Tech Design.....

Hybrid Design Philosophy: Passive crossovers with active equalization.
Hybrid design is a design philosophy in which a two or more way speaker system is designed using
simple passive crossovers and active equalization. The passive crossovers are used predominantly to control the
driver response in the stop band or crossover region while active equalization is used to compensate for such effects
as the baffle step, baffle diffraction, dipole equalization and driver sensitivity mismatches. The benefits of such a
philosophy approach many of the benefits of a fully active system without the drawback of excessive channels of
amplification. The hybrid design  philosophy results in a system with greater efficiency, greater linearity and greater
dynamic range than can be achieved with a fully passive system using the same driver compliment and having the
same frequency response. This approach has been followed in the design of the NaO family of speaker systems.
Presented here is a brief tutorial on the design procedure as applied to a simple, hypothetical 2-ways speaker system.

We begin by defining the speaker system. We would like a 2-way system with low frequency cut off in the
40 to 50 Hz range and a crossover in the 1.5 to 2K Hz area. The system is to use an 18cm woofer and 2.5cm tweeter
in a sealed box. After the design of the box we would measure the response of the woofer
and tweeter. The measured response might look as depicted in Figure 1.
Figure 1. Driver response as measure with drivers mounted in box
The next step is to design the passive, low pass filter for the woofer. To do so we set the target
level at the manufacture specified sensitivity, say 86dB/M/2.83 volts, and work forward. Examining the woofer
response we see two obvious baffle related features: the baffle step below 200Hz and the baffle related bump
centered around 700 Hz. The baffle step is ignored at this point and concentration is on flattening the response
above 200 Hz using an active Q bump filter. For the bump filter a parametric boost/cut filter is selected with
specification of center frequency, Q and dB gain/cut. These parameters are easily adjusted dynamically while
monitoring the response plot.
Form examination of the woofer response it is apparent that a center frequency of 700 Hz with a gain of -2.5dB
is a reasonable first guess. After tuning the value for Q for the filter the woofer response looks as shown in
Figure 2.
Figure 2. Woofer response with 700 Hz bump equalized.
The next step is the development of the passive low pass filter for the woofer. An initial target response is
chosen and a suitable passive circuit is place in line with the woofer. Here I chose a 2K Hz, LR4 response as the
target. The passive filter is then optimized to match the target response above 300 Hz. The result of the
optimization is shown in Figure 3. As can be seen the optimized response matches the target (black) very well
above 300 Hz. The response of the passive filter is shown in pink. Note that it is flat and only affects the
response in the stop band.  
Figure 3. Woofer passive filter response (pink) and filtered response including
bump filter (blue) compared to target response (black).
Figure 4. Tweeter passive filter response (pink) and filtered tweeter
response (blue).
Once the initial low pass woofer filter is designed the effort turns to the design of the high pass filter for the
tweeter. This is shown in Figure 4. The pink curve is the filter response and the blue curve is the filtered
tweeter response. The target is a 2k Hz LR4 high pass response. Again the passive filter response is flat
through the pass band and only controls the response of the tweeter in the stop band. Note that the tweeter
level is at 90 dB compared to the 86dB level of the woofer. The flat behavior of the woofer and tweeter
passive filters indicates that no response shaping or
attenuation is applied in the passive filters assuring that any associated insertion loss is a minimum.

With both the passive filters designed the summed system frequency response, without any equalization
applied, looks as shown in Figure 5.Clearly this is far from desirable. Additionally, the actual crossover point
appears to be somewhat below the 2k Hz point, but is well with in the target of between 1.5 K and 2 K Hz.
Figure 5. Unequalized system frequency response.
The next step is to develop the system equalization. Two additional elements are required in this simple
example; 1) a low pass shelving function to boost the response in the region of the baffle step and 2) a second
low pass shelving  function to attenuate the tweeter level. Also recognize that full baffle step correction
requires a +6dB correction and the tweeter attenuation necessary is -4 dB relative to the targeted midrange
level of 86db. Thus all that need be done is to determine the center frequencies of these shelving filters since a
shelving filter is completely specified by center frequency and boost/cut. Some additional minor optimization
may be applied to fine tune the response. The result is shown in Figure 6. Additional active equalization stages
can be added if necessary to further shape the response.
Figure 6. Equalized system response.
At this point focus is again on the passive filters. The design software allows optimization on both the system
amplitude response as well as the interdriver phase difference through the crossover region. Thus an
optimization on the passive crossover with the active equalization in place is performed to assure the phase
behavior is as desired. Then, to cross the T's and dot the I's the equalization circuit  is re-optimize. The final
result is shown in Figure 7.
Figure 7. Final, equalized response of hybrid actively equalized passive crossover system.
Figure 8, to the left, shows the polar response of the hypothetical system at the crossover frequency and one
octave above and below it.

Figure 9 shows the most significant result. The area shaded in red represents the degree to which the voltage
signal applied across the speakers terminals is attenuated by the active equalization circuit compared to that
which would be applied if the system were fully passive. If the impedance were constant, this would be a
direct measure of the amplifier power that is dissipated in a fully
passive system with the same response when playing at the same sound level. In effect, the hybrid system
takes advantage of the frequency dependent sensitivity of the system.
Figure 8. Polar response of
system at 850, 1700 and 3400
Figure 9. Lower trace is the response of the active equalization. Red area represents
reduced requirement placed on the amplifier.
The implications are far reaching with regard to the performance of the speaker system. For example, consider
a situation when a fully passive version of the speaker is asked to reproduce
two tones at equal sound pressures. Let the two frequencies be 100 Hz and 1k Hz. If the amplifier's maximum
voltage output, V
max, is referenced to 0dB then to assure that the amplifier output
remains below clipping the level of each signal must remain below a maximum value of  -6dB,
or 1/2 the maximum output voltage of the amplifier. This is because the amplifier must amplify the sum of the
two tones and apply the summed signal, unequalized and/or unattenuated, directly
to the speaker. Depending on the phase relationship of the two tones, the maximum possible magnitude of the
summed tones is 1.0 or 0dB. However, with the hybrid system the signal is equalized prior to being input to the
power amplifier. Thus, according Figure 9, for equal sound pressures of the two tones, and at the same level
produced by the fully passive system, the 100 Hz signal would be attenuated by about 2.5dB to about 0.375
max while the 1k Hz tone would be attenuated by 9 db, or 0.177 Vmax, by the equalization network. The
maximum possible sum of the two tones would be 0.552 V
max or 5.15 dB below the maximum output of the
amplifier. Thus the hybrid system, driven by the same amplifier, would have 5.15 dB of headroom when
playing at the same volume. This obviously result in more efficient use of amplifier power, and greater dynamic
range of the system throughout the region shown in red in Figure 9.

It was also stated that this approach potentially results in greater linearity of the system. This is because of the
simplicity of the passive crossover and that the response of the passive networks is flat, with minimal insertion
loss, across the pass bands of the filters. As a result, any potential variation in the passive filter transfer
functions due to variations in the load represented by the drivers is, for the most part, limited to the immediate
region of the crossover. The removal of the equalization form the passive sections to an active circuit eliminates
the potential of the
equalization to be affected by such variations. The result is greater linearity of the system.

As can be seen, there are considerable advantages to the hybrid approach to system design; simpler passive
networks, improved linearity, greater efficiency and dynamic range. At the same
time the system retains the ability to be driven by a single amplifier thus avoiding the expense of multichannel