1. DDC Signal Processing Applied to Beam Phase & Cavity Signals
Alfred Blas
Angela Salom Sarasqueta
30 March 2004

2. Input Signal: Analysis of an extreme case
I beam
Input Signal:
Very narrow single bunch
Spectrum -> ∞
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

3. Analogue Filtering Stage
The aim is to analyze one particular Harmonic of the revolution: hA FREV without being affected by the aliases
Practical limitation for the analogue Filter: 52 dB/oct (Ref: MiniCircuits)
Practical value for the Dynamic Range = 80 dB
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

4. Sampling Frequency Evaluation
MiniCircuits Reference Data:
-20 13,6 MHz
-40 15,6 MHz
Fs – FC = 3 FC  FS = 4 FC
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

5. Angela Salom Sarasqueta
Mixing Stage
FS has been evaluated for a spectrum Є [0; FNOISE] but the mixing product Є [0; FNoise + hA FREV] will be above the Nyquist Limit.
FNoise + 1*FREV will fold back to FC – FREV
FNoise + hA FREV will fold back to FC – hA FREV = 0 Hz but with an amplitude lost in Noise.
In this example with FS = 4FC all the spectrum is distorted, but with a negligible effect at very low frequency
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

6. Digital Low Pass Filter
As the spectrum is only expected to have components at the Harmonics of the Revolution (Beam Phase and cavity return), a Notch Filter can be used to get rid of them
All the FREV harmonics are filtered even the 0th harmonic which we are interested in. We might have a solution by multiplying 0 by ∞ (integrator) at DC
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

7. Digital Low Pass Filter (II)
Integrator + Notch Filter = CIC Filter!
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

8. Angela Salom Sarasqueta
Summary
Typical Values for LEIR:
FREV Є [360 KHz; 1.43 MHz]
hA max=4 (taking into account the dual harmonic mode)
FC,LEIR=4*1.43 MHz = 5.72 MHz
FS = hck*FREV ≥ 4*Fc = 4 * 5.72 MHz = 22.9 MHz
hck ≥ Fs/FREV
hck could remain = 64 if 91.5 MHz can be handled by the circuit.
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

9. Digital Filter Simulation
1st Order CIC
2nd Order CIC
CIC1 amplitude response
0.005
0.01
0.015
CIC1 Phase response
RelativeFrequency [ ]
Phase [rad]
CIC2 amplitude response
0.005
0.01
0.015
CIC2 Phase response
Relative Frequency [ ]
Phase [rad]
0.005
0.01
0.015
0.1 10
100
Relative Frequency [ ]
Gain [ ]
0.005
0.01
0.015
0.1 10
100
Relative frequency [ ]
Gain [ dB]
|CIC1(0)| = 36 dB
|CIC1(FREV-2kHz)/FS| = - 9 dB
Group Delay = 1.4 µs
|CIC2(0)| = 72 dB
|CIC2(FREV-2kHz)/FS| = - 18 dB
Group Delay = 2.8 µs
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

10. Digital Filter Simulation II
3rd Order Butterworth Filter
Filter Coefficients
fco:= Normalized to the sampling frequency
|But (FREV) | = -89 dB
|But (0) | = 0 dB
Group Delay ζ = 8 µs
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta

11. Digital Filter Simulation III
CIC2 versus Butterworth Filter
Conclusion: For the same attenuation at FREV ± ε, the Butterworth is more complicated and the group delay is almost 3 times higher.
DDC Signal Processing
Alfred Blas
Angela Salom Sarasqueta