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A rather common way to make a low noise amplifier with an equivalent input voltage noise density in the range of ~0.1 nV/rtHz, is to take a FET and place a step-up transformer in front of it.

I have done this in the past with a small commercial 1:10 microphone transformer. It did work to achieve lower equivalent input voltage noise than the amp had, but its primary winding had too high ohmic resistance for really low noise, so I made a custom transformer with approximately the following specs (I have confirmed the numbers approximately with specific measurements of resonances etc.):

enter image description here

I am feeding this into a FET amplifier with 10 fA/rtHz of current noise and 7 nV/rtHz of voltage noise.

According to spice, the output noise of the transformer with shorted primary should be approximately 7 nV/rtHz, dominated by the ohmic resistance of the primary (R2).

Taken together with the amplifier, the noise should be something like 10 nV/rtHz, or when referred to the input: ~0.2 nV/rtHz.

The issue/questions:

When I short the primary winding (Rsrc < 0.1 Ω), what I am actually getting at the output is closer to 250 nV/rtHz (or 5 nV/rtHz RTI), so 25x worse than expected. I am at a loss as to what might cause this.

When I open the primary winding, the noise reduces to a smaller value. I believe it is roughly on the same order as that of the shorted FET amp itself (will check again).

Is there any aspect of the noise contribution, that is not modeled by spice, that must be taken into account? Specifically, how should the current noise of the FET amp be treated?

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  • \$\begingroup\$ What is Rsrc in the "actual" test? Does the FET amp by itself (without transformer) match simulations? Have you tested high/low Zin? \$\endgroup\$
    – Tim Williams
    Commented Sep 5, 2023 at 14:06
  • \$\begingroup\$ @TimWilliams in the actual tests, Rsrc is short wire, with a resistance far below 1 ohm, so the primary ohmic resistance is dominated by the transformer winding. The FET amp by itself: I can confirm that its voltage noise is as stated and I can confirm that its current noise is below 10 fA/rtHz (couldn't test lower). When I open the primary short, the noise goes down, to what I would expect from the FET amp alone (as expected) \$\endgroup\$
    – tobalt
    Commented Sep 5, 2023 at 14:08
  • \$\begingroup\$ And it's not oscillating, the spectrum is flat? And, the measurement bandwidth is the same in all cases? \$\endgroup\$
    – Tim Williams
    Commented Sep 5, 2023 at 14:11
  • \$\begingroup\$ @TimWilliams yes no oscillations.. In fact there is no excitation at all for the test I am talking about here. The spectrum certainly isn't "flat" throughout.. But the voltage step-up (50x) and phase are pretty flat between ~100Hz and 10 kHz. (confirmed with function gen. + oscilloscope). I am considering this spectral range for my figures above. \$\endgroup\$
    – tobalt
    Commented Sep 5, 2023 at 16:25

1 Answer 1

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One possible problem: the shorted primary is a fairly sensitive magnetic field meter. Take a look at the output of the amplifier with a spectrum analyzer.

When I open the primary short, the noise goes down, to what I would expect from the FET amp alone

That all but confirms the magnetic noise pickup. Closing the loop turns the input circuit into a primary loop that picks up all the switchmode supplies in the vicinity, any nearby low-frequency AM sources (eg time distribution broadcast), etc.

Use a source resistance more typical of the application (i.e. higher than 0). And keep the loop area on the primary as small as possible. Ideally the primary should exit the bobbin as a twisted pair terminating directly at the source.

The transformer design must have minimal fringe field, otherwise you'll need to shield the transformer and the primary circuit - whether in a high-permeability magnetic shield or a high conductance electrostatic shield or both, I don't know off the top of my head.

With the sensitivities you're working with, without shields you just don't get any useful results - at least in my experience. Circuits like you describe can pick up ECG just by wrapping the primary loop around one wrist (just 1 turn) and joining hands so that the ECG current can flow across the arm and chest.

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  • \$\begingroup\$ The transformer is toroidal and shielded in mumetal. But the wire short is not 😬 I will experiment with the wire short geometry (will take a few weeks). In fact, I tested it once with an 820 ohm resistor instead of the short, and the noise then looked again like for the open circuit. So mag pickup of ambient noise sounds at least plausible 👍 \$\endgroup\$
    – tobalt
    Commented Sep 5, 2023 at 16:39
  • \$\begingroup\$ Now that I think of it.. the (toroidal) transformer is probably the last area I need to shield lol \$\endgroup\$
    – tobalt
    Commented Sep 5, 2023 at 16:41
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    \$\begingroup\$ Note that, as turns are wound around a toroid, a loop or solenoidal field is created, one loop for every pass around the core. That is, consider if the thickness of the toroid were reduced to zero, so the windings go from a toroidal helix to a smooth loop -- this loop is present regardless of the core. It can be compensated by winding back and forth, or with a return loop. See en.wikipedia.org/wiki/… for figures. \$\endgroup\$
    – Tim Williams
    Commented Sep 5, 2023 at 17:03
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    \$\begingroup\$ @TimWilliams good point. In this particular csse, that part of the input loop is inside the mumetal can, so ambient mag fields wouldn't be able to couple into that part of the loop as its magnetically shorted by the can.. But as I wrote above, I question the value of shielding the toroid and a good winding geometry is essential for eventually not using that shield. \$\endgroup\$
    – tobalt
    Commented Sep 5, 2023 at 17:12
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    \$\begingroup\$ @tobalt I’m glad you got unstuck with that project. I’m a measurements guy at heart and such approaches are dear to my heart :) It’d be a real travesty if someone got discouraged when we need more people who don’t shy away from the finer corners of analog world :) \$\endgroup\$
    – Kuba hasn't forgotten Monica
    Commented Sep 8, 2023 at 13:38

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