Friday, 28 June 2019

voltage - Are cutoff frequencies of bandpass and bandstop filters equal?


Consider the two filter in picture


schematic


simulate this circuit – Schematic created using CircuitLab



Are the cutoff frequencies (i.e. the two frequencies at which $V_{out}=\frac{1}{\sqrt{2}} V_{in}$) the same for the two filters? (And therefore also the bandwidth is the same for the two filters?)




I think they should be the same since in both cases the condition $V_{out}=\frac{1}{\sqrt{2}} V_{in}$ reduces to


R2=(ωL1ωC)2


Nevetheless it is strange that there is a frequency for which both $V_{out}$s taken at resistor and at LC series have the same value $\frac{1}{\sqrt{2}} V_{in}$.


Doesn't this violates Kirckoff voltage law? (At any time it should be $V_{in}=V_{R}+V_{LC\ series}$ but if $V_{R}=V_{LC\ series}=\frac{1}{\sqrt{2}} V_{in}$ then this is not true).


enter image description here




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