Thermal Compression
Subwoofers achieve deep bass response even though their enclosures are usually quite small in proportion to the driver cone area because they are equalized. Without equalization the response might extend only to 50 Hz or 40 Hz. The lowest frequencies are boosted to provide balanced system response to low frequencies.

A consequence of this boosting is that much more power is delivered to the driver than in a normal, unequalized speaker. The power supplied to the drivers at 20 Hz can be 20 or more times normal. This large amount of power results in the coils running hot even during only moderately high demands.

A significant problem stems from the fact that the electrical resistance of copper is strongly temperature dependent, having a temperature coefficient of 0.39%/°C. Therefore, when the voice coil temperature reaches 200°C, the resistance has increased by 70% which causes a reduction in current, and, therefore, output, by 4.5 dB.

The situation is actually more complicated because resistance is only one of three components of driver impedance (although the largest at most subwoofer frequencies), the others being motional and inductive impedance. The following graph shows the total impedance of the drivers in the enclosure and also the resistive, motional and inductive components that combine to produce it.

Total impedance of the SS2 (top line) and its components of resistance (at 0 dB), motional impedance and inductance.

Since the resistance is the only one of these three impedance components that is temperature dependent, the impedance does not increase with temperature uniformly at all frequencies. Where the other components are major contributors to the total impedance, near resonance and at higher frequencies, the impedance does not increase as much as it does at other frequencies.

Therefore, the shape of the total impedance curve changes and therefore the frequency response changes. The following graph illustrates, from top to bottom, the impedance at 200°C, the room temperature impedance, and the change in frequency response that results. You can see that the sensitivity has decreased 2.5 dB at 40 Hz but 4 dB at 20 and 80 Hz.

Top to bottom: total impedance at 200°C, at room temperature, and the sensitivity change at the elevated temperature.

A solution
The SmartSub incorporates a solution that consists of measuring voice coil temperature in real time and using this information to adjust the gain and frequency response of the amplifier to correct the sensitivity and response changes that would otherwise occur. This correction ensures that the output is not compressed or imbalanced during high demand.

The SmartSub uses a heat sensor on the voice coil to measure voice coil temperature in real time to allow correction of sensitivity and response changes.

Wall and corner placement problems
It is well known that placing any speaker, including a subwoofer, near a wall will cause both an increase in bass level and unevenness in the response due to reflection from the wall. The effects of corner placement are more complex than single-wall placement since there are then two sets of low frequency level and reflection effects. In fact, these effects are quite predictable.

The general increase in level affects frequencies below approximately 300 Hz and its degree is dependent on the distance from the wall. It is caused by the fact that the sound radiation is confined to a smaller and smaller solid angle as the speaker's distance to the wall becomes less and less. This effect is illustrated in this graph for wall distances of 1.8, 1.0 and 0.5 meters.

Response changes caused by reinforcement from a nearby wall at distances of 1.8, 1 and 0.5 meters.

The reflection from the wall causes a partial cancellation in a particular frequency range which is determined by the distance to the wall. The severity of the cancellation is determined by the strength of the reflection which is also determined by the speaker-to-wall distance.

So, if the speaker is a relatively large distance from the wall, the cancellation will occur at a low frequency and be mild. If the speaker is close to the wall the effect occurs at a higher frequency range and is more severe. This second graph illustrates the wall reflection effect for the same three distances. When both these effects are added together, the result is illustrated in the third graph.

Response changes caused by reflection from a nearby wall at distances of 1.8, 1 and 0.5 meters.

Response changes caused by both reinforcement and reflection from a nearby wall at distances of 1.8, 1 and 0.5 meters.

Since all three variables of the boundary effect (degree of reinforcement, cancellation frequency and cancellation severity) are determined solely by the wall distance, they can be accurately compensated for if the wall distance is known.

All SmartSubs incorporate placement compensation whereby one control setting, calibrated in distance from the wall, corrects reinforcement, cancellation amount and cancellation frequency. By incorporating two sets of wall compensation which are independently adjustable, the SmartSubs are able to accurately compensate for virtually any placement.

For example, the fourth graph illustrates the effect of placing a speaker 0.5 and 1.2 meters from a corner. The inverse compensation supplied by the SmartSub for this placement is illustrated in the last graph.

Response change caused by near-corner placement of one-half meter from side wall and 1.2 meters from rear wall.

Correction supplied for a side wall distance of one-half meter and a rear wall distance of 1.2 meters.