Matlab Guide J. Scholvin Matlab Guide for Device Characterization and Circuit Design Project This handout gives a very brief overview of useful matlab functions and code samples for handling weblab measurement data. If you have serious matlab trouble, send me an email with your code and error message(s). Simple syntax checking should be left to matlab , please :) 1. Matlab functions General reference at http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.shtml Reference listing functions by category (very useful!!) http://www.mathworks.com/access/helpdesk/help/techdoc/ref/ref.shtml Functions you may find yourself using: clf; subplot(...); plot(...); semilogy(...); hold on; axis(...); sum(...) xlabel(...); ylabel(...); title(...); floor(...) orient ...; Important: for multiplication and division, use the element by element operators .* and ./ * and / are matrix operators, which you don't want to use. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].®®®®®®2. Code Samples 2.1. Reading the Weblab data file To read directly the CSV file from matlab without having to erase the first 3 lines, create a function in a file called readWeblabFile.m , with the following content: % returns a matrix from the weblab data-file <filename> function [data]=readWeblabFile(filename) fid=fopen(filename,'r'); data=[]; if (fid==-1) disp(['ERROR: file not found or could not be opened for read. check file ' filename]); break; end % skip first lines of comments sLine=fgetl(fid); sLine=fgetl(fid); sLine=fgetl(fid); % read the data while 1 sLine=fgetl(fid); if (~ischar(sLine)) % end of file break; end % add line to table data=[data;str2num(sLine)]; end fclose(fid); 2.2. Extracting data Once you load the data, you must extract the colums that correspond to I, V, etc. Example: read mos.csv and take the first column to save in variable ID, 2nd column as VG, etc. For the correct order, look at the comment lines in the csv files. MOS = readWeblabFile('mos.csv'); ID = MOS(:,1); VG = MOS(:,2); VD = MOS(:,3); ... 2.3. Derivatives A cheap derivative is to take the difference of two neighboring data points. It won't be very smooth, but it's sufficient here. You can avoid a for loop if you use the matrix capabilities of matlab. Here we take ro = 1 / [ dID/dVDS ] roMOS = 1./( ([0;ID]-[ID;0])./([-1;VD]-[VD;-1]) ); roMOS(1)=[]; What is being done? With ([0;ID]-[ID;0]) we shift ID and subtract it. This is ID(n)-ID(n+1) = dID Similarly, dVDS is computed. The quotient is go, and 1/go = ro. The second line, roMOS(1)=[]; trims the derivative back to the original length, since we inserted an extra row to find the difference (we said [0;ID] etc). The choice of 0 and -1 in the equation is arbitrary, since the Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].®®boundary elements of the derivative are meaningless. The -1 was picked to avoid a divide by zero error. Example: for ID=[1,4,9,16,25,36] and VD=[1,2,3,4,5,6] we get row # [0;ID] [ID;0] dI = [0;ID]-[ID;0] [-1;VD] [VD;-1] dV = [1;VD]-[VD;1] roMOS 1 0 1 -1 -1 1 -2 2 2 1 4 3 1 2 1 1/3 3 4 9 5 2 3 1 1/5 4 9 16 7 3 4 1 1/7 5 16 25 9 4 5 1 1/9 6 25 36 11 5 6 1 1/11 7 36 0 13 6 -1 5 -1/13 2.4. Plotting data: Since all the data is in one table, we cannot just plot plot(VD,ID); because we would end up with nasty lines drawn through the graph (try it out to see!) Instead we can split the data up, and plot ID vs VD for every different VG. We can do this automatically: clf; % clear graph vnum=sum([inf;VG]~=[VG;inf])-1; % count the number of VG's we have vsize=floor(size(VG,1)/vnum); % for each VG there are this many data points of ID vs VD % loop through the data, and plot for each VG: for k=[0:vnum-1] idx=[(1+k*vsize):(k*vsize+vsize)-1]; % this is where the data is in the big table subplot(1,2,1); % 2 graphs on this page hold on; % we want to overlap graphs plot(-VD(idx),-ID(idx)); % I-V characteristics xlabel('VSD');ylabel('-ID'); % label it axis tight; % let's not waste figure space subplot(1,2,2); % next plot: ro vs. VSD hold on; plot(-VD(idx),roMOS(idx)); % plot ro vs VSD xlabel('VSD');ylabel('roMOS'); axis([0,3,0,1e5]); % because the boundaries of the derivative may % be some oddly large number, fix the axis to only the range of interest. % add more code here end orient tall; % options for printing: use the whole page available. Looks less shabby! Repeat this kind of loop for each file that you are processing. If you want to add more graphs, just add similar code where it says % add more code here You may want to adjust the subplot command to accommodate more graphs on one page. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].The complete example: % plot I-V and ro for mosfet measurement MOS = readWeblabFile('mos.csv'); VG = MOS(:,1); VD = MOS(:,2); ID = MOS(:,3); % take the derivative to get ro roMOS = 1./( ([0;ID]-[ID;0])./([-1;VD]-[VD;-1]) ); roMOS(1)=[]; clf; % clear graph vnum=sum([inf;VG]~=[VG;inf])-1; % count the number of VG's we have vsize=floor(size(VG,1)/vnum); % for each VG there are this many data points of ID vs VD % loop through the data, and plot for each VG: for k=[0:vnum-1] idx=[(1+k*vsize):(k*vsize+vsize)-1]; subplot(1,2,1); hold on; plot(-VD(idx),-ID(idx)); xlabel('VSD');ylabel('-ID'); axis tight; subplot(1,2,2); hold on; plot(-VD(idx),roMOS(idx)); xlabel('VSD');ylabel('roMOS'); axis([0,3,0,1e5]); % this is where the data is in the big table % 2 graphs on this page % we want to overlap graphs % I-V characteristics % label it % let's not waste figure space % next plot: ro vs. VSD % plot ro vs VSD % because the boundaries of the derivative may % be some oddly large number, fix the axis to only the range of interest. % add more code here end orient tall; % options for printing: use the whole page available. Looks less shabby! Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.