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Can anyone help me approach this quesiton? I have to derive an expression for the frequency response. How do i start this question?
Can anyone help with frequency response?
- Thread starter thisonedude
- Start date
Am i heading in the right direction? How do i get the Qaulity factor and the gain?
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You made an error.
Think of the circuit as a voltage divider. So you have one resistor: R+Rs+jwL. Second resistor is -j/(wC). You want the voltage across the second resistor. What is the voltage divider equation looks like?
Oh am i missing (-j/ωC) on the bottom summation?
Yes, you do.
Alright after adding that, what is K? It says it is the DC gain where K = H(j0). If this is true then my H(jw) = 0 from the derivation i just made. Is this correct?
Ohhh disregard that last one please, it's the MAGNITUDE! I see now. which should be 1/sqrt(1+(W/W0)^2) if i'm not wrong.
Hi,
It is more clear to write it out in terms of the variable 's' where s=jw. This makes the two complex impedances:
sL and 1/sC in shorthand notation which means s*L and 1/(s*C).
Also, for a voltage divider it is always the impedance of the lower element divided by the sum of all the element impedances.
So we would end up with:
1. The lower element: 1/sC
2. The sum: Rx+sL+1/sC
3. The division: (1/sC)/(Rx+sL+1/sC)
Note Rx=R+Rs where R and Rs are the original two resistors.
Now all that is left to do is to simplify #3 and then rearrange it into the required form to make it easier to extract the required quantities like Q.
It is more clear to write it out in terms of the variable 's' where s=jw. This makes the two complex impedances:
sL and 1/sC in shorthand notation which means s*L and 1/(s*C).
Also, for a voltage divider it is always the impedance of the lower element divided by the sum of all the element impedances.
So we would end up with:
1. The lower element: 1/sC
2. The sum: Rx+sL+1/sC
3. The division: (1/sC)/(Rx+sL+1/sC)
Note Rx=R+Rs where R and Rs are the original two resistors.
Now all that is left to do is to simplify #3 and then rearrange it into the required form to make it easier to extract the required quantities like Q.
