SAmpler Threshold Adjustment

Olivier GENTAZ IRAM/Back-End

Aug. 2006

In order a digital correlator works with a minimum loss in efficiency, the sampling thresholds of its digitizer have to be adjusted to their optimal level. Two indicators used in the Digitizer Test Equipment developed by IRAM have been defined: the offset and the amplitude relative errors.

This memo gives the mathematical definition of these two parameters. The equations hereunder are those implemented in the following test softwares:

- SHERIF_V1a1 (IRAM-PdBNG version DTE)

- ALCOR_V1a0 (ALMA version DTE)

- PDF_Viewer_V2a0 software.

1. The PDF Measurement

Assuming a relative quantization step a=q/s , the gaussian distribution of the input samples (Probability Density Function) is divided into N equally spaced bins having each a theoretical probability of occurrence P_TH(i) with iÎ[0;N-1].

Figure 1: The Ideal Sample Statistical Distribution (ALMA case: N=8).

Ideally, the N probabilities P_MES(i) measured thanks to the DTE should be compared to the N theoretical probabilities one by one in order to properly adjust the DG thresholds.

In practice, for N > 4, the DG levels cannot be adjusted individually and even so, it would be quiet cumbersome to deal with N adjustments. So, it has been chosen to only adjust the offset and the amplitude of the threshold grid. Thus the adjustment procedure will be much more convenient and moreover, as a gaussian distribution is entirely defined with only its two first statistical moments (mean and standard deviation), this method will provide a “best fit” adjustment of the comparator thresholds.

For both the offset and the amplitude, the relative difference between the expected value and the measured value is displayed along with time. The relative difference between the expected and the measured means is called the relative offset error e_m whereas the relative difference between the expected and the measured standard deviations is called the relative amplitude error e_s. Once these displayed errors are lower than a value to be defined, it is assumed that the DG thresholds are properly adjusted.

2. Equations

The displayed parameters are:

Figure 2: PDF Measurement Screenshot of the DTE test software (IRAM case: N=4).

3. measuring random signals: a tricky bussiness…