438 Practical MATLAB® Applications for Engineers
disp(‘using the final value theorem are verified returning: ‘)
V1 _ inf =limit(s*Vs(1),s,0)
V2 _ inf =limit(s*Vs(2),s,0)
disp(‘************************************’)
figure(1)
ezplot(Vs(1))
title(‘V1(s) vs s’)
xlabel(‘ complex frequency s ‘);ylabel(‘V1(s) ‘)
figure(2)
ezplot(Vs(2))
title(‘V2(s) vs s’);xlabel(‘complex frequency s’);
ylabel(‘V2(s) ‘)The script fi le nodal _eqs is executed and the results are as follows (Figures 4.83 and 4.84):
nodal _ eqs
***** RESULTS ****
The node voltages V1(s) and V2(s) are:
/ s \
(3 s + 4) s |8 ------ + 1/s|
| 2 |
(65 s + 96) s (2/s + 2) \ s + 9 /
V1(s) = 6 ---------------------------- + 90 ----------------------------
2 3 2 3
448 s + 286 s + 195 s + 72 448 s + 286 s + 195 s + 72
2 / s \
(7 s + 6 s + 4) s |8 ------ + 1/s|
| 2 |
(3 s + 4) s (2/s + 2) \ s + 9 /
V2(s) = 90 ---------------------------- + 90 -----------------------------------
2 3 2 3
448 s + 286 s + 195 s + 72 448 s + 286 s + 195 s + 72
The initial value voltages V1(t=0) and V2(t=0) (in volts)
using the initial value theorem are verified returning:
V1 0 = 4
V2 0 = 360/13
The final value voltages V1(t=inf) and V2(t=inf) (in volts)
using the final value theorem are verified returning:
V1 inf = 0
V2 inf = 0