**Resistive load**

An ideal fourth-order high-pass filter with a resistive load, looks like this:

The response of such a passive network is

The corresponding target high-pass response is

This is obtained if

,

, .

**Zobel network**

If the driver has DC resistance R_{d}
and inductance L_{d}, the component values for the Zobel
network are then

and

If the crossover frequency is much higher than the
driver resonance, the driver will behave approximately as an inductor,
and the Zobel network will equalise the driver impedance to a pure resistance
R_{d}. Unfortunately, with a tweeter the resonance is
unlikely to be more than an octave or two lower than the crossover frequency,
and even with the Scan-Speak D2905/9300 the resonance is 600HZ, a factor
of five lower than the crossover frequency 3.3kHz. I found that with a
simple Zobel network the measured response of the high-pass leg of the
filter was substantially incorrect, and this was due to the impedance of
the driver plus Zobel increasing sharply as the frequency dropped below
about 2.5kHz.

**Peter Dahl's impedance correction fix**

Peter Dahl suggested the following circuit as a substitute for the Zobel network, which he has used himself with a D2905/9300:

where R_{1} = 7.5 ohms (I used two 15 ohms in parallel),
C_{3} = 66uF (I used a 60uF reversolytic in parallel with a 6u0
polypropylene) , C_{4} = 3.3uF and L_{3} = 0.8mH. The LC circuit (L_{3} and C_{3}) has a resonance
frequency at

at which the impedance of the compensating circuit
has a minimum value of R_{1}, which presumably compensates for the impedance
maximum corresponding the main mechanical resonance at 600Hz of the D2905/9300.
I have my doubts about putting a poorly-damped LC resonant circuit in the
crossovers, but f_{r} is well outside the tweeter passband
and is quite well isolated from the midrange driver.

I constructed this, and found it gave a much better-behaved impedance characteristic, with an impedance of 5.0 ± 0.3 ohms between 1kHz and 10kHz. I think the impedance could be linearised still further, but I wonder how worthwhile this would be, given the non-ideal responses of the drivers themselves.

**The final circuit and component values**

Using R=5 ohms and w_{0}=3.38kHz,
I get the following desired component values:

L_{1} = 0.148mH, L_{2} = 0.666mH
C_{1} = 5.0uF, C_{2} = 10.0uF

The final circuit looks like this:

The values I used were:

C_{1} |
5uF |

C_{2} |
10uF |

C_{3} |
68uF |

C_{4} |
0.33uF |

L_{1} |
0.15mH |

L_{2} |
0.667mH (=1.0mH//2.0mH) |

L_{3} |
0.8mH |

R_{1} |
7.5ohms (=15 ohms/2) |

**Network Impedance**

The impedance of the high-pass crossover, with load
resistance R_{H} is

If the component values are substituted in for the 4th-order L-R filter,

As , and as , .