Instrumentation & Measurement Magazine 24-9 - 30

Fig. 10. Block diagram (1-of-4 channels) of a typical BPM signal processing front-end. (Acronyms: BPF = band-pass filter, LPF = low-pass filter, Att = attenuator,
Ctrl = control signal, LO = local oscillator signal, CLK = clock signal, ADC = analog-to-digital converter, NCO = numerically controlled oscillator, CIC = cascaded
integrator-comb filter, FIR = finite impulse response filter, WB = wide-band, NB = narrow-band.)
linear term of the normalization function, the beam position is
detected as:
pos 
11Δ ΔΔnoise
kk Σmeas Σnoise
BPM

meas
BPM Σmeas


BPM
kk
BPM
BPM
11Δ noise
= resolution 
k
with kBPM
BPM
Σ
BPM
11
ΣΣ
BPM
ΔΔ (21)

noise
BPM

resolution
BPM
AB

kA B

A BS
A BN
BPM BPM
noise


noise
and Anoise, Bnoise being uncorrelated, we find:
resolution 
2NS
2kS Nk 2 BPM

BPM
1 


 1
(23)
The noise N, contributed by the signal processing electronics,
and has a minimum level of:
N v 
noise
with k = 1.38 · 10−23
30
4 ΔkTR f
(24)
J / K (Bolzmann constant), T = 300 K (typical
operating temperature), and R = 50 Ω (typical load impedance
Performance of BPM Systems
Quantifying and comparing the performance of BPM systems
is difficult, too different are the requirements and goals among
different particle accelerators. BPM systems of single purpose
machines with a narrow range of beam parameters and formats,
such as some synchrotron light sources are advanced in
terms of resolution, accuracy, and reliability, while BPM systems
of multipurpose hadron machines may have to operate
with a wide range of beam types, energies, and formats, with
different particle species and beam intensities, and are focused
IEEE Instrumentation & Measurement Magazine
December 2021


meas
of the signal source, here: the BPM electrode). In practice the
thermal noise level of (24) defines the lower limit of vnoise
. Δf is the 3 dB overall
, passive
components including cables (counting as insertion loss),
and the so-called noise figure of gain stages (amplifiers) will
always result in a higher value of vnoise
bandwidth of the BPM processing electronics, this includes
all filter, averaging, and other bandwidth limiting elements
on the BPM signal or data (analog, digital, and software). The
signal level S = velec
noise noise
BPM BPM
≈ 2/R, see (12). Assuming small beam displacements:
(22)
can be estimated from the discussion and
equations in the previous section, selecting a frequency band
as defined by the input filters of the front-end electronics. Eq.
(23) represents the lower limit of the achievable BPM resolution,
other factors, like performance and characteristics of the
ADC can further degrade the overall resolution of a beam position
monitor.

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