Re: Capacitor-feedback for low noise


Hi Jeroen,


> Sure, here is one:
>
> J. Lepaisant, M. Lam Chok Sing, D. Bloyet, "Low-noise preamplifier
> with input and feedback transformers for low source resistance sensors"
> Rev. Sci Instrum. 63(3), March 1992, p2089
>
> This is basically a differential amplifier with series transformer
> feedback in the input. Its bandwidth is 5Hz-100kHz. It has 65pV/rtHz
> and 1.5pA/rtHz noise, so you'll want to change the transformers to
> trade current noise against voltage noise.

> In a project of mine, I used a different scheme, a folded cascode
> with transformer feedback to the sources of the input FETs. Here, the
> bandwidth is 10kHz-75MHz and the noise voltage is 650pV/rtHz. I did not
> measure the noise current, but it should be in the 30fA/rtHz ballpark.
> You can see short description at:
> http://jeroen.home.cern.ch/jeroen/tfpu/LNA.shtml
>
> There is quite a bit of flexibility trading off voltage against current


Many thanks for the references.

I've been doing a bit of thinking - quite painful when it comes to
noise analysis of multinode circuits. While your examples are
invaluable, I will have to understand the theory to optimize the design
for my particular application. Am I on the right track?

My requirement is for a transimpedance amplifier, whereas your example
has a high-impedance input. I think that my first stage must be
configured as a current amplifier, with conversion to voltage occuring
first in the second transimpedance stage. Compared to your circuit, my
bandwidth requirement is much more modest, and I plan to use
low-current-noise op amps for both stages.

Using op amps, which are inherently voltage in-voltage out, rather than
discrete components, I have to deviate significantly from your
configuration, but I think I have come up with a viable one, where the
transformer primary is between the input and output of the stage 1 op
amp, and its secondary, with much fewer turns, feeds directly the input
of the stage 2 op amp with feedback resistor Rf2. Seen from the stage 1
op amp, the feedback circuit is essentially the magnetizing inductance
M of the transformer primary, in parallel with Rf2*N/A2, where A2 is
the DC voltage gain A2 of the second op amp and N is the turns ratio of
the transformer.

The low-frequency roll-off happens at the break frequency of
Rf2*N/A2/2/pi/M, and there are no stability problems at that frequency.
The stability problems occur near the frequency 1/2/pi/sqrt(M*Ci1),
where Ci1 is the input capacitance of op amp 1. This gives a resonance
in the feedback fraction, which must be damped by a resistance
somewhere. I think the only way you can provide this resistance without
contributing to the input node noise is via the apparent resistance
Rf2*N/A2.

I think that the noise generated by this apparent resistance Rf2*N/A2
is much less than the Johnson noise from a real resistor of this value.
It will essentially be the total noise current at the input-node of op
amp 2, divided by N. Do you agree?

The resonant frequency 1/2/pi/sqrt(M*Ci1) provides a strict upper limit
to the bandwidth of the overall amplifier, and it might be hard to get
within an order of magnitude of it. This puts an upper limit on the
magnetizing inductance M of the transformer.

Thanks again for your excellent suggestion.

Best regards,

Ziggy.

.

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