Active controlled BR-system

[b_force]

Introduction
Sometimes you want to use your favourite driver or have to use a specific driver in a design, but unfortunately the BR pipe is way to long.
You can use a smaller pipe diameter, however that limits the max SPL (because of the air velocity) and would be a sin for a driver with a lot of cone excursion.

Shorten the pipe will result in a BR-system with a high Q and a (huge) peak.
Not really something that solves the problem.

A little theory
Ok, so the problem is clear but how can we find the solution?
First of all, let's translate a BR to an ideal control engineered system.
For control systems there can be said that the total Q is the product of all Q's (because the systems are in series). In other words, if you add a system with a low Q (eg. 0.5) and a high Q (eg. 1.5) the result is the product (Q=0.75).

So if we can add a second system to the BR-system (like a high pass filter or parametric EQ) maybe we get a satisfactory result.

Research and simulations
To clarify things, I've used simulation from winISD.
This little piece of software is fine to simulate control systems. (a few people know that ).

For the example I use the Adire Audio Extremis 6.8 in a box of 15 litre with a pipe of 5.1cm in diameter.
- Grey = BR-system wit no active control
- Orange = BR-system with a high pass filter with a Q of 0.5
- Yellow = with Q=0.31

The TFM:


Group Delay:


Cone excursion:


Air velocity:


All the simulations are with the same SPL.
The cone excursion and flow rate are significantly lower with the active controlled systems. Also the the pipe is shortened from 29.15cm to 20.50cm.
The disadvantages is the groupdelay and a higher -3dB point.

We can also look for the same flow rate. Therefore we need a smaller pipe diameter (thus the length is even shorter)

SPL:


Air velocity:


Or we use the same 5.1cm pipe and play louder.

Air velocity:


SPL:


Cone excursion:


Those where the results with a 2nd order high pass filter.
Why different corrections?

There are several reasons for that.
First of all you can see that the behaviour is different. (group delay)
*note:*
Group delay, cone excursion, frequency response etc are all related to each other. You can also say that systems with the same group delay have always the same frequency response etc.

Second, a 2nd order high pass with a Q of 0.5 (LR that is) can be made of to first order systems. So you need only two resistors and two capacitors (no opamp). On the opposite side, the load may not influence significantly.

What are the pros and cons?

Pros:
- With the same volume the BR pipe is shorter
- Cone excursion is lower
- Air velocity (same pipe diameter) is lower
- Smaller pipe diameter can be used with same air velocity

Cons:
- Higher group delay
- Higher -3dB point
- Correction circuit needed
- Sensitive for tolerances

A DSP can also be used. It will cost much more but you can control the variables much easier.

An other way to correct a BR system is with a parametric EQ.
- Grey = no correction
- Yellow = corrected with high pass (Q=0.11)
- Orange = corrected with parametric EQ

TFM:


Group delay:


Cone excursion:


Air velocity:


SPL: (same air velocity)


You can see that the pipe is even shorter and the group delay is also lower.
The flow rate is a little bit higher. The difficulty would be the precise settings for the parametric EQ.

Conclusion
According to the simulations there can be said that you can control the Q of the system at the expense of some group delay and -3dB point.
Benefits are a shorter pipe length and max SPL.

The main question is, how this will result (and sound) in practice.
Some drivers have huge T/S parameters tolerances and differ from the factory data.

I think there must be find a way to measure (precisely) the total Q of a BR-system.