Measuring Distortion

OK, here are NAI clipping prototypes loaded with molecular junctions and 1N4148 pairs ready for direct comparison:

​Time to put the Nanolog Audio Inc. Studio Measurements Lab to work!

In order to determine how molecular junction clipping differs from conventional diode clipping, we run a 0.3 Vpp (that's peak-to-peak) at 220 Hz into the input. Then, the output is put into an oscilloscope. As the settings on the pedal are changed, the output is monitored. Finally, in order to capture the waveforms and do further analysis, Audacity is used to record several seconds of the waves, and the data exported for plotting.

Here is a direct overlay of the resulting waveforms, showing an offset comparison of the input sine wave with the resulting clipping from a conventional 1N4148 diode pair and two different molecular junctions, one of which is 5 nm thick, and the other which is 8 nm thick:

​Two things are notable right away: the shapes are different, and the heights are different.

First, let's tackle peak height. These data were captured without adjusting the volume knob in order to show the relative amplitudes of the clipped waveforms. This is because the height of the waves will determine the overall volume, and the simple process of switching the clipping device can have a big impact on volume. As well, this height will determine the amount of dynamic range available for the player to interact with. The lower the wave height, the more compressed the signal is, and it can end up sounding "squished," which has an important impact on the tone and touch sensitivity- typically the end result of a more compressed clipped signal is less interactive feel, which is not inherently bad, but certainly different. It will depend on the intent of the player if this is desirable or not.

Second, let's get to the shapes. The more squared-off the waveform is, the more saturation or distortion there will be. That is because if we transform the time domain signal shown above into the frequency domain (more on that later), we could consider a square wave mathematically as an infinite sum of sine waves with different frequencies- this creates a very "saturated" sound perception, as if all of the available space is filled with noises.

The above data are transformed using Audacitiy's FFT algorithm, which is some fancy math that let's us see the individual frequencies the wave is composed of. For this type of clipping, we typically get harmonics- that is, integer multiples of the fundamental tone, which is 220 Hz. We therefore expect to see 220 Hz as the highest intensity, followed by 440, 660, and so on.

There are two things to note about the waveforms: a 5 nm molecular junction produces more compression and a more squared-off wave than an 8 nm molecular junction, and both of these show greater peak heights and more rounded shapes than the diode clipping.

Now, to the transform of these waveforms into the frequency domain, where we can check on how that initial single 220 Hz sine wave made out on its way through the clipping circuit:

Here, we see at far left the first peak, which is at 220 Hz (or 0.220 on this plot, where I've used kHz as the unit).We see that the diode clipping results in the most saturated frequency space, as expected from the waveforms. Both molecular junctions produce less saturation, and the frequencies fall off in intensity more as the frequency increases (follow the tops of the peaks and you'll see the steeper slope in the case of the molecular junctions. It is a bit harder to see a difference between the two molecular junctions, but it is there (I'll have to plot the heights sometime separately to show this more explicitly, but for now, this makes the point). The prediction we make from these plots is that molecular junction clipping will result in a "warmer" tone, with less high frequencies inherent, but at the same time with more dynamic range and less compression. Really cool combination!
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What does this all mean? It means there is greater control over frequency space due to the nanoscale engineering of the devices used in the clipping circuit! The differences we hear in the sound, and that we can feel when playing through the circuit with different clipping devices is indeed measurable, and now we have some extra tonal colours with which to create soundscapes: an end result that we hope is the nano-enabled musical expression of diverse ideas!