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Suppose I have a carrier signal with low-ish RF frequency (a few MHz) that I can reasonably amplify with an op-amp. How can I estimate the added phase noise due to the amplifier?

For microwave frequencies, gain blocks often have specifications of their phase noise (examples on p. 75). Op-amps do not, presumably because phase noise rarely is a concern. Can I derive the phase noise from the opamp's parameters that are specified?

For the wideband (white) noise, I think I know how I might proceed. The amplifier's noise (op-amp + feedback network) is equally distributed across both of the carrier's quadratures (corresponding to amplitude and phase). Given the carrier's input amplitude I can compute the phase noise density.

I am, however, unsure how I might estimate the close-in phase noise. By my understanding, the 1/f phase noise that an amplifier contributes is effectively its own 1/f noise, upconverted to the carrier frequency. I read that some ways by which this upconversion can happen are:

  1. non-linear gain of the amplifier;
  2. modulation of the gain with temperature, supply voltage or other fluctuations (AM -> PM);
  3. modulation of the delay (phase) of the amplifier.

In essence, all are due to a closed-loop gain that fluctuates. By design, an amplifier constructed around an op-amp is incredibly linear. With enough loop gain, the closed-loop gain only depends on the feedback network. Resistors are really quite linear (~ ppm?).

Is a feedback amplifier at these frequencies essentially that good in terms of phase noise that no one bothers?

My question is for educational purposes, I am not facing an immediate design challenge.

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  • \$\begingroup\$ There's not many op-amps that are suitable for amplification above 1MHz. Are you really using op-amps with GBW products above 50MHz with all of the layout problems that brings? \$\endgroup\$
    – TimWescott
    Aug 21, 2022 at 21:45
  • \$\begingroup\$ And can you please edit your question with some part numbers for microwave amplifiers that have phase noise specifications? I'm suspecting that they're class C or A-B or other classes where significant nonlinearities occur. \$\endgroup\$
    – TimWescott
    Aug 21, 2022 at 21:47
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    \$\begingroup\$ Yes the 1/f noise becomes the close-in noise. If the closed-loop gain is low, then this is a rather simple exercise, because the fluctuation of the op-amps gain does not matter. You will have to consider the 1/f noise of the gain setting resistors instead, however. If you run the opamp at close to its open loop gain, though, I guess matters become much more complicated. \$\endgroup\$
    – tobalt
    Aug 22, 2022 at 7:34
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    \$\begingroup\$ @polwel I'm afraid I can't. The details of how to get from the noise density to phase noise are still an "exercise", i.e. I don't know them currently. I just wanted to comment that it is indeed the low frequency noise that is upconverted as you supposed. \$\endgroup\$
    – tobalt
    Aug 22, 2022 at 18:15
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    \$\begingroup\$ If you're using a mixer, then wouldn't the main 1/f noise upconversion mechanism be in it? Sounds like you have "half" of a typical chopping amplifier scheme (i.e., only the modulator at the output), so both your carrier and 1/f noise + offset at upconverted. I don't know anyone can derive a formula for you, but perhaps you could try measuring phase noise experimentally with op-amps w/ different 1/f corners. \$\endgroup\$
    – Designalog
    Sep 19, 2022 at 9:57

2 Answers 2

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I have done some simulations and I see that the 1/f noise does not seem to have impact on phase noise only the white noise has impact as long as the amplifier is linear. I have modeled the amplifier as an adder which is just adding a noise to the clean input sine wave.

First I added a thermal noise and checked the impact of the same on phase noise

enter image description here

enter image description here

Next I added 1/f + white noise and I do not see the impact of 1/f noise on phase noise enter image description here

enter image description here

With non linear effects in the amplifier, I do not know how to calculate the phase noise impact of 1/f noise. Simulation seems the only option for me.

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  • \$\begingroup\$ But a linear amplifier is not a saturating inverter. In the latter, an offset (noise) voltage will indeed result in jitter, but in the former, it is just an offset. Put differently, the clamping of the inverter is precisely the non-linear effect that upconverts the noise of the amp to the carrier frequency. This effect is entirely absent in an op-amp that does not saturate. Of course, I am happy to be proven wrong by simulations. \$\endgroup\$
    – polwel
    Feb 25, 2023 at 20:51
  • \$\begingroup\$ I've updated the answer with simulation results. It seems that you are right. 1/f noise does not seem to have an impact on phase noise when I model the amp as a linear system \$\endgroup\$
    – sai
    Feb 26, 2023 at 3:53
  • \$\begingroup\$ I appreciate the effort you put in. Looks like we both learned something. +1 \$\endgroup\$
    – polwel
    Feb 26, 2023 at 10:17
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Op-amps don't really work well in frequencies above 1 MHz with some exceptions of high precision Op-amps. Are you sure your design is correct?

If you do a Bode plot of the gain of the op-amp with the frequency of the signal, a frequency above 1 MHz is usually above the frequency range for full power bandwidth. You get full amplification only in some frequency range and that is most likely not above 1 MHz. Your op-amp becomes a low pass filter beyond that. You will have signal attenuation outside the full power bandwidth frequency. Look at terms like full power bandwidth, gain bandwidth product of the op-amp you are using in its datasheet.

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  • \$\begingroup\$ I don't think the slew rate limits the phase noise. Certainly not when the signal amplitude is small enough. \$\endgroup\$
    – polwel
    Sep 22, 2022 at 5:11
  • \$\begingroup\$ Can you show the diagram of your circuit? Which op amp are you using? \$\endgroup\$
    – Amit M
    Sep 22, 2022 at 5:23
  • \$\begingroup\$ Per my question: "My question is for educational purposes, I am not facing an immediate design challenge." \$\endgroup\$
    – polwel
    Sep 22, 2022 at 5:25
  • \$\begingroup\$ But look here, page 208, for an example of low-phase-noise amplification of a 10 MHz signal with an ADA4895-1. Or AD8037 a page later. \$\endgroup\$
    – polwel
    Sep 22, 2022 at 5:32
  • \$\begingroup\$ The noise you talked about seems to increase with frequency in non low-noise op amps and total noise may be reasonably high at frequencies over 3 MHz.. You have to choose a op-amp with total noise which is under some range. Look at a op amp as the one below. Look at terms like total noise, phase noise, noise figure. Your op amp selection and design may be based on the above criteria. . analog.com/media/en/technical-documentation/data-sheets/… . \$\endgroup\$
    – Amit M
    Sep 22, 2022 at 5:38

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