Phono Preamp Tube Rush

Almarg, What formula did you use to calculate the Johnson noise of a phono cartridge?

@lewm

Hi Lew,

I performed that calculation in two different ways, and got the same result both ways:

Method 1: The section of the Wikipedia writeup on Johnson noise that is sub-titled "Noise Voltage and Power" contains an equation for rms noise voltage which makes clear that rms noise voltage over a given bandwidth at a given temperature is proportional to the square root of the product of that bandwidth and the resistance which is responsible for the noise. That section also states as follows:

For a 1 kΩ resistor at room temperature and a 10 kHz bandwidth, the RMS noise voltage is 400 nV.[6]

Footnote 6 indicates that a more exact result is about 403.6 nanovolts, or 0.4036 uV (microvolts).

I then extrapolated from that number to the result corresponding to the 12 ohm resistance of my cartridge, over a 20 kHz bandwidth:

0.4036 x [square root [(12 ohms/1000 ohms) x (20 kHz/10 kHz)]] = 0.0625 uV

0.0625 uV is 78 db less than the 500 uV rating of my cartridge, since:

20 x log(0.0625/500) = -78 db

Method 2: I started with the following paper, although it pertains to microphone amplifiers:

https://www.sounddevices.com/microphone-preamp-noise/

The paper states that:

The noise generated by a 10k ohm resistor (based on the thermal noise formula above) is around 1.8 uV (-114 dBV).

I assumed they were referring to a 20 kHz bandwidth, or at least to something of that order of magnitude. I then extrapolated from the 1.8 uV/10K numbers to the 12 ohm resistance of my cartridge in a manner similar to Method 1 above, and after converting to db relative to the 500 uV rating of my cartridge I got the same 78 db result.

Best regards,
-- Al

Thanks. I can’t argue with your logic, and won’t.I might wonder whether one can model a phono cartridge based solely on its internal resistance, in that calculation.  But I have no better idea.

I might wonder whether one can model a phono cartridge based solely on its internal resistance, in that calculation.

@lewm, that’s a good point. But the inductance of my cartridge is spec’d as 25 uH at 1 kHz. If we assume its inductance is also around 25 uH at 20 kHz, its inductive reactance at 20 kHz would only be about 3 ohms. And it would be progressively less than that at lower frequencies, of course. So it would appear that the cartridge’s impedance is primarily resistive throughout the audible frequency range.

Best regards,
-- Al

@lewm - Sorry I wasn't more clear.  Yes, I meant thermal noise from input resistance. 

The SUT in question had 3900 ohms on the secondary (thin wire), which generated quite a bit of noise, much more than I get from my JFET-based headamp.

And yes, you can use the ESR of a cartridge to perform a baseline minimum noise floor calculation.  You then have added noise (aka noise factor in the RF world) from the amplification (which you can break down by stage).  The first stage is by far the most important.  That's why I use special low noise matched JFETs for MC front-end.

Another good test for "tube rush" is to compare noise level between open and shorted inputs.  Most of the noise you hear open is from the 47k loading resistor.  Shorted, you hear the amplifier and tube rush.  

if executed in the balanced domain you get a maximum of 6dB less noise

Actually, that's not true.  With balanced amplification you get 6dB more signal gain, but you also get 6dB more differential noise gain.  Overall SNR is the same.  

The benefit of balanced amplification is rejection of common mode noise such as power supply crud, and crap injected on both + and - inputs together (sometimes hum).  You get a better amplifier with higher overall performance, but noise floor from a differential source such as the resistance of a cartridge is the same.