For optimal performance and accuracy in a 2+ way speaker, most crossovers will require the following networks.
The sensitivities of transducers in a multi-way speaker are typically different and their levels must be matched to achieve the acoustic design goals. As you can see from the transducer frequency response measurements, the Annex tweeter is 3 to 8dB higher in sensitivity than the woofer. The first circuit to be designed is the level matching network because it affects the circuit impedance that the filter designs are based on.
The level matching network above is typical. Depending on the frequency response and impedance requirements, resistor R2 can be eliminated. If it is required, the value can highly influence the impedance curve which of course has a lower limit ( my rule of thumb is no less than 3 ohms within the pass band ).
The transducer impedance curves confirm that their impedance magnitude and phase vary substantially throughout the pass band. One of the crossover filter calculation terms is impedance and the filter response will change if the impedance changes. To mitigate this effect, conjugate (impedance compensating) networks are used. Show above is a typical woofer impedance compensation network. As the woofer’s impedance increases with frequency due to the voice coil inductance, the capacitor impedance decreases to keep the impedance flat.
Transducer impedance variations can work in your favour to reduce the electrical crossover order requirement and/or flatten the frequency response as was at least partially the case with the Annex crossover.
Frequency response optimization
This is typically required to address the following conditions causing a deviation from a neutral frequency response.
- Baffle step / 2pi to 4pi transition/diffraction caused by the cabinet baffle size ultimately becoming smaller than wavelengths of frequencies typically below a few hundred hertz
- Transducer cone/diaphragm breakup, secondary resonances, directivity,
- Cavity resonances in the transducer or cabinet
- Listener preferences
I did not include an example of a network designed to do this because there are so many forms of them. Luckily the Annex only required a baffle step compensation network.
Low pass, band pass, high pass filters
These fundamental filters ensure the transducers only receive a defined band of frequencies to reproduce. Choosing the frequency bands and the slopes or attenuation rate of the filters can significantly affect the sound, power handling and dispersion characteristics of the speaker. For the Annex speaker, I used 2KHz Linkwitz Riley 4th order 24dB/octave (LR4) filter targets as shown in the transducer frequency response measurements.
The 2KHz crossover frequency target is based on parameters such as the tweeter’s resonant frequency, the filter slopes, directivity of the transducers and their frequency response. These are only the initial targets and depending on the results of the initial computer system simulation, they can and typically do change. LR4 is my preferred filter for this speaker because the transducer’s outputs are in phase at the crossover frequency (if the filters are correctly designed) , electrical phase inversion of one of the transducers isn’t required, the steep slope ensures good tweeter power handling capacity and the off-axis interaction between the transducers is minimized.
The crossover shown above is a textbook standard 2 way LR4 circuit. I’m targeting an acoustic LR4 filter and because the transducers already exhibit attenuation outside of their pass bands, my electrical filter order / slope requirement can be reduced to that of a 3rd or even 2nd order filter.
While summation of the transducers in the above graph isn’t too bad, the transducer phase curves (light red and blue traces) are not in phase. My target is to always face the polar vertical lobe directly forward of the tweeter which is my reference vertical axis. To accomplish this, alignment of these phase curves is required. Phase compensation will either increase the delay of the tweeter ( typical) and/or reduce the delay of the woofer. A dedicated network may not be required. Multi-order networks are not minimum phase and therefore it is possible to manipulate the phase while achieving an acceptable frequency response.
Software modeling of the speaker is a great place to start. This requires good polar transducer frequency response data, impedance measurements and accurate component models. It is usually not difficult to achieve a 2way software modeled flat on-axis speaker frequency response. That may be a good place to start but typically the best sounding speaker will not be achieved by using the software modeled network.
Even with some of the best speaker modeling software, frequency response measurements of the physical speaker will not exactly match the software model. There are several potential reasons for such discrepancies.
- Inaccurate frequency response or impedance measurements
- Incorrect modeling setup
- Parasitic(stray) inductance, capacitance and/or resistance not included in the model
- Cable resistance
- Poor electrical connections within the network
- Inconsistent setup/environment between raw transducer and speaker with network measurement stages
One either rectifies the cause of the discrepancies and/or alters the network to achieve the target response.
Once the speaker measures “well”, it’s time to evaluate the performance with music and speech. This is a step that I never skip. The speaker’s measurements may indicate that it should provide acoustic perfection but there is always room for improvement. 1dB frequency response deviations can be audible to the untrained ear. These may not appear to be problematic when examining the measurements but a voicing session can highlights issues very quickly.
My goal with the Annex speaker is a neutral speaker that doesn’t add any specific character to the sound. No excessive bass or hyper accentuated treble allowed. The initial voicing session consists of critical listening to a single speaker in an IEC calibrated room (average of most listening rooms) at an average level of 80dBA with about six to eight music and speech tracks. Subsequent voicing sessions include comparisons with well received reference speakers behind a blind screen and a broader range of source material. These are also conducted with single speakers to ensure the differences aren’t masked as is the case when comparing pairs of speakers in stereo mode. Final voicing is conducted in stereo mode.
It’s not usual to cycle between crossover design, measurements, voicing, and on-the-fly crossover tweaking extending over weeks or months in the pursuit of sonic perfection.