Audio Science Guide

In an ongoing effort to investigate, understand, and then produce a tutorial on current source amplifiers, I've done a first round of Bakoon HPA-21 measurements. One of the tricky things about investigating this type of amplifier is that there seem to be a variety of interpretations of this type of amplifier technology. Evidently, not all current source amps are equal.

For example, the Apogee Groove is claimed to have a circuit design that prevents changes to headphone frequency response with changes in its impedance vs. frequency response. I'll be doing some measurements of the Groove sometime soon.

Anyway, to establish a base line, and to make sure the model in my head had some grounding in reality, I felt the need to grab a little real data.

Single Tone Response
A pure current source amp (sometimes called a transconductance amplifier) takes a voltage signal in, and outputs a current signal.

Let's say we have a 1 Volt RMS 500Hz tone incoming voltage signal and set the volume control for 1 Amp RMS output. If we have a 1 Ohm load resistor, we will measure 1Vrms across the resistor. If we switch to a 2 Ohm resistor, the amp will output the same 1Arms current signal and we'll get 2Vrms across the resistor.

If an amp behaves this way, we can likely say that it's a pure current source amplifier. I hooked up the Bakoon so that I could place varying resistive loads on the amp to see if it exhibited this behavior.

In this case, I had a 500mVrms 500Hz tone going into the Bakoon, and set it up for a 1mArms output into a 150 Ohm load, which will give a 150mVrms across the load. I then put various other resistive loads to see if the output current signal remained constant.

You can see from the images at right that I got a fairly constant 1mVrms/1 Ohm response with all loads. It's off just a bit with the 600 Ohm and 16 Ohm loads. Probably a resistor tolerance issue with the 600 Ohm load, and cable resistance issues with the 16 Ohm load.

It is close enough though to say the Bakoon is acting as a pure current source amp.

Effects on Frequency Response with Varying Headphone Impedance
Some headphones have dramatically changing impedance with frequency. For example, the Sennheiser HD 800 has about 630 Ohms impedance at 100Hz, but has about 340 Ohms impedance at 2kHz.

In the plot above we can see the wildly swinging impedance of the HD 800. As we saw from the single tone experiment above, as we change the load impedance, we change the voltage across the load. This means that the HD 800 will get about twice the drive voltage at 100Hz than it gets at 2kHz. With a pure current source amplifier, the tonal balance of the headphones will be modified by the impedance curve of the headphones.

In the above plot, the blue traces are the HD 800 being driven by a traditional voltage output amplifier. The red traces are the HD 800 being driven by a current source amplifier. At 100Hz, the HD 800 is almost double the impedance relative to its impedance at 2kHz. It should therefor have about double the voltage drive from a current source amplifier. We can see in the above plot that the HD 800 is about 6dB (double in amplitude) at 100Hz relative to when being driven by a typical voltage amplifier. Science!!!

The HD 800 also has a rising impedance after about 7kHz. In the above plot we can also see, if we look closely, that the red plots start to increase above the blue plots above 7kHz.

The big impedance swings of the HD 800 is a bit of a rarity these days; most headphones are lower impedance and have less severe swings. Lets look at the V-Moda M-80 as a more typical headphone.

The M-80 hoovers around 33 Ohms impedance, and while it varies, it's no where near the HD 800. Let's take a look at the frequency response plots.

As you can see, there's a little difference in the bass due to the primary driver resonance hump centered at 40Hz, but not much difference otherwise.

Planar magnetic headphones have a virtually flat impedance response; I performed this test with the Mr. Speakers' Ether. You could just imagine a flat line, but why not show it.

This means that there should be very little difference between the Ether's frequency response with voltage and current output amplifiers. Here's the FR plot.

While the two response curves are nearly identical, they do seem to be somewhat different below 40Hz. I thought this might just be a difference between the output coupling of the two amps, but it doesn't appear in the other headphone plots. Not sure what's going on here. Feel free to brainstorm your ideas in the comments.

Bottom line: these plots show clearly that current source amplifiers will effect the frequency response of headphones that have significant impedance swings with frequency.

Transient Response
As you can see, current source amplifiers have the potential of not working well for headphones with varying impedance response. One area of performance where they may excel is transient speed. We're going to look at response when driving the leading edge of a square wave. The thing to get a grip on to understand what's going on is the relationship between voltage and current at the output when driving an inductive load.

When you drive current through a wire, a magnetic field forms around the wire. An inductor is a coil of wire—like the voice coil of a headphone. When current flows through and inductor, the magnetic field around each winding adds to the whole forming a larger magnet.

Here's the important thing to know: It's the current flowing through the coil that makes the magnetic field, not the voltage across the inductor. When, at the leading edge of a square wave, the amplifier output rises in voltage almost instantaneously, but the current going through the coil does not rise immediately. This is because it take some time for the current to build up the magnetic field around the coil. So, the current lags behind the voltage when driving an inductor. While the voltage output from the amp may be very fast and responsive, the speed of the current output will be dependent on the reactive impedance of the coil and the output impedance of the amplifier.

In a current source amplifier, the output current will follow the incoming voltage transient exactly and will force the current through the coil immediately. But in so doing, the output of a current amplifier will have a very high voltage spike as it deals with the initially very high reactive impedance of the voice coil.

In the diagram above, you can see that in a voltage drive amp the current (green) lags behind the desired voltage waveform (red). With a current drive amp, the output current (and therefor motive force of the voice coil) will achieve it's desired level immediately—but the voltage will have a significant spike on it.

In an effort to verify this characteristic, I set up a current and voltage amp (Bakoon HPA-21 and Simaudio Moon NEO 230HAD) each driving one channel of a pair of headphones. I then set up an oscilloscope to look at the voltage of the two types of outputs simultaneously to see if it looked like the red voltage traces in the above illustration.

The o'scope display above shows the voltage signal from the two amps driving the Mr. Speakers Ether. The top trace is the current source amp, the bottom is the voltage amp. Please note the timescale of 1uSec/division—while the voltage rise time might look slow, it's actually quite fast.

You can see that the voltage step with the Moon is a simple voltage rise. But the step from the current amplifier (top) wiggles around quite a bit. I can't measure the current waveform, but it probably looks quite like the voltage waveform on the bottom trace. The reason the transient shape of the voltage on the Bakoon wiggles so much is because the voice coil, and its movement through the permanent magnet of the driver, is reactive and is "fighting" against the current being pushed through it. I can assure you that with a voltage amplifier, if you were to look at the current output from the device you would see similar wiggling about.

When driving a reactive load, you can control the voltage, or you can control the current, but in either case the uncontrolled parameter will do some wiggling about.

Here's the V-Moda M80.

You can see in this case that the V-Moda voltage waveform from the Bakoon has larger swings than the Ether. This is probably because the long zig-zag conductor traces on the diaphragm on the Ether has less inductive reactance than the tightly wound voice coil of the M-80.

And here's the HD 800...I'm not exactly sure what's going on here except to say it might be much more inductively reactive than even the V-Moda, but I'm not sure.

Regardless, the big question is whether or not the current source amp is able to product faster transient response at the ear. So I set up a similar test, but this time looking at the acoustic waveform from the headphones. Top traces are the Bakoon, bottom are the Moon.

Here's the Ether. Remember this is the left and right channels being driven simultaneously, so there are some slight differences due to being mounted on separate ears. You can see that while there are some small differences between channels, there is no obvious difference in the speed of the leading edge, or the amount of control of the signal. Both traces are fairly similar.

The V-Moda delivers some difference in response. The changing angle of the trailing edge is more about frequency response than speed. The rise of the leading edge is about the same. The Bakoon has markedly larger swings after the initial spike than the Moon. My guess is this might be related to the better damping factor of the low output impedance Moon compared with the very high output impedance of the Bakoon.

The HD 800 also shows no remarkable difference in the transient speed. While the shape of the wave form is slightly different due to the frequency response differences imposed on the HD 800 by the current source amp, the magnitude and shape of the wiggles is roughly the same.

Summary
First, it does seem that the Bakoon is a pure current source amplifier. It's going to be interesting to compare this traditional transconductance amp with the Apogee Groove, which includes circuitry intended to rid it of frequency response changes due to varying headphone impedance curves.

Second, boy I wish there was some hard evidence the Bakoon delivered faster transient response...but there doesn't seem to be so far. I'll keep poking around more though, you never know when something will turn up.