Ocharaku Flat4-粋 (SUI) part.3: In-depth analysis

Continued from part 2, General analysis.

According to Ryo Yamagishi 山岸亮, the representative & the director of acoustic research at Ocharaku Inc., Ocharaku Sound Customize's ultimate goal is to create a gentle sound signature with high frequency well-extended, derived from a ground-breaking technological innovation. 

And that is how Flat4-SUI is created, after Full-range 2-element 4-way effect, with two dynamic driver connected with an acoustic transfer tube, which is named as Phase Correction tube. The placement of the tube is claimed to be precisely calculated in order to achieve optimum performance of the IEM. 

Yamagishi-san claims that Flat4-SUI's double driver configuration not only expands the low frequency bandwidth by cancellng off any anti-resonance induced mechanical vibration, but also improves the sensitivity of the low-mid frequency range. Moreover, while the proprietary Phase Correction tube offsets acoustic interference caused by closing off the ear canal, without using any acoustic resistance at the output of the IEM, an ultra high frequency reproduction is acquired. 

And of course, Yamagishi-san does not end there. By utilizing a driver with no tangential grooves corrugated on the diaphragm, Ocharaku successfully reduces distortion in the mid-high frequency range. If all five of these claims happen to be for real, it is no doubt that Ocharaku would surely become one of the most technologically advanced headphone manufacturers, along with Sennheiser and Etymotic Research.

In this in-depth analsis, two of Ocharaku's claims will be discussed:

1. The principle of 特許第４９５３４９０号
2. A driver without tangential corrugation




特許第４９５３４９０号

The basic principle of Ocharaku's patent, 特許第４９５３４９０号, is rather simple: It is cancelling off any resonance-related interference caused by closing off the ear canal, especially when the IEM is shallow inserted.

Closed at both ends Open at single end

It all starts out by assuming the external ear meatus as a simple tube, which is 25 to 30 mm long, with one end open. Such tube has quarter-wavelength resonance at 2.8 to 3.4 kHz and 8.5 to 10.2 kHz, which are equivalent to n=1 and n=3 respectively. However, once it is sealed with an IEM, the resonance property changes to half-wavelength resonance at 5.7 to 6.8 kHz and 11.3 to 13.6 kHz, which are also equivalent to n=1 and n=2 respectively. Yamagishi-san believes that if resonance property of a closed ear canal can be tamed by utilizing anti-phase cancellation, a natural tonal signature can be realized.

So here comes critical thinking, translated from the original patent document. When the ear canal is open,
SPd: Sound pressure at the ear drum 
SPc: Sound pressure at the ear canal 
SPs: Sound pressure from the driving source
SPo: Sound pressure at the IEM's output
TFo: Transfer function of a tube with one end open
TFc: Transfer function of a tube with both ends closed

SPd = SPe * TFo

SPc = SPs

SPd = SPs * TFo

And once the ear canal is closed with an IEM,
SPd = SPc * TFc
SPc = SPo = SPs * Bore resonance

Thus,
SPd = SPs * Bore resonance * TFc
SPs * TFo = SPs * Bore resonance * TFc
Bore resonance = TFo / TFc


From the logic derived from above assumptions, simple mathematical equations can be deduced:
A sine wave is wave form as a function of time(t), Y = Asin(ωt)

A = amplitude or maximum value of the function Y

ω = angular frequency = 2π/t = 2*π*frequency

t= time in sec to complete one full cycle

V= speed of sound 
L = the difference in length from Kb to Ka = Kb - Ka


Ya(ω) + Yb(ω) = 2Asin(ωt)

As sound waves from two paths with different length emerge at Q,
Q(ω) = Ya(ω) + Yb(ω) = Asin(ωt) + Asin(ωt+ωL/V)

And introduce the delay of L/2V (of a tube with both ends closed):
Q(ω) = Asin(ωt-ωL/2V) + Asin(ωt+ωL/2V)
= 2Asin(ωt)*cos(ωL/2v)
= Ya(ω)*cos(ωL/2V)
= Yb(ω)*cos(ωL/2V)

From Pa/Pb to Q, the resulting transfer function Tpq is,
Tpq ∝ cos(ωL/2V)

Inversely,
Tpq' ∝ |cos(ωL/2V)|
Tpq' ∝ |cos(πfL/V)|

Finally, in order to negate the half-wavelength resonance at 6.07 kHz, which is occurred when the IEM is situated at 28 mm away from the ear canal, L is set at (340,000/6,071)/2 = 28 mm, and the transfer fuction from P to Q becomes proportional to cosine of (π*frequency*28)/340,000.

Although anti-phase cancellation is utilized, the conceptual goal of Oharaku's patent is totally identical to that of T-PEOS' crossover network(@ 7.5 kHz = 23 mm), Sennheiser's D2CA resonator(@ 7 kHz & 8 kHz = 24 mm & 21 mm), and Sead Smailagic's idea of designing an IEM from shallow insertion depth(@ 8 kHz = 21 mm). While these techniques effectively offset any ill effects caused by shallow insertion, Yamagishi-san's approach is relatively destructive and is only applicable to users with very long ear canals, longer than 28 mm, not to mention there is a need for extra 3 mm for ear sleeves to fit in, at least.  Considering the effective length of conventional simulators is no longer than 25.5 mm, the benefit from 特許第４９５３４９０号 is hard to quantify.


A driver without tangential corrugation

Yamagishi-san states that by removing the tangential grooves corrugated on the diaphragm of Flat4-SUI's driver, a distortion reduction in the mid to high frequency range has been achieved. According to Kim and Park, such grooves are placed in order to increase the stiffness of the diaphragm. Consequently, such diaphragm forming technique increases sensitivity of the driver and lowers the resonant frequency. And unlike what Yamagishi-san states, Flat4-SUI's distortion measurement result from part.2 indicates the IEM's distortion is rather high for a dynamic driver, suggesting the sign of a false claim by the manufacturer.

Conclusion

Although Ryo Yamagishi of Ocharaku Sound Customize really tries to pull off a great innovation by compensating the half-wavelength resonance of a closed ear canal, not only the innovation interferes fidelity due to overly emphasized treble, but also fails to approach the insertion depth related issue practically. In addition, the scientific principle behind the smooth diaphragm is nowhere to be seen.

1. Flat4-SUI's double driver configuration does expand the low frequency bandwidth, but the claimed low-mid sensitivity increase is not observed.
2. The proprietary Phase Correction tube works as how it is supposed to, only when the tip of the IEM is situated exactly at 28mm away from the eardrum, but cuts off the high frequency bandwidth by a great degree.
3. Acoustic damperless design turns out to be extremely harsh, juxtaposing against Ocharaku's philosophy of making a gentle sound signature ironically.
4. Finally, grooveless diaphragm does not lower distortion in the mid to high frequency range.

References

K.M. Kim, and K. Park, "Analysis of Vibration Characteristics of Micro-Speaker Diaphragms with Various Shapes," presented at the Korean Society of Mechanical Engineering (KSME) Annuals Spring & Fall Conference, Daejeon, Korea (June 26-27, 2012).