From: jch@alexander.cs.umn.edu (J.C. Hamlin)
Newsgroups: rec.audio.car
Subject: Passive Crossover Networks (was Re: crossover networks)
Keywords: crossover
Date: 26 Jan 93 22:59:46 GMT
Article-I.D.: news2.C1HH7L.ss
Organization: University of Minnesota

In article <1jqms8INNbrt@tamsun.tamu.edu>, wdevine@andrew.cea.pvamu.edu (William Devine II) writes:
|>    anybody ever built their own crossover (that is, themselves without
|>    buying inductors?) if so please send me any and all info possible
|>    on the subject.. as i might be able to use this as a circuits lab
|>    project! *8-P......

		 Simple Passive Crossover Contruction
		    by J.C. Hamlin (jch@Cray.COM)

First, how to choose the proper values:

   For a first order, high pass filter (a capacitor):

      Let C = The needed capacitance of the capacitor, in Farads.
      Let f = The desired frequency of cutoff, in Hertz.
      Let R = The resistance of the the circuit (driver), in Ohms.
         pi = 3.1415926535...

                 1
      C = ----------------
          (2 * pi * f * R)
                                                          6
      C is more useful in microfarads, so multiply by 1x10  (1,000,000).
      Remeber that the values listed for capacitors aren't exact.  So you 
      may not get the desired frequency unless the actual value is near 
      the computed one.  

      Also remeber that capacitors are polarized unless explicitly stated 
      "bipolar".  Since the voltage in your speaker lines is AC, you need 
      to use a "bipolar" capacitor, or two polarized capacitors of half 
      the value, in parallel and opposite polarity.

      There are two types of common capacitors, NP electrolytic and solid
      dielectric.  Solid dielectric capacitors are a better choice for
      high frequency uses.  But for low frequency uses, the NP electrolytics
      will work just fine, and at a lower cost.

      The last point is to make sure the capacitor will be able to handle
      the power you will be using it with.  Most capacitors are rated in
      the maximum voltage they can handle.  This value can be computed by:

         V = SQRT( Power in the circuit * Resistance of the circuit )

      The cut-off for a first order high pass filter is 6dB/octave.

   For a first order, low pass filter (an inductor coil):

      Let L = The needed inductance of the inductor coil, in Henries.
      Let f = The desired frequency of cutoff, in Hertz.
      Let R = The resistance of the the circuit (driver), in Ohms.
         pi = 3.1415926535...

               R
      L = ------------
          (2 * pi * f)
                                                           3
      L is more useful in millihenries, so multiply by 1x10  (1,000).
      Remeber again, that the values listed for inductors aren't exact.
      You may not get the desired frequency.

      There are two types of common inductors, air-core coils and
      iron-core coils.  An air core can a core made of any nonmagnetic
      material.  Iron core coils can be smaller, but it is likely that
      a cheap iron core coil will cause distortion.  In almost all cases,
      it pays to get the best air-core coil you can afford.

      It is desirable to keep the DC resistance of the coil as small as
      possible.  As a rule of thumb, it is desirable to use a coil that
      has a DC resistance of no more than 5 percent of the resistance
      of the circuit (driver).

      The last point is to make sure the capacitor will be able to handle
      the power you will be using it with.  Most capacitors are rated in
      the maximum voltage they can handle.  This value can be computed by:

         V = SQRT( Power in the circuit * Resistance of the circuit )

      The cut-off for a first order low pass filter is 6dB/octave.


> What is the difference between using a cap and buying a "real" crossover?

Now for the theory:

   A capacitor is truly a first order, high pass crossover.  So this is
   a "real" crossover.  Most "common" crossovers are a second order
   crossover, and contain both a high pass and a low pass section,
   prepackaged in a black box with inputs and outputs.

   Most crossovers are two-way or three way.  They either split the signal
   into the highs and the lows, or they split it into the highs, mids, and
   the lows.  Some can even split it five ways, highs, mids, mid-basses, 
   basses, and sub-basses.

   This discussion is about passive crossovers.  That is, they don't require
   any power to do their job other than the power from the speaker lines.

   An active crossover goes in-line somewhere with your preamp cables, and
   electronically does the filtering.  This is often better if you have
   the money to invest in a seperate amplifier for each band of frequencies
   that you want to use--it allows you to adust many factors of the crossover
   like the slope, frequencies, and number of input and output channels.
   You will need a stereo pair of amplification for every frequency range
   you wish to use (highs, mids, mid-basses, basses, sub-basses).  You can
   get away with some woofer and subwoofer frequencies in mono, however.

   A passive crossover goes in-line with your speakers and does the filtering
   at a cost, some of your amplifier power.  The is often better if you
   have only one amplifier to amplify the signal.  You can then split the
   signal after amplification.  Passive crossovers are usually not adjustable,
   but usually come matched with a set of seperate drivers.  In this cass,
   adjustment is usually not nescessary.

   A crossover "rolls off" the frequencies equal to:
     (6dB / Octave) * order of the crossover.

   FIRST ORDER:
   A first order, two way, parallel crossover is shown below:

                 C1
 +  -------+-----||------  +
  in       |             tweeter
 -  -------|----+--------  -
           |    |
           |    |  L1
           |    +--OOO---  +
           |              woofer
           +-------------  -

   Where C1 and L1 can be computed directly, using the formulas given above.

   SECOND ORDER:
   A second order, two way, parallel crossover is shown next:

                 C1
 +  -------+-----||-----+---  -
           |            |  
  in       |        L1 OOO   tweeter
           |            |
 -  -------|----+-------+---  +
           |    |
           |    |  L1
           |    +--OOO--+---  +
           |            |
           |        C1 ===   woofer
           |            |
           +------------+---  -

   Notice the polarity reversal of the tweeter.  This is because a second 
   order crossover network produces a 180 phase shift.

   There are three types of second order crossover networks common today:
    - The first is the Linkwitz-Riley (L-R), and is characterized 
      by a null in the frequency response at the crossover point.
    - The second is called a Butterworth network, and is more common.  
      With this type you get a peak in the response curve at that point.  
    - The third is called a Bessel network, and is characterized by a 
      smaller peak at the crossover point than the Butterworth.

   The values for C1 and L1 can be computed using the formulas above
   as a basis.  Find C and L from the formulas above, and then multiply
   them by the following constants to get the proper values for your
   choice of network.

          L-R      Butterworth    Bessel
       ----------  -----------  ------------
   C1   x 0.50      x 0.71       x 0.57
   L1   x 2.00      x 1.41       x 1.74

   There are other factors that make a greater difference in the sound
   of your system than the choice of networks, so it really isn't that
   important.

   There are also third, fourth, fifth, and even higher order crossover
   networks, or three-way networks that can be constructed, but I will 
   not go into detail about those here.  If you are interested, you can
   email me or buy the book.

J.C. Hamlin
Automotive Sound & Security by Hamlin, Minneapolis, MN
jch@cs.umn.edu

P.S.  The answers to, "How to wind your own inductors coming right up!"