Symbolsk løsning av nodeligninger med Matlab - Revision history

Nfyku: Added calculation for all capacitors

2020-09-23T11:39:47Z

Added calculation for all capacitors

← Older revision		Revision as of 11:39, 23 September 2020
Line 3:		Line 3:
	% Using Kirchoff's current law (KCL) on a source follower configuration		% Using Kirchoff's current law (KCL) on a source follower configuration
	% to find Vo as a function of Vin		% to find Vo as a function of Vin
	~~% Only Cgd is considered (Zc)~~		% Kjetil Ullaland, 2020
	% Kjetil Ullaland

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

			%%
			disp('Only Cgd with series resistor is considered (Zc)')

	eq1=(Vo-Vgs)/(R+Zc)+gm*Vgs+Vo/Rl == 0;		eq1=(Vo-Vgs)/(R+Zc)+gm*Vgs+Vo/Rl == 0;
	eq2=(Vgs-Vo)/(R+Zc)+(Vgs-Vin)/Rs == 0;		eq2=(Vgs-Vo)/(R+Zc)+(Vgs-Vin)/Rs == 0;
	eq1=subs(eq1,Zc,1/(s*C));		eq1=subs(eq1,Zc,1/(s*Cdg));
	eq2=subs(eq2,Zc,1/(s*C));		eq2=subs(eq2,Zc,1/(s*Cdg));
			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));
			%%
			disp('All MOST capasitors are considered')

			syms s Cdg Cgs Cds Vin Vo Vgs gm Rl Rs Av Avo

			eq1=(Vo-Vgs)sCdg + gmVgs + Vo/Rl + Vos*Cds == 0;
			eq2=(Vgs-Vin)/Rs + VgssCgs + (Vgs-Vo)sCdg == 0;
	disp('KCL for circuit node 1:');		disp('KCL for circuit node 1:');
	pretty(eq1);		pretty(eq1);

Nfyku at 11:13, 23 September 2020

2020-09-23T11:13:48Z

← Older revision		Revision as of 11:13, 23 September 2020
Line 29:		Line 29:
	% Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18		% Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18
	% to find Vo as a function of Is		% to find Vo as a function of Is
	% Kjetil Ullaland, ~~2015~~		% Kjetil Ullaland, 2020

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

	%% With feedforward capacitor		%% With feedforward capacitor
	eq1=~~sym('~~(Vo-V1)/Zc+gmV1+Vo/R2+Vos*C2=0');		eq1=(Vo-V1)/Zc+gmV1+Vo/R2+Vos*C2==0;
	eq2=~~sym('~~(V1-Vo)/Zc+V1sC1+V1/R1+Is=0');		eq2=(V1-Vo)/Zc+V1sC1+V1/R1+Is==0;
	eq1=subs(eq1,Zc,'1/(s*C)');		eq1=subs(eq1,Zc,1/(s*C));
	eq2=subs(eq2,Zc,'1/(s*C)');		eq2=subs(eq2,Zc,1/(s*C));

	~~solV1=solve~~(~~eq2,~~V1);		disp('Solve for Vo and V1 and calculate Vo/Is with capacitor only in feedforward loop');
	~~eq3~~=~~subs~~(eq1,V1,~~solV1~~);		solved=solve(eq1,eq2,Vo,Is);
	~~SolVo~~=~~simplify(solve(eq3,[~~Vo~~]));~~		VoOnIs=solved.Vo/solved.Is;
	~~disp('With capacitor only in feedforward loop')~~;		pretty(simplify(VoOnIs));
	pretty(simplify(~~SolVo/Is~~));

	%% With series resistor and capacitor in feedforward loop		%% With series resistor and capacitor in feedforward loop
	eq1=~~sym('~~(Vo-V1)/(Zc+Rz)+gmV1+Vo/R2+Vos*C2=0');		eq1=(Vo-V1)/(Zc+Rz)+gmV1+Vo/R2+Vos*C2==0;
	eq2=~~sym('~~(V1-Vo)/(Zc+Rz)+V1sC1+V1/R1+Is=0');		eq2=(V1-Vo)/(Zc+Rz)+V1sC1+V1/R1+Is==0;
	eq1=subs(eq1,Zc,'1/(s*C)');		eq1=subs(eq1,Zc,1/(s*C));
	eq2=subs(eq2,Zc,'1/(s*C)');		eq2=subs(eq2,Zc,1/(s*C));

	~~solV1=solve~~(~~eq2,~~V1);		disp('Solve for Vo and V1 and calculate Vo/Is with resistor and capacitor in feedforward loop');
	~~eq3~~=~~simplify(subs~~(eq1,V1,~~solV1)~~);		solved=solve(eq1,eq2,Vo,Is);
	~~SolVo~~=~~solve(eq3,[~~Vo~~]);~~		VoOnIs=solved.Vo/solved.Is;
	~~disp('With series resistor and capacitor in feedforward loop')~~;		pretty(simplify(VoOnIs));
	pretty(simplify(~~SolVo/Is~~));
	</pre>		</pre>

Nfyku: Updated for newer Matalb versions (tested on R2020b)

2020-09-23T11:02:34Z

Updated for newer Matalb versions (tested on R2020b)

← Older revision		Revision as of 11:02, 23 September 2020
Line 6:		Line 6:
	% Kjetil Ullaland		% Kjetil Ullaland

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

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

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

	~~disp('Solve for Vo~~(~~vin)');~~		pretty(subs(Av,Rl*gm,Avo));
	~~eq3=~~subs(~~eq1~~,~~Vgs~~,~~vgs_solved~~);
	~~Vo_solved=solve(eq3,Vo~~);
	~~pretty(simplify(Vo_solved/Vin))~~
	</pre>		</pre>

Nfyku at 08:46, 13 September 2016

2016-09-13T08:46:07Z

← Older revision		Revision as of 08:46, 13 September 2016
Line 2:		Line 2:
	<pre>		<pre>
	% Using Kirchoff's current law (KCL) on a source follower configuration		% Using Kirchoff's current law (KCL) on a source follower configuration
	% to find ~~Vout~~ as a function of Vin		% to find Vo as a function of Vin
	% Only Cgd is considered (Zc)		% Only Cgd is considered (Zc)
	% Kjetil Ullaland		% Kjetil Ullaland

	~~ligning1='(Vout-~~Vgs)/Zc+gm*Vgs+Vout/Rl~~=0';~~		syms s Vin Vo Vgs Zc gm Rl Rs R
	~~ligning2='(Vgs-Vout)/Zc+(Vgs-Vin)/~~Rs~~=0';~~
	~~ligning1=subs(ligning1,'1/(jwC)','Zc');~~
	~~ligning2=subs(ligning2,'1/(jwC)','Zc');~~
	~~pretty(ligning1);~~
	~~pretty(ligning2);~~

			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 doc prettynode 2:');
			pretty(eq2);

	disp('Solve for Vgs');		disp('Solve for Vgs');
	vgs_solved=solve(~~ligning2~~,'Vgs');		vgs_solved=solve(eq2,Vgs);
	pretty(simplify(vgs_solved));		pretty(simplify(vgs_solved));

	disp('Solve for ~~Vout~~(vin)');		disp('Solve for Vo(vin)');
	~~ligning3~~=subs(~~ligning1~~,vgs_solved~~,'Vgs'~~);		eq3=subs(eq1,Vgs,vgs_solved);
	~~Vout_solved~~=solve(~~ligning3~~,~~'Vout'~~);		Vo_solved=solve(eq3,Vo);
	pretty(simplify(~~Vout_solved~~))		pretty(simplify(Vo_solved/Vin))
	</pre>		</pre>

Nfyku at 07:58, 9 October 2015

2015-10-09T07:58:46Z

← Older revision		Revision as of 07:58, 9 October 2015
Line 1:		Line 1:
			=== Using Kirchoff's current law (KCL) on a source follower configuration to find Vout as a function of Vin ===
	<pre>		<pre>
	% Using Kirchoff's current law (KCL) on a source follower configuration		% Using Kirchoff's current law (KCL) on a source follower configuration
Line 23:		Line 24:
	</pre>		</pre>

			=== Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18 to find Vo as a function of Is ===
	<pre>		<pre>
	% Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18		% Using Kirchoff's current law (KCL) on single transistor stage, fig. 9.18
Line 29:		Line 31:

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

			%% With feedforward capacitor
			eq1=sym('(Vo-V1)/Zc+gmV1+Vo/R2+Vos*C2=0');
			eq2=sym('(V1-Vo)/Zc+V1sC1+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)+gmV1+Vo/R2+Vos*C2=0');		eq1=sym('(Vo-V1)/(Zc+Rz)+gmV1+Vo/R2+Vos*C2=0');
	eq2=sym('(V1-Vo)/(Zc+Rz)+V1sC1+V1/R1+Is=0');		eq2=sym('(V1-Vo)/(Zc+Rz)+V1sC1+V1/R1+Is=0');
Line 36:		Line 52:
	solV1=solve(eq2,V1);		solV1=solve(eq2,V1);
	eq3=simplify(subs(eq1,V1,solV1));		eq3=simplify(subs(eq1,V1,solV1));
	SolVo=~~simplify(~~solve(eq3,[Vo]));		SolVo=solve(eq3,[Vo]);
			disp('With series resistor and capacitor in feedforward loop');
	pretty(simplify(SolVo/Is));		pretty(simplify(SolVo/Is));
	</pre>		</pre>

Nfyku: Nfyku moved page Nodeligninger for en source-følger to Symbolsk løsning av nodeligninger med Matlab without leaving a redirect

2015-10-09T07:37:02Z

Nfyku moved page Nodeligninger for en source-følger to Symbolsk løsning av nodeligninger med Matlab without leaving a redirect

← Older revision	Revision as of 07:37, 9 October 2015
(No difference)

Nfyku: Added single transistor stage, fig. 9.18

2015-10-09T07:32:47Z

Added single transistor stage, fig. 9.18

@@ Line 21: / Line 21: @@
 Vout_solved=solve(ligning3,'Vout');
 pretty(simplify(Vout_solved))
 </pre>

Nfyku at 08:17, 9 September 2014

2014-09-09T08:17:03Z

← Older revision		Revision as of 08:17, 9 September 2014
Line 2:		Line 2:
	% Using Kirchoff's current law (KCL) on a source follower configuration		% Using Kirchoff's current law (KCL) on a source follower configuration
	% to find Vout as a function of Vin		% to find Vout as a function of Vin
			% Only Cgd is considered (Zc)
	% Kjetil Ullaland		% Kjetil Ullaland

Nfyku at 08:13, 9 September 2014

2014-09-09T08:13:57Z

← Older revision		Revision as of 08:13, 9 September 2014
Line 2:		Line 2:
	% Using Kirchoff's current law (KCL) on a source follower configuration		% Using Kirchoff's current law (KCL) on a source follower configuration
	% to find Vout as a function of Vin		% to find Vout as a function of Vin
	% Kjetil Ullaland~~, 10. september 1996~~		% Kjetil Ullaland

	ligning1='(Vout-Vgs)/Zc+gm*Vgs+Vout/Rl=0';		ligning1='(Vout-Vgs)/Zc+gm*Vgs+Vout/Rl=0';
Line 12:		Line 12:


	~~Vgs_solved~~=~~simplify(~~solve(ligning2,'Vgs'))		disp('Solve for Vgs');
	~~pretty~~(~~Vgs_solved~~)		vgs_solved=solve(ligning2,'Vgs');
	ligning3=subs(ligning1,~~Vgs_solved~~,'Vgs');		pretty(simplify(vgs_solved));
	Vout_solved=~~simplify(~~solve(ligning3,'Vout'))
	pretty(Vout_solved)		disp('Solve for Vout(vin)');
			ligning3=subs(ligning1,vgs_solved,'Vgs');
			Vout_solved=solve(ligning3,'Vout');
			pretty(simplify(Vout_solved))
	</pre>		</pre>

Nfyku at 09:52, 22 September 2009

2009-09-22T09:52:55Z

← Older revision		Revision as of 09:52, 22 September 2009
Line 1:		Line 1:
			<pre>
	% Using Kirchoff's current law (KCL) on a source follower configuration		% Using Kirchoff's current law (KCL) on a source follower configuration
	% to find Vout as a function of Vin		% to find Vout as a function of Vin
Line 16:		Line 17:
	Vout_solved=simplify(solve(ligning3,'Vout'))		Vout_solved=simplify(solve(ligning3,'Vout'))
	pretty(Vout_solved)		pretty(Vout_solved)
			</pre>