EP500 Port Tuning and Setup

The relative similar amplitude peaks of FL and FH indicate good port tuning while Fm and Fb being only 1.8Hz apart is one attribute that demonstrates it to be a well-executed and linearly-tuned system.

For those who like to get down to the inner details of subwoofer designs, Mark Sanfilipo (our resident loudspeaker engineer) has provided the following equations in the editorial note below to determine a good first-order approximation of the box tuning based on the physical port dimensions we furnished to him on the design of the EP500.

Editorial Note on Port Tuning by Mark Sanfilipo (updated June 23, 2005 )

Driver Branch                                                      Enclosure Branch

First approximation electrical equivalent          Simplified driver/vented box circuit 

Driver Branch
Revc = voice coil DC resistance
Levc = voice coil inductance
Res = resistive electrical equivalent of suspension losses
Cmes = capacitive electrical equivalent due to the cone's moving mass
Lces = inductive electrical equivalent due to suspension compliance

Enclosure Branch 
Lceb = inductive electrical equivalent of the acoustic compliance of air in the enclosure
Rel = resistive electrical equivalent of acoustic resistance of enclosure losses caused by leakage
Cmep = capacitive electrical equivalent of the acoustic mass of the port or vent, including air load.

The vented loudspeaker enclosure is a Helmholtz resonator. Ignoring for a moment the presence of the driver, this resonator is modeled here by the 2nd-order Cmep/Lceb/Rel series tuned-resonance circuit seen at the right side of the circuit pictured above. It's a very simplified electrical equivalent of a Helmholtz resonator.

The driver (in combination with the enclosure) forms the basic system. It's modeled here by the 2nd-order Res/Cmes/Lces parallel resonance circuit, along with Revc & Levc, as seen in the center and left portion of the circuit pictured above. It too is very simplified.

The acoustical inertance provided by the air within and very near both entrances of the port, along with the compliance of the air enclosed by the cabinet, together form a resonant system. The system's driver forms a second resonant system. Together, they form the 4th-order vented box loudspeaker.

At their respective resonance frequencies, the driver branch hits an impedance peak and the enclosure branch hits a minimum. The two impedance peaks typically seen in the usual vented box Z-curve result from the enclosure branch's shunting the driver branch's impedance. The amplitude and shape of the peaks depend upon, among other things, both enclosure and driver losses.

When a given vented cabinet is tuned by altering port dimensions, the values of Cmep & Rel are altered. This, in turn, alters the impedance minimum of the enclosure branch that, running in parallel with the driver's parallel resonance tank, results in an impedance minimum unique to the interaction of the two branches. For most vented box systems, the enclosure branch resonance frequency resides (by design) in general proximity to the driver branch resonance frequency.

In the context of loudspeaker design, when reference is made to "fb" it's used to describe not the resonance frequency of the box as just a simple Helmholtz resonator, but the frequency to which the system is tuned. Though it seems counterintuitive, the frequency to which the system is tuned and the frequency where the inter-peak impedance minimum, fm, occurs by the driver & enclosure circuit branches running in parallel are not necessarily the same. Large voice coil inductance values can result in an fb higher in frequency than fm, for example.

Helmholtz Resonator Equation
fb = resonant frequency
C = speed of sound in air
r = radius of neck
a = area of neck
L = length of neck
L' = effective length of neck

k = correction factor, port with 1 end flanged, the other, not flanged. k = 1.4488 - 1.464 (common range of values)

L' = L + 1.4488r (outer end unflanged)
vb = volume of enclosure

From Kinser & Frey's " Fundamentals of Acoustics "
fb = (c/2*pi) * [a/(L' * v)]^.5
= (179.845) * [a/(L' * v)]^.5

EP500 Approximates
@ port depth = 19"

a = .1191 ft^2
r = 0.1947 ft
l = 1.58 ft
l' = 1.8622 ft
vb = 3.47 ft^3

fb = (s/2*pi) * [a/(L' * v)]^.5
= (179.845) * [a/(L' * v)]^.5
= (179.845) * [.1191/(1.8622 * 3.47)]^.5
= (179.845) * [0.1357]

fb = 24.42 Hz @ L = 19"

I found the EP500 easier to place than most subs. Both myself and Ray Adkins are finding that the more linear the frequency response and bass extension a sub exhibits, the less fussy it is about placement to some extent. The EP500 makes it even easier with its variable trim settings. I settled on rear placement of the EP500 directly behind my listening position and found the "half" trim setting most appropriate to combat a room mode with the subwoofer placed in this location as indicated in the graph below.

By engaging the "Half" setting I minimized the frequency response dip between 42Hz to 50Hz at the primary listening position. Though it did provide more output from 35-40Hz, the overall summed response from all three subwoofers in my system helped to smooth this out. Using a PEQ to flatten the excessive output in the 35-40Hz region is certainly a valid measure to take for achieving the most accurate response.

Upon power up, I did notice an unusual amount of hum, which prompted the words "ground loop" to immediately pop into my head. Just when I was about to start tracing the source of the ground loop, I consulted the handy Axiom manual. It recommended to unscrew the little back panel screw for instances such as these. This physically floats the chassis ground and eliminates a current path between earth ground and the return line. I obliged and my ground loop problem was immediately resolved. Now, if only all of our daily troubles could be resolved this easily, the world would be a much happier place.

After several minutes of idle, I noted the EP500 back panel light remained illuminated green, indicating amplifier power was present. I questioned Axiom about this and they informed me there is no Auto On/Off feature on this sub, unless you utilize the 12V trigger connection. This was a concern to me at first until Axiom informed me the sub goes into auto mute mode when no signal is present, thus the power consumption is negligible since it's a Class D amplifier design. I opted not to use the 12V trigger since I didn't have one pre-wired for the location where I was testing this subwoofer.

Editorial Note on Auto Off (update 07/14/05)
In our investigative studies we actually discovered that there really isn't a true auto off on any powered subwoofer which doesn't have an independent DC trigger line. In reality most subs simply remove the connection between the power output devices and the subwoofer driver during the auto off state. But the power transformer and associated amplifier electronics are still active.