Hi!
I'm trying to derive the argument of H(jw) for hi and lo pass filters.
So far I've gotten the following:
for low pass:
From the voltage dividor I've gotten: H(jw) = 1/ (1 + j(w/w_c)) (w_c = ang. cutoff freq.)
Then I found the angle by converting it to polar form and I get:
arg H(jw) = arctan (w / w_c)
But to my knowledge, it should be H(jw) = - arctan(w/w_c). Where is this minus coming from?
Same thing with hi pass. Following the same procedure as above, starting with H(jw) = 1 / (1-j( w_c / w ) ), I get:
arg H(jw) = arctan (w_c / w)
I also know I "should" be getting H(jw) 90 - arctan (w_c / w).
I can see this by recognizing how the filters work and how the output voltage lags the input voltage. But I don't see how this happens mathematically?
Any help would be much appreciated!
I'm trying to derive the argument of H(jw) for hi and lo pass filters.
So far I've gotten the following:
for low pass:
From the voltage dividor I've gotten: H(jw) = 1/ (1 + j(w/w_c)) (w_c = ang. cutoff freq.)
Then I found the angle by converting it to polar form and I get:
arg H(jw) = arctan (w / w_c)
But to my knowledge, it should be H(jw) = - arctan(w/w_c). Where is this minus coming from?
Same thing with hi pass. Following the same procedure as above, starting with H(jw) = 1 / (1-j( w_c / w ) ), I get:
arg H(jw) = arctan (w_c / w)
I also know I "should" be getting H(jw) 90 - arctan (w_c / w).
I can see this by recognizing how the filters work and how the output voltage lags the input voltage. But I don't see how this happens mathematically?
Any help would be much appreciated!