Test Setup

It’s quite straight forward. Table was suspended on some 20cm of acoustic foam, to isolate it from outside world vibrations as much as possible. Next in chain, there was low noise measurement preamp, set for 40dB gain. It’s output was fed to Esi Julia sound card. There is no need too apply RIAA equalization in analog chain nowadays. It can be done digitally with far more ease and precision using any modern recording software. If you have a phono stage, that is able to go lower then 20Hz, you can certainly use it too.

I’m using Reaper for recording. You can’t get better for ~50Eur/license (discount price). It supports VST, so applying RIAA equalization is a breeze, you just need a plugin. This one from Olaf Matthes works flawlessly. After applying RIAA, exported WAV file is analysed in SpectraPlus SC. Why Spectra ? Because again, I have license from a project long time ago. There are good freeware alternatives, like RMAA or Audacity.

Hi-Fi News Analogue Test LP was used as a test record. It doesn’t have 3.15kHz pilot tone for wow&flutter measurement, or 1kHz reference tone. And as later will be evident, there are a lot of other quirks, but it will do the job.

Measurement System Check&Calibration

We will be concentrating our efforts in a subsonic end of the audio spectrum, so let’s make sure that what we are measuring is really the D.U.T and not our equipment measuring itself. Let’s run couple loop-back tests and see how low we can go.

Black trace in first graph is a 10 sec. -40dB sweep from 0.1 to 40Hz, with large enough FFT window, to give us 0.09Hz resolution. That’s not bad, -3dB corner is at 1.3Hz! But we can do better. Let’s export this overlay and make a compensation file using this data. Now, taken with some grain of salt, we have useful bandwidth down to 0.1Hz (Red). Next graph is same setup, but with a 30Hz – 20kHz sweep. No problems further down the line.

Next, we need something to reference our measurements to. Widely accepted 0 dB level for vinyl is 5 cm/s RMS lateral velocity adjusted for RIAA equalization. HFN test record has 300 Hz tracks from +12dB to +18dB, but it doesn’t mention any references. After some digging, I found this thread, which has a clear microscopic picture of +12dB track.

I totally agree with OP, that it translates to a level of +7dB at 5 cm/s RMS lateral velocity.

Here is why ! Formulas ahead, skip if you are allergic…

Magnetic MM or MC phono cartridge, is “velocity sensitive” device. It means that cartridge electrical output is proportional only to it’s stylus tip velocity, with which it tracks LP groove, and not the frequency.

That’s why manufacturers declare cartridge output voltage at 5 cm/s RMS velocity and don’t include any frequency. It will have this rated output at all frequencies within it’s usable bandwidth, provided velocity will stay constant. Let’s find out how this velocity relates to amplitude of a record groove. From a simple equation for motion that follows a sine wave:

$x(t)=A\, sin\, (wt)$

Follows a derivative of velocity at time t being:

$v(t)=\frac{dx}{dt}=A\, \omega \, cos\, (\omega \, t)$

Which at 0⁰, when peak velocity is reached, becomes:

$v=A\, \omega =A\, 2\,\pi \, f$ $A\, -\: peak\, amplitude; f\, -\, frequency;$

Now, let’s find out what amplitude has a standard 1kHz groove at 5 cm/s RMS:

$5\, cm/s\,RMS=\frac{5}{1/\sqrt{2}}=7.07\, cm/s \,\, peak$

$A=\frac{v}{2\, \pi \, f}=\frac{7.07}{2\, \cdot 3.14\cdot 1000}=11.2\cdot 10^{-4}\, m=11.2\, \mu m$

So, for a 300Hz tone at the same 5 cm/s RMS, this groove has to be:

$A=\frac{v}{2\, \pi \, f}=\frac{7.07}{2\, \cdot 3.14\cdot 300}=37.52\, \mu m$

This means, that cartridge tracking 1kHz groove with 11.2 μm wide amplitude, will output the same voltage, as 300Hz groove with 37.52 μm amplitude. Sounds simple enough ? But there is a catch. We are feeding this cartridge voltage to our phono preamp, which has RIAA equalization. There is no problem for 1kHz, as this is unity gain EQ frequency, but for 300Hz – there will be 5.48 dB boost applied. To retain the same 0dB level, we must compensate by lowering velocity:

$5.48\, dB=1.879\: ratio$ $\frac{7.07\, cm/s}{1.879}=3.762\, cm/s$

And the resulting groove amplitude becomes:

$A=\frac{v}{2\, \pi \, f}=\frac{3.76}{2\, \cdot 3.14\cdot 300}=19.96\, \mu m$

This is our 0dB reference for 300Hz after RIAA equalization. So, what about HFN record +12dB 300Hz track with 45.5 μm groove?

$\frac{45.5\, \mu m}{19.96\, \mu m}=2.27\: ratio=7.12\, dB$

That’s far out man… (pun intended)

It’s little beyond me why HFN labeled it +12dB, but you can’t complain, when there are no specifications in the first place. Using this track, calibration was made and from here on, all amplitude sensitive measurements are referenced to this level.

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