A Simulation Study for Time resolution of ANITA-Lite
This is an analytic approach to
understand the time resolution of the ANITA-Lite system.
But this is not full simulation, including only the digitization part
of the ANITA-Lite.
Sampling clock time error
We are assuming the 25ps of sampling time error. This assumption means
that every time interval of each sampling is very accurate comparing
with 0.5ns bin size. This 25ps of error is a kind of free parameter in
our simulator and obtained by comparing the instrinc time resolutions
of the simulation and the data.
In order to simulate the dt = T2-T4 measurement, we generate two independent signals and apply the same dt measurement algorithm as the real data analysis. The amplitude of signal is varied from 1 sigma to 15 sigma of the noise level. Figure 1 compares the simulation and data for the distribution of the time resolution as a function of threshold. The Agreement is satisfactory.
Figure 2 shows the intrinsic time resolution as a function of the signal amplitude. The intrinsic timing was obtained by measuring the time interval between consecutive cycles in a given antenna. For the simulation we generate the single waveform and apply the same method as the real data measurement. It also shows an agreement with data.
We use our simulator to expect the time resolution for the several frequencies of the signal in two different sampling rates. Figure 3 shows the expected time resolution for the 2GHz sampling (top) and 4GHz sampling (bottom). The 2GHz sampling provides good time resolution up to about 800MHz. The higher frequency signal above the 800MHz requires more fast sampling rate. For the 4GHz sampling rate, the frequcy coverage is up to 1.5 GHz or higher.
May 6 2004, Jiwoo Nam
Model
Signal
We generate a sine wave to simulate the ANITA-Lite calibration pulse. The amplitude and frequency can be specified by user. The phase of the signal is randomly varied within 1 cycle.Random Noise
The noise is modeled by the Gaussian distribution. The width of Gaussian is measured at the real data. Also we tested this model by embedding the simulated signal into the noise part of the real waveforms where no calibration signal exists. And no different result was found.Sampling rate
We use 2 GHz sampling rate which is as same as ANITA-Lite system. Furthermore 3 GHz and 4 GHz are used for an estimation of ANITA-Heave system.Sampling clock time error
We are assuming the 25ps of sampling time error. This assumption means
that every time interval of each sampling is very accurate comparing
with 0.5ns bin size. This 25ps of error is a kind of free parameter in
our simulator and obtained by comparing the instrinc time resolutions
of the simulation and the data.Voltage error
We don't introduce the error of voltage measurement. In the real experiment the limited number of bits for the voltage digitization must carry the error within 1 bit of digitization. But we are assuming the negligible effect on it because the random noise is much larger than the size of digitization.Results
Figure
1. Time resolution of time difference between two antennas
In order to simulate the dt = T2-T4 measurement, we generate two independent signals and apply the same dt measurement algorithm as the real data analysis. The amplitude of signal is varied from 1 sigma to 15 sigma of the noise level. Figure 1 compares the simulation and data for the distribution of the time resolution as a function of threshold. The Agreement is satisfactory.
Figure
2 instrinc time resolution as a function of amplitude
Figure 2 shows the intrinsic time resolution as a function of the signal amplitude. The intrinsic timing was obtained by measuring the time interval between consecutive cycles in a given antenna. For the simulation we generate the single waveform and apply the same method as the real data measurement. It also shows an agreement with data.
We use our simulator to expect the time resolution for the several frequencies of the signal in two different sampling rates. Figure 3 shows the expected time resolution for the 2GHz sampling (top) and 4GHz sampling (bottom). The 2GHz sampling provides good time resolution up to about 800MHz. The higher frequency signal above the 800MHz requires more fast sampling rate. For the 4GHz sampling rate, the frequcy coverage is up to 1.5 GHz or higher.
Figure
3. Expectation of the time resolution for the several frequencies.
2GHz sampling (top), 3GHz sampling (middle) and 4GHz sampling(bottom)
2GHz sampling (top), 3GHz sampling (middle) and 4GHz sampling(bottom)
May 6 2004, Jiwoo Nam