The Fourier series expansion of a sawtooth wave with a peak-to-peak amplitude of 5V and a frequency of 100 kHz can be represented as:
f(t)=52−5π∑n=1∞1nsin(2πnft)f(t) = frac{5}{2} - frac{5}{pi}sum_{n=1}^{infty}frac{1}{n}sin(2pi n f t)f(t)=25−π5∑n=1∞n1sin(2πnft)
To determine the first four terms of this Fourier series expansion, we need to calculate the coefficients for n = 1, 2, 3, and 4. The coefficient for each term is given by:
an=2T∫0Tf(t)sin(2πnft)dta_n = frac{2}{T}int_{0}^{T}f(t)sin(2pi n f t)dtan=T2∫0Tf(t)sin(2πnft)dt
where T is the period of the sawtooth wave, which is given by T=1fT = frac{1}{f}T=f1</span