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Prime Number Spirals

Prime numbers on a Sacks spiral.  The prime numbers are depicted as dots. 

The line with the arrow was discovered by Euler. x2 + x + 41,

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Group Theory Using Rubics Cube



MOSFET Transistor Array CD4007 Parameters

From Foty 1987: Device parameters for this version of the CD4007 are:

  • W = 190 pm
  •  L = 4.0 pm
  • tOx =1200 A
  • NA = 2.8 X 10^16 (boron).

From Foty 1989: Device parameters for this version of the CD4007 are: 

  • W = 495 pm
  • L = 6.35 pm
  • to = 120 nm
  • ND = 3.0 X lOI5 (phosphorus)

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Agilent 4156C Precision Semiconductor Analyzer

GnuPlot Summary and How to Plot Data From a CSV File

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You can download this file and follow along: Processed_P1-Data.csv

Point Gnuplot to the correct directory to find the file full of data that you want to plot

The button with the folder icon and ChDir is what you want:


Set up GnuPlot to recognize comma as the field separator

set datafile separator "," 

This needs to match the field separator in your file.  My file has commas.  Watch out for excel files that export sometimes with only a CR and no LF character.  This will drive you crazy because it looks just fine when you look at the file with a text editor unless you are using something like NotePad++.  Then you will see it.  You need a right handed karate chopped n & r.  That would be \n\r.


Set the title of the plot


Setting up X axis to be log scale

Use the following command to select a log scale on X:

set logscale x 10

When you need to switch back out of this mode:

unset logscale x

It appears they do not have an explicit command for "linear" mode.


Setting the range to avoid taking log(0) and getting an error

When you try to plot a Log(X) axis you will see the following error

   x range must be greater than 0 for log scale

If you have not already done so set your X range so it does not include zero with:    set xrange[1e-10:1e-4] 

or whatever you like for the first value just make it >0.


Plotting Log(X) axis values correctly   Without this statement your X axis is labeled:  00000 00000 00000 .00001 .00010 etc and what you want is shown below.

If you use a log scale you will probably also want to format the log axis value labeling.

set logscale x 10
set format x '10^{%L}'  #<- enhanced text.


At this point the plot function should probably start working

plot "Processed_P1-Data.csv" using 4:8


If you want more than one plot on the same graph

In order to plot multiple lines in a single plot, simply put them in a single plot command like

plot 'AAA' u 1:2, 'BBB' u 1:2


If you want lines instead of only data points use:

plot "Processed_P1-Data.csv" using 2:3 with lines


Paper Size


Because I always seem to need it.

Space Saving Architecture


For if you have one of those tiny houses.

SubThreshold Slope Measurement Lab Using SPICE

MOSFET-Gm-Over-Id.7z Archive with this file included

Run: Diode-Connected-FET-SubVt_Slope.asc


Diode Connected MOSFET

The subthreshold slope is a feature of a MOSFET's current–voltage characteristic.

In the subthreshold region the drain current behaviour – though being controlled by the gate terminal – is similar to the exponentially increasing current of a forward biased diode. Therefore a plot of logarithmic drain current versus gate voltage with drain, source, andbulk voltages fixed will exhibit approximately linear behaviour in this MOSFET operating regime. Its slope is the subthreshold slope.

Click Image for higher resolution


This simulation demonstrates

  • slope factor in weak inversion: Purple Curve
  • Extraction of specific current: Is  - by setting cursor to point where gm/Id = 1/2 gm/Id max
  • Threshold Vt by setting if=3


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