Memory effects in transducers are the number one obstacle to achieving higher fidelity sound. This is because the sound signal is dynamic. A low level signal following a large signal can be easily masked and modulated by the memory effect left in the system by the large signal. As a result, the low level resolution is compromised. Often this is described as the system being "slow", and unable to keep up with the front speakers.

Many audiophiles are aware of the concept of thermal compression, which refers to the loss of efficiency of a driver with the increase of power as the voice coil heats up and causes the voice coil resistance to change. Thermal memory is not as commonly understood. The following chart gives an illustration.

The above graph shows how temperature affects the frequency response of a driver. The blue line shows the response when the voice coil is at room temperature and the red line shows the response when the voice coil is at 300 degrees Celsius. As one can see the output is reduced by up to 6 dB except in the region around the impedance peak. In this particular example, it is around 45 Hz. In addition, the Q value of the bass roll-off is also increased by almost a factor of 2. So thermal compression not only reduces the output, it also changes the Q value of the alignment, and thus the phase angle of the response.

When the thermal compression changes dynamically, it causes both amplitude modulation and phase modulation distortion.

For instance, the above graph shows the frequency response at two different voice coil temperatures. As the temperature changes between low and high, it causes amplitude modulation. This amplitude modulation distortion is not measured in the conventional harmonic distortion measurement. While the above graph does not show the phase response, one can easily understand that similar modulation on the phase angle is also generated, commonly referred to as phase modulation distortion. Phase modulation distortion is also related to Doppler Effect. As the phase modulation distortion occurs, it is often perceived as the movement of sound image.

The latter can be resolved using Alnico or rare-earth magnets. What Direct Servo subs address is the compression caused by the temperature of the voice coil.

The thermal memory effect comes about because the heat from the voice coil cannot be immediately dissipated into the air within the driver. Normally a voice coil has several layers of copper wires. The heat is dissipated through the outermost layer into the air and through the innermost layer into the former. This heat dissipation process takes time. Before the heat can be dissipated, the voice coil resistance increases and the output is reduced. After the heat is dissipated, the temperature recovers, the voice coil resistance drops, and the output is regained. Alternatively, one can view thermal memory is a "delayed" thermal compression. The rate of the temperature recovery resembles an RC network discharging the capacitor and therefore can be characterized using a time constant, which we have found to be around 5 seconds without forced ventilation. What makes the problem more complex is at the resonance peak of impedance curve, the power consumption is low, but the cone movement is high. This forced ventilation makes the time constant shorter. As a result, the time constant in the real world is not a time-invariant quantity. At low bass frequencies, the temperature profile of a voice coil resembles a delayed rectified version of the applied signal. At high frequencies on the other hand, the temperature profile resembles a delayed rectified version of the applied signal envelope.

Thermal compression vs thermal memory

Thermal memory occurs any time the cone makes a movement, no matter if the voice coil temperature is high or low. Thermal compression, on the other hand, is worst when the voice coil is at high temperature. So how serious is this memory effect? A simple mathematical calculation can give us some ideas. The heat specific of copper is 0.4 joule/(g x degrees Celsius). A typical copper voice coil weighs about 50g. 200 watts RMS power (less than half of the full power of today's amplifiers) in one second generates energy of 200 joules. That means an input power of 200 watts RMS in one second will increase a typical voice coil temperature by 10 degrees Celsius. In 2 seconds the temperature increases by 20 degrees Celsius. For every 20 degrees Celsius increase in temperature, the output is reduced by 7%. If the voice coil changes within a range of 20 degrees Celsius, the amplitude modulation distortion is around 7%.

Thermal memory- non servo subwoofer

The above is the actual microphone measurement of thermal memory (delayed compression) on a supposedly constant 60 Hz sine wave using a 370WRMS non servo subwoofer operating at half power, i.e., 200WRMS. The thermal compression is -2%/sec. In 6 seconds, the output is reduced by 12%. Thermal memory leads to modulation distortion and conventional Harmonic Distortion Analyzer cannot measure it as explained in the spectral plot of the above waveform.

Note that there is a tree trunk center at 60hz. Even the second harmonic at 120hz shows a small trunk. So thermal compression creates a side band energy that spread around 50hz to 70hz, and starts at around 40db level. It has 61hz, 62hz, 63hz,..etc. It also has 59hz, 58hz. 57hz..... This is "warbling" and "jittering". The memory effect creates a warbling and jittering that is dependent on voice coil temperature. And the harmonic distortion analyzer only look at components at multiple of fundamental frequency. All others are lumped as "noise". But these sideband energry is not noise. If we use the analogy between sound and image, harmonic distortion is like an image is distorted (for instance,a straight line becomes slightly bent), but the compression is like a shadow or jitters in the image (because the camera man cannot hold the camera steady or something like multiple exposure) and even a slight shadow can blur the image. Even worse it is the blurring depends on how fast the signal change. Which one is more tolerable? Furthermore, thermal compression is not the same as amplifier overload or clipping. It happens at all power levels with the worst at full power. The root cause is the voice coil being heated up and voice coil resistance increased as a result. It is this type of variation that makes the non servo subs not only sound "compressed", but also less coherent (that is, it can vary from one moment to next). In the following is the same measurement with our Direct Servo sub, same 200WRMS operating power. There is absolutely no thermal compression because the servo loop enable the power amplifier to supply more power to the subwoofer driver to sustain the output level.

Thermal memory - Direct Servo

The improvement is quite remarkable. The spectral plot shows very little side band energy. No more warbling and jittering. This has correlated very well with bass sound from DirectServo subwoofers: defined, clear, articulate, coherent, and revealing (by being able to preserve microscopic details). A lot of customers are surprised to hear new sounds in the music that they've listened for many many years.

The best example is the hysteresis effect of a spider, as shown in the above graphs. If one stretches a spider and then lets it go (that is, no force), the spider will not immediately return to zero position. It takes a finite amount of time for it to return to zero. When the signal is repetitive, the relation between force and displacement shows a hysteresis loop. The hysteresis loop has nothing to do with the non linearity of the spider. It is a problem inherent in the shape and form of the spiders. And the spider is not the only component in a driver that exhibits hysteresis, though a full discussion of hysteresis effects in driver components is beyond the scope of this discussion. As ever increasing excursion requirements necessitate larger and larger spider, this inherent hysteresis effect can only get worse.

The ability to dramatically reduce this effect is a unique advantage of Direct Servo Subwoofers. It is not possible to overcome this problem with good driver design, hence even the most expensive drivers will be plagued by this problem.

The effects of mechanical memory are also discussed in our discussion of the benefits of a closed loop servo system compared to an open loop in a conventional subwoofer.

Direct Servo Subwoofers

The following figure shows the connection between a Direct Servo amplifier and driver. It is a closed loop system in which there is a servo (or velocity) feedback from the driver to the amplifier so the amplifier will linearize the velocity of the cone movement, instead of just at the amplifier output. At any time when the velocity signal deviates from the expected value, the amplifier will adjust its output to correct it. As a result, this arrangement offers additional distortion reduction that is not available in conventional open-loop subwoofers.

Benefits:

Frequency response is independent of voice coil resistance
Spider and surround distortion reduced by 6 - 9 dB
No thermal induced distortion

The frequency response of Direct servo subs is almost independent of the voice coil resistance/temperature. To demonstrate this, we add a serial resistor of 3ohms to the driver to emulate a scenario where the voice coil temperature increases to 300 Celsius and then compare it with the frequency response without this 3ohm resistor. The volume control is at exactly the same position for both cases. The two curves are plotted below. They almost track each other. The actual difference between the two curves is less than 0.2 dB whereas in non servo subs, the difference can be up to 6 dB as we have previously demonstrated. As a result, not only do Direct servo subs maintain the same frequency response over any voice coil temperature, they do not have any thermal-induced memory distortion either.

To demonstrate the distortion reduction capability of Direct Servo subs on spider non linearity and memory effect, we set up a 2 cu ft sealed box with our DS12TC driver in both non servo and servo configurations. The test signal is a 10 Hz sine wave that produces 1/4" peak-to-peak excursion. The purpose is to examine the low level distortion characteristics. At this excursion level, the distortion is mainly caused by the non linearity in the spider and surround. The results are plotted below. Each horizontal division is 10 Hz. The results for the non servo and servo are offset horizontally to provide a better visual comparison. In reality, both of them use the same 10 Hz sine wave and produce the same excursion. The distortion reduction of the Direct servo sub for the 2nd, 3rd, 4th, and 5th harmonic distortion is 3db, 5db, 8db, and 5db, respectively. One thing to note is the 2nd order harmonic distortion at 20 Hz is mainly due to flux modulation with low memory effect. Also the 2nd order harmonic distortion is less audible than higher order distortions. Also worth noting is that dB scale is logarithmic so that a difference of 5 dB is a factor of 3x in terms of power whereas a difference of 8 dB is a factor of 6x in terms of power. The ability of the Direct Servo subs to reduce harmonic distortions above 2nd order is an indication of their ability to reduce the non linearity of the spider, including the memory effect. The actual mechanism by which Direct Servo subs achieve this distortion reduction is through the servo feedback. If the cone velocity (and therefore position) deviates from the expected value, additional power will be supplied by the amp to force the cone to follow correct velocity and therefore reduce distortion.

Since the isolation between the amplifier and the driver in non servo subs is the largest when the voice coil temperature is high, one can expect that distortion is subsequently higher. After we put in a series resistor of 3ohms to the driver to emulate the high voice coil temperature scenario, the new results are plotted below. The distortion reduction of Direct servo sub for the 2nd, 3rd, 4th, and 5th harmonic distortion is 3 dB, 8 dB, 14 dB, and 6 dB, respectively. Again, as the dB scale is logarithmic, a 14 dB difference is a factor of 16x in terms of power. The improvement over the room temperature case is mainly because the distortion increases in the non servo setup. Again, in the Direct servo sub, the distortion is hardly affected by the voice coil temperature.

While so far we have only discussed the distortion reduction part of our servo sub, in reality our servo subs also have higher usable output than conventional non-equalized servo subs. The secret is in the so-called "excursion utilization".

To summarize, Direct Servo offers the following benefits:

No voice coil thermal-induced compression or distortions.
Spider and surround distortion reduced by 6 - 9 dB
Flat frequency response that is less dependent on T/S parameters.
Audiophile bass sound at an affordable price: articulate, tight, transparent, and well-defined bass
Applicable to all subwoofer configurations (including horns, dipole, infinite baffle and others)
Higher output (with better excursion utilization) for sealed, IB, and Dipole subs.