I am working a Bandpass filter problem in my circuits class. The circuit is very basic. It is a cap in series with an inductor and resistor in parrellel.
If you work out the transfer function for this filter you will see that there is an s^2 in the numerator and nothing else.
My question is this: According to my book the standard form for a bandpass filter is (s x beta)/(s^2 + beta x s + wo). The transfer function for this circuit does not work out to have a beta on the top and the bottom. I am thinking that the circuit was set up wrong in the problem, but I am not sure.
Must beta be in both the numerator AND the denominator in a bandpassfilter transfer function? I am getting 1/RC in the beta position on the denominator, but nothing except s^2 in the numerator.
In my first post I assumed the cap and inductor were in series, and the resistor was in parallel with V[sub]out[/sub]. This gives the following transfer function:
[s*(R/L)] / [s^2 + s*(R/L) + 1/(LC)]
This is a bandpass filter.
In my second post I assumed the cap (alone) was is “in series,” while the resistor, inductor and V[sub]out[/sub] were all in parallel. This gives the following transfer function:
Maybe you knew this, but it’s not beta you need to worry about being missing, it’s the s. If you’re trying to build a bandpass filter and you don’t have any zeros at all ( i.e. no s in the numerator) you know something’s wrong. You need both poles & zeros to ‘cancel out’ for some portion of the spectrum in order to get a band.
Of course just having the zeros doesn’t mean you have a bandpass filter, as is obvious in the highpass filter given by CrafterMan.
I think the capactor and the resistor/inductor are in series with Vout.
-{{-
--||--< >--o**Vout**
-ww-
No? This is a bandpass filter, too, with an R there to limit (half, in principle, though without the values I can’t say for sure) the inductor’s inherent resistance due to the conductor length.
I’m having a hard time understanding the topology of his filter.
Is he talking about a capacitor and inductor in series; with a resistor in parallel with V[sub]out[/sub]? That’s what I assumed in my first post.
Is he talking about a capacitor in series; with an inductor, resistor, and V[sub]out[/sub] all in parallel? That’s what I assumed in my second post.
Now you seem to being describing a third possibility.
Does your drawing show that nothing is in parallel with V[sub]out[/sub]? If so, then it is not a filter, bandpass or otherwise, and cannot be analyzed as such. (Unless, of course, you include a finite load impedance.)
Ok, I am confused as hell now. I got the exact same transfer function that you have above. s^2/[s^2+s blah blah
How is this a high pass filter? A high passfilter looks like such:
s/s+wo correct? What am I supposed to do with an s^2 term. On top of that, I have a quadratic in the denom that is not a perfect square. I have not seen a high pass that has a quadratic in the denom?!?
I’d suggest that you visit the Troubleshooting Forum at www.carsound.com. The moderator there, Dave Navone, is a physicist, and very smart; he’ll know.
Welcome to the world of EE, Phlip. And relax; after we get this solved I’ll buy you a few pints of Guinness, O.K.?
As s goes to 0 the transfer function H(s) also goes to 0, and as s goes to infinity H(s) goes to 1.
Perhaps you’re confused because you’re not taking the limit correctly.
To take the limit, divide the numerator by s[sup]2[/sup] and divide the denominator by s[sup]2[/sup]. H(s) will then be:
1 / [1 + 1/(sRC) + 1/(LCs[sup]2[/sup])]
As s goes to 0 the second and third terms in the denominator explode toward infinity. This means the entire denominator goes toward infinity, and thus H(s) goes to 0.
As s goes to infinity the second and third terms in the denominator simply go to 0. This means H(s) = 1/1 = 1.
Do you believe it’s a (2[sup]nd[/sup] order) highpass filter now?
As far as it “not being a perfect square,” is there someone who says it has to be?
You also asked “what to do with the quadratic” in the numerator. All I can say is that it’s part of the transfer function.
Can I ask what you’re trying to solve for? Are you doing a Bode plot? Do you need to find the –3dB frequency? Are you trying to plot the magnitude over frequency? Or perhaps the phase?
