1. MTE2 Review 2nd Order Transient Ckt
Engineering 43
MTE2 Review 2nd Order Transient Ckt
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer

2. The Problem Find for the Circuit Below vC(t) io(t) + vC(t) − io(t)
110 Ω
33 μF
300 mH
125 mA
8 V
180 Ω
t = 0
+ vC(t) −
io(t)

14. MATLAB Code - 1 % Bruce Mayer, PE % ENGR43 * MTE2 Review Problem
% File = E43_MTE2_2ndOrder_Vc_ m %
% Component Values
R1 = 110
R2 = 180
L = 300e-3
C = 33e-6
% Calulate the Roots of the Characteristic Equation by Quadratic Formula
% * Yields the Time Constants for Exponential Decay of OverDamped Ckt
Splus = (-(R1+R2)*C + sqrt(((R1+R2)*C)^2 - 4*L*C))/(2*L*C)% in Rads/sec
Sminus = (-(R1+R2)*C - sqrt(((R1+R2)*C)^2 - 4*L*C))/(2*L*C)% in Rads/sec
tauPlus = 1000/Splus % in mS
tauMinus = 1000/Sminus % in mS
% use Ax = b to solve for K1 & K2
A = [1 1; ] % unitless coefficients
b = [-8; 0]; % units are volts
K = A\b % in
K1 = K(1)
K2 = K(2)
% Define function for the total solution
vtot K1*exp(y/tauMinus) + K2*exp(y/tauPlus)
t = linspace(0, 60, 500); % in mS
vc = vtot(t);
% graph Solution
plot(t,vc), grid, xlabel('time (ms)'), ylabel('vc (V)')
disp('Showing FULL-time plot. Hit AnyKey to show the 2nd-Order IC CHECK-Plot')
disp(' ‘)

15. MATLAB Code - 2 pause % % make the [dvc/dt](0+) =0 check plot
tdv = linspace(0, 0.5); % in mS
dvcdt = vtot(tdv);
plot(tdv,dvcdt), grid, xlabel('time (ms)'), ylabel('vc (V)')
disp('Showing SHORT-time plot. Hit AnyKey to show the FULL-TIME io(t) Plot')
disp(' ')
% the solution for io(t)
Kio = 36.61; % in mA
io Kio*(exp(Splus*t) - exp(Sminus*t));
tio = linspace(0, 0.04, 1000); % in SECONDS
ioplot = io(tio);
plot(tio*1000, ioplot), xlabel('time (mS)'), ylabel('io (mA)'), title('MTE2 2nd-Order Problem Exam Review'), grid
% Find ioMax and tioMax using MAX command
[ioMax,ItioMax] = max(ioplot);
disp('Maximum value for io in mA = ')
disp(ioMax)
tioMax = tio(ItioMax);
disp('TIME for Maximum value for io in mS = ')
disp(1000*tioMax)
disp('Showing FULL-time plot. Hit AnyKey to show the Short-TIME io(t) Plot')
tio = linspace(0, 0.008, 1000); % in SECONDS
plot(tio*1000, ioplot, 1000*tioMax, ioMax, 'h'), xlabel('time (mS)'), ylabel('io (mA)'), title('MTE2 2nd-Order Problem Exam Review'), grid

16. vC(t) MATLAB Plot

17. CHK: dvC(t)/dt|t=0+ = 0
Slope at t=0 looks FLAT; thus 1st Order IC is CONFIRMED

18. io(t) MATLAB Plot
Note io,max at about 3 mS

19. io,max(2.683 mS) = mA