The Bemidji mini


Here is a simple simple cost effective bookshelf speaker design that will yield superior results compared to commercial offering from manufacturers at similar or greater price tags.  The performance of this speaker should be superior to the sum of the parts.

 

I chose the above drivers carefully to transition well together with a low part count in the crossover.  I have selected a small Vifa polypropylene woofer.  The on and off axis response is excellent, and there is nothing troublesome with the out of band response.  There is a small I KHz peak and as is the norm with small polypropylene bass/midranges a step response.  Here is the manufacturer’s specification.

 

The tweeter is by Morel.  This is one of their cheaper offerings.  The roll off and dispersion characteristics are excellent.  Fs is 900 Hz.  This is the full specification.

 

The crossover needs to make a smooth transition at crossover without ripple, correct the step response, as far as possible take care of response irregularities.  It should have a respectable, impedance, phase, and time response.  It should also be the most elegant solution with the smallest part count compatible with achieving goals.  These crossovers have five components on each board.

 

Now this crossover has a combined fourth order acoustic and electronic slopes.

The crossover is very symmetrical without ripple.  As you work with a design you find the design begins to tell you where the crossover needs to be.  In this case it is 3 KHz.  This is a very good place for a two way crossover point by the way.  There is no zobel impedance equalization.   This is for a good reason.  I took advantage of the rising impedance to correct the step response.  The low pass filter is in fact first order over most of it operative range.  It changes to second order.  Now please note that the program does not let me write in and show R1.  If you look at the component values you will see that C2 shows an internal resistance of 4 ohms.  No cap has this value, so you need to put a 4 ohm resistor in series with C2.  This is VERY important.  This resistor is operative in the model.

 

The HF filter has the Q of the filter aligned to combine with the acoustic roll off of the tweeter and make for symmetry with the woofer response and make a very smooth transition.  This crossover also optimizes the off axis response of the speaker.  The tweeter is 33db down at F3, which is excellent.   This filter also switches order.

 

The step response is corrected.  A small remnant of the small woofer peak remains, however the Q of the peak is changed.  It is lower in magnitude and moved down to 750 Hz.  It is 400 Hz broad from 600 to 1000Hz, and less now about 2db.  I have made the judgment that in that range and at that magnitude it will do no arm.  Also I suspect that if the speaker is around 10 inches from room boundaries that the response below the slight peak will be lifted by that small amount and help compensate for cabinet diffraction loss.

 

A word about sensitivity,  note that the average sensitivity is now 86db 1 watt one meter.  That is because with any passive network does not allow for boosting a signal, only attenuating it.  This reduction in sensitivity is a consequence of correction of the step response.

 

Now impedance.   Now the bass curve will be the one shown in the woofer alignment.  The published spec is sealed, and has one impedance hump.  This woofer requires reflex loading and there will be two impedance humps.  One is at 20 Hz the other at 73Hz.  There is a dip to 6 ohms between the peaks.  Now although these are 8 ohm drivers, correcting the step response, which in my view is essential, always drops the impedance.  The impedance is 6 ohms from 200 Hz to around 650 Hz and then rises.  This is where a good deal of the power is, so regard these speakers as 6 ohm.  There is an impedance rise to 14 ohms in the crossover region.

 

These speakers should be an easy amp drive.  Any amp the over heats driving those, should never have seen the light of day.

 

Now to phase, this crossover puts woofer and tweeter out of phase at crossover.  There is an unusually good phase and time response.  The shift at crossover is 2.2 inches or 0.17msec.  Now a woofer’s acoustic center is the geometric center of the cone, which for me is impossible to visualize and certainly calculate.  However the tweeter will be ahead of the woofers acoustic center, so will modify this.  I would start with the wiring as shown, but when the speaker is constructed see which polarity has the greatest output at crossover.  I have a hunch that with the drivers lined up on a flat panel recessed flush, the polarity switch will not change the output.  If that is the case, I would wire the tweeter in phase.  This is something that is hard to predict from modeling.

 

For the crossover use good quality air cored inductors and mount them as far away from each other as possible, with one horizontal and the other vertical.  This will minimize cross inductance.  Please select polypropylene caps.

 

This should be an easy low budget speaker to construct.  I would welcome comments from anyone who builds a pair.

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