Change the aspect ratio of MOSFETs

Experimenters were continue studying the voltage transfer characteristics this week. According to supervisor's advice, experimenters should  change the aspect ratio of P-Channel (PMOS) and N-Channel(NMOS) to observe the change of voltage transfer characteristics curve. Then, the experimenters fix the MATLAB code as shown in below:
V_tn=0.7;V_tp=-0.7;

K_n=100;K_p=50;

y_p=0.05;y_n=0.04;

V_DD=5;

y = zeros(1,5/0.005+1);z = zeros(1,5/0.005+1);m = zeros(1,5/0.005+1);

i = 1;j = 1;k = 1;

for V=(0:0.005:5);

    WLR_n=2;WLR_p=4;

    B_n=K_n*WLR_n; B_p=K_p*WLR_p;

    if(V>=0)&&(V<0.7)

        y(i)=V_DD;

    elseif(V>=0.7)&&(V<y(i-1)-0.7)

        y(i)=V+abs(V_tp)+sqrt((V_DD-abs(V_tp)-V)^2-(B_n/B_p)*(V-V_tn)^2);

    elseif(V>=y(i-1)-0.7)&&(V<y(i-1)+0.7)

        y(i)=((B_p*(1+y_p*V_DD)*(V_DD-abs(V_tp)-V)^2)-B_n*(V-V_tn)^2)/(B_n*y_n*(V-V_tn)^2+B_p*y_p*(V_DD-abs(V_tp)-V)^2);

    elseif(V>=y(i-1)+0.7)&&(V<4.3)

        y(i)=V-V_tn-sqrt(abs((V-V_tn)^2-(B_p/B_n)*(V_DD-abs(V_tn)-V)^2));

    elseif(V>=4.3)&&(V<5)

        y(i)=0;

    end;

    i = i+1;    

end;

for x=(0:0.005:5);

    WLR_n=3;WLR_p=4;

    B_n=K_n*WLR_n; B_p=K_p*WLR_p;

    if(x>=0)&&(x<0.7)

        z(j)=V_DD;

    elseif(x>=0.7)&&(x<z(j-1)-0.7)

        z(j)=x+abs(V_tp)+sqrt((V_DD-abs(V_tp)-x)^2-(B_n/B_p)*(x-V_tn)^2);

    elseif(x>=z(j-1)-0.7)&&(x<z(j-1)+0.7)

            z(j)=((B_p*(1+y_p*V_DD)*(V_DD-abs(V_tp)-x)^2)-B_n*(x-V_tn)^2)/(B_n*y_n*(x-V_tn)^2+B_p*y_p*(V_DD-abs(V_tp)-x)^2);

    elseif(x>=z(j-1)+0.7)&&(x<4.3)

        z(j)=x-V_tn-sqrt(abs((x-V_tn)^2-(B_p/B_n)*(V_DD-abs(V_tn)-x)^2));

    elseif(x>=4.3)&&(x<5)

        z(j)=0;

    end;

   j = j+1;    

end;

for n=(0:0.005:5);

    WLR_n=5;WLR_p=4;

    B_n=K_n*WLR_n; B_p=K_p*WLR_p;

    if(n>=0)&&(n<0.7)

        m(k)=V_DD;

    elseif(n>=0.7)&&(n<m(k-1)-0.7)

        m(k)=n+abs(V_tp)+sqrt((V_DD-abs(V_tp)-n)^2-(B_n/B_p)*(n-V_tn)^2);

    elseif(n>=m(k-1)-0.7)&&(n<m(k-1)+0.7)

        m(k)=((B_p*(1+y_p*V_DD)*(V_DD-abs(V_tp)-n)^2)-B_n*(n-V_tn)^2)/(B_n*y_n*(n-V_tn)^2+B_p*y_p*(V_DD-abs(V_tp)-n)^2);

    elseif(n>=m(k-1)+0.7)&&(n<4.3)

        m(k)=n-V_tn-sqrt(abs((n-V_tn)^2-(B_p/B_n)*(V_DD-abs(V_tn)-n)^2));

    elseif(n>=4.3)&&(n<5)

        m(k)=0;

    end;

   k = k+1;    

end;

plot(0:0.005:5,y,'k',0:0.005:5,z,'b',0:0.005:5,m,'r');

title('CMOS Inverter Voltage Transfer Characteristics Curve (Xu.Zhao and Shuoshi.Zhang)');

xlabel('Vin');ylabel('Vout');

legend('B_n/B_p=1','B_n/B_p=1.5','B_n/B_p=2.5','location','NorthEast')

grid on;

axis square;

And the output voltage transfer characteristic curve is shown in Figure 1.

Figure 1: Voltage Transfer Characteristic Curve with Different Mosfet Aspect Ratio



When change the aspect ratio of MOSFETs, the transconductance parameters beta of PMOS and CMOS and transconductance parameters ratio will also change. According to the figure above, transition is pushed lower as transconductance parameters ratio increases.