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REVIEW 3 major objections 6 minor 29 references

Experimental Study of AM and PM Noise in Cascaded Amplifiers

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read For a fixed output power, adding amplifier stages can lower the effective noise figure.

desk verdict Solid experimental study with a useful NF design rule, but the coherence-peak story needs a clear statement about per-power quadrature calibration before I'd trust it. read the letter →

arxiv 2501.18235 v1 pith:X7JMOPC5 submitted 2025-01-30 physics.ins-det

Inari Badillo , Joaquín Portilla This is my paper · ORCID
classification physics.ins-det
keywords AMnoisePMcascadedamplifierseffectivefigureflickerwhiteAM-PMcorrelationgaincompression
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports simultaneous measurements of amplitude-modulation (AM) and phase-modulation (PM) noise in chains of one to four identical 2 GHz amplifier stages, from small-signal operation into strong compression, using an in-phase/quadrature (I-Q) receiver that also measures the AM-to-PM coherence function. The central experimental result is that the effective noise figure, computed from the white-noise parts of both AM and PM spectra, decreases as the number of stages grows when the comparison is made at a fixed carrier output power. At a fixed input power the opposite trend appears: more stages compress earlier, and their AM/PM noise performance degrades faster with drive. The paper also finds that AM and PM noise are largely uncorrelated, but in particular amplifier types the coherence shows peaks near the 1 dB compression point, coinciding with peaking in the measured AM-to-PM derivative. If the cascade result holds, receiver and radar front ends can trade extra stages for lower effective noise at a required output power.

What carries the argument

The argument is carried by the I-Q receiver measurement setup, which simultaneously demodulates AM and PM noise and computes the coherence function, the normalized cross-power spectral density between the two noise channels, ranging from zero for uncorrelated to one for fully correlated. The cascade analysis rests on a simple noise-accounting rule: each stage amplifies the AM and PM modulation noise arriving from earlier stages and adds its own noise, so when the output power is held fixed the last stage's added noise is identical and the earlier stages' contributions are weighted down by the gain that follows. For the correlation result, the key object is the measured AM-to-PM derivative, whose peaking near the 1 dB compression point tracks the peaking of the coherence function.

What would settle it

Measure the effective NF of one-, two-, three-, and four-stage chains while keeping the final stage's output power fixed but changing only the gain placed before it, for example by inserting a calibrated attenuator between stages; if the final stage's noise contribution changes with the number or gain of preceding stages, the cascade argument fails.

Watch

Extended reading notes

Core claim

The authors claim that, for a cascade of identical amplifier stages, the effective noise figure at a given carrier output power is improved by increasing the number of stages. Their reasoning is that at equal output power the final stage adds the same noise regardless of how many stages precede it, while the noise added by earlier stages is reduced by the gain of the stages after them and is generated at lower drive levels. Measured effective noise figures from AM and PM white noise in one- to four-stage amplifiers support this: at low input power the cascade follows the standard noise-figure behavior, and under compression the effective NF rises for all chains, but the absolute degradation is larger for the chains with fewer stages. A separate finding is that AM-to-PM coherence is generally low, yet some amplifier configurations show clear correlation peaks close to the 1 dB gain compression point, in both flicker and white noise regions, and the same peaking appears in the derivative of the AM-to-PM characteristic, linking the underlying noise-conversion mechanisms to the device's large-signal AM-PM response.

Load-bearing premise

The conclusion that more stages improve effective noise figure at a fixed output power assumes that each identical stage adds a noise power depending only on its own output power, so the final stage contributes the same noise whether it is preceded by one stage or by three.

Editorial extensions

If this is right

  • For a fixed carrier output power, a cascade with more identical stages can exhibit a lower effective NF than a shorter chain, even though the same chain has worse AM/PM noise figures when compared at the same input power.
  • Adding stages moves the onset of gain compression to lower input power levels, so input-referred AM/PM noise performance degrades faster with drive as the stage count grows.
  • Under small-signal conditions the effective NF is nearly independent of the number of stages, and slightly worse with more stages, consistent with the standard cascade noise-figure formula.
  • AM and PM noise in the tested amplifiers are mostly independent, so an amplifier's AM noise performance cannot be inferred from its PM noise performance; both must be measured.
  • In some devices, operating near the 1 dB compression point can create significant AM-to-PM correlation at specific offset frequencies, meaning noise at those offsets should not be treated as two independent channels.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable design extension: if the cascade result generalizes to other transistor technologies, system designers could deliberately lower the drive level of early stages and add gain later to reduce effective NF at a fixed output power, accepting extra stages and DC consumption.
  • The coincidence of coherence peaks with AM-to-PM derivative peaks suggests that a static AM-PM measurement could serve as a screening test for operating points where AM and PM noise become correlated, before full noise measurements are made.
  • The load-bearing assumption that a stage's added noise depends only on its own output power is unlikely to hold in strong compression, where noise conversion becomes input-dependent; the reported NF improvement may vanish or reverse in that regime.
  • Because cyclostationary noise theory allows AM-PM correlation to grow under strong periodic drive, the observed near-compression peaks are consistent with that picture, but the device-dependence of the peaks points to a role for specific bias and matching conditions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript reports an experimental study of AM and PM noise in cascaded amplifier chains built from one to four identical stages, measured at 2 GHz from small-signal to strong compression. Using an I-Q receiver with simultaneous AM and PM detection, the authors determine flicker and white noise contributions, compute an 'effective noise figure' from the white AM and PM noise spectra, and measure the AM-to-PM coherence function. The main reported findings are (i) that effective noise figure degrades with input power but, for a fixed output power, improves as the number of stages increases, and (ii) that AM-PM coherence is generally low but shows peaks near the 1 dB compression point in a second amplifier family, coinciding with peaking in the measured AM-PM derivative. The paper includes measured spectra, coherence plots, and effective NF curves, with comparisons across one to four stages.

Significance. If valid, the result that adding stages can improve effective noise figure at a fixed output power is of practical interest for amplifier chain design, and the observed coherence peaks near compression are relevant for nonlinear noise modeling. The paper's strengths are its simultaneous AM/PM measurement capability, the use of a previously published calibration procedure [17] giving a 0.15 dB uncertainty claim, and the lack of any fitted parameters in the reported trends. The experimental data are presented clearly and the main trends are internally consistent. However, the two central claims (effective NF comparison and coherence peaks) rely on the I-Q receiver actually separating AM and PM noise, and the manuscript does not document that the quadrature condition is maintained as the DUT's AM-PM phase shift varies with power. This unresolved calibration issue is the key correctness risk and prevents acceptance in the present form.

major comments (3)
  1. [Section 2 (Measurement Setup) and Figures 11–13] The paper does not state that the 90° phase condition between the DUT path and the LO path is re-optimized at every carrier input power. The text only says the phase shifter 'must be adjusted to obtain proper settings' and refers to [17] for the calibration procedure. Since Figure 13 shows that the AM-PM derivative (and hence the DUT insertion phase versus power) peaks near the 1 dB compression point, a fixed phase-shifter setting would produce a quadrature error that grows with power in exactly that region. This would cause AM noise to leak into the PM channel and PM noise into the AM channel, artificially raising the coherence function near compression and biasing the white-noise levels used to compute effective NF. The authors need to either document that the quadrature is re-optimized at each power step or provide a quantitative error budget for quadrature misalignment in the nonlinear regime; without one, the coherence peaks in Figures 11 and 12 and the effective NF comparison in Figures 8 and 9 are not fully trustworthy.
  2. [Section 4 (Discussion), argument on last-stage noise contribution] The sentence 'achieving an identical output power implies that the noise power contribution of the last stage is identical for all of the amplifiers, independent of their number of stages' assumes that each stage's added noise depends only on its own output power and is independent of the noise content of its input or the compression state of preceding stages. This assumption is not tested or justified in the paper. While the reported NF improvement is an experimental observation, this argument is used to explain it, and a failure of the assumption could alter the interpretation. The authors should either provide a direct test (for example, comparing the output noise of a single stage driven at the same output power as the final stage of a chain) or explicitly state this as a limitation.
  3. [Figures 11–13 and Section 3] The coherence peaks are reported for a second amplifier family ('another type of amplifier component') with only the linear gain and noise figure stated (over 26 dB and around 1 dB at 2 GHz). No details of the device technology, bias, or matching conditions are given, even though the paper's own introduction notes that AM and PM noise levels depend on bias and matching conditions. Without this information, the claim that these peaks occur in 'some particular amplifier configurations' is not reproducible, and the reader cannot assess whether the effect is specific to the device or an artifact of the measurement conditions.
minor comments (6)
  1. [Abstract and Section 3] The abstract states the effective noise figure 'decreases with the number of stages for a given carrier output power level,' but the results in Section 3 (Figure 9) are phrased as 'significantly improved by adding some amplification stages, except under small-signal conditions for which it remains essentially constant or, more precisely, slightly worse.' Please harmonize the wording so the small-signal caveat is reflected in the abstract or in the conclusion.
  2. [Section 2] There is a typo: 'allowing for the simultaneously measuring of AM and PM noise' should read 'allowing the simultaneous measurement of AM and PM noise.'
  3. [Section 2] The sentence 'The desired phase difference can be obtained simply by tuning the phase shifter' is misleading: the phase shifter may introduce loss and its own noise, and the word 'simply' understates the need for the calibration procedure of [17]. Consider rewording.
  4. [Figures 8 and 9] No error bars are shown on the effective NF data. Since the paper cites a 0.15 dB uncertainty from the calibration procedure, it would be helpful to include error bars or a statement that the uncertainties are smaller than the symbol size.
  5. [Section 4] The sentence 'the fact of adding stages does not produce an improvement in AM and PM noise performances' appears to contradict the later statement about improved effective NF. Clarify that AM and PM noise in dBc/Hz worsen with the number of stages, while the effective NF computed from those spectra can nonetheless improve at a fixed output power because the carrier power also increases with gain.
  6. [References] Reference [15] (Adamian and Uhlir) is listed in the bibliography but not cited in the text; reference [19] (Friis) is cited in Section 3 and 4 but appears after [18] in the reference list. Please check the citation order.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central measured trends and the cascade argument rest on new experimental data, while prior self-citations supply definitions and calibration methods rather than the reported results.

full rationale

The paper's central claims are the measured effective noise-figure trend versus stage count at fixed output power and the measured AM-to-PM coherence peaks near the 1 dB compression point. These are presented as raw measurement results (Figures 6-13), not as outputs of a fitted model. The cascade argument in Section 4 uses standard Friis-type reasoning that each stage amplifies prior noise and adds its own contribution; this is an explanatory model consistent with the data, not a quantity fitted to the data and then renamed as a prediction. The effective NF definition is imported from the authors' earlier work (ref. 12) and the measurement/calibration procedure from ref. 17, and the AM-PM derivative link from ref. 13, but those citations provide definitions, calibration methodology, and a qualitative hypothesis, not the reported data or the central trend. No parameter is fitted to a subset of the data and then used to predict a closely related quantity, and no quantity is defined in terms of the quantity it is said to explain. The observed coherence peaks and the measured AM-PM derivatives are independent measurements that are compared qualitatively. The skeptical concern about quadrature crosstalk is a measurement-validity question, not a circularity of the derivation chain, and therefore does not raise the circularity score. Overall, the derivation chain is self-contained once the cited measurement definitions are accepted.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities or fitted parameters. Its conclusions rest on standard noise-modeling assumptions and on prior results by the same group for effective NF and AM-PM derivative behavior.

assumptions (5)
  • domain assumption Noise in amplifiers can be modeled as small-index AM and PM modulation sidebands superimposed on the carrier.
    Invoked in Section 4 to justify describing noise conversion as a linear perturbation of the steady state, in the paragraph starting 'More generally, whether the noise is flicker or white...'.
  • domain assumption The coherence function computed from measured cross-spectral density gives the true AM-PM correlation of the DUT.
    The paper uses the coherence function definition from ref [16] without discussing how measurement noise biases the estimate, especially when the true correlation is low.
  • domain assumption Effective NF derived from AM and PM white noise spectra equals the standard noise figure under linear operation.
    Taken from ref [12] (Garmendia and Portilla) and used to compute effective NF in Figures 8 and 9; the assumption is stated in the Introduction.
  • domain assumption The AM-PM derivative of the amplifier's steady-state input-output characteristic is directly related to the mechanisms producing AM-PM noise correlation.
    Used in Section 4 to interpret the coherence peaks; based on refs [13,20]. The paper notes a 'similar peaking behavior' but does not derive a quantitative relation.
  • domain assumption Noise contributions of individual stages add in power and are amplified by the gain of subsequent stages following the Friis formula, even under mild compression.
    Used in Section 4 to argue that the last stage's noise contribution is identical for all chains at a given output power; this is standard for linear operation but is applied here near compression.

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Cite this review

Pith. "Pith review of Experimental Study of AM and PM Noise in Cascaded Amplifiers." pith.science (2026). https://pith.science/paper/X7JMOPC5

@misc{pith2026250118235,
  author       = {Pith},
  title        = {Pith review of: Experimental Study of AM and PM Noise in Cascaded Amplifiers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X7JMOPC5}},
  note         = {Machine review of arXiv:2501.18235}
}
read the original abstract

An experimental study of amplitude modulation and phase modulation noise spectra in cascaded amplifiers was carried out as a function of the number of amplification stages and the input power. Flicker and white noise contributions were determined, as well as effective noise figure from AM and PM noise spectra from small signal to large signal regimes. Simultaneous measurements of AM and PM noise were performed, and associated correlation was measured as a function of the offset frequency from the carrier. Measurements exhibited, in general, quite low AM PM correlation levels both in the flicker and white noise parts of the spectrum. In some particular amplifier configurations, however, measurements showed some peaks in the correlation at some specific input power levels in the transition zone, from a quasi-linear to strong compression. The results show that the effective noise figure decreases with the number of stages for a given carrier output power level.

Figures

Figures reproduced from arXiv: 2501.18235 by the authors.

Figure 1
Figure 1. Schematic of the experimental setup for the measurements. The system is settled in orderto measure the DUT AM noise from the I branch output, eliminating PM noise contributions from the source and the DUT itself, and to obtain the PM noise produced by the DUT from the Q branch output, eliminating in this case the DUT AM noise contribution, as well as the AM and PM noise introduced by the source. With the appropriate… view at source ↗
Figure 4
Figure 4. AM-to-PM coherence function in the white noise region versus carrier input power, measured for one- to four-stage amplifiers [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. AM-to-PM coherence function, measured at 1 KHz offset frequency, versus carrier input power for one- to four-stage amplifiers. AM and PM noise performances as a function ofinput power and for 1–4 amplification stages are showninterms of single-sidebandnoisepower,withrespectto carrierpower[18], in Figures 6 and 7 for the white portion of the spectra and for flicker noise at the 1 kHz offset, respectively. It can be n… view at source ↗
Figures from the paper (5 more)
Figure 6
Figure 6. Figure 6: Measured AM and PM white noise versus carrier input power, produced in one- to four￾stage amplifiers [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: AM and PM noise measured at 1 KHz offset frequency versus carrier input power, corre￾sponding to one- to four-stage amplifiers. Itis also interesting to observe the noise behaviorin terms of effective NF (see [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 11
Figure 11. Figure 11: AM-to-PM coherence function versus carrier input power for the one-stage amplifier, measured at 1 KHz offset, at 10 KHz offset and in the white noise region. In [13], it is shown that the dependence on the carrier power of AM and PM noise behavior in one stage could b…
Figure 12
Figure 12. Figure 12: AM-to-PM coherence function versus carrier input power for the two-stage amplifier, measured at 1 KHz offset, at 10 KHz offset and in the white noise region [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 13
Figure 13. Figure 13: Measured AM-to-PM derivative versus carrier input power. It is well known that the correlation is zero as far as additive white noise is con￾cerned [22]. Due to the particular noise mechanisms that control AM and PM noise conversion around the carrier, it can be conje…

Discussion (0). Continue with ORCID to comment.

Reference graph

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