- #1

Gwozdzilla

- 81

- 0

## Homework Statement

Determine the center frequency and bandwidth of the bandpass filter.

## Homework Equations

center frequency of bandpass filter = ω

_{c}occurs when the magnitude of H = 1

H = V

_{0}/V

_{s}

Center frequency occurs when Im(Z) = 0

Z

_{c}= 1/(jωC) = 1/s

Z

_{L}= jωL

Z

_{R}= R

I don't know a formula for finding bandwidth.

## The Attempt at a Solution

Z

_{series}= 1 + 1/s

Z

_{ll}= ((1/s)(1 + 1/s))/(2/s + 1)

Z

_{eq}= 1 + Z

_{ll}

Simplifying gives...

Z

_{eq}= (1 + 3s + s

^{2})/(2s + s

^{2})

V

_{s}= IZ

_{eq}

V

_{ll}= IZ

_{ll}

V

_{0}= I

_{2}(1Ω)

V

_{series}= I

_{2}Z

_{series}= V

_{ll}

V

_{0}Z

_{series}= V

_{ll}= IZ

_{ll}

V

_{0}Z

_{series}= (V

_{s}Z

_{ll})/Z

_{eq}

V

_{0}/V

_{series}= Z

_{ll}/(Z

_{eq}Z

_{series})

Plugging in values from above and simplifying gives...

V

_{0}/V

_{series}= s/(s + 3s + 1) = H

s

^{2}= -ω

^{2}

How do I find the magnitude of H? What is a bandwidth?