Tweeter crossover question.

[sugarn]

I've attached my speaker crossover for tweeter. I plan to upgrade the old VIFA D26TG to Peerless HDS 810921 tweeter.
I have a few questions.
1. Is this crossover 1st order or 2nd order?
2. What is the purpose of resistor 1.5R and inductor 0.82mh in parallel with tweeter?

[CeramicMan]

The inductor shunts low frequencies, making the filter second-order. (A first order one would be just the capacitor and maybe a couple of padding resistors.)

The 1.5 ohm resistor might be the internal resistance of the inductor windings. Or, most likely: a fudge-factor to tweak the response, either by ear or on a simulation program.

[Jay_WJ]

Yes, you're right. The 1.5 Ohm resistor makes the effect of the shunt inductor a bit weaker (i.e., the slope becomes a bit less steep or less 2nd order-lke).

[Svante]

This is a tricky question that has several answers.

First, the term "filter order" needs to be defined. Originally, it was a pure mathematical definition that said something about the order of the polynomials in the transfer function. For simple filters, it turns out that multiplying the order by 6 gives the slope of the filter. This has lead to a slightly different popular interpretation of what "filter order" means; 6 dB/oct= 1st order, 12 dB/oct=2nd order etc.

So, looking at the filter alone, with a resistive load, it is a second order filter in the strict mathematical sense. Polynomials become second order due to the capacitor in series and the inductor in parallel. However, still with a resistive load, the resistor in series with the inductor introduces a zero in the transfer function, which effectively reduces the slope to 6 dB/oct at low frequencies (~100Hz). Actually, in this configuration it never reaches 12 dB/oct. Between 1000 and 2000 Hz (1 octave), for example, the level difference is only 8 dB (red curve).

Furthermore; the driver has a transfer function too, typically second order high pass. This makes the acoustic slope of the driver and filter combined at least 4th order, as seen in the figure.

To make things even more complicated; the driver is not a resistive load. It has a system resonance, in this case at 650 Hz, and an impedance peak at the same frequency. This affects the response of the filter, as shown in the figure below. One can determine the mathematical order of this system too, but it is rather meaningless.

The bottom line here is that filter theory and cookbook formulas don't last too long when it comes to filter design. If one want good results, the response of the filter needs to be simulated with the actual load of the driver, and combined with the other drivers in the system.

Solid lines: Acoustic output
Dashed lines: Voltage at the output of the filter



Edit: The purpose of the 1.5 ohm resistor can only be guessed. Probably it is the DC resistance of the copper wire in the coil. The resistance is rather high, though, so the wire in the coil must be rather thin. It is possible that this is the case and the reason is probably economical. It could also be so that the resistance is actually a physical resistor, separated from the coil. It is hard to find a reason for putting the resistor there though, since the effect of it is reducing the slope of the filter. Replacing the 1.5 ohms with 0.1 ohms results in a steeper slope for rally low frequencies, but also a change in the amplitude around the resonance. It might be that that is the reason.

Edit2: I do not have the data for the 6 ohm version of the Vifa driver, so there is a bit of guesswork involved in the curves. The conclusions are the same though.

[CeramicMan]

Originally posted by Svante
First, the term "filter order" needs to be defined. Originally, it was a pure mathematical definition that said something about the order of the polynomials in the transfer function. For simple filters, it turns out that multiplying the order by 6 gives the slope of the filter. This has lead to a slightly different popular interpretation of what "filter order" means; 6 dB/oct= 1st order, 12 dB/oct=2nd order etc.... [snip]

Also note that the so-called 'orders' only represent the slopes of asymptotes, which are never quite reached anyway.

[Svante]

Originally posted by CeramicMan



Also note that the so-called 'orders' only represent the slopes of asymptotes, which are never quite reached anyway.

Yes, the ultimate slopes in the stop band, far away from the crossover frequency.

The 6 dBs "per order" originate in that the transfer function ultimately gets proportional to either of f^n or 1/f^n, where n is the order. So, for a frequency shift of 1 octave (a factor of 2), the amplitude is changed by 2^n. The level of that change, in dB is 20*log(2^n)=n*20*log(2)=n*6.0206.

[sugarn]

Thank you for answering my questions.
Svente,
1. The resistor 1.5 ohm is a real resistor. My speaker is commercial speaker, not diy. I wrote crossover schematic from the actual crossover in my speaker.
2. Here is the data of Vifa tweeter.
http://www.speakerbits.com/net/catal...aspx?ID=VF026B

[ssmith]

sugarn,
when you complete the project do give some feedback on your upgrade the HDS is reputed to be a great tweeter -- so would be nice to hear how it works out.

[Svante]

Originally posted by sugarn
Thank you for answering my questions.
Svente,
1. The resistor 1.5 ohm is a real resistor. My speaker is commercial speaker, not diy. I wrote crossover schematic from the actual crossover in my speaker.
2. Here is the data of Vifa tweeter.
http://www.speakerbits.com/net/catal...aspx?ID=VF026B

Ah, ok, then it seems plausible that they wanted to reduce the peak at the resonance then. It also seems that my guesswork was pretty ok.