crossover with baffle step compensation.

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 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.

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 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.

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.

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.

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.

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.

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