Topic: The true horror of passive crossovers !
A while ago on this forum there was some discussion about loudspeaker crossover networks and the relative merits of the active and passive approach. This prompted me to investigate passive crossovers further.
First, some background:-
Loudspeaker drive units are designed to be driven by a very low impedance, and the published frequency response plots from the manufacturer will always be shown with the drive unit driven directly from an amplifier, without any intermediate crossover network. If the driving impedance is not low, the response will be adversely affected, and the amplifier will lose control over the speaker cone motion. The degree of control is termed 'damping' and is defined by a 'damping factor', which is simply the ratio of the nominal speaker impedance (usually 8 ohms) to the driving impedance. So for example, an amplifier having an output impedance of 0.5 ohms would have a damping factor of 16.
Amplifier designers generally strive to achieve a damping factor of 50 or more, and for good ones it can be several 100s. But what happens when you insert a passive crossover network in between the amplifier output and the speaker drive units ?
The effect of the passive crossover :-
To quantify this, we need to establish the impedance of the crossover network output, since this becomes the new driving impedance for the speaker unit. The plot below shows this impedance for a 2nd order passive Linkwitz-Riley crossover network with a crossover frequency of 2kHz.

As you can see, over most of the audio band the impedance is not very low, reaching a maximum value of 8 ohms at the 2kHz crossover frequency. By calculating the ratio of this impedance to 8 ohms, we can establish the effective damping factor when the crossover network is in circuit. This is shown in the plot below.

At 30Hz, the damping factor is a just about tolerable 34, but it drops sharply as the frequency is increased, dropping to less than 2 right from 500Hz to over 7kHz. At the 2kHz crossover frequency the damping factor is just 1 !
So what does this mean ?
The results show that a typical passive crossover has an absolutely disastrous effect on speaker damping. Over most of the audio band, the damping factor is very low, so the amplifier will have almost no control over the cone movement at all. Were it not for the mechanical self damping in the drive unit suspension, the cone would be flapping around wildly. As it is, the cone movement will certainly not be accurately following the applied signal voltage from the amplifier.
What about active crossovers ?
With an active speaker, the crossover network is connected at the amplifier inputs, and the amplifier outputs drive the speaker drive units directly. In this case, the excellent damping factor of the amplifiers is maintained, and the cone motion is accurately controlled at all frequencies. In the past, the main argument against the active speaker approach has been the cost. But these days, power transistors are cheap, so there really is no excuse !
Chris.

