The GXO Page
10/02 A short study on the validity of a generic 2-way
crossover with baffle step compensation.

The Objective:
In the forum postings, I have often read of the trials of aspiring speaker builders overcoming the pitfalls of
beginning crossover design without the benefits of design software. I wondered if a generic 2-way crossover
could be devised that would take into account some of the variables implicit in such a design, such as BSC
(baffle step compensation), and whether it could accommodate a wide variety of 5 inch to 8 inch mid/woofers
and tweeters in a simple enclosure and still provide an acceptable on axis FR (frequency response) of within +/-
3 db.  

The Assumptions:
Of course no crossover can be truly universal, so certain limitations and assumptions must be made to define
the scope of the design.

> Accuracy of the data:
Manufacturers specifications and plots are prone to changes in lots, materials, manufacturing processes, etc.
For the purposes of this study, it is assumed the published information is accurate, and that the crossover
topology will be sufficiently adjustable so as to accommodate minor response variations.

> Crossover frequency:
I looked at the FR of many 5 in. to 8 in. drivers, as well as many different tweeters to determine an acceptable
crossover point. On one hand you have the Fs of the tweeters, which should be at least one octave below the
crossover frequency. On the other hand many mid woofers can start showing response abnormalities above 3 -
4KHz. With this in mind, as well as the driver spacing limitations, I chose 2350 Hz as the target crossover point.

> Baffle configuration:
One consideration necessary in order to achieve flat frequency response is to account for the diffraction effects
caused by the baffle size and the location of the drivers on the baffle. I chose a 9 in. by 20 in. front baffle for
MT designs and a 9 in. by 28 in. for MTMs. For ease of construction, no chamfering or rounding was modeled.
These sizes should accommodate most drivers and their required enclosure volumes.

> Driver spacing:
On the MT baffle the tweeter center was modeled orientated 4 inches from the top of the baffle. The mid
woofer was centered 10 inches from the top of the baffle. On the MTM, the top woofer was modeled centered
6 inches below the top of the baffle, the tweeter centered 12 inches below the top of the baffle, and the bottom
woofer centered 18 inches from the top of the baffle. The center-to-center spacing between the mid/woofer and
the tweeter was 6 inches. This is very close to 1 wavelength at the crossover frequency. This spacing limits the
maximum size of the mid/woofer to approximately 8 inches.

> Acoustic centers:
A difference in signal propagation time will occur if the distances from the acoustic centers of the woofer and
tweeter to the listener are not equal. The differing path lengths effect the relative phase of the individual drivers,
and cause frequency response abnormalities in the crossover region. In the MT crossover, no attempt was made
to compensate for the difference between the acoustic centers of the drivers. I felt a better choice would be to
tilt the baffle to align the centers. This can be done either by sloping the front baffle, or tilting the entire
enclosure back. In the MTM, I assumed a relative difference of 15mm, and a vertical baffle.

> Driver impedance:
The crossover was designed using the average Re and Le of several 8-ohm nominal drivers. For the woofer I
assumed 6 ohms and 1.0 mh. For the tweeter, 5 ohms and 0.05 mh.

> Driver FR:
The drivers should have a flat FR throughout the pass band, and ideally at least one octave past the crossover
frequency.

> Driver mounting:
All drivers assumed to be flush mounted.

The Design Process:
To compensate for diffraction effects, I first determined a target response for the system. This is required as
manufacturers normally only publish anechoic half space or 2pi frequency response curves. I modeled the baffle
and driver orientation using
Paul Verdone's BDS program, and determined the woofer diffraction effects (gain)
caused by the baffle. This curve was inverted and exported to Ingemar Johansson'sLspCAD to provide the
target response, or attenuation required to obtain a flat on axis frequency response. Different target responses
were modeled for the MT and MTM formats.
Next, I modeled various crossover topologies using idealized drivers, optimizing them to track the target
response and the transfer functions of the crossovers selected. My initial investigation was to see if an acoustic
2nd order LR low pass crossover would have sufficient roll off to mitigate the woofer FR irregularities above
the crossover frequency. Importing various driver FR files however, indicated insufficient attenuation with some
drivers, and caused unacceptable changes in FR above the crossover frequency. A zobel circuit was added, but
the attenuation was still insufficient in some cases. I then modeled an acoustic 4th order LR, and found
the
attenuation was adequate to mitigate the response irregularities of most drivers, including some with some
serious cone resonance / break up modes. For example, I modeled a 6.5-inch driver which has a 10 db peak at
4100 Hz. This peak was attenuated acceptably using this modeled crossover. A zobel circuit was used to allow
the Q of the low pass roll off to be easily adjusted. The tweeter circuit was also modeled as a 4th order LR, and
provided acceptable results with a variety of tweeters. Phase tracking was good, assuming proper alignment of
the acoustic centers of the drivers.
Once I had an acceptable circuit for a TM design, I imported the
target curve for the MTM baffle, and modified
the low pass circuit to provide similar results. Phase tracking through the crossover region may be poorer due to
the assumption of the tweeter and woofers relative acoustic centers, but due to the sharp roll off rates of the
crossover, this aberration should be limited to a small frequency band around the crossover frequency. The
impedance curves for the MTM remained above 4 ohms for all the drivers I modeled.

The Circuits:
MT woofer network   MT tweeter network    MTM woofer network    MTM tweeter network
The circuit topology turned out to be quite simple and is the same for both designs. Any resistors with values
less than an ohm are the DCR of the adjacent inductors. The MTM design assumes the woofers are paralleled.
For the low pass network, a third order electrical filter with zorbel was used to achieve the BSC and the 4th
order acoustic slope at the crossover frequency. The high pass network is also a third order electrical providing
a 4th order acoustic slope. The two resistors after the network represent an L-pad, or fixed resistors for tweeter
attenuation.

The Tweaks:
For most of the drivers I modeled, the frequency response criteria of +/- 3 dB could be achieved by merely
adjusting the tweeter attenuation and the resistor in the woofer zorbel. If you want to experiment with this
design, I would suggest purchasing a pair of L-pads for each speaker to do the initial voicing adjustments. The
L-pad for the woofer would be wired as to utilize only the middle terminal and the terminal with the maximum
resistance with respect to the middle terminal when the L-pad is turned fully clockwise. On the ones I tested,
this was the left and center terminals as viewed from the shaft side. It had a maximum resistance of 40 ohms,
but abruptly went open circuit at the full clockwise position.. To obtain the best response, additional resistance
in series with the L-pad may be required for some drivers. Wired this way, turning the L-pad counter clockwise
will reduce the resistance, and reduce the woofer output from roughly 700 Hz to 2 KHz. Note that while the
results are driver dependent, in many cases the BSC of the speaker system can be adjusted somewhat by raising
or lowering both L-pads simultaneously.   

Additional Tweaks:
While the modeled frequency response of most drivers fell acceptably within my +/- 3 db target using only the
zorbel resistor and tweeter attenuator, small changes in the component values may improve the FR of the actual
system.

>Low pass section:
Reducing the value of L1 will have the effect of lessening the baffle step. Note that this will also raise the
crossover frequency of the woofer.  Using a coil with increased DCR will reduce the baffle step with little
change in the crossover frequency, at the expense of making the system slightly less efficient.
Increasing the value of C1 will lower the crossover frequency and affect the FR around the crossover
frequency. It will also affect the slope of the roll off at the crossover frequency.
Increasing the value of L2 will have an effect similar to that of C1.

>High pass section:
Increasing the value of C1 will lower the crossover frequency.
Changing the value of L1 and C2 will affect the slope of the roll off and affect minor changes in FR around the
crossover frequency.

Modeled Results:
After determining the final values and topology for this circuit, I wondered if it would model well with a woofer
exhibiting extreme breakup modes near the crossover frequency. Metal cone drivers came immediately to mind.
I selected the response curves of a SEAS L17REP, a 6.5 inch aluminum cone driver to model with my TM
circuit. The results  are shown in the
accompanying snapshot. The blue curve is the SEAS woofer without the
crossover. The green curve is with the crossover applied. Note the effects of the breakup modes appear
sufficiently far down in the pass band as to mitigate their audible effects. The red curve is an SS9500 with
crossover applied and suitably attenuated. The violet curve is the combined modeled frequency response, and
the black band is the combined response with the tweeter out of phase, showing good phase tracking through
the crossover region with the acoustic centers aligned. No zorbel was required for this particular driver.

Conclusions:
This was a design study. I have not used this crossover in an actual design. However, the modeling of various
drivers and predicated on the assumptions made, it appears that the  crossover should provide acceptable
results. A reasonably flat  modeled frequency response is accomplished in most instances with no adjustments
other than adjusting the zorbel resister and tweeter attenuation.
Of course, this design is no substitute for one that uses the measured specifications and response curves of the
actual drivers in the intended enclosure with an optimized crossover design unique for that specific application.
However, for those who wish to expand their design knowledge but do not have access to the measurement
equipment or design software, I suggest the topologies presented here might be used as a template for further
experimentation.

Erratum:
While I made every attempt to insure the validity of my procedures, data, and results. I do not profess to
possess any superior abilities with regards to speaker and crossover design. Please email me with any
constructive comments or suggestions you may have.


Copyright 2002 by Curt Campbell