Student199
New Member
Hi,
I am a postgraduate engineering student.My thesis surrounds VCOs. I am currently writing my thesis and came across the following maths problem. It intruiges me,and I am not sure if I am interperating it correctly.
The gain response of a two port resonator is usually that of a Band Pass Filter's response.
The phase of a resonator also has the phase response of Band Pass Filter's as well.
It is very common practice to differentiate the phase response of a resonator, to find the group delay,and from the group delay,the resonator's Q. Literature defines group delay as
GD=-dΦ/dω
Which simply is the change in resonator phase, with frequency.From the phase response of the resonator,it is clear that the phase slope is negative.Here however they deliberately add a negative in front of the derivative.
It is my understanding that they make the assumption that the phase response of the resonator can be linearized as
Φ=ωt
in the center of the phase response.Therefore, the GD has a unit of time.I understand that the negative is added in front of the derivative,to gain an answer in positive units of time. What bothers me however is that clearly from the phase response plot this gradient, and thus the answer in units of time, is in fact negative and not positive.
My ultimate question really is, does this then mean that in a two port resonator system such as this,the output signal arrives at the output before the input signal was ever even applied?Is this then in fact a non-causal system? And did the output signal then go back in time?
I am a postgraduate engineering student.My thesis surrounds VCOs. I am currently writing my thesis and came across the following maths problem. It intruiges me,and I am not sure if I am interperating it correctly.
The gain response of a two port resonator is usually that of a Band Pass Filter's response.
The phase of a resonator also has the phase response of Band Pass Filter's as well.
It is very common practice to differentiate the phase response of a resonator, to find the group delay,and from the group delay,the resonator's Q. Literature defines group delay as
GD=-dΦ/dω
Which simply is the change in resonator phase, with frequency.From the phase response of the resonator,it is clear that the phase slope is negative.Here however they deliberately add a negative in front of the derivative.
It is my understanding that they make the assumption that the phase response of the resonator can be linearized as
Φ=ωt
in the center of the phase response.Therefore, the GD has a unit of time.I understand that the negative is added in front of the derivative,to gain an answer in positive units of time. What bothers me however is that clearly from the phase response plot this gradient, and thus the answer in units of time, is in fact negative and not positive.
My ultimate question really is, does this then mean that in a two port resonator system such as this,the output signal arrives at the output before the input signal was ever even applied?Is this then in fact a non-causal system? And did the output signal then go back in time?
