SpeakerBuilding.com - Series Notch Filters

Series Notch Filters

By Roy Viggo Pedersen
31 Jan 1996

Printed from SpeakerBuilding.com, 04 Feb 2012 08:49
URL: http:///content/speaker_design/1041/

What is a series notch filter?

The function of the series notch filter is to dampen the effects the driver resonance has on filter networks. Most drivers has a large impedance peak at it's resonance. For crossovers to works as expected, it's important to have a nearly resistive impedance, at least in the crossover frequency region. Most drivers benefits from using notch filters, specially tweeters and midranges where the component values can be kept small. Using this filter on bass drivers calls for very large (and expensive) components. Many modern tweeters are using magnetic oil (Ferrofluid) in the voice coil gap to mechanically damp the resonance. These tweeters will probably not need such a curcuit, or does not depend so much on it.

When is it used?

The series notch filter is most useful when the crossover frequency in a highpass filter is near the driver resonance. But this depends on the filter damping. Example: If you're using a tweeter without ferrofluid with a 1. order filter (damps 6 dB/octave) and the crossover frequency is two octaves above the driver resonance, you certainly need a notch filter. Lets say driver resonance is at 1000 Hz (typical) and the crossover frequency is at 4000 Hz (also typical, and two octaves above the resonance). Then the filter only damps 12 dB at driver resonance, and this will strongly affect the network, as this graph shows Fig. 1. Crossover response without notch filter.

We are using a capacitor of 5 microFarads for this filter at (approximately) 4000 Hz. You can see that the undamped driver resonance causes a big peak in the SPL responce curve at driver resonance.

The circuit

This circuit is also called a LCR circuit because it consist of a Inductor (L), a capacitor (C) and a resistance (R). They are wired in series Fig. 2. The circuit.

Formulas

Use the following formulas to calculate the values if you know the Q values of the driver:

0.1592
C = -----------
Re Qes fs

0.1592 (Qes Re)
L = -----------------
fs

Qes Re
Rc = Re + --------
Qms

Explanation of the symbols used:
fs = Drivers resonance frequency
Re = Drivers DC resistance
Qes = Drivers electrical Q value
Qms = Drivers mechanical Q value

If you don't know the Q values of the driver (typical for most tweeters), you can use this method:

0.03003
C = ---------
fs

0.02252
L = ---------
fs^2 C

Rc = Nominal impedance of the driver

With this method you should measure the impedance of the driver, and try different values for Rc. Dickason[1] suggest you can try increasing Rc in increments of 0.5 Ohm at each time until you reach your goal.

Back to the example

In our example above we get the following values (using the second method):

0.03003
C = --------- = 0.00003  (or 30uF)
1000

0.02252      0.02252
L = ---------- = --------- = 0.00075 (or 0.75mH)
1000^2 C        30

R = 8 Ohm

If we try these values, we get this impedance curve Fig. 3. Impedance of tweeter.

We got right on the spot with these values. Now we can make a crossover that works properly. If we try the above filter, a 5 microFarads capacitor, we get this result Fig. 4. Crossover response with notch filter.

Quite a change, huh? That was a lot better! Note that the driver+filter responce rolls off with a higher order than the target. That's normal because the rolloff of the driver and the filter are summed.

Summary

We have showed that using notch filters are beneficial, specially when dealing with low-order filters, and tweeters that don't have a mechanical damping in form of magnetic oil in the voice coil gap. We have also showed that these filters are not so critical that we had to use measurement tools to get a decent flat impedance curve, we got right on our first try. So we state that series notch filters is a "must have" under the above conditions, for amateurs not "knowing what they do" (can't measure).

Roy Viggo Pedersen

References

[1] Vance Dickason, "The Loadspeaker Design Cookbook"

Figures

Fig. 1. Crossover response without notch filter
This graph shows tweeter response without crossover, with a 6dB/oct filter and target response. Target is 6dB/oct at 4000Hz.

Fig. 2. The circuit
A LCR circuit consist of a inductor (L), a capacitor (C) and a resistance (R). They are wired i series of each other, and in parallell of the driver.

Fig. 3. Impedance of tweeter
This graph shows the impedance of a tweeter with and without a notch filter.

Fig. 4. Crossover response with notch filter
This graph shows the tweeter response without any filter, with a 6dB/oct filter + a notch filter, and the target response.