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Re: Possible designs for a Ultra low noise 1 Hz to 100kHz amplifier for Phase Noise Analyzer?

 

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On 21/08/2022 00:30, F1EKU wrote:
Paralleling transistors or amplifiers simply increases the current of phase correlated signals by a factor of N and of non-phase correlated signals (Gaussian noise for example) by a factor of square root of N.
Thus, we obtain an improvement of the signal-to-noise ratio of 6 dB for 4 transistors, 12 dB for 16 transistors, and so on.
This solution was widely used in Hi-Fi several decades ago in the glory days of vinyl records, particularly for moving coil type cells.
This is not true.

The S/N and hence noise figure may decrease with addition of more parallel transistors, but it doesn't improve by 3dB for every doubling of the number. Paralleling transistors only reduces the noise contributed by the transistors, the source noise remains the same. It is really only useful if the noise figure of the transistor is significant to start with. If a transistor stage has a noise figure of 3dB, for example, it means that half the noise is contributed by the transistor. If you add another identical transistor in parallel (all other things being unchanged), the transistors' contribution will reduce by half, but the total noise is still ? of what it was. The noise figure will now be 1.75dB - an improvement of 1.25dB. If you double again to 4 transistors, the resulting noise figure will now be 0.96dB - incremental improvement of 0.79dB. The benefit of each doubling of the number of transistors rapidly diminishes.

Here's a table with more cases:

<------------------------------------------------------- Noise Figure of n transistors in parallel ----------------------------------------------------->
?1??? ? 2??? ???? 3? ?? ??? 4??? ? ?? 5??? ? ?? 6? ?? ??? 7?? ? ? ? 8???????? 9?? ? ? ? 10?? ? ?? 11?? ? ?? 12? ? ??? 13?? ? ?? 14 ? ?? ? 15? ? ? ? 16
1dB??? 0.53dB??? 0.36dB??? 0.27dB??? 0.22dB??? 0.18dB??? 0.16dB??? 0.14dB??? 0.12dB??? 0.11dB??? 0.10dB??? 0.09dB??? 0.09dB??? 0.08dB??? 0.07dB??? 0.07dB
2dB??? 1.11dB??? 0.77dB??? 0.59dB??? 0.48dB??? 0.40dB??? 0.35dB??? 0.31dB??? 0.27dB??? 0.25dB??? 0.22dB??? 0.21dB??? 0.19dB??? 0.18dB??? 0.17dB??? 0.16dB
3dB??? 1.75dB??? 1.24dB??? 0.96dB??? 0.79dB??? 0.67dB??? 0.58dB??? 0.51dB??? 0.46dB??? 0.41dB??? 0.38dB??? 0.35dB??? 0.32dB??? 0.30dB??? 0.28dB??? 0.26dB
4dB??? 2.45dB??? 1.77dB??? 1.39dB??? 1.15dB??? 0.98dB??? 0.85dB??? 0.75dB??? 0.67dB??? 0.61dB??? 0.56dB??? 0.52dB??? 0.48dB??? 0.45dB??? 0.42dB??? 0.39dB
5dB??? 3.18dB??? 2.36dB??? 1.88dB??? 1.56dB??? 1.34dB??? 1.17dB??? 1.04dB??? 0.94dB??? 0.85dB??? 0.78dB??? 0.72dB??? 0.67dB??? 0.62dB??? 0.58dB??? 0.55dB
6dB??? 3.96dB??? 3.00dB??? 2.42dB??? 2.03dB??? 1.75dB??? 1.54dB??? 1.38dB??? 1.24dB??? 1.13dB??? 1.04dB??? 0.96dB??? 0.90dB??? 0.84dB??? 0.79dB??? 0.74dB
7dB??? 4.78dB??? 3.69dB??? 3.02dB??? 2.56dB??? 2.22dB??? 1.97dB??? 1.77dB??? 1.60dB??? 1.46dB??? 1.35dB??? 1.25dB??? 1.17dB??? 1.09dB??? 1.03dB??? 0.97dB
8dB??? 5.63dB??? 4.42dB??? 3.67dB??? 3.14dB??? 2.75dB??? 2.45dB??? 2.21dB??? 2.01dB??? 1.85dB??? 1.71dB??? 1.59dB??? 1.49dB??? 1.40dB??? 1.32dB??? 1.24dB
9dB??? 6.50dB??? 5.20dB??? 4.37dB??? 3.78dB??? 3.34dB??? 2.99dB??? 2.71dB??? 2.48dB??? 2.29dB??? 2.13dB??? 1.98dB??? 1.86dB??? 1.75dB??? 1.65dB??? 1.57dB
10dB?? 7.40dB??? 6.02dB??? 5.12dB??? 4.47dB??? 3.98dB??? 3.59dB??? 3.27dB??? 3.01dB??? 2.79dB??? 2.60dB??? 2.43dB??? 2.28dB??? 2.16dB??? 2.04dB??? 1.94dB
11dB?? 8.32dB??? 6.87dB??? 5.91dB??? 5.21dB??? 4.67dB??? 4.24dB??? 3.89dB??? 3.59dB??? 3.34dB??? 3.13dB??? 2.94dB??? 2.77dB??? 2.62dB??? 2.49dB??? 2.37dB
12dB?? 9.26dB??? 7.74dB??? 6.73dB??? 5.99dB??? 5.41dB??? 4.94dB??? 4.56dB??? 4.23dB??? 3.95dB??? 3.71dB??? 3.50dB??? 3.31dB??? 3.14dB??? 2.99dB??? 2.85dB
13dB?? 10.20dB?? 8.64dB??? 7.59dB??? 6.80dB??? 6.19dB??? 5.69dB??? 5.28dB??? 4.92dB??? 4.62dB??? 4.35dB??? 4.12dB??? 3.91dB??? 3.72dB??? 3.55dB??? 3.39dB
14dB?? 11.16dB?? 9.56dB??? 8.47dB??? 7.65dB??? 7.01dB??? 6.48dB??? 6.04dB??? 5.66dB??? 5.33dB??? 5.04dB??? 4.79dB??? 4.56dB??? 4.35dB??? 4.16dB??? 3.99dB
15dB?? 12.12dB?? 10.50dB?? 9.37dB??? 8.53dB??? 7.86dB??? 7.30dB??? 6.84dB??? 6.44dB??? 6.09dB??? 5.78dB??? 5.50dB??? 5.26dB??? 5.03dB??? 4.83dB??? 4.64dB
?
In practice, it is difficult to see these improvements.
--
Regards,
Tony
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