Sennheiser HD800 part3: In-depth analysis #2

Previously, by fully analyzing the European patent DE102007005620, a theoretical concept of Sennheiser HD800's driver has been discussed. The driver is in an annular configuration, metal coated with capricious crassitude, acoustically vented in the rear, and enclosed in a non-reflective baffle. By utilizing all the above, high-frequency phase intereference, oscillation, distortion are minimized, while the reflection-related contortion can be effectively controlled. The general analysis surely confirms Sennheiser's claim, but one factor still remains equivocal: a peak at 5~6 kHz. According to a Head-Fi user, arnaud, his FEM simulation indicates that HD800's asymmetrical geometry is the cause of such anomaly.

Above polar pattern represents HD800's positioning pattern on my dummy-head, EURI. It is clear that the peak is present at all positions except at the front(90°), where the peak is slighly reduced.

( v / frequency ) = wavelength for fundamental modes

(340,000 mm/s) / 5,000 Hz = 68 mm

(340,000 mm/s) / 6,000 Hz = 57 mm

And considering the role of a quarter-wavelengh resonance, the reflection has to be occuring approximately 14 mm to 17 mm away from the driver in the housing. However, even if the housing is acousically treated with modification, the peak is more or less still present. Then what is the ultimate cause of the peak? Is it possible that the source is from the center hole?

A ring radiator transducer simulated

In order to figure out the effect of a center hole, a Kobitone 25CE500-RO driver has been used for experiment. Its datasheet is here.

Frequency response

A calibrated free-field microphone placed at 10 mm distance

First of all, as a center hole is created in the middle of the diaphragm, the motion break-up of the cone is gone. And the consequential frequency response change is as seen above. The bandwidth remains unaltered, but the high frequency resonances are shifted downwards. And surely enough, a familiar pattern emerges:

Relative difference with the stock as a reference

Impedance

The mechanical resonance has been increased by a great degree with an upward shift.

Thiele-Small parameters

		Stock	Radiator
DC R	Res (Ω)	550	550
Free Air Resonance	Fs (Hz)	121.01	139.4
L of coil	Le (uH)	2342.59	2255.72
L due to ind coupl of eddy current	L2 (uH)	3427.82	1952.33
R due to eddy currents	R2 (Ω)	44.08	52.11
Total Q	Qts	0.62	1.09
Electrical Q	Qes	2.19	1.89
Mechanical Q	Qms	0.87	2.58
Effective mass	Mms (g)	0.18	0.12
Mechanical R of driver loss	Rms (kg/s)	0.16	0.04
Compliance	Cms (m/N)	0.0096	0.011
Air volume equivalent	Vas (liters)	2.13	2.45
Effective area of cone	Sd (cm^2)	12.57	12.57
Force factor	Bl (Tm)	5.76	5.33
Reference efficiency	ETA (%)	0.17	0.34
SPL @ 1 m for 2.83 V	Lp(2.83V/1m) (dB)	66.1	69.27

According to Dr.Wolfgang Klippel, mechancal & acoustic losses are dominant source for microspeakers's nonlinear distortion. Thus, the most importance parameters in this analysis are Bl, Cms, and Rms. Compliance of the suspension and mechanical resistance have definitely improved, while the force factor slightly decreased.

Total harmonic distortion

Interestingly, while the overall harmonic distortion figures are pumped up, distortions at 3~4 kHz, at which the human hearing is the most sensitive, have been reduced.

Directivity index

0-degree measurement data as reference

As a ring driver radiates soundwaves more uniformly than a dome, although its perceptual effect is not subjectively evaluated yet, it can be expected that the spatial distribution of a ring driver should be more like that of a electrostatic driver.


The role of a concha

Apart from electroacoustic properties of the driver, it is also vital to look into the physioacoustic properties of our body parts. Naturally, a concha boosts input signal up to 10 dB at 5~6 kHz due to Helmholtz resonance of its own cavity volume.

And of course, if the input signal has a peak at such frequency range, the result can be expected to be even more amplified, just like the case of HD800.


Conclusion

By simulating a ring radiator driver by making a hole in the middle of a Kobitone unit, its electroacoustic effect has been predicted. Thus, it can be assumed that the peak at 5~6 kHz of Sennheiser HD800 is deriving from these causes:

1. Resonant housing
2. Resonance shift due to center hole
3. Concha resonance

While the overall sound signature can be altered with modifications, it is virtually impossible to totally eliminate the peak.

(The deviation between Sennheiser's official frequency response data and conventional HATS measurement data shall be discussed in the next entry, as Gennadiy is expecting to receive the frequency response chart from Sennheiser soon)