In audio, we often come across the Q of a speaker. What exactly is it and how does it affect the sound. I will try to explain it in very simple terms and later show how I use it in designing a loudspeaker.
The letter Q actually stands for Quality Factor. It’s just a number to express how a woofer resonates in an enclosure. A woofer has it’s own resonating frequency. This is the Fs in the Thiele & Small parameters. When the woofer is mounted onto a box, it interacts with the air enclosed within the box. This will create a new resonating frequency known as Qtc. It stands for the total Q in a closed box.
In the graph above, there’s a collection of plots with different Q. Right at the top is a Q of 2. What this number indicates is the woofer rings like a bell. It acts like a pendulum. This is not something we want because the bass will lack definition. As the number goes lower, the ringing gets less and less.
For best bass, we target a Q of 0.50. This is known as critically damped. When a woofer has a Q of 0.50, the cone will stop when the signal is removed. In other words, no ringing. So why don’t we always use 0.50. Well for one, not every woofer can do this. Even if it can, the other problem is a Q of 0.50 is not loud. Beautiful tight bass but very soft.
A Q of 0.7 is generally regarded as the best compromise. It gives adequate bass with minimal ringing. It doesn’t mean that all speakers must have a Q of 0.7 or 0.5. It all depends on the quality of the woofer, the size of the box and other factors. One aspect of Q that we should avoid is a Q of more than 1.4. The ringing will become so bad that the bass quality suffers considerably.
Practical use of Q
As an example, I would like to design a 2-way bookshelf with enough bass. I don’t want to apply EQ to boost the bass. The bass must be loud enough on it’s own. It would also be advantageous if the box is small too.
This is a very common request, small box with bass. Small box means small woofers. And small woofers, as we all know, are not optimized for bass. Can it be done?
After going through my collection of woofers, I ended up with my 5″ Tang Band W5-1685 midwoofer. The box modelling in Fig 1 predicts how the bass will be when mounted onto a 10 liters bass reflex.
Fig 1 – Tang Band W5-1685 Box Modelling
In box modelling, the parameter I watch for is the System Q. With the W5-1685 in a 10 liters bass reflex, the Q is 0.9. I think I can live with that. I then tune the port to 50Hz. This results in a bass boost of +3dB at 80Hz. After that, the woofer begins to roll off. Will it work? Will I get the bass that I’m after?
Fig 2 – Frequency Response of W5-1685.
Fig 2 is the frequency response of the Tang Band W5-1685 in the 10 liters bass reflex tuned to 50Hz. Measurements below 500Hz includes reflections in my room. Ignore the deep notch at 150Hz. It is an anomaly in my measurement setup. It’s a floor bounce picked up by my measuring microphone 1 meter away.
It is reassuring that the tip of the 80Hz is at 85dB. It just so happens that 700Hz~5kHz is also at 85dB. We can take this as the normalized spl. This measurement was made with no crossover and other networks in place. Just the raw W5-1685 in the box.
How does it sound like?
Overall, very good. Actually, the first thing that struck me is how well behaved the Tang Band W5-1685 is. It is remarkably flat from 700Hz~5kHz. After that, there’s the cone breakup. This midwoofer can be used as a full range if need be. I can’t detect any harshness in the treble. The highs are not as sweet as a tweeter but which full range driver is. What about the bass?
It’s loud enough without overwhelming the midrange which is important. I find that when I don’t have to strain my ears to hear the bass, it is more relaxing. This Q does just that. Is the highish Q an issue?
Well, the bass is not as tight and detailed as I would like it to be but it’s perfectly acceptable for most listeners. All I want is nice music from a pair of compact speakers for general use and this design meets my objective.
So far, this exercise only establishes the bass character of my intended design. There is still a tweeter, the crossover and total cost to take into consideration. But it does demonstrate the importance of Q in designing speakers. If the bass is wrong, the quality of the speaker will be affected. The best or most expensive tweeter will not help.
That’s why the first thing I do is to model the box response. It gives me an idea of the character of the bass. But that is only in simulation. I still have to build a test box and listen to the bass.
March 22, 2020Articles