Equivalent Noise Resistance

[7N7]

Hello all.

Could some kind and clever person explain the concept of Equivalent Noise Resistance?

I have made a little research based on the data sheets supplied on Frank's site:

E810F EQR 110 ohms gm 50
E282F EQR 220 ohms gm 26
E280F EQR 330 ohms gm 26
E83F EQR RF: 1k gm 9
AF: 36k

It would appear that EQR is related to gm, the higher the gm the lower the EQR. And that's as far as I have got. Interesting too that in the case of E83F Philips gives data for RF & AF EQR - with very different numbers.

Thanks

7N7

[Brian Beck]

Resistors by themselves produce a broadband thermal noise voltage that is described by the well-known equation V = SQRT(4kTBR). Req is that resistance that would produce the same noise as the tube in question if it were placed in series with the grid of an imaginary noiseless tube having the same parameters (gm, mu, etc.). It's just a way to put noise considerations onto a common footing with other resistive noise sources in the same system, for analysis purposes. This perspective comes from the radio frequency world, and is most useful when tubes are used at RF frequencies. The noise power density of an ideal resistance is "white"; it has the same energy in each Hertz of bandwidth anywhere in frequency. It is somewhat less useful for audio, where other noise mechanisms, mainly flicker noise and hum, also factor in, and can even dominate. A triode has a theoretical relationship between gm and Req as follows: Req = 2.5/gm. The similar equation for a pentode is more complicated since there is an additional source of noise called "partition" noise that comes from the statistical separation of the electron flow into the plate and screen currents. Specified Req values are usually a bit worse than would be predicted by this ideal equation. But as a general rule, high gm triodes will make less noise than low gm triodes. Hence the use of tubes like the 6DJ8 and 417A in RIAA stages where noise is a big problem because signal levels are so low. At audio frequencies, particularly at lower frequencies, flicker noise, which declines in energy density with increasing frequency, comes from any of a number of sources, and is harder to predict as it varies a lot from tube to tube depending on manufacturing techniques, etc. For audio, Req comparisons give only a first blush idea of relative noise performance. Generally, tubes with lower Req will have relatively lower sources of other kinds of noise, but this is not always true.

[7N7]

Brian,

Thanks very much for that most erudite explanation.

And it is now clear to me as you say, why high-gm types are preferred for RIAA applications.

It is frustrating that sometimes noise is defined in other ways; for example, Philips quotes 2µV for EF86; presumably this is more flattering than EQR in this case since EF86 has low gm!

7N7