I want to plot an implicit equation

2 次查看（过去 30 天）
mohd ayaz
mohd ayaz 2022-4-21
回答： Sam Chak 2022-4-21
I have attached the equations and its all variable I don't know how to plot.
  4 个评论
显示 2更早的评论
mohd ayaz
mohd ayaz 2022-4-21
phit1=0.026;
Nd1=1e19;
phim1=5.2
ni=1.5e10;
chi=4.1;
Eg=1.1
Vfb1=phim1-(chi+(Eg/2)-phit1*(log(Nd1/ni)))
ni=1.5e10;
q=1.6e-19;
eox=3.9*8.8*1e-14
tf1=6*10^-7
tox=0.7*10^-7
Cox=eox/tox
esi=8.8*11.7*1e-14
Qss1=3*10^-6
Qc1=2*10^-5
Ec1=1.4*10^6;
Tsc1=1*10^-6;
p1=q*Nd1*Tsc1
alpha_1=-((3*sqrt(3))/4)*(Ec1/Qss1)
beeta_1=((3*sqrt(3))/8)*(Ec1/(Qss1^3))
damma_1=0
alpha1=2*tf1*alpha_1
beeta1=4*tf1*beeta_1
damma1=6*tf1*damma_1
Vgd1=1;
N=30;
Vds=linspace(0,1,N);
Qd1=zeros(1,N);
for i=1:N
syms x
assume(x,'real')
eqnLeft = (Vgd1-Vfb1-Vds(i)+((Tsc1/(8*esi))*(x+p1)))-0.026*(log(2*sqrt(((x+p1)*Tsc1)/(8*3.14*0.026*esi))*(1-((x+p1)/(p1)))));
eqnRight =((alpha1+(1/Cox))*((x+p1)/2))+(beeta1*(((x+p1)/2).^3))+(damma1*(((x+p1)/2).^5));
Qd1(1,i)=vpasolve(eqnLeft == eqnRight,x);
end
%Qd1(1,i)=vpasolve(eqnLeft == eqnRight,x,"What should be here?");

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

David Goodmanson
David Goodmanson 2022-4-21
编辑：David Goodmanson 2022-4-21
Hi mohd,
This is not really an implicit equation since Vgs appears only once, by itself, on the lhs. So you can take all the other stuff to the rhs and use Qm as the independent variable and Vgs as the dependent variable. You can experiment around for the range of Qm that gives the correct range for Vgs, assuming there is one. When you fine the right range, don't be reluctant to use lots of points in the Qm array. Ater you find the corresponding Vgs array you can plot(Vgs,Qm). One catch is if Qm+qNdtsi goes negative, in which case you will run into problems with the log term.
Sam Chak
Sam Chak 2022-4-21
Hi @mohd ayaz
I tried to plot this way to first visualize how the curve looks like for the positive part of .
Qm = linspace(-1, 0, 1001);
Vgs = (1 + 1)*(Qm + 1)/2 + 1*((Qm + 1)/2).^3 + 1*((Qm + 1)/2).^5 + 1 + 1 - 1*(Qm + 1) + 1*log(- Qm.*sqrt((Qm + 1)/(1)));
plot(Qm, Vgs, 'linewidth', 1.5)
grid on
xlabel('Q_{m}')
ylabel('V_{gs}')
So, you want to invert the axes to plot(Vgs, Qm). You can check this documentation:
https://www.mathworks.com/help/matlab/ref/fimplicit.html
f = @(Vgs, Qm) Vgs - ((1 + 1)*(Qm + 1)/2 + 1*((Qm + 1)/2).^3 + 1*((Qm + 1)/2).^5 + 1 + 1 - 1*(Qm + 1) + 1*log(- Qm.*sqrt((Qm + 1)/(1))));
fimplicit(f, [-5 2 -1 0])
grid on
xlabel('V_{gs}')
ylabel('Q_{m}')
Now, make the substitution of the original constants.

类别

在 Help Center 和 File Exchange 中查找有关 Mathematics 的更多信息

标签

产品


版本

R2020a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by