Confidence Level and Test Time Excel Calculator at Specified BER and Data Rate

     For those who have the experience of receiver jitter tolerance (RXJTOL) test using a bit error rate tester (BERT) build-in function are mostly likely familiar with the configuration parameters such as the measurement BER depth, confidence level, error gating time or transmitted bits. On the one hand, most of the industry standards will specify these test requirements explicitly such as "test at a BER value of 1E-12 with 95% confidence level" and leave you with no choice but to follow. But some will not specify explicitly, thus you need to make a wise engineering judgement for BER, confidence level settings considering the data rate of the DUT to strike a balance between test accuracy and test time. On the other hand, when there is a requirement of DUT and BERT interactions during the RXJTOL test, you have to write your own test codes instead of using the BERT build-in test function. In this case, you again need to have a good understanding of the relationship among BER, CL, data rate and measured error numbers so that your test algorithm can be properly implemented.

    To serve the above-mentioned purpose without sweat on the mathematics, you can actually make use of some online calculators such as the one from JitterTime. You can input target BER, data rate, measured errors and test time to calculate the confidence level. However, if you has a target CL in mind and want to know the test time or number of bits transmitted, then you need to "play with" the test time iteratively until you hit your CL target if use this online calculator. Alternatively, you need to look at the graph on the same website to find your answer indirectly.

    To make life easier, I implemented similar calculators in Excel based on the same Poisson equation. It not only provides the flexibility of using the calculator without the access of the Internet but also provides the capability of calculating the test time and transmitted number of bits for specific CL targets using bisection root finding method with a 0.01 second accuracy. It can be downloaded here and hopefully can be of some use for you.

    Take note, if you find that the Excel calculator doesn't response to your input. It's most likely because of your Excel disabled the Macro.  If that is the case, you need to enable the Macro by going to "Options..." to "Enable the contents" first.

Measurement Automation: How to Save Screens of 86100C DCA-J, SDA830 and E4440A/E4445A to Local PC Through GPIB

Picture from agilent.com

Measurement automation can save you a lot of pain in many cases on top of the advantages of higher productivity and greater accuracy in case of performing repeated day-to-day test and measurement tasks. Several examples using simple GPIB commands to capture screen pictures from different instruments to a local PC are given in this article with the complete workable VEE codes shown how to implement. They are easily portable with any programming languages such as Matlab and C or scripts like Perl and Python. If you are interested in how to:

• Save screen image from Agilent DCA-J 86100C to local PC as GIF files.
• Save screen image from LeCroy SDA830ZI-A to local PC as PNG files.
• Save screen image from Agilent E4440A/E4445A spectrum analyzer to local PC as GIF files.
• Dump raw spectrum data from Agilent E4440A/E4445A spectrum analyzer to local PC as text files.
• Dump raw phase noise log plot data from Agilent E4440A/E4445A spectrum analyzer to local PC as text files.

Please read on here ...

Finally, 50G Hz electrical BW with 32Gbps hardware CDR module is available for DCA from Agilent

    I have been looking for high bandwidth, high fidelity CDR modules for high speed (25Gbps and beyond) SerDes characterizations and finally it's here! It is Agilent 86108B Precision Waveform Analyzer which claimed to have "industry best intrinsic jitter below 50 femtoseconds, channel bandwiths to 50GHz, and clock recovery to 32Gbps ...."

If you are interested to know more, "Tips and Techniques for Accurate Characterization of 28Gb/s " is one of their good application notes to start with.

AC Signal RMS vs. Peak Value

    A lot of times, we need to relate the signal peak-to-peak amplitude to its root-mean-squared value, this is required to understand the system performance impact caused by different aspects of signal characteristics. For example, when you are trying to estimate the maximum current carrying capability of copper traces, wire bonds etc. or how much power the system consumes, how much heat the system generates and need to be dissipated, you could be more interested in signal RMS values while signal peak-to-peak value is of more importance when you are trying to figure out the dielectric break down voltage or device punch through limit and you probably like to consider both parameters when you are interested in not only instantaneous value but also long term averaged power such as complying with IC electromigration design rules.
  
If you are interested, please read the full article here ...

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Gaussian PDF, CDF, Error Function and Q-Transformation

How time flies! My blog is six-months' old now and I've been trying to update it with one post per month on average. Contents here may not be fantastic, but all are originally created by myself so far. :)

Original also means the contents are my own understandings, thus may not be 100% correct. This is why I tried to give as more details as possible and attach the sample codes, if any, that used for preparing all the figures presented in the articles. Thus, your comments to correct wrong observations and conclusions, contributions to extend the scope of the articles are certainly warmly welcomed and greatly appreciated.

With that said, let me go back to the fields to continue today's topic: "PDF and CDF of Normal/Gaussian-distributions, Error Function and Q-transformation".

If you are an electrical engineer who want to brush up the very basic statistics that leads to a better understanding of random jitter modeling, dual-Dirac model based DJ, RJ decomposition and jitter extrapolation using bath-tube curve, you may like to read on here ....

You may also have interest in one of my previous articles talking about similar topics: "From Jitter Statistics to System BER"

Or simply look for it in May/2011 archives ...

From Jitter Statistics to System Bit-Error-Ratio(BER)

A magic factor of 14 is most frequently cited in publications and literature when scale the unbounded system random jitter expressed in terms of its root mean square(RMS) value to the bounded peak-to-peak value at the specified system bit error ratio(BER) value of 1E-12. A good example is its use in the dual-Dirac model to calculate system total jitter from an estimated DJ and RJrms. This article tries to walk through the necessary mathematical equation derivations in detail and understand the physical meanings underlying the general statistical models involved.

The full article can be read here ....