benbingham

Greetings, I'm struggling with a signal analysis electrical engineering college assignment. We need to a derive differential equation for a low-pass filter, high-pass filter and a band pass filter (made by connecting the output of a low pass filter to the input of a high pass filter). Here are diagrams for reference: Low pass filter: High pass filter: Band pass filter (buffer can be removed): The equations I derived are: - low pass filter: Vo=Vi-RC(dVi/dt) - high pass filter: Vo=RC(dVi/dt) - band pass filter: Vo=R2C2((1-C1-R1)-R1C1(d^2Vi/dt^2)) The equation for the band pass filter I found by making the input of the high pass filter the output of the low pass filter. So I derived the equation of the low pass filter with respect to time and got dVo/dt = dVi/dt - R1*dVi/dt - C1*dVi/dt - R1C1*(d^Vi/dt^2). I substituted in this rate of change of voltage into the equation of the high pass filter to get the equation I derived for the band pass filter. Could anyone please tell me if what I have done is valid and if not, please explain to me what the correct strategy is. Thank you kindly.