/68MHz LO

GAIN

352.5
MHz
LO

DAC’s &
PGA’s

DFE

PCI
DAQ

TIMING
MODULE

CLK

2.5 MHz
Reference

Event
Link

RTDL

RACK MOUNT
PC

PCI BUSS

CONTROL

LabVIEW

CONTROL

SYSTEM

7/22/02

Ring BPM FDR

8

BPM Configuration

ANALOG FRONT END

and BAND
-
LIMITING

DIGITIZER

DIGITAL INTERFACE

Averaging, Circular Buffer, Gain Memory,

Gain Correction, Baseline Restore,

Integration, Time
-
stamp

DATA

TIMING

REFERENCES

60MHz Sampling Clock

RING Ref., etc.

DIFFERENTIAL

INPUT

DIFFERENTIAL

INPUT

SENSOR

STATUS


SETTING INFO

Gain, Ref., etc.


SETTING INFO

Gain, Ref., etc.

STATUS

Separate Boards

7/22/02

Ring BPM FDR

9

Processing Techniques


RF
-

HEBT


Identical to Linac unit


Down convert to 50MHz


IF sample at 40MHz and Demodulate


Base
-
band


Ring and RTBT


Amplify, Filter, digitize at 64 times revolution freq.


Eases transient response and anti
-
aliasing filter
requirements


Process signals digitally to suit specific requirements


Process signals using mean square to provide an
average signal for an entire mini
-
pulse.


Use Log ratio approach to improve linearity with
displacement

7/22/02

Ring BPM FDR

10

S/N Ratio Estimate


50 Ohm Noise

Estimated BPM Output Signal
for 38ma Beam
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
1.4E-05
0
5
10
15
20
25
30
Harmonic Number
MS Voltage (Volts-
squared)
0
10
20
30
40
50
60
70
S/N (dB)
S/N
PWR in BW
PWR in Signal from BPM
S/N 15ma
Beam
7/22/02

Ring BPM FDR

11

Processing


Goals


Avoid sensitivity to edge


Develop a position measurement weighted over an entire mini
-
pulse



Methods investigated


Diff over sum



(favors beam edges)


Mean
-
squared difference over sum

(averages over mini
-
pulse)


Log(ratio)




(favors beam edges)


Log(ms ratio)




(averages over mini
-
pulse)

7/22/02

Ring BPM FDR

12

Linearity to Displacement

100
80
60
40
20
0
20
40
60
80
100
6
5
4
3
2
1
0
1
2
3
4
5
6
4.576605
4.576605

log
Ir
r
(
)
Il
r
(
)






Ir
r
(
)
Il
r
(
)

Ir
r
(
)
Il
r
(
)

log
Ir
r
(
)
2
Il
r
(
)
2






0.032
r
0.016
r
100
100

r
7/22/02

Ring BPM FDR

13

Simulation


S/N Estimate Table

15ma beam
-

5 MHz Bandwidth

S/N 50 Ohms

49dB

Amp noise


10dB

Cable atten.


2dB

Add’l atten.


6dB

Switches & filter

6dB

RESULT S/N=

25dB

Signal simulations confirmed by comparing results
of LabVIEW, PSPICE, MathCAD, and EXCEL
spreadsheets computing Shafer’s equations.

7/22/02

Ring BPM FDR

14

Processing Simulation Comparison


15ma
Beam 1mm displacement 210mm diam BPM

COMPARISON OF RESOLUTION ERROR FOR
DIFFERENT PROCESSING ALGORITHMS
15ma - 1mm on axis displacement to 210mm diameter
22cm 70 degree BPM
0.01
0.1
1
10
15
20
25
30
35
40
45
50
S/N (dB)
RMS Resolution Error for 1mm Offset
(mm)
Log(Rms/Lms)^2
Rms-Lms/Rms+Lms
pk R-L/R+L ms to noise
0.15mm Resolution
0.5mm Resolution
Best Guess
0.15mm resolution - target
0.5mm resolution - spec.
diff/sum vs. ms pwr to noise
log(Rms/Lms)
ms diff/ms sum
Best Guess S/N ratio
1*en50
2*en50
6*en50
12*en50
20*en50
40*en50
7/22/02

Ring BPM FDR

15

Processing Conclusions


Difference over sum provides best % error (using
peak
-

signal detection at time of peak). Not being
used since it favors edges.


Mean
-
square difference/ mean
-
square sum
provides about the same resolution as
log(Rms/Lms).


Log Ratio improves linear range at little loss in
resolution compared to pk difference over pk sum.


Resolution near 0.5% of half aperture is
achievable using log ratio of mean
-
square for
S/N=25dB.

7/22/02

Ring BPM FDR

16

Processing Conclusions

To achieve a resolution near 0.15% half aperture
for a 15ma beam requires averaging.



This could be accomplished with a narrow
band filter (approx. 22KHz, Q=91) at the 2
nd

harmonic (producing a sinusoidal signal for
a single injected bunch). This is readily
accomplished digitally.



Requires averaging over about 46 turns.

7/22/02

Ring BPM FDR

17

Mean Square processing

Defining Variables:

Right stripline voltage = vr(t) (volts)

Left stripline voltage = vl(t) (volts)

Beam position =

r,
q

stripline angular width =

f (
rad
)

noise at right channel = vnr(t) (volts)

noise at left channel = vnl(t) (volts)

rms noise at right channel = vnrrms (volts)

rms noise at left channel = vnlrms (volts)

signal at stripline for r=0 is: V(t) (volts)

Gain of right channel = Gr

Gain of left channel = Gl

BPM sensitivity variable = a (mm
-
1
)


7/22/02

Ring BPM FDR

18

Log ratio processing


Calibrated by Beam
Based Alignment
-

1

Output
log
1
T
0
T
t
vr
t
(
)
2



d

1
T
0
T
t
vl
t
(
)
2



d
















Output
log
Gr
2
Gl
2






4
a

r



+ (noise) + (cross
-
correlation)

After storing the beam based alignment data and subtracting:

vr
t
(
)
Gr
V
t
(
)
1
a
r


(
)

vnr
t
(
)

[
]


vl
t
(
)
Gl
V
t
(
)
1
a
r


(
)

vnl
t
(
)

[
]


+/
-

resolution errors

Out put
4
a

r
Ro

(
)

vnrrms
2
vnlrms
2

(
)
Vrms
2

2
Vrms
2
1
T
0
T
t
V
t
(
)
vnr
t
(
)




d

1
T
0
T
t
V
t
(
)
vnl
t
(
)




d













7/22/02

Ring BPM FDR

19

Log ratio processing


Calibrated by Beam
Based Alignment
-

2


This indicates it is not necessary to calibrate
the electronics as long as one does beam
-
based
alignment periodically.



Changes in gain will contribute to a position
error term. Therefore, it is useful to calibrate
to assure gain has not changed between beam
based alignment procedures.

7/22/02

Ring BPM FDR

20

Dual AFE Motivation


We have some RF in the recently injected turns in the Ring. To
examine the RF we need 402.5MHz BPM systems.


Motivations
-

incoherent tune, first turn sensitivity, commission to
target as transfer line,…


If costs are considered it may pay to put our money into a dual
AFE.

Crude cost estimate for 2 independent

402.5MHz BPMS in the RING


Bergoz Card

$1300


Digitizer


$1000


PCI


$2000


Timing generator

$10000


PC


$2000


Approx Total

$28600


How many locations can we equip

with dual AFE approach?

How useful is the capability to
commission thru the Ring and RTBT
to the Target as a Transfer line?

7/22/02

Ring BPM FDR

21

Bergoz
® Dual AFE

7/22/02

Ring BPM FDR

22

Bergoz
® Dual AFE

7/22/02

Ring BPM FDR

23

Bergoz
® Dual AFE

7/22/02

Ring BPM FDR

24

Back
-
up Slides

7
-
22
-
02 FDR

7/22/02

Ring BPM FDR

25

Mean Square processing
-

1

Defining Variables:

Right stripline voltage = vr(t)

Left stripline voltage = vl(t)

Beam position =

r,
q

stripline angular width =

f

noise voltage at right channel = vnr(t)

noise voltage at left channel = vnl(t)

rms noise voltage at right channel = vnrrms

rms noise voltage at left channel = vnlrms

signal voltage at stripline for r=0 is: V(t)

Gain of right channel = Gr

Gain of left channel = Gl

BPM sensitivity = a (mm
-
1
)


7/22/02

Ring BPM FDR

26

Mean Square processing
-

2

The BPM sensitivity is (given by Shafer):

a
4
1
b







cos
q
(
)
sin
f
2







f


The signals at each PUE are: (using only the linear term)

vr
t
(
)
Gr
V
t
(
)
1
a
r


(
)

vnr
t
(
)

[
]


vl
t
(
)
Gl
V
t
(
)
1
a
r


(
)

vnl
t
(
)

[
]


b= radius (mm)

7/22/02

Ring BPM FDR

27

Mean Square processing
-

2

The BPM sensitivity is (near center):

Position= Output/0.03107/mm

Output
log
1
T
0
T
t
vr
t
(
)
2



d

1
T
0
T
t
vl
t
(
)
2



d
















Where:

7/22/02

Ring BPM FDR

28

Mean Square processing
-

3

Defining the signal rms voltage:

The Output for small displacements is:

Vrms
1
T
0
T
t
V
t
(
)
2



d


Out put
log
Gr
2
Gl
2
1
a
r


(
)
2
2
1
a
r


(
)
Vrms
2

1
T
0
T
t
V
t
(
)
vnr
t
(
)




d











vnrrms
2
Vrms
2









1
a
r


(
)
2
2
1
a
r


(
)
Vrms
2

1
T
0
T
t
V
t
(
)
vnl
t
(
)




d











vnlrms
2
Vrms
2

























7/22/02

Ring BPM FDR

29

Mean Square processing
-

4

This simplifies approximately to:

Output
log
Gr
2
Gl
2






4
a

r



+ (noise) + (cross
-
correlation)

Noise is:

Cross
-
correlation terms are:

Out put
log
Gr
2
Gl
2
1
4
a

r


vnrrms
2
Vrms
2

vnlrms
2
Vrms
2

2
Vrms
2
1
2
a

r


(
)
1
T

0
T
t
V
t
(
)
vnr
t
(
)




d

1
2
a

r


(
)
1
T

0
T
t
V
t
(
)
vnl
t
(
)




d






























2
Vrms
2
1
2
a

r


(
)
1
T

0
T
t
V
t
(
)
vnr
t
(
)




d

1
2
a

r


(
)
1
T

0
T
t
V
t
(
)
vnl
t
(
)




d











vnrrms
2
Vrms
2
vnlrms
2
Vrms
2

7/22/02

Ring BPM FDR

30

Simulating the Sensitivity to Noise

Output
log
1
T
0
T
t
vr
t
(
)
2



d

1
T
0
T
t
vl
t
(
)
2



d
















msdiffoversum
1
T
0
T
t
vr
t
(
)
2



d

1
T
0
T
t
vl
t
(
)
2



d


1
T
0
T
t
vr
t
(
)
2



d

1
T
0
T
t
vl
t
(
)
2



d



vr
t
(
)
Gr
V
t
(
)
1
a
r


(
)

vnr
t
(
)

[
]


vl
t
(
)
Gl
V
t
(
)
1
a
r


(
)

vnl
t
(
)

[
]


diffoversum
vr
tpk
(
)
vl
tpk
(
)

vr
tpk
(
)
vl
tpk
(
)


Error
Output
noise
(
)
Output
ideal
(
)

Output
ideal
(
)

Gr = Gl = 1

7/22/02

Ring BPM FDR

31

Normalized Spectrum of a Pulse 645ns
duration 945ns Period

Spectrum for Ring Single Turn Study
-4.00E-01
-2.00E-01
0.00E+00
2.00E-01
4.00E-01
6.00E-01
8.00E-01
0
5
10
15
20
25
30
35
40
Harmonic Number
Peak Amplitude
0
5

10
7
1

10
6
0
0.02
0.04
0.038
0
Ib
t
(
)
1
10
6


0
t
Bunch Shape

7/22/02

Ring BPM FDR

32

BPM Signal Components for 38ma Beam

ms signal voltage
0.00E+00
1.00E-07
2.00E-07
3.00E-07
4.00E-07
5.00E-07
6.00E-07
7.00E-07
8.00E-07
0
5
10
15
20
25
30
35
Harmonic Number
Mean Squared BPM Signal
Voltage (V^2)
0
5

10
7
1

10
6
0
0.02
0.04
0.038
0
Ib
t
(
)
1
10
6


0
t
Bunch Shape

7/22/02

Ring BPM FDR

33

Processing Conclusions

To achieve a resolution near 0.15% half aperture
for a 15ma beam requires averaging.



This could be accomplished with a narrow
band filter (approx. 22KHz, Q=91) at the 2
nd

harmonic (producing a sinusoidal signal).



This will require averaging over about 46
turns.

7/22/02

Ring BPM FDR

34

Improved Transient Resonse by Increasing
Clock Rate to 64 times Frev.

Comparison of anti
-
aliasing capabilities of
increasing Sampling Frequency. The signal
is down by about 92dB at 34MHz, while the
other provides about 79dB at 20MHz. If a
single Gaussian filter were used the signal
would be down about 70dB at 20 MHz.


Comparison of pulse response for the two
choices of filtering and sampling
frequency. The transient response is
drastically improved by increasing the
Nyqist frequency to 34MHz.


7/22/02

Ring BPM FDR

35

Bergoz’s Block Diagram

Gain 20dB

7/22/02

Ring BPM FDR

36

HEBT Instrumentation

Type

BNL

LANL

BPM PUE 12cm

31

0

BPM PUE 21cm

4

0

BPM Electronics

0

35

Phase
-

BPM TOF

0

2

BLM

52

0

FBLM

3

0

BCM

5

0

WS

0

11

Foil Video

2

0

Harp

0

2

7/22/02

Ring BPM FDR

37

Ring Instrumentation

Type

Qty

Comment

BPM (2 shared
with RF)

44

28 ea 21cm, 8 ea
26cm, 8 ea 30cm

IPM

2

H + V

BLM

75

Ion chamber

FBLM

12

PMT

Beam Current

2

BCM, WCM(RF)

Coh tune

1

Kicker + PU

Incoh tune

2?

BTF, QMM

WS (LANL)

1

H + V + 45 deg

Beam
-
in
-
Gap

1

Kicker + PMT

E detector

5

Octupole

1

7/22/02

Ring BPM FDR

38

RTBT Instrumentation

Type

BNL

LANL

BPM 21cm

15

0

BPM 36cm

2

0

BLM

40

0

FBLM

3

0

BCM

5

0

WS

0

5

Harp

0

2

7/22/02

Ring BPM FDR

39

Processing Simulation
-

1

y
t
(
)

1


1

(
)
3

2

exp
t









1


1

(
)
3

2

exp
t


1








1


1

(
)
2


1

t

exp
t


1








1
2

1
2


1

(
)






t
2

exp
t


1
















yy
t
(
)
y
t
(
)
y
t
T

(
)

t
T

(
)



0
5

10
7
1

10
6
0.1
0
0.1
0.077985
0.077985

yy
t
(
)
1
10
6


0
t
0
2

10
7
4

10
7
6

10
7
8

10
7
1

10
6
0.01
0.0083
0.0067
0.005
0.0033
0.0017
0
0.0017
0.0033
0.005
0.0067
0.0083
0.01
5.229398
10
3


5.229398

10
3


Y
t
(
)
.015
0.038
Y
t
(
)

1
10
6


0
t
Approximate the signal (response to exponential):

Modify to include response to pulse:

Provide Scaling:

0
5

10
7
1

10
6
0
0.02
0.04
0.038
0
Ib
t
(
)
1
10
6


0
t
Current Pulse

7/22/02

Ring BPM FDR

40

Processing Simulation
-

2

RTms
1
10
6

0
10
6

t
15
38
Y
t
(
)






2





d


LFms
1
10
6

0
10
6

t
15
38
Z
t
(
)






2





d


Simulate noise sources and signal

en1
t
(
)
0
Y
t
(
)

3
.91

k

10
9


f
0.5

rnd
2
(
)
1.0

(
)



en2
t
(
)
0
Y
t
(
)

3
.91

k

10
9


f
0.5

rnd
2
(
)
1.0

(
)



en3
t
(
)
0
Y
t
(
)

3
.91

k

10
9


f
0.5

rnd
2
(
)
1.0

(
)



en4
t
(
)
0
Y
t
(
)

3
.91

k

10
9


f
0.5

rnd
2
(
)
1.0

(
)



yn
t
(
)
Y
t
(
)
15
38

en1
t
(
)


15 ma beam with noise, Right pickup
15 ma beam with noise, Lef t pickup
zn
t
(
)
Z
t
(
)
15
38

en2
t
(
)


0
2

10
7
4

10
7
6

10
7
8

10
7
1

10
6
0
2

10
6
4

10
6
6

10
6
4.286087
10
6


0
zn
t
(
)
2
yn
t
(
)
2
1
10
6


0
t
0
5

10
7
1

10
6
1

10
5
5

10
6
0
5

10
6
1

10
5
en1
t
(
)
t
0
5

10
7
1

10
6
1

10
5
5

10
6
0
5

10
6
1

10
5
en2
t
(
)
t
yn
t
(
)
Y
t
(
)
15
38

en1
t
(
)


zn
t
(
)
Z
t
(
)
15
38

en2
t
(
)


7/22/02

Ring BPM FDR

41

Compute Output and Calculate Errors

num
1
10
6

0
10
6

t
yn
t
(
)
2
zn
t
(
)
2

(
)



d


den
1
10
6

0
10
6

t
yn
t
(
)
2
zn
t
(
)
2




d


Gout put
num
ems3

ems4

den
ems3

ems4


Gout lograt io
log
1
10
6

0
10
6

t
yn
t
(
)
2



d

1
10
6

0
10
6

t
zn
t
(
)
2
(
)



d


















mserror
Gout put
Gout ideal

Gout ideal

mserror2
num
den
Gout ideal

Gout ideal

Gout ideal
RTms
LFms

RTms
LFms


Diffoversumerror
diffoversumnoise
diffoversum

diffoversum

Gout logideal
log
RTms
LFms







Gout logerror
Gout lograt io
Gout logideal

Gout logideal

Mean
-
Square Difference Over Sum:

Peak Signal
-

Difference Over Sum:

For no noise:

Log Ratio of Mean
-
Square signals:

With noise subtraction:

7/22/02

Ring BPM FDR

42

Interfering Signals

Out put ramp
k
(
)
log
1
P
0
P
t
0.015
Io
Y
t
(
)
k
P
t















2





d

1
P
0
P
t
0.015
Io
Z
t
(
)
k
P
t















2





d






















P=Pulse Period

Out put
k
(
)
log
1
P
0
P
t
0.015
Io
Y
t
(
)
k

(
)







2





d

1
P
0
P
t
0.015
Io
Z
t
(
)
k

(
)







2





d






















7/22/02

Ring BPM FDR

43

Interfering Signals

0.1
1
10
1

10
4
1

10
3
0.01
0.1
1
10
2.993
.0001
Outcoserror
h
1

(
)
Outcoserror
h
.31

(
)
Outcoserror
h
.1

(
)
Outcoserror
h
0.031

(
)
10
0.1
h
ERROR INTRODUCED BY AN INTERFERING COSINE SIGNAL of PEAK
VALUE A FRACTION OF THE PEAK SIGNAL for a LOG(MS RATIO)
ALGORITHM

Out cos
h
A

(
)
log
1
P
0
P
t
0.015
Io
Y
t
(
)
n
t
h

A

(
)

(
)







2





d

1
P
0
P
t
0.015
Io
Z
t
(
)
n
t
h

A

(
)

(
)







2





d






















Out coserror
h
A

(
)
Out cos
h
A

(
)
Out put
0
(
)

Out put
0
(
)

HARMONIC NUMBER

Out put
k
(
)
log
1
P
0
P
t
0.015
Io
Y
t
(
)
k

(
)







2





d

1
P
0
P
t
0.015
Io
Z
t
(
)
k

(
)







2





d






















n
t
h

A

(
)
A
pksig

cos
2
h


P

t









P=PULSE PERIOD

7/22/02

Ring BPM FDR

44

Interfering Signals

HARMONIC NUMBER

Out put
k
(
)
log
1
P
0
P
t
0.015
Io
Y
t
(
)
k

(
)







2





d

1
P
0
P
t
0.015
Io
Z
t
(
)
k

(
)







2





d






















P=PULSE PERIOD

0.1
1
10
1

10
5
1

10
4
1

10
3
0.01
0.1
1
10
1.03
1.231
10
5


Outsinerror
h
1

(
)
Outsinerror
h
0.31

(
)
Outsinerror
h
0.1

(
)
Outsinerror
h
0.031

(
)
Outsinerror
h
0.01

(
)
10
0.1
h
Out sinerror
h
A

(
)
Out sin
h
A

(
)
Out put
0
(
)

Out put
0
(
)

Out sin
h
A

(
)
log
1
P
0
P
t
0.015
Io
Y
t
(
)
nsin
t
h

A

(
)

(
)







2





d

1
P
0
P
t
0.015
Io
Z
t
(
)
nsin
t
h

A

(
)

(
)







2





d






















nsin
t
h

A

(
)
A
pksig

sin
2
h


P

t









ERROR INTRODUCED BY AN INTERFERING SINE SIGNAL of PEAK VALUE A
FRACTION OF THE PEAK SIGNAL for a LOG(MS RATIO) ALGORITHM

7/22/02

Ring BPM FDR

45

Bergoz
® Linac AFE

7/22/02

Ring BPM FDR

46

Protected Amplifier Front
-
End


Gain =6

Zi=50

OPA680

Gain = 1

Two state

Amplifiers

(100ns


switch time)

Maximum Z change 0.16%

6dB

Attenuator

Diplexer

Switch

Matrix

CALIBRATION

SIGNAL

40 TO 65MSa/S

DIGITIZER

G=4.4

100:50 Ohm

29.5db Atten.

100 Ohm

Protected Amp

G= 25

G=150

G=30

666

150

25

5

1

7/22/02

Ring BPM FDR

47

Log ratio processing


Calibrated by Beam
Based Alignment
-

1

7/22/02

Ring BPM FDR

48

Log ratio processing


Calibrated by Beam
Based Alignment
-

2

After beam based alignment the constant terms subtract:

The output is approximately given by:

+/
-

Resolution errors during alignment

7/22/02

Ring BPM FDR

49

BPM Processing Linearity to Displacement


100
80
60
40
20
0
20
40
60
80
100
2
1.6
1.2
0.8
0.4
0
0.4
0.8
1.2
1.6
2
1.8
1.8

Ir
r
(
)
Il
r
(
)

Ir
r
(
)
Il
r
(
)







.018
r
100
100

r

100
80
60
40
20
0
20
40
60
80
100
50
40
30
20
10
0
10
20
30
40
50
45.766
45.766

20
log
Ir
r
(
)
Il
r
(
)







0.31
r

100
100

r
A plot of sensitivity along the axis of a pair of pick
-
up
elements for a 70 degree stripline designed BPM with a
half aperture of 105mm. The sensitivity is shown to be
0.31dB per mm. Linearity is shown to be “reasonable”
over a range of +/
-

65mm.



A plot of sensitivity along the axis of a pair of pick
-
up
elements for a 70 degree stripline designed BPM with a
half aperture of 105mm. The sensitivity is shown to be
0.018A/A per mm. Linearity is shown to be “reasonable”
over a range of +/
-

20mm.