This very small introduction to the Central Limit Theorem is probably something worthwhile before the Shannon paper. The main point is that as we take more and more samples from a random variable, tadalafil medicine with a fixed mean and variance, medical the samples approach a normal (Gaussian) distribution. That is, irregardless of the distribution of the random variable, if it meets the criteria, it will behave like a normal ly distributed random variable in the limiting case. The typical application engineering application of this theorem is making the assumption that some measured quantity is normally distributed and use that assumption to define things like confidence limits and so forth. The requirements for this assumption are that the process is second-order stationary, meaning the mean and variance do not change in the window of observation, and that the number of samples is approaching infinity. The requirement for a large number of samples can sometimes be loosened since the residual differences between the sample distribution and a normal distribution can sometimes be determined. The requirement for a stationary process cannot. For example, it would be foolish to apply Gaussian statistics to a random-walk (Brownian motion).
The key message is that the normal/Gaussian assumption is typically a good one, as long as the statistical nature of the random variable under investigation is constant through the period of observation and the number of samples is large.
( sec_4_f.pdf ) ( Image is from Wikipedia )
I found this surprisingly well-written manual for I2C serial communication protocol today. In short, ailment this is a fairly popular message-based protocol that can be found in many embedded systems in consumer electronics, hospital test and automation and automotive fields. There are low-speed alternatives and the structure of the protocol is fairly user-friendly making it a good option for hobbyists. There also schematics available on-line for rs232 and USB to I2C adapters available on-line like this open-source platform.
( an10216_1.pdf )
The inaugural paper for the Journal Club is titled “Power-constrained high-frequency circuits for the IBM POWER6 microprocessor” by Brian Curran et al. and is published in the November 2007 issue of the IBM Journal of Research and Development. I have much respect for the whole POWER micro-architecture, check consequently, I am interested in learning a little bit about their design methodology which lead to a near-5GHz core logic clock rate. The IBM design team responsible for the POWER6 applied a three-direction strategy to achieving this performance goal: cutting edge technology, manual circuit optimization and thorough testing.
The processor was designed at a 65um manufacturing node so various technologies needed to be employed to keep leakage current to a minimum and thereby maintain an acceptable power usage. The first method involved using silicon-on-insulator (SOI) which reduced back-gate current due to parasitic capacitances and can CMOS latch-up. The processing steps to implement SOI are well understood, however, extra care must be given to design layout as it is no longer possible to drive the back-gate by connecting the whole substrate to a fixed potential. Another technological advance employed was the use of dielectrics with low relative permittivity between traces to further reduce transmission line effects and the associated propagation delay of interconnects. Since less energy is stored in the dielectric material between interconnects, this also reduces power consumption.
From a design stand point, the goal of the team was to distribute the clock properly and to maintain the latency of the core logic circuits below “13FO-4”. Propagation delays, loading and transmission line effects play a very important role in the 5GHz regime. It was very interesting to see how multiple layers of buffers and clock delays were included to guarantee that clock pulses would be synchronized around various cells while maintaining an adequate slew rate. The 13FO-4 latency means that each processing cycle had to be accomplished in the time it would take for a signal to propagate along a chain of thirteen inverters that were loaded with four devices each. This is the criteria which allowed for a 5GHz core logic clock rate. It was mentioned that threshold voltages were tuned, probably through ion implantation, to minimize leakage while maximizing speed.
Simulations, being the last major piece of the paper, were less interesting as they relied mostly on proprietary tools. The piece that may have been important for readers was the iterative cycle of debugging and performance tuning. Going from schematic overview to transmission line calculations to back-annotation, to placing and routing made some sense.
Please feel free to contribute your thoughts on this paper, my interpretation or another paper that would be an interesting read in the comments section. Lets look at Claude Shannon’s paper titled ‘A Mathematical Theory of Communications’ as suggested by Adam. As the full paper is quite long, we may want to look at only the first thirty pages in detail. Those that want to brush up on their mathematics before attempting the paper should start on page thirty-two.
Here is a short application note (AN-404) from Analog Devices that deals with high performance analog and digital layout on the same printed circuit board. The specific example deals with AD1845 and CS4231 codecs and demonstrates some ideas for clean power and ground plane separation, order among others. The application note provides some handy numbers, such as a “ballpark” estimate inductance of a PCB trace of 1nH/mm. Another helpful hint is that the note helps prioritize the various pins of the codec on page six to optimize noise management.
While on the subject of PCB design, here is a nice tutorial covering various dielectric materials used in printed circuit board fabrication. Its main goal is to give an overview of the various properties of the materials so the designer has a better judgement of which to use for higher performance RF boards and which is most economic for medium-speed digital designs.
( an-404.pdf )