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Copyright 2011, Free use of program governed by statement in About dialog which is repeated below.
Updated June 2, 2012.  See Document History at end for details.
SPICE verified.




FETCurve

A FET parameter calculator

 

Introduction

In the context of desiring to match or scale FET parameters for the purpose of distortion cancelation, it becomes desirable to calculate these parameters.  Few would have access to transistor testers for their high cost.  Here I show how these parameters can be calculated from measurements made with just a power supply and a multimeter and provide a dedicated calculator to make them.
 

Calculations

These calculations are exact for enhancement MOSFETs.  The program makes minor adjustments for JFET's depletion mode bias range.

Simple Calculations are based on the idea that the VGS measured with the highest bias resistor is approximately VT.  RBIAS determining VT would have to be very high compared to any anticipated circuit bias like 1MΩ.  The other measurement would then determine kn (or KP in SPICE terms).

If VGS1 ≈ VT then

(1)
ID2 =
VBIAS - VGS2
RBIAS2
(2)
kn ID2
(VGS2 - VT)2


Two-Point Calculations
mathematically fit a curve to the data instead.  Three data points are usually required to define a second order polynomial.  Two data points suffice because a constant preexisting boundary condition satisfies the function of the third data point.  That di/dv = 0 when i = 0 at VT defines this boundary condition.

If the MOSFET equation

(3)
ID = kn(VGS - VT)2

is rearranged in the form

(4)
      
ID
kn
 + VT = VGS

A pair of simultaneous non-linear equations suitable for solving for kn and VT can be written:

(5)
      
ID1
kn
 + VT = VGS1
(6)
      
ID2
kn
+ VT = VGS2

The following substitutions in the rearranged MOSFET equation

(7) x0 =
     
1
kn
(8) x1 = VT
(9) aX0 =
     
IDX
(10) aX1 = 1
(11) aX2 = VGSX

where X is the data point and equation number, yields solvable simultaneous linear equations in the form of:

(12)
a10x0 + a11x1 = a12
(13)
a20x0 + a21x1 = a22

or in standard matrix form:

(14)

a10 a11 a12
a20 a21 a22

Continuing with the substitutions in the matrix:

(15)

     
ID1
1
VGS1
     
ID2
1
VGS2

By matrix reduction, the matrix is transformed to diagonal format with the last column containing the results:

(16)

1
0
     
1
kn
0
1
VT

Because the reduced a22 term returns VT in its final form, it remains only to solve for kn from the reduced a12 term.

(17)
kn =
1
a122



Calculator

Based on above calculations, I am offering a simple calculator for download.  It is tested in Windows XP, Windows 98, and under Linux using Wine (Windows Emulator)1 as well.

Screenshot


EULA

I retain copyright.  You may freely use this software for personal, non-commercial, use (that is you cannot offer it for sale).  You may share it with others as long as it is provided to them complete and unmodified as you get it from this website.  Because this program is free, although it works, I do not guarantee its operation or application

Download

Download FETCurve 1.2.1.zip

Download FETCurve 1.2.1.zip (13KB)

Download FETCurve 1.1.0.zip

Download FETCurve 1.1.0.zip (12KB)

Download FETCurve 1.0.0.zip

Download FETCurve 1.0.0.zip (12KB)

After download, copy the executable into the desired directory.  You will have to manually create links on the desktop or the start menu, as you desire.


Instructions

(These are to serve in place of a program help file)

1.  Test Circuit Setup

Enhancement MOSFETs tested must be connected so that VBIAS drops across the selected bias resistor and VGS in series.  JFETs tested must be connected with selected bias resistor placed between gate and source and sufficient voltage applied to the drain to ensure device is biased out of its linear range into saturation.  Depletion MOSFETs can be tested the same as JFETs.  If depletion MOSFETs are tested with enhancement bias, drain voltage cannot be connected with gate voltage as the enhancement circuit, but sufficient voltage above gate voltage must be applied to the drain to ensure device is biased out of its linear range into saturation.  Experimentation may be required to determine the best RBIAS values.  At least use values one above and one below the operating point of your expected circuit.

Figure x:  Example Test Circuits.

                  Depletion Mode                                          Enhancement Mode
        NJFET                      PJFET                        NMOSFET                PMOSFET
test circuits



2.  Soft ware Operation



SI prefixes

Factor

Name

Symbol

1024

yotta

Y

1021

zetta

Z

1018

exa

E

1015

peta

P

1012

tera

T

109

giga

G

106

mega

M

103

kilo

k

 

Factor

Name

Symbol

10-3

milli

m

10-6

micro

10-9

nano

n

10-12

pico

p

10-15

femto

f

10-18

atto

a

10-21

zepto

z

10-24

yocto

y



SPICE verification

Program is now SPICE verified.  SPICE verification was held up by confusion of transconductance factor kn with SPICE tranconductance bulk factor KP.

(18)
kn =
KP
2

W
Leff


Previously, SPICE verification did not seem necessary because of mathematical correctness to textbook MOSFET equation.

SPICE model for JFET test set.
SPICE model for enhancement MOSFET test set.


Software Input Limitations

Because I did not want to accidentally restrict the usefulness of the program, I have not placed any range limits on the inputs to the program.  At some later time I may place thoughtful and modest input limitations.  Until then, the user is responsible to input well-formed input data.  Therefore, there are a few pitfalls to beware:

It would be well to have or gain a good understanding of FET characteristics to use and interpret the output of this program.


Can it run on Windows 95? 

Windows 95 may not have the shared Visual C++ 6.0 dlls needed to run this program.  If you have any problem that implicates a missing file, mfc42.dll or msvcrt.dll, download here, and copy into the directory with the program or into the windows system directory (c:\windows\system\  or c:\windows\system32\  whichever contains system dlls).

 

download mfc42.dll

Download mfc42.dll  (1004KB)

download msvcrt.dll

Download msvcrt.dll (335KB)

 


1Specifically, Wine version 1.2.2 under Kubuntu 10.10 Maverick Meerkat.  You will have to copy mfc42.dll and/or mfc42u.dll to ~/.wine/drive_c/windows/system32 directory for proper operation.

Document History
June 26, 2011  Created.
June 26, 2011  Added section on software input limitations specifying some data pitfalls, made minor improvements, and clarified a wordy sentence.
May 31, 2012  Added SPICE verification.  Updated program to version 1.1.0 to flag alias error and to show kn for transconductance factor to avoid confusion with SPICE parameter KP.
June 2, 2012  Updated program to version 1.2.0 adding input checking for numeric entries.  Immediatedly released version 1.2.1 to allow negative number entry.