- #1
ChasW.
Gold Member
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This is my first post here. I hope I have found the correct place to do it. This is not actual coursework, but as it is this type of work, I am posting here per the guidelines.
I am trying to solve for angular frequency for a given output voltage, so I am seeking to get ω on its own.
This problem applies to a series R to parallel LC circuit.
The formula in bold at the end of this post is what I am trying to solve for ω.
1) Vo = Xtotal / ((Rs + Xtotal)(Vi)) see below
2) Xtotal = jωL / (1 - ω2LC) see below
3) Vo/Vi = jωL / ((Rs - ω2RsLC) + jωL)
where,
Vo = voltage out
Vi = voltage in
ω = angular frequency
Rs = series resistance
L = inductance
C = capacitance
Formula #3 in its above form can be used for plotting band pass filter response for various frequencies of interest.
So what I am seeking to do is identify frequencies for voltage output levels of interest.
For example if the voltage input was 5V and I wanted the frequencies for the -3dB point, I would input for Vo 5V x 1/(√2) or 3.5355. Proof: 20log10(3.5355/5) ≈ -3.0103
The above formula #3 is derived from #1:
Vo = Xtotal / ((Rs + Xtotal)(Vi))
where,
Xtotal is the total inductor capacitor reactance
Vo is output voltage
Vi is input voltage
where,
Xtotal = XcXL / Xc + XL
where,
XC = 1/jωC
XL = jωL
Xtotal becomes formula #2
= jωL / (1 - ω2LC)
Assuming Vo < Vi, I believe there are going to be 2 solutions for ω which would make sense given that for example, there are 2 -3dB points for a given center frequency of this circuit type.
How do I solve for or begin to solve for ω when
Xtotal = jωL / (1 - ω2LC) ?
A strong nudge in the right direction is most welcome.
Charles
Homework Statement
I am trying to solve for angular frequency for a given output voltage, so I am seeking to get ω on its own.
This problem applies to a series R to parallel LC circuit.
The formula in bold at the end of this post is what I am trying to solve for ω.
Homework Equations
1) Vo = Xtotal / ((Rs + Xtotal)(Vi)) see below
2) Xtotal = jωL / (1 - ω2LC) see below
3) Vo/Vi = jωL / ((Rs - ω2RsLC) + jωL)
where,
Vo = voltage out
Vi = voltage in
ω = angular frequency
Rs = series resistance
L = inductance
C = capacitance
Formula #3 in its above form can be used for plotting band pass filter response for various frequencies of interest.
So what I am seeking to do is identify frequencies for voltage output levels of interest.
For example if the voltage input was 5V and I wanted the frequencies for the -3dB point, I would input for Vo 5V x 1/(√2) or 3.5355. Proof: 20log10(3.5355/5) ≈ -3.0103
The Attempt at a Solution
The above formula #3 is derived from #1:
Vo = Xtotal / ((Rs + Xtotal)(Vi))
where,
Xtotal is the total inductor capacitor reactance
Vo is output voltage
Vi is input voltage
where,
Xtotal = XcXL / Xc + XL
where,
XC = 1/jωC
XL = jωL
Xtotal becomes formula #2
= jωL / (1 - ω2LC)
Assuming Vo < Vi, I believe there are going to be 2 solutions for ω which would make sense given that for example, there are 2 -3dB points for a given center frequency of this circuit type.
How do I solve for or begin to solve for ω when
Xtotal = jωL / (1 - ω2LC) ?
A strong nudge in the right direction is most welcome.
Charles