Tuesday, April 26, 2005
40 years ago (19 April 1965), Gordon E. Moore published his famous paper in "Electronics" magazine and predicted that after 10 year, as many as 65000 components would be integrated on a single chip. This prediction was based on changes in number of integrated components during 1962-1965 which was doubled every year. In 1975, Moore amended the law to state that the number of transistors doubled about every 24 months.
Maybe at the first glance it seemed that exponential behavior in the growing of number of transistors, would fail after a while but interestingly, now after 40 years the number of transistors in CPU's manufactured by Intel is following Moore's law. How long will this law be valid? It seems that there should be an end for this rule after 40 years. The inventor of this law, Gordon Moore believes that this law is dead. Should we believe Moore's opinion again?!!
Monday, April 25, 2005
Peak-to-peak and RMS jitter
What does jitter mean? Jitter is very common word in oscillatory systems vocabulary. In an ideal oscillator, time difference between transitions (for example two rising or falling edges) is constant. In practice, due to existence of noise these spacings are varying. Assume Vout is referred as output voltage of an oscillator and t(n) as the time point of the nth zero crossing of rising edge of Vout. The nth period of Vout can be defined as T(n)=t(n+1)-t(n). As we mentioned earlier, this difference is constant for an ideal oscillator but not in a practical one. This variation in T(n) can be called as jitter. If T(n) is deviated from mean period (Tm), then we can define: d(T)=T(n)-Tm.
The RMS value of d(T) for infinite number of cycles is called as "RMS jitter" while the difference between maximum and minimum value of d(T) is called as "peak-to-peak jitter". For more detailed definitions and calculations refer Yamaguchi et al.
On the other hand random jitter can be specified by Gaussian distribution. Standard deviation of this distribution gives RMS jitter. If Bit Error Rate (BER) of a jittery system is specified, the relationship between RMS and peak-to-peak (pp) value of jitter can be written as:
where k is BER-dependent constant and can be calculated by solving following equation:
0.5*erfc(k/(8^0.5))=BER. (in "x^y" y is power for x)
In this equation erfc(x) is "error function" and it is tabulated in different references. Using such a table gives the values for k. For example:
In measurements BER=10^-12 will cover 99.99999% of time interval of Gaussian distribution to calculate pp value of jitter.
Friday, April 22, 2005
I think sometimes everyone needs to think about what s/he has done in her/his life. Sometimes writing about your problems and ideas help you to summarize them to get a better feeling about them. This was the first thing which forced me to start such a blog. I know that there are lots of people who are doing in the same way as mine, but it does not prevent me to write. In my first start I would like to thank Jalal, one of my friends who gave me this idea to start this blog.
Please read it and share your ideas with me.