I want to be able to find the resonant frequency and bandwidth of any circuit if I know the values of its components.
For example, let's say I have a standard parallel RLC circuit (a resistor in parallel with a capacitor in parallel with an inductor) with resistance R, capacitance C, and inductance L.
The admittance of the circuit can be calculated easily by adding the admittance of each individual parallel component:
Ytotal(s) = YR(s) + YC(s) + YL(s) = 1/R + C*s + 1/(L*s)
For some reason that I can not understand since the teacher skipped this in class and just assumed we knew it I'm now supposed to combine the terms and the equation eventually becomes
YTotal = C/s * (s^2 + s*1/(C*R) + 1/(L*C))
I know that the resonant frequency of a parallel circuit is Sqrt(1/LC) and the bandwidth is 1/(R*C) for this circuit.
On the other hand, if I look at a standard series RLC circuit the total impedance boils down to
ZTotal = L/s(s^2 + s*R/L + 1/LC)
I know that the resonant frequency of a series circuit is Sqrt(1/LC) and the bandwidth is R/L for this circuit.
My question is the following:
Is it a rule of thumb that the equation of total admittance or total impedance is of some form K/(s+c)*(s^2+s*BW+w0^2) where c and K are constants, BW is the bandwidth, and w0 is the resonant frequency in radians / second?
Why is it admittance for a parallel circuit and impedance for a series circuit? I would rather understand why these things are true than just memorize the equations...
If this is not the case, how does one calculate BW and w0 from a given circuit. I read the contents of this site: http://www.allaboutcircuits.com/vol_2/chpt_6/6.html
I know w0 is given when XL = XC, but I'm still confused on the topic and I don't understand how BW is calculated so much.
Thank you for your help,
-blazed
For example, let's say I have a standard parallel RLC circuit (a resistor in parallel with a capacitor in parallel with an inductor) with resistance R, capacitance C, and inductance L.
The admittance of the circuit can be calculated easily by adding the admittance of each individual parallel component:
Ytotal(s) = YR(s) + YC(s) + YL(s) = 1/R + C*s + 1/(L*s)
For some reason that I can not understand since the teacher skipped this in class and just assumed we knew it I'm now supposed to combine the terms and the equation eventually becomes
YTotal = C/s * (s^2 + s*1/(C*R) + 1/(L*C))
I know that the resonant frequency of a parallel circuit is Sqrt(1/LC) and the bandwidth is 1/(R*C) for this circuit.
On the other hand, if I look at a standard series RLC circuit the total impedance boils down to
ZTotal = L/s(s^2 + s*R/L + 1/LC)
I know that the resonant frequency of a series circuit is Sqrt(1/LC) and the bandwidth is R/L for this circuit.
My question is the following:
Is it a rule of thumb that the equation of total admittance or total impedance is of some form K/(s+c)*(s^2+s*BW+w0^2) where c and K are constants, BW is the bandwidth, and w0 is the resonant frequency in radians / second?
Why is it admittance for a parallel circuit and impedance for a series circuit? I would rather understand why these things are true than just memorize the equations...
If this is not the case, how does one calculate BW and w0 from a given circuit. I read the contents of this site: http://www.allaboutcircuits.com/vol_2/chpt_6/6.html
I know w0 is given when XL = XC, but I'm still confused on the topic and I don't understand how BW is calculated so much.
Thank you for your help,
-blazed
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