Ultrabass, psychoacoutstic low bass for little speakers

[phase_accurate]

In the aforementioned JAES article form November 2011 there was a list of nonlinear mathematical functions that were used to synthesise bass and which were evaluated in terms of subjective bass enhancement effect and how they affect other frequency bands with unwanted byproducts. They even found some of the functions to be "bass-killers". One function that was rather simple and that belonged to the best ones was the the following one. It could be implemented via the "classic" analog exponential function using the nonlinear properties of a transistor. If the trnasistor variant will not work it could maybe also approximated with a diode-resistor network.

The Nominator is just a scaling factor. The difference e - exp (1-x) is making the output voltage zero for an input voltage of zero. The exponent 1 - x instead of just x or - x is shifting the function. The total function is a nonliear, continuous and monotonic.

[phase_accurate]

Here is the flow diagram of an analog implementation of the function, a circuit diagram will follow a soon as I find some time to fiddle around:

[danielwritesbac]

Originally Posted by Elvee

Here is the tube circuit converted to jFET.
First pic shows the output at 30Hz (distorted) Second pic at 1KHz (undistorted) All the pots are centered. Other values can be tweaked too (corner frequency of lowpass, etc). If you want to make a virtual test, LTspice can accept a wav file as input voltage, process it and write it to an output file. The operation will be similar to the original tube circuit (ie. pretty crude) The nominal voltage is around 0.5Vrms

Thank you sir! This real circuit will make an excellent comparison point. I just love having the first Ultrabass converted to Solid State.

[rcw666]

There you have it Daniel, four schemes, I am sure you can find at least one to suit.
rcw

[danielwritesbac]

Originally Posted by rcw666

There you have it Daniel, four schemes, I am sure you can find at least one to suit. rcw

Yes, the one with component values looks build-able.

[phase_accurate]

I derived a circuit that delivers the following output spectrum when fed with 1 kHz. There is one or another cap that would have to be redimensioned when used with low frequencies.

Unfortunately it is very level-dependent. Not so much the output spectrum (i.e. the ratios between the different harmonic almost stay the same) but the ratio of input to output voltage is input level dependant.

Regards

Charles

[rcw666]

It looks like the JAES article is recommending a scaled anti log function.

Maybe putting it through a two op amp two transistor antilog generator is what is needed.
rcw

[phase_accurate]

I tried it with a one transistor/one op-amp variant. An additional OP-AMP is used for stabilisation but it isn't satisfactory so far. The approximation with a diode-transistor network isn't that good either.
The best so far (from looking at the simulation curves, not listening tests !) was something like a pseudo antilog circuit with one op-amp and two transistors - one of them in the forward path and one in the feedback path. A simple signal dependant biasing circuit makes it work over a larger range of levels than the other ones that I have tried so far.

I will also try the classic two-transistor/two op-amp antilog variant because it seems to be the only one that can be really made to work in practice. But to be useful one would have to use a pair of transistors that are tightly coupled from a thermal point of view.

Regards

Charles

[rcw666]

Gluing two together, and then wrapping some copper wire around them works well enough in practice.
rcw

[danielwritesbac]

Originally Posted by phase_accurate

The best so far (from looking at the simulation curves, not listening tests !) was something like a pseudo antilog circuit with one op-amp and two transistors - one of them in the forward path and one in the feedback path. A simple signal dependent biasing circuit makes it work over a larger range of levels than the other ones that I have tried so far.

I will also try the classic two-transistor/two op-amp antilog variant because it seems to be the only one that can be really made to work in practice. But to be useful one would have to use a pair of transistors that are tightly coupled from a thermal point of view.
Regards
Charles

Yes, it would be very interesting to have a device that matches up with that research paper.

The prospect seems very useful for several applications:
The majority of full range, even the biggest full range have very limited x-max.
Very low power amplifiers have limited potential for replaying large fundamentals.
Compact speakers are plagued with bass distortion for the same reason that Steinway doesn't make pianos the size of toasters.
(and a portable application usually has all 3 caveats, plus boomy tuning for the only impact it could do)

In all of the above cases, rolling off the fundamental in exchange for psychoacoustic bass processing could decrease audible distortion. In the case of removing a terrible noise in exchange for something more favorable, having a selectable frequency response will have the largest effect on listening tests.