# Symbolsk løsning av nodeligninger med Matlab

### Using Kirchoff's current law (KCL) on a source follower configuration to find Vout as a function of Vin

```% Using Kirchoff's current law (KCL) on a source follower configuration
% to find Vo as a function of Vin
% Only Cgd is considered (Zc)
% Kjetil Ullaland

syms s C Vin Vo Vgs Zc gm Rl Rs R Av Avo

eq1=(Vo-Vgs)/(R+Zc)+gm*Vgs+Vo/Rl == 0;
eq2=(Vgs-Vo)/(R+Zc)+(Vgs-Vin)/Rs == 0;
eq1=subs(eq1,Zc,1/(s*C));
eq2=subs(eq2,Zc,1/(s*C));
disp('KCL for circuit node 1:');
pretty(eq1);
disp('KCL for circuit node 2:');
pretty(eq2);

disp('Solve for Vo and Vin and calculate Av (Vo/Vin):');
solved=solve(eq1,eq2,Vo,Vin);
Av=solved.Vo/solved.Vin;
pretty(simplify(Av));

pretty(subs(Av,Rl*gm,Avo));
```

### Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18 to find Vo as a function of Is

```% Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18
% to find Vo as a function of Is
% Kjetil Ullaland, 2015

syms Vo V1 s gm R1 R2 C C1 C2 Is Zc Rz;

%% With feedforward capacitor
eq1=sym('(Vo-V1)/Zc+gm*V1+Vo/R2+Vo*s*C2=0');
eq2=sym('(V1-Vo)/Zc+V1*s*C1+V1/R1+Is=0');
eq1=subs(eq1,Zc,'1/(s*C)');
eq2=subs(eq2,Zc,'1/(s*C)');

solV1=solve(eq2,V1);
eq3=subs(eq1,V1,solV1);
SolVo=simplify(solve(eq3,[Vo]));
disp('With capacitor only in feedforward loop');
pretty(simplify(SolVo/Is));

%% With series resistor and capacitor in feedforward loop
eq1=sym('(Vo-V1)/(Zc+Rz)+gm*V1+Vo/R2+Vo*s*C2=0');
eq2=sym('(V1-Vo)/(Zc+Rz)+V1*s*C1+V1/R1+Is=0');
eq1=subs(eq1,Zc,'1/(s*C)');
eq2=subs(eq2,Zc,'1/(s*C)');

solV1=solve(eq2,V1);
eq3=simplify(subs(eq1,V1,solV1));
SolVo=solve(eq3,[Vo]);
disp('With series resistor and capacitor in feedforward loop');
pretty(simplify(SolVo/Is));
```