# resonant frequency in passive filters

#### ninjaman

Joined May 18, 2013
336
hello

what role does resonant frequency play in passive filters. I know XL = XC, but why would this be used in passive filters.

1. is the resonant frequency the crossover frequency?
2. XL would equal XC. this is were maximum power transfer takes place?
3. there would be little power loss?

if any of this is correct please could you just say yes to the number that is correct.

I started looking at complex impedance and angular frequency to try and figure this out but I think there is a rather large gap to fill in my education before I do that!

cheers

simon

#### LvW

Joined Jun 13, 2013
1,228
ninjaman, at least you should mention which filter type you are speaking about.

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#### Papabravo

Joined Feb 24, 2006
15,730
If you look at various filter designs what you see is a more complicated interaction of the components than when there are just two components. I can tell you what a filter will be doing if you tell me where the poles and zeros of the transfer function are located. That might be a good place to start. Since various combinations of L and C are available you should ask yourself:
1. What is the transfer function?
2. Where are the poles and zeros?
Now you have a set of simple geometries that you can use to understand what is going on that is generalizeable to more components.

#### ninjaman

Joined May 18, 2013
336
poles and zeros....yes......erm......what?

I don't know that stuff. I haven't been taught that on my course. please could you point me in direction of a good explanation of that stuff please

I have a third order butterworth, two actually. one with two inductors (and cap in parallel)and one with two capacitors(inductor in parallel).

I will have to get back after looking at poles and zeros.

#### LvW

Joined Jun 13, 2013
1,228
I will have to get back after looking at poles and zeros.
Ninjaman, in case you come back after learning some basics, please try to ask a clear question and tell us - at least - if you speak about a low pass, high pass or band pass.
A clear answer requires a clear question.
Good luck

#### ninjaman

Joined May 18, 2013
336
two speakers in one cabinet.

one speaker is a tweeter and requires high pass, I chose butterworth third order, two capacitors and one inductor with L pad

one speak is a woofer and requires a low pass, I chose butterworth third order, two inductors and a capacitor with zobel circuit

where does resonant frequency fit into the crossover circuit of the two filters?

#### gootee

Joined Apr 24, 2007
447
Speakers are difficult to analyze because you don't have the equvalent RLC circuit of the drivers themselves. They are not purely resistive.

Forgetting that difficulty for a moment, you can often analyze filters by treating the reactive components as frequency-dependent resistances. If you can then reduce the circuit to a frequency-dependent voltage divider, you're home and can even directly write the transfer function (assuming you can write the equation for the output voltage of a voltage divider). It's just of the form output voltage = (transfer function) x input voltage. For a resistive voltage divider, the TF would just be Rshunt/(Rseries+Rshunt), for example.

The poles are then the frequencies where the denominatir of the transfer function goes to zero (i.e. the output "blows up", to infinity). The zeros are the frequencies where the numerator goes to zero.

Anyway, if you can derive the expression for the output voltage in terms of the input voltage and the frequency, then you can plot vout/vin versus frequency, which will show the filter's frequency response. But that will change, significantly, when you add the speaker driver onto the output.

I recommend downloading the free LTSPICE from linear.com, and using that to see what your circuits would do. That will be a valuable tool but it still won't help with what will happen with the actual drivers connected. And even knowing that wouldn't be enough, because the box or however they're mounted will have significant effects.

If you had a measurement microphone, there is free software that would enable you to measure your speaker drivers' Thiele-Small parameters, using your computer's sound card input. You would need those parameters in order to be able to design the correct crossover (and enclosure) to get the speaker response you want.

#### ninjaman

Joined May 18, 2013
336
unfortunately transfer functions are out, I don't know how those work. you were talking about voltage dividers. please could you explain that a little more please. I thought that I may be able to do that, I mentioned it in another post but someone said otherwise.

I understand that poles are components, I don't know zeros. im guessing that is transfer function related. so ill leave that out.

I have these formulas for inductor and capacitor values

L1 1.6 * RL/ 2 PI Fc
L2 RL/ 2 PI Fc
L3 RL/ 4 PI Fc

C1 1/ PI Fc RL
C2 1/ 3.2 PI Fc RL
C3 1/ 2 PI Fc RL

this is for two speakers, tweeter and woofer, third order butterworth. this takes into consideration the speakers and impedance stabilization circuits(I believe)

if someone could add the voltage divider for the three components. unless
shunt/ first component + shunt *input voltage, then that voltage through the third component?

I got some of those values, but some others were out.

#### gootee

Joined Apr 24, 2007
447
Can you post a picture of your filter schematics? Or describe them better. i.e. What is in series with the signal and what goes to ground (probably from after the series stuff?), for each one.

#### ninjaman

Joined May 18, 2013
336
there are two speakers
tweeter has capacitors in series with an inductor shunt to ground
woofer has inductors in series with an capacitor shunt to ground

#### #12

Joined Nov 30, 2010
18,217
It's an LCL Butterworth for the bass speaker and a CLC Butterworth for the tweeter.
ninjaman wants to know the resonant frequency of the components...as if that has anything to do with speakers.

#### ninjaman

Joined May 18, 2013
336
so resonant frequency has nothing to do with filters?

#### gootee

Joined Apr 24, 2007
447
there are two speakers
tweeter has capacitors in series with an inductor shunt to ground
woofer has inductors in series with an capacitor shunt to ground
So, which ones are C1, C2, C3, L1, L2, and L3, in that arrangement?

Note that if you want to calculate their response, you would also want to know the DC series resistance of each inductor, and the Equivalent Series Resistance (ESR) or each capacitor. Or, if you are designing the filters, you would want to at least see what effects those parasitic resistances might have, and the sensitivity to their values.

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#### gootee

Joined Apr 24, 2007
447

http://www.diyaudioandvideo.com/Calculator/XOver/Help.aspx

http://www.diyaudioandvideo.com/Calculator/XOver/

http://www.diyaudioandvideo.com/FAQ/Crossover/

You might notice that two Linkwitz-Riley types of crossover filters would give a flat summed response in the crossover region, whereas two Butterworth types give a 3 dB peak, there.

FYI:

In terms of both sound quality and the cost and quality of the crossover components, it would be far better to put the filters BEFORE the power amplifier(s), and drive the speaker drivers directly. That's called a "line-level crossover" setup. But you would need two amplifiers, for speakers that have two drivers each.

Since the line-level crossovers would be operating at low voltages and low currents, you could use the very highest-quality types of capacitors and inductors (and probably no inductors, using active opamp-based filters), and it would still cost a fraction of what even run-of-the-mill components for in-speaker crossovers would cost. The difference (possibly $100 to$200, or even more) would easily pay for a nice used power amplifier, like an Adcom GFA-535 or 545 (designed by Nelson Pass), or a Hafler DH-220 (designed by David Hafler), from ebay.com. (I have bought several of each. You can't even get a high-quality new empty CASE for a power amplifier, for those prices! All were (and are) in excellent working and physical condition. And they are built like TANKS. Astounding values are there to be had...)

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#### gootee

Joined Apr 24, 2007
447
so resonant frequency has nothing to do with filters?
Yeah, it can crop up, with filters above first order. Sometimes you can get a peak in the response, around the cutoff frequency of the filter. If you don't want a peak, there, you can usually add some damping (resistance) to get rid of it. But that can also change other characteristics in ways you don't want.

#### Papabravo

Joined Feb 24, 2006
15,730
Yeah, it can crop up, with filters above first order. Sometimes you can get a peak in the response, around the cutoff frequency of the filter. If you don't want a peak, there, you can usually add some damping (resistance) to get rid of it. But that can also change other characteristics in ways you don't want.
A Butterworth filter is maximally flat by design. It cannot produce peaks or any other evidence of resonance.

I'm sorry but there is no other way to understand the behavior of filters without understanding the algebra of complex numbers. Learn it on your own if you have to, but learn it.

#12

#### #12

Joined Nov 30, 2010
18,217
Are we starting to get through here? One of the primary goals of a Butterworth filter is that it does not have a resonant response.

#### gootee

Joined Apr 24, 2007
447
A Butterworth filter is maximally flat by design. It cannot produce peaks or any other evidence of resonance.

I'm sorry but there is no other way to understand the behavior of filters without understanding the algebra of complex numbers. Learn it on your own if you have to, but learn it.
I was just musing about filters at that point, not Butterworth specifically, and was trying to respond on the OP's level. Please, you don't need to explain, to me, what mathematics it takes to understand anything in electrical engineering.