Transfer Function Solving Process w/ Example - Revision history

Brett at 02:26, 2 July 2026

2026-07-02T02:26:43Z

← Older revision		Revision as of 19:26, 1 July 2026
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	Hout_Homo = subs(Hout, {R1,R2,C1,C2}, {R,R,C,C}) %Assuming R1=R2 and C1=C2.		Hout_Homo = subs(Hout, {R1,R2,C1,C2}, {R,R,C,C}) %Assuming R1=R2 and C1=C2.
	</syntaxhighlight>'''~~Final~~ Transfer function:'''		</syntaxhighlight>


			'''Transfer function:'''

	<math>H(s) = \frac{C_1 R_2 s}{C_1 C_2 R_1 R_2 s^2 + C_1 R_1 s + C_1 R_2 s + C_2 R_2 s + 1}</math>		<math>H(s) = \frac{C_1 R_2 s}{C_1 C_2 R_1 R_2 s^2 + C_1 R_1 s + C_1 R_2 s + C_2 R_2 s + 1}</math>

	'''~~Final~~ Homogeneous Transfer Function:'''
			'''Homogeneous Transfer Function:'''

	<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>		<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>

Brett at 21:41, 1 July 2026

2026-07-01T21:41:01Z

← Older revision		Revision as of 14:41, 1 July 2026
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	<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>		<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>

	~~{{Infobox core}}~~

Brett at 21:39, 1 July 2026

2026-07-01T21:39:52Z

← Older revision		Revision as of 14:39, 1 July 2026
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	<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>		<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>

			{{Infobox core}}

Brett at 02:31, 1 July 2026

2026-07-01T02:31:44Z

← Older revision		Revision as of 19:31, 30 June 2026
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	== Base KVL / KCL Equations: ==		== Base KVL / KCL Equations: ==
	[[File:~~ExampleCir~~.~~svg~~\|thumb]]		[[File:ExampleCircuitFixPNG.png\|thumb]]
	'''KVL Equations:'''		'''KVL Equations:'''

Brett at 02:23, 1 July 2026

2026-07-01T02:23:58Z

← Older revision		Revision as of 19:23, 30 June 2026
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	== Base KVL / KCL Equations: ==		== Base KVL / KCL Equations: ==
	[[File:~~ExampleCircuitFix~~.svg\|thumb]]		[[File:ExampleCir.svg\|thumb]]
	'''KVL Equations:'''		'''KVL Equations:'''

Brett: transfer function solving process

2026-07-01T02:12:05Z

transfer function solving process

New page

== Base KVL / KCL Equations: ==
[[File:ExampleCircuitFix.svg|thumb]]
'''KVL Equations:'''

# ''Vin - Vc1 - Ir1*R1 - Ir2*R2 = 0''
# ''-Vc2 + Ir2*R2 = 0''

'''KCL Equations:'''

# ''-Ir1 + Ic1 = 0''
# ''-Ir2 + Ic1 - Ic2 = 0''

'''Additional Equations:'''

# ''Ic1 = s*C1*Vc1''
# ''Ic2 = s*C2*Vc2''

== MATLAB Code for Computing Reduced Equation Set: ==
<syntaxhighlight lang="matlab" line="1">
syms Ir1 Ir2 Ic1 Ic2 Vc1 Vc2 Vin R1 R2 C1 C2 s

equs = [Vin - Vc1 - Ir1*R1 - Ir2*R2 == 0;
-Vc2 + Ir2*R2 == 0;
-Ir1 + Ic1 == 0;
-Ir2 + Ic1 - Ic2 == 0];

vars = [Vin Vc1 Vc2 Ir1 Ir2 Ic1 Ic2];

[A, b] = equationsToMatrix(equs, vars);

equ1 = A(1,:)*vars.' == b(1,:); %equ1 = Vin - Vc1 - Ir1*R1 - Ir2*R2 == 0;
equ2 = A(2,:)*vars.' == b(2,:); %equ2 = - Vc2 + Ir2*R2 == 0;
equ3 = A(3,:)*vars.' == b(3,:); %equ3 = - Ir1 + Ic1 == 0;
equ4 = A(4,:)*vars.' == b(4,:); %equ4 = - Ir2 + Ic1 - Ic2 == 0;

equ5 = Ic1 == s*C1*Vc1;
equ6 = Ic2 == s*C2*Vc2;
</syntaxhighlight>

== MATLAB Code for Computing the Transfer Function: ==
<syntaxhighlight lang="matlab" line="1">
sol = solve([equ1,equ2,equ3,equ4,equ5,equ6], [Ir1,Ir2,Ic1,Ic2,Vc1,Vc2])

Hout = simplify(sol.Vc2/Vin)

syms R C

Hout_Homo = subs(Hout, {R1,R2,C1,C2}, {R,R,C,C}) %Assuming R1=R2 and C1=C2.
</syntaxhighlight>'''Final Transfer function:'''

<math>H(s) = \frac{C_1 R_2 s}{C_1 C_2 R_1 R_2 s^2 + C_1 R_1 s + C_1 R_2 s + C_2 R_2 s + 1}</math>

'''Final Homogeneous Transfer Function:'''

<math>H_h_o_m_o(s) = \frac{C R s}{C^2 R^2 s^2 + 3 C R s + 1}</math>