Find the cut-off frequency of this filter:
My attempt:
H (ω)=R1+jωLR1+R2+jωL=R1+jωLR1+R2+jωL⋅R1+R2−jωLR1+R2−jωL= R21+R1R2+(ωL)2+jωLR2(R1+R2)2+(ωL)2
So when you're looking for the cut-off frequency you can say:
ℜ(H (ω))=ℑ(H (ω))
So we get:
R21+R1R2+(ωL)2=ωLR2⟺ (ωL)2−ωLR2+R21+R1R2=0⟺ ω2L2−ωLR2+R21+R1R2=0⟺ ω=LR2±√(−LR2)2−4⋅L2⋅(R21+R1R2)2⋅L2⟺ ω=LR2±√(LR2)2−4⋅L2⋅(R21+R1R2)2⋅L2
Am I doing something wrong?
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