Series Notch Filters

By Roy Viggo Pedersen
31 Jan 1996

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"

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