Question

Determine the center frequency and bandwidth of the bandpass filters

Answer 1

2. Relevant equations center frequency of bandpass filter = ωc occurs when the magnitude of H = 1 H = V0/Vs Center frequency occurs when Im(Z) = 0 Zc = 1/(jωC) = 1/s ZL = jωL ZR = R I don't know a formula for finding bandwidth. 3. The attempt at a solution Zseries = 1 + 1/s Zll = ((1/s)(1 + 1/s))/(2/s + 1) Zeq = 1 + Zll Simplifying gives... Zeq = (1 + 3s + s2)/(2s + s2) Vs = IZeq Vll = IZll V0 = I2(1Ω) Vseries = I2Zseries = Vll V0Zseries = Vll = IZll V0Zseries = (VsZll)/Zeq V0/Vseries = Zll/(ZeqZseries) Plugging in values from above and simplifying gives... V0/Vseries = s/(s + 3s + 1) = H s2 = -ω2 How do I find the magnitude of H? What is a bandwidth? Attachments

Reference https://www.physicsforums.com/threads/center-frequency-and-bandwith-of-bandpass-filter.813960/