Power Transconductance Amplifiers
This is a fancy name for a power current source. An input voltage causes the amplifier to deliver a proportional output current. Of course this same sort of thing would occur with an ordinary amplifier driving a pure resistance but a loudspeaker circuit is not purely resistive. It possesses numerous reactive elements, some due to inductance and capacitance in the electrical circuit, some from the reaction to motion of the voice coil in a complex mechanical system. Fed by a voltage amplifier, the current through the driver's voice coil is not directly or instantly proportional to the input to the amplifier. Ordinarily, loudspeakers are designed around this assumption but the "pistonic model" of loudspeaker design assumes that the acoustic output mirrors the acceleration of the voice coil/cone assembly over a specific range. This is reflected by the current through the voice coil.

The most precise way to develop that specific current is with a current-source amplifier. Such an amplifier ignores the impedances in series with the circuit, the resistance and inductance of the wire and voice coil and the back electromotive force (EMF) produced by the cone motion. As I said, most speakers are designed around voltage sources but there are a few instances where a current source can be used to advantage. One of the best ones is the category of full-range high-efficiency drivers.

Why is that? First, such drivers are able to take advantage of acoustic and suspension resistance to achieve some or all of the damping that they need to prevent excessive overhang because their moving mass is very light. With their efficient motors, even a high source impedance is often enough to give critical damping. Second, their impedance curve tends to reflect their needs - more current both at low frequency resonance and in the treble, two areas where frequency response has fallen off with increased speaker impedance. If you want, the current through the voice coil can be made constant regardless of the variations in the acoustic environment. The voice coil force is invariant whether the cone is loaded into a horn, sealed box, bass reflex or whatever else you care to mount it in.

Third, they are very easy to adjust in the upper midrange and high end where you typically run into peaking problems. Most of these drivers are too hot in the upper midrange and quite a few of them fail to make it to 20KHz. With a simple parallel network, you can arrange for a midrange dip followed by an increase at the top, evening out the loudspeaker response. With the higher quality drivers, you more often than not simply want an equalized 'shelf' where everything above a specific frequency is evenly attenuated.

The adjustments for damping at the low end and the mid/high peaking are easily accomplished using R, RC or RLC (resistor/inductor/capacitor) networks wired in parallel with the output of the amp. You occasionally see this sort of equalization with full-range high-efficiency drivers using voltage-source amplifiers, but there the elements are paralleled and then placed in series with the driver. With a current source, the equivalent circuit becomes the elements placed in series and then paralleled with the driver.

Of course with a current source, there's the added benefit that the resistive element of the speaker cable and the connection points can be made to largely disappear. To obtain the best results, the loading network is placed close to the driver instead of the amplifier. The following pages will show what we found with a variety of full-range efficient loudspeaker transducers when we drove them with an active current source and experimented with parallel networks to shape the response to our liking.

Most of the examples we will examine do not require true current-source amplifiers, only amplifiers of quite high output impedances. Most of these cases will be happy with an output impedance of approximately 47 ohms or so and prefer 47 ohms loaded in parallel with the output of a current source. That being the case, you can build a Thevenin Equivalent of such a current source by placing a large resistor (here later referred to as R0) in series with the output of a high wattage voltage source amplifier and get similar results.

I'm not saying it will equal a spiffy First Watt F1 (being Class A, zero feedback and all), and your resistor will run hot. On the other hand, you probably already have such a voltage-source amplifier and some of these speakers are quite cheap, allowing you a taste of these forbidden pleasures without high expense.

I want to emphasize that this does not serve as any sort of comprehensive guide to designing systems around this approach. You can build up the examples and they will probably measure about the same. But remember that we are mostly restricting ourselves to the sealed box case for simplicity's sake. In the real world and most of time, these drivers are used in an enclosure that also utilizes the back wave of the driver. Additionally, the best measured curve is often not the best sounding one so be prepared to try various values to get satisfactory sound.

Amplifier/Loudspeaker/EQ network Model
The above schematic will be referenced through the rest of the article. This diagram shows a current-source amplifier, the simplified model of the loudspeaker's impedance and the generalized network that we can parallel with the speaker to enhance its performance. The speaker model consists of L2/R2/C2 that model the fundamental resonance, and R3/L3 give us its DC resistance and high frequency inductance. A good example of this is the simulation of the Pioneer b20fu20-51 driver. The values L2 = .05 H, R2 = 27 ohms, C2 = 300 uF, R3 = 7 ohms and L3 = .1 mH give a reasonable facsimile of the measured free-air impedance curve shown below.

Unless otherwise noted in this discussion, we will be addressing the driver mounted in a sealed box of a given volume because it is the easiest design to consider. Horns and rear-loaded acoustic systems are more complicated to simulate and measure and test results are more difficult to duplicate and interpret. One advantage to a sealed box for full-range drivers is that the excursion becomes limited below resonance, which can reduce distortion particularly at higher levels. Driven by a voltage source, we usually see a response loss anywhere from -6 to -15dB at low-frequency resonance and a treble that increases or declines (or both) depending mostly on the cone construction and voice coil inductance.

Driven by a current source, we note that the bottom end is bumped up at resonance and the top end is increased when compared to the performance of the voltage source. Let's assume that we want to achieve optimal frequency response for a given system. This is not necessarily the best-sounding system possible but causes less subjective arguments. We can trim the damping "Q" of the low frequency roll-off knee by trying different values for R0 (L0 = 0 in this case) until it flattens out to our taste. Most of the drivers we worked with were happy with values from about 22 ohms to about 47 ohms. It is surprising that so little damping gave such dramatic results but as previously pointed out, this category of loudspeaker responds well to small amounts of damping.

Usually we also want to adjust the upper midrange and high end. Often these drivers will exhibit an upper-mid peak followed by a decline before the upper-most treble is reached. We can compensate for this by our selection of R1, C1 and L1, which can be used either to create a shelf or a dip to flatten out the response. With these models in mind, we measured all the sample speakers of interest, developing networks to optimally flatten out their response with a current source, and comparing this with the same speaker driven by a voltage source. We used a Vidsonics 'virtual crossover' substitution box to play with the parallel loading and took both near-field (from an inch or so) and far-field (from 1 meter) response measurements using Mlssa. Again, the results here are not necessarily the best-sounding ones achievable and I am not attempting to address this subject as such, given the wide range of source material, listening environments and subjective tastes. Typically, these exact network figures are not the ones listeners will subjectively prefer. Usually this is because listeners tend to prefer a higher value for R1 than is shown on the table. If you decide to use one of these networks, consider the possibility that R1 is the minimum value and use a switch or high-power (5 watt) potentiometer to variably increase the value to as much as twice R1. Less often you might consider a different value for L1 to trim the treble.

I repeat: Consider this as an experimental guide and a good starting point. Be prepared to change the values to suit your needs and remember that these figures were obtained in stuffed sealed enclosures in a large room placed well away from the wall. Your results will certainly vary. Also remember my comments reflect off-hand reactions. Please do not treat them as reviews.

The following table shows the values that resulted in improved frequency response curves with current sources for different speakers in different sized boxes: * Mini-Me is the Lowther Mini-Medallion rear-loaded horn enclosure. Horn is the KleinHorn [below], a 20-foot long 30Hz rear-loaded horn with a 30sqft. mouth. Article to follow shortly.

Now that you have an overview of the interface networks, let's look at the individual drivers in more detail. In the following pages, you will see a picture of the driver, an impedance curve and the near- and far-field response curves for the loudspeaker in the box described above. The dotted line is the response driven by a voltage source and the solid line is a current source with the parallel network in the above table.