1. Status report on the fast front-end design for Layer0-3 strip detectors
L. Ratti, M. Manghisoni
Università degli Studi di Pavia
INFN Pavia
SuperB FE chip phone meeting, 24/02/202

2. Fast front-end block diagram
Charge sensitive amplifier with gain selection (1 bit)
2nd order unipolar semi-Gaussian shaper with polarity (1 bit) and peaking time (2 bits) selection
Symmetric baseline restorer for baseline drift suppression (1 bit, might be advisable to have one, especially for high rate operation)
Threshold generator, discriminator
3-4 bit A to D conversion with TOT technique or through a flash ADC

3. Present performance
Charge sensitivity: ~5.5 mV (high gain configuration)
Power consumption: ~1.3 mW (not including the stages following the shaper)
Output dynamic range: ~15 MIP (240 ke- for layer 0, 360 ke- for layers 1 to 3)
Response linearity: ~3%
S/N: >20 for all the layers

4. Plans for the very next future
New simulations with updated capacitance and resistance values (mainly to evaluate noise related issues)
Noise hit rate estimation/simulation
Threshold generation and comparator design
Threshold dispersion simulation – do we need a threshold DAC?
Baseline drift/dispersion simulation – do we need a baseline restorer?

5. Hit time resolution under A to D conversion
L. Ratti
Università degli Studi di Pavia
INFN Pavia

6. Hit time estimation
Consider a readout channel with threshold discrimination
The time of arrival of a particle, t0 (corresponding to the signal start time, drift time of the charge in the detector is considered negligible), is given by
with tth the threshold crossing time and twalk the time needed by the signal to reach the threshold (depending on the signal amplitude and, in turn, on the input charge). The uncertainty in the estimation of t0 is given by
depends on time stamping
can be estimated through amplitude measurement

7. Time over threshold
In a TOT system, tth can be estimated based on the time stamp latched in the register upon transition of the discriminator output
The uncertainty depends on the time stamp clock period TCK,TS. Since the probability of the discriminator firing is uniformly distributed inside a clock period, then
Estimation of twalk can be performed based on the amplitude measurement, which in the case of the TOT is performed by means of an amplitude-to-time interval conversion
The uncertainty in the estimation of the time walk depends on the amplitude-to-time interval relationship, i.e. on
the shaping function,
the peaking time
the TOT clock frequency

8. Time over threshold: amplitude-to-TOT counts
TOT clock
RC2CR shaping
TOT
When converting from amplitude to TOT counts, a ±1 counting error has to be taken into account (e.g., a shaper signal staying over threshold for 7.5xTCK,TOT can result in 7 or 8 TOT counts)

9. Time over threshold: TOT counts-to-TOT (and Q)
When going back from TOT counts, or TOTDIG, to TOT and Q, if TOTDIG=i (i≠0), then
and
RC2CR shaping
with TOT=f(Q)
For example, if TOTDIG=8, then the original analog TOT value might have been anywhere between 7xTCK,TOT and 9xTCK,TOT

10. Analytical calculations
Given a value i (i a natural number) for TOTDIG, estimation of the time walk and of its uncertainty can be calculated analytically provided that analytical expressions for
the probability density function pQ,i(Q) (for the charge in the interval [f-1((i-1)TCK,TOT), f-1((i+1)TCK,TOT)])
the relationship between twalk and Q, twalk=g(Q)
are known. In this case
with
This can be done for example in the case of a triangular shaping processor (calculations have been performed in this case and the results confirmed by Monte Carlo simulations)

11. Monte Carlo simulations
In the case of an RC2CR shaping processor, an analytical expression for g(Q) is not available – Monte Carlo simulations are needed
In the MC simulations
106 events generated for each of the possible digital words in the charge-to-TOT counts (A/D) conversion characteristic
uniform or Moyal (Landau-like) distribution for the input charge
triangular and RC2CR shaping functions
TOT processing and standard A to D conversion with uniform and non uniform (compression type) distribution of the ADC levels
also the case of peaking time measurement by means of a flash ADC (operated as a digital peak stretcher) has been considered
Moyal distribution

12. Monte Carlo simulation: amplitude measurement resolution
σTOT/TCK,TOT depends on the tp/Tck ratio (and not on tp)
in the figures, Tck=TCK,TOT

13. Monte Carlo simulation: time walk estimation
<twalk>/tp depends on the tp/Tck ratio (and not on tp)

14. Monte Carlo simulation: time walk uncertainty
σwalk/TCK,TOT saturates between 0.24 and 0.25 for TOTDIG0
σwalk/TCK,TOT depends on the tp/TCK ratio (and not on tp)

15. Uncertainty in the estimation of t0
Based on MC simulation results, the uncertainty in t0 can be expressed as
where the worst case value of σwalk, ~0.25 TCK,TOT for TOTDIG0, is assumed
Layer
tp [ns]
tp/TCK,TOT
fCK,TS [MHz]
σwalk [ns]
σt0 [ns] 25 3 30
2.1
9.8 1
100
8.3
12.7 2
200
16.7
19.2 4
500
41.7
42.8 5
1000
83.3
83.9
Actually σwalk gets smaller for larger values of TOTDIG, so better resolution in t0 could be obtained

16. A to D conversion
As in the case of the TOT processor, uncertainty in the threshold crossing time is given by
Time walk can be estimated based on the amplitude measurement
Uniform and non uniform distributions of the ADC levels have been considered – variable quantization can be used to implement a compression type characteristic, like in the TOT case

17. Monte Carlo simulation: time walk estimation
for large n, the first ADC levels may be below the threshold – would be even worse for the parabolic distribution case (ADC levels are denser towards lower values of the dynamic range)
possible solution: the starting ADC level corresponds to the discriminator threshold
like in this case (and in the figures in the following slides)

18. Monte Carlo simulation: time walk uncertainty
parabolic ADC level distribution offers slightly worse performance in terms of time walk resolution

19. Monte Carlo simulation: amplitude measurement resolution
ADC with parabolic level distribution has better behavior from the standpoint of amplitude measurement resolution, especially at smaller amplitudes (typical of a compression type characteristic)

20. TOT vs ADC (uniform level distribution)
Amplitude measurement and time walk resolution

21. TOT vs ADC (parabolic level distribution)
Amplitude measurement and time walk resolution