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 .... 

Periodic Jitter and Phase Modulation

It's been a while since my last working on this blog. To keep going on, I combed my PC and found some articles written some time ago which may worth sharing here.

Posted here is a topic briefly talking about periodic jitter caused by phase modulation and its extraction from the measured time interval error. The derivation of the analytical form relating the timing error and the signal spectrum is also shown in detail.

If you are interested, please read on ...

Spectrum analysis of clock-like signals

The purpose of this article is to briefly study the rise/fall time and DCD effects on clock-like signal spectrum. If you are interested, please read on....

Real-time Oscilloscope Spectrum Analyzer and Matlab

This article is trying to understand a typical clock-like signal measured and interpreted in different domains(time domain and frequency domain) and try to correlate the different results produced from different sources such as measurements, analytical math equations or Matlab functions bridged by Discrete Fourier Transforms(DFT).
   
If you are interested, please read on....