Finding the Phase Angle & Understanding Bandstop Filters

[lucy_b14]

Hi

Does anyone know the equation for the phase angle by which v0 leads v1 in a bandstop (parallel resonant) circuit?

also, can anyone tell me how (in terms of the equation for the transfer function) a bandstop filter works?

Thanks a lot, any help appreciated.

 

[Ouabache]

For your first question, it is not clear what circuit elements you are using and also what you are labelling v0 and v1. Please attach a diagram.

Before I elaborate on your second question (which is easy actually), can you tell me what does a bandstop filter do? If you had a BODE plot (frequency versus gain) of this filter, describe the plot (you may attach a drawing).

 

[ravenprp]

Hi there,

To find the phase angle between v0 and v1 in a bandstop circuit, you can use the following equation:

Φ = tan^-1(2ζω/ω0 - ω^2/ω0^2)

where ζ is the damping factor, ω is the angular frequency, and ω0 is the resonant frequency.

As for understanding how a bandstop filter works in terms of the transfer function, it can be represented by the following equation:

H(s) = (s^2 + ω0^2) / (s^2 + ω0^2 + ω0/Qs)

where s is the Laplace variable, ω0 is the resonant frequency, and Q is the quality factor. This transfer function shows that at the resonant frequency, the output voltage will be attenuated due to the presence of the pole at s = jω0/Q. This means that the filter will block or attenuate signals at the resonant frequency, hence the name "bandstop" filter.

I hope this helps! Let me know if you have any other questions.