Circuit Analysis Resistors, Capacitors, Voltage sources

Impedance A way to introduce circuit elements with complex numbers. Z R = R Z c = 1/(j*ω*C) = 1/(j*2*pi*f*C)

Voltage source Function V s can be expressed by a Fourier series V s_n = c n *e i*2pi*n*t/T /(i*pi*n)

Fourier series for periodic source

Fourier series cont’d c o =1/2 c n =1/(i*pi*n) if n odd, 0 if n even V s = Σ n c n e i*2*pi*n*t/T

Output Voltage In general, V o = V s /(1+R/Z c ) V o = V s /(1+j*2*pi*f*C*R) We need to use this formula but in a Fourier series. V o_n = V s_n /(1+j*2*pi*(n/T)*C*R) V o_n = c n e i*2*pi*n*t/T /(1+j*2*pi*(n/T)*C*R) V o = Σ n V o_n