I have tried to solve, but do not know if the answer is correct or not.
A person has a periodic voltage input to a circuit. The input repeats itself every 0.02 seconds i.e. the fundamental period is 0.02 seconds. The person measures the input with a voltmeter and finds that the input may be approximated by:
Vin(t) = V0*exp(a*t) ; 0 sec <= t < 0.02 sec ; V0= 2 Volts a = -100sec^-1
Graphically the function may be represented by:
B)Evaluate the integral analytically for the DC-term (often referred to as c0 ). Looking at the graph, how can you check if your answer is reasonable?
I know I need to use these formulas:
I've tried to calculate a0 and here I got approx 2, according to this matlab code:
v0 = 2; a = (-100^-1) T = 0.02 a_0 = (1/T)*int((v0*exp(a*t)),t,0,T)
a0 calculated to
I stuck with the an and bn, because i'm not sure if that is correct or not...
an = ((2/T)*int((v0*exp(a*t))*cos(n*w0*t),t,0,T))
an calculated to
(20000*exp(-1/5000)*(exp(1/5000) - 1))/(100000000*pi^2 + 1)
bn = (2/T)*int((v0*exp(a*t))*sin(n*w0*t),t,0,T)
bn calculated to
(200000000*pi*exp(-1/5000)*(exp(1/5000) - 1))/(100000000*pi^2 + 1)