![]() ![]() Use a protractor to measure the angle between the two and calculate the inverse hyperbolic arc-cotangent. Next the peak of the column values is located (called out here with a green circle), and a line is drawn between that peak and the tip of the blowback arrow. The accuracy of this arrow is imperative! Standard methods can be used for this process. At the end of the line a series of concentric circles is used to help center the blowback arrow that is drawn in the following figure. This entire process must be repeated for each column of the matrix. In the second frame one column of matrix values is plotted onto the chart. This shows as a red dot in the first figure. (You can click on any of the charts to view an enlarged rendition.) First a point is drawn to indicate the current year and state of the present economy. The following series of pictures illustrates the process for a single column of the forecast matrix. I am sure that readers will recognize the parallels between these and common forecast methods, and that I need not further explain. In the world of RF this is used to determine the Radially-Scaled Parameters: The SWR (the Standing Wave Ratio) both toward the load and toward the generator, attenuation, standing wave loss coefficient, reflection & return losses, and the transmission & reflection coefficients. For forecasting DRAM these obviously will be translated to the partial derivative of the dollar value of the average transistor over the node migration.Īlong the bottom is a separate and very useful little linear nomogram that I will show how to use in a future post. The circles around the outside of the chart can be used for any of three things: the resistance or conductance component, the wavelengths toward the signal generator or toward the load, or the angle of reflection and transmission coefficient. For forecasting these would naturally be proxies for the components of economic versus temporal stability. The chart is beautifully symmetric, with the capacitive reactance component or inductive susceptibility accounting for the lower half of the nomogram, while inductive reactance component or capacitive susceptibility is accounted for in the upper half. It dissolves complex equations into simple sketches that, once drawn onto the chart, can determine the answers to the enormous complexities of antenna designs. Although I have tried to use mental arithmetic, it’s a little too challenging to keep all the numbers in my head. The resultant matrix is then easily transposed to create a set of dimensions that can be applied to the Smith chart.Īlthough much of the above work can be done with a calculator or in an Excel, spreadsheet, I prefer to calculate it with pencil and paper. Those who prefer can use a Hadamard transform, with appropriate compensation. This bears some resemblance to the algorithms applied in computational lithography.Īfter the data has been groomed we determine the weighted frequency of the cycles, which can be achieved easily enough by performing a Laplace transform on each row. This multiplication must be applied both vertically and horizontally through the matrix. This assures that the next step includes no sampling aliases. ![]() To avoid edge effects each row must be multiplied by a sinc function. By applying Boltzman’s Constant to these cells you create a neutral ground for the calculations to continue. What do you do with the cells that aren’t filled when you do this? That’s easy. Since the intervals are of different durations, these lines need to be centered below one another. It helps to have a frequency analysis of the actual shapes of the waves, and that can be done relatively easily by taking the values from one peak to the next and arranging them in a matrix, with the revenue for each peak-to-peak curve constituting a single row in the matrix. The big peaks occur roughly every 5 years on average, so the base frequency is about 157 micro Hertz, or μHz. These cycles can be observed in the chart below, which shows both DRAM and NAND flash revenues since 1991. The first thing to do is to determine the frequency of the industry’s cycles. Its relation to regular cycles leads it to immediate use in predicting the cycles of the memory market, or semiconductors, or for any other cyclical market. This chart is a nomogram, presented in an angular/logarithmic format (as opposed to the semi-logarithmic format that I often use in this blog) which was originally devised to help antenna designers determine the effects of impedance and standing waves. My answer is always that I use the Smith Chart. Many of my clients ask The Memory Guy how it is that I am able to come up with such consistently-acurate forecasts in a seemingly-unpredictable market. Forecasting the memory market can be quite daunting unless you use the appropriate tools, then it becomes enormously simple.
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