Passive to active
Copyright 2021 © Troels Gravesen

Why it is not so easy to convert a passive speaker into an active speaker

I sometimes have the question on converting a passive design into an active one by buying a 3-way plate-amp with DSP, like the Hypex FA253, apply the specified points of crossover and the slopes used, let's say 2nd order, LR2, at 400 and 3000 Hz.
In order to do this you have to replicate the transfer function of the passive crossover with regard to amplitude and phase in the DSP software.
Not that easy! Here's why:

Below in fig. 1 you see the situation in an ideal world, where we have three drivers, bass, midrange and tweeter, all with linear frequency response from 20-20000 Hz. Impedance not shown, but this will be a perfect 8 Ohm impedance also from 20-20000 Hz.
I have here made the tweeter have a sensitivity of 90 dB (orange), the midrange with a sensitivity of 88 dB (blue) and the bass 86 dB (red), which means we should be able to make speaker with a system sensitivity of 86 dB as the bass driver obviously determines that value. We can't make the bass driver play louder than it can with a passive crossover, but we can attenuate the midrange and tweeter to match the bass driver. In an active set-up we can make the bass play as loud as the others by increasing gain.

This wonderful world does not exist!


Fig. 1.


In fig. 2 below you see a tweeter (red), a midrange (green) and a bass driver (orange) on a real-world baffle. It may come as a surprise to many that the frequency response is also dependent on the baffle size, and where on that baffle the driver is placed, but so it is. Even on an infinite baffle the frequency response is not linear.
Manufacturers usually display a frequency response on an infinite baffle (except SEAS) and this is very useful.
The bass in this example is reasonably linear from 100-500 Hz, the midrange is reasonably linear from 300-3000 Hz and the tweeter reasonably linear from 2 kHz to 20 kHz. The midrange is quite a bit more sensitive compared to the other two and should require some attenuation to match the others.




Fig 3 below: In the wonderful world of perfection we could do as shown, apply a 2nd order low-pass to the bass, a 2nd order low- and high-pass filter to the midrange and a 2nd order high-pass filter to the tweeter. We connect the midrange driver with opposite polarity as we should from a 2nd order crossover, and we assume the drivers have the same sensitivity (SPL/2.8V) and we have a beautiful straight line, the green one - and we're happy.
Not so, because, again, drivers aren't linear. We also assume drivers are time-aligned, not so. The tweeter is mostly some 20-30 mm in front of the other drivers. Please read here what it means: You need to be able to analyse the dZ to apply the proper delay of the tweeter in microseconds if your tweeter is at ear-height and you want to listen with tweeter on-axis.


Fig. 3.


Fig. 4 below:
If we insert the drivers shown in fig. 2, we get this. The midrange and tweeter is way too high in amplitude and also the point of crossover between mid and tweeter is too high. It doesn't work and it would rip off your ears.
You may argue we just add some attenuation to tweeter and midrange and we're flying. That would certainly help, but the ragged roll-off the midrange will still distress your ears because the passive crossover attenuates this peaky roll-off from R6+C3 (see fig. 5).

This can very well be done, but the thing is:
You need measuring equipment to fine-tune the DSP software. You need to be able to measure what is going on when designing the software.

Fig. 4.


Fig. 5 below:
In this you see the result shown in fig. 4 compared to the result from the passive crossover. Point is there is a lot more to be done that "just" applying points of crossover and driver attenuation. The passive crossover applies a lot of equalisation and we need to replicate this in the DSP software - and we need measuring equipment to do so.

Fig. 5.


Fig. 6 below:
This shows the transfer function of the active crossover (left) compared to the transfer function of the passive crossover (right). Not quite the same...

Fig. 6.


Fig. 7.
Above an example of a low-pass filter for a 2-way speaker.
As can be seen, a lot of equalisation and lots of boosts and dips have to be done to make target frequency response like seen below. This can only be done by having good measuring equipment.


Fig. 8.