After completing my ML TQWT speakers, using the Fostex FE-164 six inch drivers, I decided I wanted to do another full range speaker project but with an eight inch driver. For this new project, I selected the top of the line Fostex FE-208 Sigma full range driver and ended up building a mass loaded transmission line enclosure. The speaker uses quarter wavelength standing waves to produce the bass response that is reinforced by the port at the bottom of the enclosure.
After purchasing two FE-208 Sigma drivers, I played music through them for over 100 hours before measuring the Thiele/Small parameters. The average Thiele/Small parameters for Driver #1 and Driver #2 are shown below.
I originally bought the Fostex FE-208 Sigma drivers with the idea of building a back-loaded horn enclosure. I modeled back-loaded horn designs that I found on the Internet, including the popular Jericho horn, and several designs that I generated myself using my MathCad worksheets. I looked at over twenty different back-loaded horn enclosure designs. Most of the back-loaded horn designs I analyzed produced adequate bass response but also contained a significant number of higher frequency SPL nulls that I associated with quarter wavelength standing waves in the truncated horn geometry. The back-loaded horn enclosures were acting more like rapidly expanding undamped transmission lines. The time domain impulse response of the back-loaded horn designs typically showed a pair of pulses separated in time by the length of the back-loaded horn divided by the speed of sound. The first pulse comes directly from the front of the driver. A second inverted pulse comes from the back of the driver with a time delay consistent with the pulse having traveled the additional length of the horn. The SPL frequency response nulls as described above, and this potential time domain "echo" troubled me enough that I decided not to pursue a back-loaded horn enclosure. I am still working on this style of enclosure, but I have not found a configuration that I believe will produce mathematically an optimized fairly flat SPL response.
I started looking at bass reflex, transmission line, and TQWT enclosures. The FE-208 Sigma driver's low Qtd presented a problem for achieving an extended flat bass response for all of these cabinet styles. I decided to add a resistor in series with the driver to simulate a higher Qtd system. Adding a 3.5 ohm resistor in series raised the Qtd from 0.224 to 0.335 while at the same time dropping the SPL, for 1 watt at 1 m, from 96 dB to 94 dB. To help control the influence of the series resistor at the higher frequencies, a Zobel circuit was placed across the driver terminals to offset the rising impedance created by the voice coil inductance.
A couple of observations need to be made concerning the role of the series resistor in shaping the system SPL response. The series resistor does not change the performance characteristics of the driver one bit, it only forms a voltage divider that modifies the signal level seen at the driver's terminals. Below 100 Hz, the driver's impedance is quite high (> 20 ohms) so well over 85% of the voltage signal from the amplifier is seen across the driver terminals. Above 100 Hz, the driver's impedance approaches a constant 8 ohms (due to the Zobel circuit) so only 70% of the voltage signal from the amplifier is seen across the driver terminals. The series resistor attenuates the SPL response above 100 Hz by simple voltage division, it does not impact the performance of the FE-208 Sigma driver. No details in the recorded performance are lost.
Adding the series resistance was a predictable change for my particular set-up. I am using a solid-state amplifier with a very high damping factor and 200 watts of power per channel. A reduction in the speaker's SPL rating was not a big concern for my system. If I were using a tube amplifier, with a low damping factor, then the series resistance could probably be reduced or maybe even eliminated. The SPL rating would then increase towards the originally measured value. If you decide to build this project, set the value of the series resistor to be consistent with the type of amplifier being used.
I used the MathCad worksheet "ML TQWT.mcd" to design the enclosure. I ran simulations until I settled on a design that was both compact and met my low frequency performance goals. I used the same construction techniques as the ML TQWT project to build and finish the speaker cabinet. After installing the driver, the Zobel circuit, and the 3.5 ohm series resistor I measured the impedance and SPL as functions of frequency using the LAUD computer software. These measurements were used to design a Baffle Step Correction circuit. The MathCad design simulation, the enclosure drawing, the complete correction circuit, and the final impedance and SPL measurements are presented below.
After reviewing the smoothed SPL response, notice that there are several significant dips in the frequency response curve below 1000 Hz. At approximately 190 Hz, 570 Hz, and 950 Hz the calculated differences in the path lengths, for a straight path from the driver to the microphone and a second path between the driver and the microphone that reflects off the floor, are equal to odd multiples of one half wave length. This is the floor bounce cancellation often discussed when designing speaker enclosures. Just above 200 Hz, there is another cancellation that occurs due to the differences in the path length and the relative phase of the output from the driver and the port at the microphone position. As the distance between the listener's position and the speaker increases, the depth of these dips should decrease producing a much smoother SPL frequency response curve.
In the project title, an implied question is raised concerning the classification of this enclosure design as a simple bass reflex cabinet or as a mass loaded transmission line cabinet. To try and answer this question, an ANSYS acoustic finite element model was constructed and used to calculate the natural frequencies and mode shapes of the air in the enclosure. The plotted output from this model is included below. Based on these plots, I concluded that quarter wavelength standing waves occur and that this enclosure behaves as a mass loaded transmission line. The quarter wavelength standing waves are what generate the bass output from the port. A uniform compression of the air volume, typically associated with a bass reflex enclosure design, does not occur.
Now we reach the bottom line. After all the math and measurements, how do the speakers really sound? There are some similarities and some differences when comparing these speakers to the original ML TQWT's using the smaller Fostex FE-164 drivers. The FE-164 drivers exhibit visibly larger cone motion when acoustic bass and drum recordings are being played at moderate listening volumes. The FE-208 Sigma has much less cone motion for the same recordings played at the same listening levels. The larger FE-208 Sigma driver delivers significantly more bass punch. This is one big advantage of the eight inch FE-208 Sigma driver. At the other end of the frequency spectrum, the FE-208 Sigma does not produce as forward a presentation or seem to extend into the higher frequencies as far as the smaller FE-164 driver. If this were to become a significant disadvantage, it could be handled by a super tweeter crossed over above 10 kHz. I change my thinking on the high end extension almost every time I listen to the two pairs of speakers. On a few recordings, I feel that the high end from the FE-208 Sigma might be lacking just a little bit. But on most recordings, I do not feel that anything is really missing at the very top end. If there is a difference in the high frequency response, between the eight inch FE-208 Sigma and the six inch FE-164, it is small and probably more subjective based on a listener's personal taste.
I have not spent as much time tweaking the correction circuitry as I would like, so some of the perceived high frequency roll-off might be improved by playing with the Zobel circuit components and the value of the series resistor. The addition of a super-tweeter is not obviously necessary and I am not contemplating adding one at this time. Overall, the sound produced by the larger eight inch full range driver has been promising enough to increase my interest and got me thinking about higher performance eight inch full range drivers. But that is another story that may develop in the coming months.
These speakers eventually found a permanent home in my family room. They are positioned on either side of the fireplace right up against the back wall. Being against the wall really reinforced the bass response. I started to consider redesigning the baffle step correction circuit (BSC circuit) to reduce the 6 dB of attenuation that I had originally applied. My first quick attempt was to reduce the parallel resistor value which did improved the mid and high frequency performance of the speakers.
While considering a complete redesign of the baffle step correction circuit, I received an excellent recommendation from Jean-Philippe Bondy. Jean-Philippe recommended placing a capacitor in parallel with the filter to form a by-pass at the high frequencies. The capacitor would cause the high frequency response to rise. If an appropriate capacitor value was used this rise in response could be designed to occur where the driver's natural high frequency response starts to roll-off. High frequency extension of the SPL response could be realized without requiring a super-tweeter.
The result of this redesign was a schematic and parts list for the new BSC circuit. The following picture shows the assembled circuit. The measured impedance and the measured SPL are also shown below for the old and new style BSC circuit designs.
From the impedance measurements shown above, you can see the capacitor starting to bypass the BSC circuit just above 3 kHz. The SPL response shows that the overall efficiency has been improved and the high frequency response does extend further then with the original BSC circuit design. The room reinforcment of the bass frequencies, by the back wall, helps produce a nicely balanced result. The speakers sound brighter and the need for a super-tweeter is not so evident.
