Subwoofer setup 101: subwoofer crossover frequency, slope and phase for two channel systems

In this educational article we describe how to properly setup and integrate subwoofer in a stereo or two channel system using the XTZ Room Analyzer II Standard package.

Two channel vs. home theater crossover considerations

There are a number of factors which make sub integration more involved in a stereo system than in a home theater system. More involved because there is greater reliance on acoustical measurements and calibration skills. Here are the major differences:

No line level crossover. A line level crossover splits the audio signal before power amplification into two parts, one of which feeds the sub and the other the main amplifier. This is the type of crossover used in home theater systems. Audiophiles, however, have been conditioned that extra components in the signal chain introduce degradation. Most audiophiles would sell their grandmother before introducing a line level crossover in the signal chain! There are good, high quality, solutions out there to introduce a line level crossover, including the Bryston Sub-10B (analog) and the DEQX HDP-3 / DEQX HDP-Express (digital). These devices introduce very little to no audible changes and are an option for more open minded people. Introducing a line level crossover has a number of benefits including the ability to choose a different crossover point and slope than that dictated by the raw acoustical characteristics of the main speakers. Setting a higher crossover point can often lead to sound quality benefits since the main speakers - and the amplifiers driving them - are subject to lower power handling demands. Furthermore most main speakers will not be able to reproduce bass with the same low level of distortion as the best subwoofers out there today.

 

 

 

No industry standard crossover frequency. The vast majority of home theater systems are setup using an 80Hz crossover. 80hz was chosen to be a good compromise between the need to support the main speakers and localization. In a home theater setup the main speakers are most often smaller 'monitor' types with limited low frequency extension and power handling which require support from a subwoofer if the system is to reproduce bass with any degree of fidelity. At frequencies of 80Hz and below there is a simple rule defined from psychoacoustic research that shows that humans cannot localize sound. In essence we cannot tell where a sound at these frequencies is coming from. This allows the sub to be physically separated from the main speakers. This simple rule does have some complications, however. For one the crossover between mains and sub is not a brick wall. With a 12dB per octave crossover the sub will only be 12dB down at 160Hz. That is why more progressive calibrators are using either steeper crossover slopes, moving the crossover down to 50Hz or both. In a two channel system we have no 'industry standard'. Furthermore most two channel systems have no line level crossover. The choice of crossover frequency must therefore take into account the acoustical characteristics of the left and right speakers and in particular the frequency at which the sound pressure they output starts to fall off.

With these two points in mind let's look at how to integrate a sub with a stereo system.

What you need: an acoustical measurement package

Our approach relies heavily on acoustical measurements. You will need an acoustical measurement package such as XTZ Room Analyzer II Standard that has a real time analyzer (RTA) and 1/3rd octave resolution frequency response capability. The instructions provided below are for the Room Analyzer but you should be able to follow along if you are using other software.

Can't I just use some music cuts? Some people may claim that a sub can be calibrated by ear just by listening to music and twiddling the controls back and forth. Well, if you can do that then you are one in a million! Even if your ear and brain has the ability to analyze frequency and level of a musical note down to a couple of Hz and dB you are still left with the problem that there is no piece of music on the planet that equally energizes the low frequencies. Good luck with that!

What about test tones and a sound pressure level (SPL) meter? This is a potential alternative, but only if you want to spend hours playing test tones and recording SPL at different frequencies. It's ok to maybe do this once but what if you want to try a different crossover slope or frequency? You'll have to redo all your measurements again. I'd rather be drinking beer and listening to music than grappling with that.

Presenting the Acoustic Frontiers sub integration methodology

Ok! Let's get down to business. Connect your XTZ Room Analyzer to your computer and to the left and right channel inputs on your pre-amplifier or integrated via the included Y-RCA adaptor. The sub should be disconnected. Once you've done that open the XTZ software and go to the 'Room Analyzer' tab. Using the SPL meter function set to 'C-Weighting' and 'Slow-1s' set the volume control on your system so that the 'LCS' (Level with C-weighting and Slow averaging) reads 75dB or thereabouts. This ensures that there is sufficient signal to noise ratio to get a good measurement. Now press the 'Measure' button on the top right to take a measurement of your left and right speakers without the sub.

Screenshot from XTZ Room Analyzer II Standard showing how to set SPL levels and take a measurement

The Room Analyzer will now take a frequency response measurement and display it to you in the main window. Analyzing this measurement will allow you to set the crossover slope and frequency on the sub. You will see that it is not an exact science, and multiple iterations are often necessary to find the best sub to mains integration. But before we look at your system's measurement, let's briefly discuss crossover slopes.

Crossover slope. This control on a sub, most often called the 'Low Pass' filter, is specified as xxdB per octave and comes most often in 12dB and 24dB options, although sometimes you find 6dB and 18dB. The slope defines the rolloff above the crossover frequency. In a situation where there is no line level crossover in the system, as will be the case in most audiophile two channel setups, the appropriate crossover slope to choose will match the acoustical rolloff of the left and right speakers. To find the acoustical rolloff you need to try and fit a straight line to the frequency response measurement. This isn't an exact science as quite often there are few different ways you can fit the straight line to the measurement. Room modes and speaker boundary interference effects also create peaks and dips in the measurement that are not speaker related. Our advice is to focus most on the section of the frequency response after rolloff begins as this is the part that will dictate the smoothness of integration with the sub.

The chart below shows the results of a straight line fit for our measurement. To find the crossover slope you need to find two points on that line separated by one octave. One octave represents a doubling of frequency. Looking at the chart below we can see that the rolloff of the main speakers is around 24dB per octave. The chart makes this easy to see because each set of three squares represents one octave e.g. 31.5Hz to 63Hz is one octave, 63Hz to 125Hz is one octave, 125Hz to 250Hz is one octave. If we start at the square at 25Hz (the square just below 31.5Hz) and count three squares up we get to 50Hz which is one octave. The difference in SPL is 24dB (40dB at 25Hz and and at 64dB at 50Hz).

Frequency response measurement of main speakers taken with XTZ Room Analyzer II Standard - the 25Hz and 50Hz points on the rolloff slope have been annotated

Crossover frequency. Choosing the most appropriate crossover frequency is complicated by the fact that the point to choose depends on the crossover that is built into the sub. Most subs use either Butterworth (BW) or Linkwitz-Reilly (LR) filters. BW filters sum to +3dB at the crossover point whilst LR filters sum flat. The crossover point for a BW filter is the -3dB point and for a LR it is the -6dB point. The diagram below, from this Wikipedia article, shows this clearly.

There is a catch, however, which is that whilst the low pass leg of the sub might be a LR the high pass leg (the natural rolloff of the mains) is not following any particular crossover function in terms of magnitude and phase response. Furthermore most subs do not specify if they use BW or LR filters so you have to guess. You can often tell by the slope options they have. LR filters only come in 12dB and 24dB versions therefore if your sub only has those choices it is likely to be using LR filters. If it has 6dB and 18dB options then it is likely to be using BW filters. So the choice of crossover frequency is arbitrary. We normally use the -6dB point to start with and find this by looking at the average SPL across the range above the crossover point. Looking at the diagram above this is around 65dB so the -6dB point relative to that is around 40Hz.

We're ready to take a measurement of the sub now! Dial those crossover values into the sub crossover, open the Room Analyzer and take another measurement. This time you want to measure the sub only. Have a close look at the chart, because it will tell you if the crossover frequencies and slopes marked on the sub actually measure that way in real life! In our case (we used a JL Audio Fathom F112) they were spot on. You'll see there is a bump in the frequency response at 75Hz or so, which is a room mode. If you see things like this you should try and see 'through them' by extrapolating the straight line above the problematic frequency.

Frequency response of sub taken with XTZ Room Analyzer II Standard - extrapolate the straight line and ignore bumps and dips due to room modes and boundary interference effects

Once you've selected the crossover slope and phase on your sub the next step is to use the RTA function to examine the frequency response of the whole system playing together i.e. Left / Right speakers and sub. So open up the XTZ software again and go to the 'RTA' tab and click on 'Measure'.

Level Part 1. The level of the sub should be 'eyeballed' by looking at a RTA measurement of the whole system playing together and approximately matching the level below the crossover point (i.e. the sub level) with the level above the crossover point (i.e. the left and right speakers). Remember that there might be big dips in the frequency response at the crossover since you haven't set phase properly yet. You will fine tune level after setting phase correctly.

Polarity and Phase. Many people get confused by polarity and phase. The thing to remember is that both controls are adjusting the same thing. The phase control is normally variable between 0 and 360 and the polarity has two settings 0 and 180. Both controls are changing the phase at the crossover frequency. If you set polarity to 180 and phase to 0 you'd get 180 degrees of phase shift at the crossover. If you set polarity to 0 and phase to 180 you get exactly the same result. So they are interchangeable. Theoretically speaking a 6dB filter has 90 degrees of phase shift at the crossover frequency and each extra 6dB adds 90 degrees, so a 12dB filter is 180 degrees out of phase and so on. Theory goes out of the window at this point, however, since the phase of the main speakers at low frequencies is very hard to pin down since not only is there the main rolloff of the speakers, there is also ports and other things that cause strange phase shift effects at low frequencies. Therefore the method we use involves using a RTA. What you do adjust the phase controls on the sub to get the maximum SPL at the crossover frequency. When you find the phase setting that produces the most SPL at the crossover frequency it means that the sound waves from the sub and mains are properly in phase and not causing any phase based cancellation.

In the XTZ software take another RTA measurement, but this time slowly change the phase control on your sub whilst watching the RTA bar corresponding to the crossover frequency you have chosen.

 RTA taken with XTZ Room Analyzer II Standard showing the frequency band we care about in this example - that of the crossover point between the sub and main speakers

Once you've found this point a quick check can be done - flipping the polarity switch will then change the phase relationship 180 degrees which should result in a nice deep null at the crossover point. To measure this go to the 'Room Analyzer' tab and take a measurement. Save this as Overlay '1'. Now flip the polarity switch on the sub and take a second measurement. Now take a look at the null in this second measurement. If it is not symmetrical or deep then keep on tweaking that phase control!

The chart below shows what it should look like - the mains and sub when measured together with the phase set correctly should be virtually flat (green line) and when they are 180 degrees out of phase should have a nice symmetrical null at the crossover point (blue line).

In phase / out of phase - green line is response of mains and sub when they are in phase. Flipping the polarity switch for a check gave the blue line. The deep symmetrical null is what we expect when the phase control is set correctly.

I know what you are thinking! You are looking at the graph and wondering why it isn't a perfectly flat straight line. The chart above is actually very good - it's within 5dB over most of the range below 300HZ. You have to remember the other major factors at play - room modes and speaker boundary interference. Even if you get your sub and mains properly integrated there will still be peaks and dips in the frequency response caused by room acoustics. To mitigate these effects you need to start looking at subwoofer placement relative to room modes / boundaries, using multiple subwoofers in mode canceling arrangements and using parametric EQ. Those aspects are beyond the scope of this blog post but if you want to learn more follow the links above.

Level Part 2. This is the point at which you play some music and find the best level for the sub. It's best to play a variety of music. Aim for the point at which the sub doesn't draw attention to itself but rather provides a solid foundation for the presentation. It will take a little while but soon you will find the best level and once you've found it you shouldn't need to move it.

After this process you should note down and live with your sub settings for a few days. It's often worth experimenting with different slopes and crossover points as these can sometimes lead to slightly improved results. If you don't have patience then don't worry, following the instructions above should result in a well integrated sub.

Conclusion

In this educational blog post we've tried to explain how to set the crossover frequency, slope and phase controls appropriately in a two channel system without a line level crossover. Following the instructions here will get you a properly integrated sub. You may still have frequency response anomalies related to room modes and boundary interference that you can solve through sub placement or EQ.

Acoustic Frontiers is based in Kentfield, Marin, California and sells the XTZ Room Analyzer II Standard package mentioned in this article (which we ship globally) and subs from Velodyne and JL Audio. We also offer subwoofer calibration services if you'd like a professional calibrator to setup your sub(s) for you.

What do you think of the methodology? Please leave a comment!