Question

The input to a certain filter is given by vin(t)=2cos(104πt−25∘) and the steady-state output is given by vout(t)=6cos(104πt+20∘). Part A Determine the (complex) value of the transfer function of the filter for f = 5000 Hz. Enter your answer to three significant figures using polar notation. Express argument in degrees.

Answer 1

`H(5000) = 3 \angle45\°`

Step-by-step explanation:

Easy, we know that

`v_(in)(t)= 2cos(104\pi t -25\°)\\v_(out)(t)= 6cos(10 \pi t +20\°)`

Transforming to polar:

`V_(in) = 2 \angle -25\° V\\V_(out) = 6 \angle 20\°V`

For
`f=5000Hz`

`H(5000) = (V_(out))/(V_(in))`

`H(5000) = (6 \angle 20\°V)/(2 \angle -25\° V)`

`H(5000) = 3 \angle45\°`