21-S-Domain and General RLC Example 1 modified Lecture

21-S-Domain and General RLC Example 1 modified Lecture -...

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Unformatted text preview: General SOC Example & S-Domain Analysis © Fred Terry all, 2008 Fall, 2008 1 General RLC Example 1 • Find Governing Differential Eqn. • Find Natural Response • Find Forced Response otal soln=nat+forced i o (t) C R 2 L • Total soln=nat+forced • Find Initial (Boundary) Conditions R 1 • Match total solution to Initial Conditions 2 General RLC Example 1 • Find Diff Eqn • KCL/KVL Approach L i o (t) C R 2 R 1 3 i o (t) C R 2 L R 1 4 i o (t) C R 2 L R 1 5 Step Response Example • Find s 1 ,s 2 , damping type (nat response) • orced response i o (t) C R 2 L Forced response • B.C.’s R 1 5 5 1 5 ( ) 1 ( ) R K C F L H i t u t A Ω = Ω = = = 1 2 2. 5 5 1 5 ( ) 1 ( ) R R K C F L H i t u t A μ μ = Ω = Ω = = = 6 Initial Conditions & Forced Response i o (t) C R 2 L R 1 5 5 1 5 ( ) 1 ( ) R K C F L H i t u t A Ω = Ω = = = 1 2 2. 5 5 1 5 ( ) 1 ( ) R R K C F L H i t u t A μ μ = Ω = Ω = = = 7 Match Initial Conditions i o (t) C R 2 L R 1 5 5 1 5 ( ) 1 ( ) R K C F L H i t u t A Ω = Ω = = = 1 2 2. 5 5 1 5 ( ) 1 ( ) R R K C F L H i t u t A μ μ = Ω = Ω = = = 8 i o (t) C R 2 R 1 L 1 2 2.5 5 1 5 ( ) 1 ( ) R R K C F L H i t u t A μ μ = Ω = Ω = = = 9 10 Matlab Code for Plots % general RLC example clear all; 1=2 5; t=0:1e-2/a:8/a; iL=(b1*cos(wd*t)+b2*sin(wd*t)).*exp(-a*t)+iLf; R1=2.5; R2=5e3; C=1e-6; L=5e-6; vL=L*((-a*b1+b2*wd)*cos(wd*t)+(-a*b2- b1*wd)*sin(wd*t)).*exp(-a*t); vc=vL+R1*iL; ic=i0-vc/R2-iL; a=0.5*(R1/L+1/(C*R2)) w0=sqrt((1+R1/R2)/(L*C)) s1=-a+sqrt(a^2-w0^2) =- - rt(a^2- 0^2) subplot(2,1,1); h=plot(t,iL,t,ic); set(h,'linewidth',2); xlabel('time (s)'); s2 a sqrt(a 2 w0 2) wd=sqrt(w0^2-a^2) %set for underdamped response i0=1; %source ylabel('Current (A)'); legend('i_L','i_C'); grid on; subplot(2,1,2); iL0=0; %boundary condition iLf=R2/(R1+R2)*i0 b1=iL0-iLf c0=0; %boundary condition h=plot(t,vc,t,vL); set(h,'linewidth',2); xlabel('time(s)'); ylabel('Volts (V)'); 11 Vc0 0; %bou da y co d t o b2=((Vc0-iL0*R1)/L+a*b1)/wd legend('V_c','V_L'); grid on; Transient Circuit Analysis...
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This note was uploaded on 01/31/2011 for the course EECS 215 taught by Professor Phillips during the Spring '08 term at University of Michigan.

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21-S-Domain and General RLC Example 1 modified Lecture -...

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