β-Sine (Beta Sine): a discussion on geometry
As I have teased out a bit to this point, I have been busy at work creating Hapa Audio's next generation of Hapa Audio balanced products. In order for these products. It has been a long time in the making. New geometry is deceptively difficult to accomplish. For one, rarely is it ever as straightforward as merely understanding what the geometry looks like. And for two, implementing said geometry in the real world is an engineering feat in and of itself. Thus began my journey. If you are curious about what lead me to this point, I have a short writeup about it https://www.audiocircle.com/index.php?topic=173480.0]here.
Without further adieu!
Introducing our new balanced geometry- β-Sine or βalanced Sinusoidal Isolated NEtwork. β-Sine is my engineering expression using geometry to create an inductive environment that is ideal for a balanced signal.
The math behind the geometry:
Conceptually β-Sine started out as a mathematical expression. 4 sine waves 90 degrees out of phase with each other. Simple to understand, hard to implement! If done correctly, the leads can be placed close enough to allow for inductive interplay without the conductors exceeding the appropriate distance from each other, which would cause inductive thievery. Here's what β-Sine looks like trigonometrically:
The actual geometry utilized in β-Sine geometry
And graphed out:
Note: the only time each line intersects another is strictly at 90 degree angles reducing crosstalk to a statistical minimum while allow conductors to be close enough to allow inductive interplay.
Thinking in 3 dimensions + time:
In order to truly understand β-Sine geometry, it is important to understand the design parameters I required in order to improve on my other geometries.
- First, the design needed to be lightweight for user comfort and portability.
- Second, it needs to meet or exceed DCSG in noise rejection and signal transfer.
- Third, left and right channels inductive fields need to be isolated from each other to reduce crosstalk.
- And fourth, time-domain for signal arrival needs to exceed that of my previous designs.
β-Sine geometry in the upcoming silver headphone cable.
β-Sine utilizes a sinusoidal geometry wherein 4 separate leads are woven in the shape of a sine wave that propagates on the interior of the cable for each channel (4 per channel, 8 leads in total). This sinusoidal geometry allows for a constant distance between phase original pathway and phase inverted pathway through the length of the cable. This allows for inductive interplay between the two pathways allowing for near-ideal transmission for a balanced signal, while simultaneously segregating the left channel from the right by placing them at 90 degrees from each other.
β-Sine utilizing our new Gold plated Silver. Yum Yum!!!
The result of this carefully engineered geometry:
- A cable with the most accurate phase delivery of any cable on the market.
- A cable that is incredibly lightweight.
- A cable that is not only flexible along it’s entire length, but retains it's geometry throughout
- A cable that can be stretched significantly, taking the stress off of the connectors and delicate Angel Hair Litz I utilize in the design.
β-Sine split for left and right channel.
The work I put into this design was extensive. I had to create tools and new methods of weaving that were at times, frustrating! :duh: In the end, the sonic merits of β-Sine were immediately apparent and well worth the research and development. first and foremost β-Sine allows for a lushness in sound that I have [i]never heard before[/i]. The clarity and pristine vision of the performance presented has never occupied so much dimensionality. And finally, β-Sine geometry is applicable wherever an analog balanced signal is used, thus Hapa Audio will soon be proudly releasing an XLR cable and a headphone cable both of which utilize this extraordinary geometry.
