Path 05 · Module 04

Blockers, Linearity
& Gain Control

A receiver can hear a whisper in a quiet room and lose it beside a transmitter. Follow the unwanted energy, find the first stage that loses its margin, and decide what filtering and gain control can actually protect.

Wanted at the antenna feed
−105 dBm · 2.450 GHz
Recurring decision
Which stage fails first?
Gain control is causal
Detect → qualify → switch → settle
01 / 10

Failure: sensitivity passes, the nearby transmitter wins

The gateway meets its quiet sensitivity allocation. Why does a nearby transmitter still stop reception?

Continue the fictional telemetry gateway from Sensitivity, Gain & Noise Budget. Its wanted input is −105 dBm at R2, the antenna-feed plane. The matched quiet chain has 42.5 dB gain, 2.799879362 dB NF and conditional sensitivity −118.165007875 dBm. That gives 13.165 dB above the quiet threshold. None of those numbers says how much unwanted energy its LNA, mixer or converter can tolerate.

Now admit one −10 dBm CW blocker, 20 MHz above the wanted carrier. With no extra rejection, the front-end loss makes its LNA input −11.5 dBm. The synthetic LNA input P1dB is −15 dBm: the blocker alone is 3.5 dB above the supplied compression point. The small wanted signal must traverse that same device. A later IF gain reduction cannot restore the lost linear relationship.

Think about itIf IF gain drops by 40 dB, does the LNA recover its input headroom?
Answer

No. The LNA still receives −11.5 dBm from the blocker. IF gain acts after the LNA and mixer. It can lower the converter level only if the preceding analog amplitude model remains valid. After this LNA failure, later levels are uncompressed extrapolations; neither quiet sensitivity nor a calculated downstream SNR qualifies reception.

Opening contrast · R2 input, high gain, matched synthetic gateway
CornerFirst evidenceDecision
Quiet · all blockers offNF 2.799879362 dB; sensitivity −118.165007875 dBmConditional weak-signal screen only.
−10 dBm at +20 MHzRX-LNA input −11.5 dBm vs IP1dB −15 dBmLinear domain exceeded at R1-LNA-in. Stop downstream fidelity claims.
−25 dBm burst at +1 MHzMixer input −6.5 dBm vs IP1dB −5 dBm1.5 dB margin fails 6 dB reserve; this is not proof of exactly 1 dB compression.
Common misconceptionExcellent small-signal NF guarantees blocker performance.

NF measures small-signal SNR degradation under a specified noise convention. Strong signals can change gain, create products or push converter peaks across the rail. Build a separate dynamic-range argument from actual threats and stage conditions.

Begin that argument at the point where each unwanted source enters, not at the output where the failure becomes visible.

02 / 10

Catalogue every blocker and coupling path

What must you know about a blocker before adding a number to the budget?

A threat row names frequency, on-time level, waveform and occupied width, duty/timing, receiver mode, coupling path and entry plane. Antenna coupling enters at R2; a board clock coupled at the mixer input skips the front-end filter and LNA. A conducted level at a transmitter output is not a receiver input level until a coupling model or measurement connects the ports.

Four canonical gateway threats · illustrative engineering case, not conformance levels
ID / waveformFrequency / widthLevel and entryTiming / mode / path
Quiet · no blockerWanted 2450 MHz; 13.5 kHz ideal signal supportWanted −105 dBm at R2High gain; continuous wanted.
B1 · nearby CW screen2470 MHz; +20 MHz; zero-width tone−10 dBm at R2[0,2000) µs; high gain; antenna-feed coupling.
B1 + B2 · two CW tones2451 and 2452 MHz; zero-width tones−55 dBm EACH at R2[0,2000) µs; high gain; two distinct source frequencies.
B1 · coexistence burst2451 MHz; +1 MHz; gated CW screen−25 dBm on-time at R2[50,150) µs; 5% of 2000 µs; automatic starts high.

Blockers default to off, represented by absence, not a magic −999 dBm input. A CW burst is a plateau screen: the exact event times are modeled, but spectral splatter from its edges is not. A wideband or modulated source keeps its frequency support for overlap inspection while losing supported CW amplitude claims. Do not quietly turn Wi-Fi into this exact two-tone fixture.

Reference-plane contract · semantic portfolio names and local suffixes
PlaneWhat crosses itLocal convention
R2 → R1-LNA-inAntenna feed → RX-FE → LNA input50 Ω matched available power; RX-FE at physical 290 K.
R1-LNA-outLNA output = mixer RF input50 Ω; real LO drive and image response require evidence.
A1-IF → A1-ADC-inMixer 100 MHz IF → driver → converter100 Ω differential teaching power at A1; actual ADC impedance is not asserted resistive.
R0 / R3RF demodulator boundary / detector decision boundaryR3 is not an antenna connector. A0 codes and D3 80 kcomplex-sample/s remain separate.
Common misconceptionThe strongest blocker is always the dominant failure.

A weaker pair can place a cubic product exactly on the wanted channel. A closer blocker may sample a much noisier part of the LO mask. Rank paths and mechanisms, not only a list of dBm values.

Exact technology test levels belong to Path 07, coupling distributions to Path 06, and repeatable receiver tests to Path 08. Here, preserve a source’s identity as it moves through the chain.

03 / 10

Propagate levels and compression headroom

Which local input margin fails before you ever reach the ADC?

Carry each wanted, blocker and product frequency through its own transfer. The nominal stage gains are −1.5/+20/−6/+30 dB and NFs 1.5/1/6/4 dB. We retain p05-m03-receiver-ledger-v1, including its effective wanted-channel mixer NF. We add synthetic input P1dB/IIP3 conditions in p05-m04-blocker-agc-v1; these do not replace the different bilateral device fixture in 04.4.

Pinned local CW conditions · nominal bias, active devices 25 °C, matched interfaces
StageGain / NF · dBInput P1dB / IIP3 · dBmCondition
RX-FE−1.5 / 1.5not modeled / not modeledLinear passive teaching network; no real power-handling claim.
RX-LNA+20 / 1−15 / −5CW compression; two equal CW tones near 2.450 GHz, 1 MHz spacing.
RX-MIX−6 / 6−5 / +10LO 2.350 GHz; adequate fixed drive assumed; effective wanted-band product convention.
RX-DRV+30, +10, −10 / 4−10 / +5100 MHz IF. Fixed NF and input intercepts across gain states are synthetic assumptions.

The screening law pins flat parameters over RF 2.430–2.470 GHz and IF 80–120 MHz. Outside that window the frequency map remains useful, but amplitude evidence stops. RF/IF band edges, input P1dB and the independent detector range are different limits.

Ptotal,in=10log10(i10Pi,in/10)Mstage=IP1dBPtotal,inOP1dB=IP1dB+Gsmall1dB\begin{aligned}P_{\mathrm{total,in}}&=10\log_{10}\left(\sum_i10^{P_{i,\mathrm{in}}/10}\right)\\M_{\mathrm{stage}}&=\mathrm{IP1dB}-P_{\mathrm{total,in}}\\\mathrm{OP1dB}&=\mathrm{IP1dB}+G_{\mathrm{small}}-1\,\mathrm{dB}\end{aligned}Pi in dBm; mW conversion is 10^(Pi/10). M is conditional margin to an INPUT compression point, not a peak or absolute-damage rating.

For the LNA, OP1dB = −15 + 20 − 1 = +4 dBm. Omitting the final −1 dB mistakes the uncompressed output extrapolation for the compressed output point. Negative input margin leaves the small-signal domain. Margin below 6 dB fails this lesson’s local reserve; a positive margin alone is not measured fidelity. Intercept estimates need the stricter 10 dB guard.

Common misconceptionP1dB at the output is enough without stage input levels.

Use the local input total and its waveform against IP1dB. A small final output can hide a compressed upstream stage. Absolute maximum voltage, current, temperature and input-power ratings are unknown here; P1dB is not a damage limit.

Once a predecessor compresses, retain the first invalid stage and label every downstream level as an uncompressed extrapolation. Do not carry a fabricated nonlinear gain correction into an apparently precise SNR.

04 / 10

Intermodulation products and intercept approximations

Can two harmless-looking frequencies create an unwanted signal right on the carrier?

Think about itFor f1 = 2451 MHz and f2 = 2452 MHz, where does 2f1−f2 land?
Answer

At 2450 MHz, exactly on the wanted channel. The other close-in permutation is 2f2−f1 = 2453 MHz. A channel filter that preserves wanted energy at 2450 MHz cannot separate an already coincident IM line by frequency alone.

An intercept is where extrapolated fundamental and intermodulation lines would meet. It is not a safe input power. Use the approximation only while contributing parents remain at least 10 dB below each pinned CW input P1dB, under compatible frequency, spacing, bias and match. Unknown IIP2 permits frequency enumeration but no numeric IM2 level.

P2fafb,out2Pa+Pb+G2IIP3Equal tones:PIM3,out3P+G2IIP3\begin{aligned}P_{2f_a-f_b,\mathrm{out}}&\approx2P_a+P_b+G-2\mathrm{IIP3}\\\text{Equal tones:}\quad P_{\mathrm{IM3,out}}&\approx3P+G-2\mathrm{IIP3}\end{aligned}Third-order cubic normalization at one stage. Pa and Pb are individual INPUT CW tone powers, G is small-signal gain, and IIP3 is input-referred, all in dB/dBm as labelled. Unequal-tone normalization retains the doubled parent.
Independent −55 dBm EACH R2 fixture · zero extra rejection, high gain
Stage outputPer-tone powerGenerated in-band IM3 propagated to A1Origin calculation
RX-FE → R1-LNA-in−56.5 dBmnot modeledPassive transfer only.
RX-LNA → R1-LNA-out−36.5 dBm−115.5 dBm3(−56.5)+20−2(−5)−6+30
RX-MIX → A1-IF−42.5 dBm−105.5 dBm3(−36.5)−6−2(10)+30
RX-DRV → A1-ADC-in−12.5 dBm−107.5 dBm3(−42.5)+30−2(5)

Increasing both parents by 1 dB raises each cubic product by 3 dB while the model remains valid. Increasing only the doubled parent gives 2 dB; increasing only the other parent gives 1 dB. Intercept estimates near compression display “inspect—intercept extrapolation unreliable.” ADC clipping invalidates the digital result but does not erase a valid analog contribution generated before the ADC.

Pbound=(iPi)2Bound for the three A1 contributions=99.012062399dBm\begin{aligned}P_{\mathrm{bound}} &= (\sum _{i} \sqrt{P_{\mathrm{i}}})^{2} \\ \text{Bound for the three A1 contributions} &= -99.012062399 \mathrm{dBm}\end{aligned}Common-plane powers in mW. Coincident products from different stages have unknown relative phase. This is a constructive bound, not a measured level or random-noise sum.
Go deeperCascade orientation, phase and the separate IM2 fixture

In a separate flat-gain, aligned-product cascade, constructive cubic coefficient addition gives 1/IIP3total = Σ(Gpreceding/IIP3i), with gains and intercept powers in linear units. The corresponding aligned second-order normalization is 1/√IIP2total = Σ√(Gpreceding/IIP2i). Gains include only preceding stages. Frequency-selective gains, mixing conversions and unknown phases prevent treating either shortcut as a general receiver truth. ADI’s selectivity derivation explicitly uses an in-phase worst case and different parent/product filtering.

A separate one-stage example supplies IIP2 = +30 dBm, G = +10 dB, and two −40 dBm tones: PIM2,out = Pa + Pb + G − IIP2 = −100 dBm. Raising both tones by 1 dB gives −98 dBm, a 2:1 slope. At 101 and 102 MHz, the sum is 203 MHz and difference 1 MHz; neither is the wanted 100 MHz IF. These values do not invent IIP2 for the gateway.

Common misconceptionIP3 predicts all modulated blocker behavior.

Memory, bias dynamics, cross-modulation, waveform peaks and frequency-dependent coefficients need their own evidence. The pairwise table omits three-distinct-tone cubic terms, wanted/blocker mixing, self harmonics and higher orders. No complete spur-free or modulation-quality claim follows.

IM is one mechanism. Next distinguish it from gain change and noise contamination so the proposed remedy addresses the cause.

05 / 10

Cross-modulation, compression, and NF degradation

What exactly changed when the receiver became less sensitive?

“Desense” describes a degraded receive threshold; it does not identify its cause. A strong signal can change the incremental gain experienced by a weak wanted signal. If the blocker’s envelope changes, the weak signal’s gain can vary with it: cross-modulation. That requires a waveform-dependent nonlinear model, not a single interpolated IP3 line.

Mechanism ledger · keep each failure and evidence request distinct
MechanismCausal pathDiscriminating next evidence
Direct leakageUnwanted spectrum enters the wanted passbandMeasure coupling and the actual channel response with the declared waveform.
Compression / cross-modulationStrong envelope changes gain at an upstream deviceWanted-plus-blocker AM/AM, modulation transfer and recovery at named bias and temperature.
IntermodulationTwo or more parents generate a new in-band lineChange parent levels/spacing; preserve origin and receiver/instrument residual checks.
Reciprocal noiseBlocker translates LO noise into wanted bandBlocker offset/power and LO SSB density over exact integration bounds.
Gain-state noise / converter noiseReduced gain changes input-referred later contributions or converter allocationState-specific gain/NF and actual in-band converter noise.
AGC blanking / clippingFinite response or rails remove samplesTime-aligned source, detector, gain command and valid-code capture; packet/preamble overlap.
Common misconceptionOut-of-band means irrelevant.

The label depends on the reference filter and plane. A blocker outside the digital channel may still reach the LNA, mixer and ADC. Filtering after those blocks cannot prevent the distortion or clipping they already created.

Small-signal NF at one bias is not a large-signal NF-degradation curve. Once compression invalidates the incremental linear model, the ledger suppresses current downstream noise claims. It retains the quiet NF as an explicitly separate reference, so you can still see what the design was trying to preserve.

Before changing gain, inspect the oscillator path: it can move blocker energy into the wanted band without the same two-tone mechanism.

06 / 10

LO phase noise causes reciprocal mixing

How can an offset blocker raise the wanted-band noise even before strong compression?

A real LO has phase-noise sidebands. Mixing a CW blocker with that LO translates a slice of those sidebands into the wanted channel. Keep the LO at 2.350 GHz, wanted RF at 2.450 GHz and IF at 100 MHz. In the anchor, the blocker is +1 MHz from wanted and −35 dBm at the mixer RF input, not at R2.

Nrm,mixerin=Pblocker×H(f)210L(Δff)10df\begin{aligned}N_{\mathrm{rm,mixer-in}} &= P_{\mathrm{blocker}} \times \\ &\int |H(f)|^{2} 10^{\frac{L(|\Delta f-f|)}{10}} d f\end{aligned}CW narrowband teaching proxy. Pblocker is linear power at mixer RF input. L is LO SSB density in dBc/Hz at positive offset |Δf−f|. H is normalized amplitude response. Integrate signed wanted f = −10…+10 kHz.
Think about itThe wanted integral runs from −10 to +10 kHz. Should a factor of two be added for SSB phase noise?
Answer

No. One blocker translates one relevant LO side into that full 20 kHz wanted interval. The signed integral already covers both edges of the wanted band. Doubling it again would add an unjustified 3.0103 dB. A second independent symmetric blocker supplies a second contribution; that is a different physical source.

Independent one-side reciprocal anchor · H = 1 in ±10 kHz; L = −120 dBc/Hz over 990–1010 kHz offset
Quantity / planeCalculationResult
Mixer RF input equivalent−35 −120 +10log10(20000)−111.989700043 dBm
R2 input equivalentMixer result −18.5 dB preceding wanted gain−130.489700043 dBm
R2 baseline noiseSame quiet receiver, same 20 kHz ENBW−128.165007875 dBm
Noise-limited degradation10log10(1 + 10^[(Nrm−Nbaseline)/10])2.001676806 dB

Common-plane power addition is essential. The −111.99 dBm mixer figure cannot be added directly to −128.17 dBm at R2. Two equal, independent reciprocal contributions add 3.010299957 dB to the reciprocal noise, not automatically 3.0103 dB to total receiver degradation.

Common misconceptionReciprocal mixing is additive thermal noise.

Its source is the blocker and oscillator phase-noise process, not a new resistor temperature. This lesson adds its proxy to thermal/receiver noise only under an explicit independence assumption at the same plane and bandwidth. The resulting SNR degradation is not PER or measured Wi-Fi desense.

Go deeperBounded masks, deterministic integration and spurs

The anchor is flat only from 990 to 1010 kHz. Shifting the blocker so any required LO offset leaves that mask makes the integral unknown. The optional synthetic mask has knots (10 kHz, −90), (100 kHz, −105), (1 MHz, −120), (10 MHz, −140), (30 MHz, −145), in dBc/Hz. It interpolates in log-frequency/dB and uses 1024 equal signed-frequency Simpson panels across ±10 kHz; both continuous integration limits must lie inside the mask. Discrete spurs are excluded and require separate lines. Wideband convolution and phase correlations are deferred.

Build on 04.7’s LO plane and mask discipline. Its different 2.550 GHz observation-receiver handoff and real device drive examples are not transplanted into this 2.350 GHz synthetic system fixture.

Reciprocal noise is born at the mixer. Filtering parents before that point and filtering already translated noise afterward are different interventions.

07 / 10

Place filtering, linearity, and gain together

Where can a filter stop the unwanted cause before it creates an in-band effect?

The zero-extra-rejection corner is a deliberately broad-front-end screen. It keeps 05.3 wanted gain/NF but does not claim to implement 05.2’s narrow IF selection. The interaction adds ideal filters at pre-LNA and post-mixer planes: each passes ±10 kHz with its declared wanted insertion loss and applies extra rejection outside it. These are transparent allocation models, not realizable sharp-edge component responses.

Filter-placement counterexample · −10 dBm, +20 MHz blocker; zero added wanted loss
Extra rejectionLNA inputConsequences
20 dB before LNA−31.5 dBm16.5 dB LNA margin; parent also reaches mixer 20 dB lower. ADC can still be limiting in high gain.
20 dB after mixer−11.5 dBmLNA remains above P1dB; a low downstream extrapolated level cannot qualify the chain.
20 dB after mixer, −55 dBm pairParents into driver drop 20 dB eachDriver-generated cubic product drops 60 dB; existing in-band LNA/mixer IM sees only wanted insertion loss.

For the −55 dBm pair, post-mixer rejection of 20 dB leaves the LNA/mixer A1 in-band terms at −115.5 and −105.5 dBm when wanted insertion loss is zero; it changes the driver-generated term from −107.5 to −167.5 dBm. The parent frequencies and the product frequency must follow different filter transfers.

Common misconceptionFilters can be placed after the overloaded stage with the same result.

They can remove the parent after the damage has happened. In-band products or cross-modulation may remain. Put the necessary rejection before the vulnerable stage, then check the noise cost and what the next stage now sees.

An extra 1 dB matched loss before the LNA at 290 K increases nominal receiver NF by 1 dB and reduces wanted gain by 1 dB. Loss after substantial gain usually costs less input-referred noise, but protects fewer upstream blocks. The noise calculation inserts each extra passive loss in its physical position; it does not subtract blocker rejection from wanted gain indiscriminately.

Go deeperLinearity, noise and stability are a joint allocation

Moving gain forward suppresses later noise but raises later blocker inputs. Changing bias may improve intercept at an energy cost and change NF. A real filter’s impedance can change amplifier gain, stability and noise match. This scalar matched model cannot approve that termination; request the S/noise parameters and stability review from Path 04. ADI’s selectivity example supports tracking off-channel parent attenuation separately from the coincident product, under its stated phase assumptions.

With the placement choices explicit, add time. Gain changes do not happen the instant a blocker appears.

08 / 10

AGC needs states, thresholds, hysteresis, and time

What reaches the converter while the AGC is still deciding to act?

The three driver states are +30/+10/−10 dB, giving total gains 42.5/22.5/2.5 dB. This diagnostic observer sits at A1-ADC-in and reports composite average dBFS relative to the full-scale sine. It sums tracked wanted/blocker powers over 80–120 MHz, omits noise/error and remains ideal through +30 dBm even if ADC codes clip. It never reconstructs unclipped power from clipped codes.

Down qualifies at detector ≥−12 dBFS continuously for 20 µs; up qualifies at ≤−36 dBFS for 1000 µs. Between thresholds, hold the state and reset both timers. A broken condition resets its timer. Each event moves one adjacent state, then ignores and resets timers during [transition, transition+5) µs. Qualification restarts when the new state settles. Bound states hold.

Think about itThe burst starts at 50 µs. Does automatic gain control protect its first sample or immediately reach low gain?
Answer

Neither. High→medium occurs at 70 µs, settles at 75; a new attack hold then reaches medium→low at 95 and settles at 100. Earlier clipped samples and blanked intervals stay lost or exposed. The gain switch cannot improve the mixer’s upstream 1.5 dB reserve.

Independent timed fixture · blocker −25 dBm at R2, +1 MHz, interval [50,150) µs
Boundary / intervalState / eventCausal interpretation
0…49 µsHigh, quietNo blocker source; detector below lower, already at high bound.
50…69 µsHigh, attack qualifyingUncompressed A1 blocker +17.5 dBm; rail screen fails before AGC reacts.
70 → 75 µsHigh→medium; blank [70,75)At 75, restart qualification from settled medium.
95 → 100 µsMedium→low; blank [95,100)No skipping a state; low output follows settling.
150 µsBlocker removed before detector evaluationStart low-state release hold; stop endpoint is exclusive.
1150 → 1155 µsLow→medium; blank [1150,1155)Next release starts at 1155; high would occur at 2155, outside the horizon.

At the burst plateau, LNA input is −26.5 dBm, mixer input −6.5 dBm and driver input −12.5 dBm. LNA margin 11.5 dB clears the screens; mixer/driver margins 1.5/2.5 dB fail the 6 dB reserve in every gain state. This conditional timing exercise is allowed while inputs remain below P1dB. If a predecessor leaves the linear domain, quantitative AGC timing becomes unavailable from that boundary.

Common misconceptionAGC prevents front-end overload.

This AGC changes IF driver output gain. It cannot reduce LNA/mixer input or undo prior clipping. Real receivers may distribute attenuation and detectors elsewhere, which changes the noise trade and timing contract.

Go deeperHysteresis, chatter and a real implementation evidence request

The 24 dB default threshold separation exceeds the 20 dB state step. This avoids the simple deterministic toggle in which a down-step immediately demands an up-step. Custom separation ≤20 dB warns about chatter; threshold ordering is still mandatory. Hysteresis does not remove detector noise or delay in real hardware.

ADRV9001-family UG-1828 Rev. A, Receiver Gain Control, distinguishes detector functions, gain modes and gain-block timing. Use those categories to request detector bandwidth/range, gain table, gain-dependent noise, settling and source/packet timing. Its implementation does not validate the three-state synthetic timers here.

At every time boundary the model applies source events, evaluates the settled detector, then tests holds and transitions. This ordering makes the event trace reproducible without a browser clock. Now compare those states with the converter’s instantaneous rail.

09 / 10

Protect converter full scale and digital headroom

Does an average level below full scale leave enough room for the largest peak?

The ADC boundary is a 2 Vpp differential sine across a teaching 100 Ω load. Sine RMS is Vpp/(2√2), so PFS = 6.989700043 dBm. The rail-equivalent instantaneous power is PFS+3.010299957 = 10 dBm. Average dBFS uses the first number; a peak-to-rail comparison uses the second.

PFS=10log10[Vpp28Rload×1mW]Ppeak=Paverage+CFMrail=PFS+3.010299957Ppeak\begin{aligned}P_{\mathrm{FS}} &= 10 \log_{10}[\frac{V_{\mathrm{pp}}^{2}}{8R_{\mathrm{load}} \times 1 \mathrm{mW}}] \\ P_{\mathrm{peak}} &= P_{\mathrm{average}} + \mathrm{CF} \\ M_{\mathrm{rail}} &= P_{\mathrm{FS}} + 3.010299957 - P_{\mathrm{peak}}\end{aligned}Differential voltage across 100 Ω. CF is a supplied composite peak/average power ratio; reserve R is additional distance below rail. Generic CF = 6 dB; two equal CW tones have exact worst-envelope CF = 6.020599913 dB.
Independent pair-only peak anchors · excludes the much weaker wanted signal; A1 high gain, two equal CW tones
R2 eachA1 each / total averageWorst peakRail reserve / decision
-55 dBm-12.500000000 / -9.489700043 dBm-3.469100130 dBm13.469100130 dB · clears 3 dB reserve
-45 dBm-2.500000000 / 0.510299957 dBm6.530899870 dBm3.469100130 dB · clears 3 dB reserve
-43 dBm-0.500000000 / 2.510299957 dBm8.530899870 dBm1.469100130 dB · reserve fails; no clipping

At −45 dBm each, reserve is 3.469100130 dB: it clears the 3 dB allocation by 0.469100130 dB. At −43 dBm each, reserve is 1.469100130 dB: the reserve fails, but the 10 dBm rail has not been crossed. These exact anchors concern the blocker pair alone. The live composite average also sums wanted power, so its final digits differ. Applying the exact-pair CF to any additional waveform is a declared proxy, not an exact envelope reconstruction.

Common misconceptionADC average level alone proves clipping margin.

Two tones sum to each+3.0103 dB in average power; their coherent peak needs the separate 6.0206 dB crest factor. An unknown coherent peak cannot be obtained by RSS. A supplied worst-envelope bound or a declared waveform/CCDF is needed.

For an exact two-tone envelope, crossing the deterministic worst-peak screen establishes possible rail crossing in the stated waveform, not a packet-error rate. For a modulated signal, clipping probability requires a CCDF with sample population, oversampling, filtering and observation time. The current model reports a peak-bound screen only; its clipping probability is unknown. A generic 6 dB crest factor cannot supply a probability.

Reducing driver gain by 20 dB reduces analog output signal and noise by 20 dB in this fixed-NF fixture. It leaves this receiver’s input-referred analog NF unchanged, but makes fixed converter input noise more significant. Reuse 05.3’s converter-noise allocation rather than claiming gain reduction always improves the full receiver.

Clipping prevention also does not prove alias clearance. At A0’s 80 MS/s teaching rate, the 100 MHz IF folds to 20 MHz. A 140 MHz IF tone also folds to 20 MHz; such an input is outside the current 80–120 MHz amplitude fixture and still geometrically dangerous. D3’s 80 ksample/s is a different boundary. Carry anti-alias response, clock noise and actual converter spectra into 05.6.

10 / 10

Build wanted-plus-blocker operating corners

Can you defend a gain/filter decision for every threat without hiding an invalid assumption?

  1. Load Quiet. Reproduce 05.3 gain, NF and sensitivity with all blockers explicitly absent.
  2. Load Strong. Find R1-LNA-in before looking at the converter. Compare 20 dB rejection pre-LNA versus post-mixer.
  3. Load Two-tone. Identify 2f1−f2 and its three origins; compare −55, −45 and −43 dBm each without confusing reserve and clipping.
  4. Load Reciprocal anchor. Verify mixer→R2 referral and the one-side integral; switch the LO mask to unknown.
  5. Load Timed. Use Next event through 50, 70, 75, 95, 100, 150, 1150 and 1155 µs. Name the earlier samples and upstream margins that AGC cannot repair.
  6. Record the stage, plane, time, invalidated claim, filter/linearity requirement and next waveform-specific test for each corner.
Interactive · Class 1 · p05-m04-blocker-agc-v1

Wanted/Blocker Headroom Map

Predict the first failure. Load a corner, compare filter placement and gain, then step through the burst. Apply commits a complete valid input; unsupported physics remains inspect.

Wanted and gain mode
-130…-20 dBm; step 0.5. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.

Driver edits change the high-state gain; medium/low remain exactly 20/40 dB below it. Automatic mode always starts high.

Blocker catalogue · three stable source slots
B1 · independent source
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
-130…0 dBm; step 0.5. Reset restores the quiet fixture.
-200…200 MHz; step 0.001. Reset restores the quiet fixture.
0…40 MHz; step 0.001. Reset restores the quiet fixture.
0…2000 µs; step 1. Reset restores the quiet fixture.
0…2000 µs; step 1. Reset restores the quiet fixture.

Offset is relative to 2450 MHz at RF entries or 100 MHz at A1-IF. On-time level and [start, stop) define duty within the 2000 µs horizon. Entry is before any named extra filter at that stage. Frequencies outside ±20 MHz retain geometry only.

B2 · independent source
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
-130…0 dBm; step 0.5. Reset restores the quiet fixture.
-200…200 MHz; step 0.001. Reset restores the quiet fixture.
0…40 MHz; step 0.001. Reset restores the quiet fixture.
0…2000 µs; step 1. Reset restores the quiet fixture.
0…2000 µs; step 1. Reset restores the quiet fixture.

Offset is relative to 2450 MHz at RF entries or 100 MHz at A1-IF. On-time level and [start, stop) define duty within the 2000 µs horizon. Entry is before any named extra filter at that stage. Frequencies outside ±20 MHz retain geometry only.

B3 · independent source
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
-130…0 dBm; step 0.5. Reset restores the quiet fixture.
-200…200 MHz; step 0.001. Reset restores the quiet fixture.
0…40 MHz; step 0.001. Reset restores the quiet fixture.
0…2000 µs; step 1. Reset restores the quiet fixture.
0…2000 µs; step 1. Reset restores the quiet fixture.

Offset is relative to 2450 MHz at RF entries or 100 MHz at A1-IF. On-time level and [start, stop) define duty within the 2000 µs horizon. Entry is before any named extra filter at that stage. Frequencies outside ±20 MHz retain geometry only.

Stage allocations and conditional metadata

Fixed stage order preserves RF → mixer → IF. Editing a stage clears its fixture metadata; supply your custom conditions before applying. This records a conditional assumption, not verified data. Default RX-FE has no compression/IP3 model.

RX-FE · R2R1-LNA-in
-30…60 dB; step 0.1. Reset restores the quiet fixture.
0…30 dB; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
Reset restores the quiet fixture. Changes need Apply corner.
RX-LNA · R1-LNA-inR1-LNA-out
-30…60 dB; step 0.1. Reset restores the quiet fixture.
0…30 dB; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
-40…30 dBm; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
-30…50 dBm; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
RX-MIX · R1-LNA-outA1-IF
-30…60 dB; step 0.1. Reset restores the quiet fixture.
0…30 dB; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
-40…30 dBm; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
-30…50 dBm; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
RX-DRV · A1-IFA1-ADC-in
-30…60 dB; step 0.1. Reset restores the quiet fixture.
0…30 dB; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
-40…30 dBm; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
-30…50 dBm; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.
Filter placement and LO phase noise
0…80 dB; step 1. Reset restores the quiet fixture.
0…80 dB; step 1. Reset restores the quiet fixture.
0…6 dB; step 0.1. Reset restores the quiet fixture.
0…6 dB; step 0.1. Reset restores the quiet fixture.
Reset restores the quiet fixture. Changes need Apply corner.

Both extra filters pass wanted ±10 kHz with their stated insertion loss and apply extra rejection outside it. Synthetic mask knots (Hz, dBc/Hz): (10⁴, −90), (10⁵, −105), (10⁶, −120), (10⁷, −140), (3×10⁷, −145). Interpolate in log-frequency/dB; integrate signed ±10 kHz with 1024-panel Simpson quadrature. No outside-mask extrapolation or discrete spurs. This ideal filter is not the 05.2 acquisition design.

ADC peaks and AGC timing
0.5…4 Vpp; step 0.01. Reset restores the quiet fixture.
3.010299956639812…15 dB; step 0.1. Reset restores the quiet fixture.
0…12 dB; step 0.1. Reset restores the quiet fixture.
-60…0 dBFS average; step 0.1. Reset restores the quiet fixture.
-60…0 dBFS average; step 0.1. Reset restores the quiet fixture.
1…200 µs; step 1. Reset restores the quiet fixture.
50…1500 µs; step 1. Reset restores the quiet fixture.
0…20 µs; step 1. Reset restores the quiet fixture.

100 Ω differential teaching load. CF is a declared composite screen; exact two-tone CF is 6.020599913 dB only for two equal CW tones. Unknown coherent phases are not an RSS peak. Observer covers 80–120 MHz, composite average relative to full-scale sine, ideal linear response through +30 dBm, no detector noise/error. It is separate from ADC codes.

View only: source/gain settings are unchanged. Results stay at the last selected valid time until Show time.

Quiet receiver · committed corner

Illustrative CW screen; nominal bias, 25 °C active devices, matched 50 Ω RF / 100 Ω differential A1. RX-FE and extra losses at 290 K. Flat RF 2430–2470 MHz / IF 80–120 MHz; LO 2350 MHz, adequate fixed drive assumed. IIP3 normalization: CW pair, 1 MHz spacing. Not measured or normative. Custom stage conditions are listed with the stage outputs below.

t = 0 µs · high · settled-state screen. W is the −105 dBm default wanted signal (current R2 input -105.0 dBm); B1–B3 are distinct-frequency blocker sources. A1 levels are before digital channel selection.

Blocker-free reference NF / gain · current state
2.799879 / 42.500000 dB
Blocker-free R2 sensitivity · 20 kHz, SNR 8 dB + implementation 2 dB
-118.165008 dBm
Current analog noise estimate · R2 / A1, same ENBW
-128.165008 / -85.665008 dBm
A1 composite average / sine-referenced average dBFS
-62.500000 dBm / -69.489700 dBFS
A1 composite peak / rail-equivalent instantaneous power
-56.500000 / 10.000000 dBm
Rail reserve · required 3.0 dB
66.500000 dB · reserve clears

Sensitivity above is a separate blocker-free reference, before optional converter loss. Fixed RX-DRV NF = 4.0 dB is a synthetic assumption in all states. A reduced final-stage gain changes output noise, but its own input-referred NF term stays the same. Actual converter noise, modulation quality and PER remain unmodeled.

Stage input headroom map

Stage input power versus input P1dBVertical axis dBm at each stage input. Circles show composite average, squares wanted average, dashed horizontal marks input P1dB. Crosses mean unsupported amplitudes: uncompressed extrapolations, not predicted output. Complete values and conditions follow in the tables.Input plane · dBm · illustrative CW screen10-25-60-95-130RX-FERX-LNARX-MIXRX-DRV● total □ wanted ┄ input P1dB × extrapolation
Average powers sum in mW. P1dB comparisons use stage inputs. A marker above P1dB ends the linear model; a 6 dB reserve failure asks for evidence sooner.
Input / output composite average powers · dBm; conditional margins in dB
Stage / planesGainTotal input → outputInput P1dB marginEvidence / first failure
RX-FE
R2R1-LNA-in
-1.5 dB-105.000000 → -106.500000unknownLinear passive teaching network; power rating not modeled
RX-LNA
R1-LNA-inR1-LNA-out
20.0 dB-106.500000 → -86.50000091.500000Conditional CW screen; ≥10 dB below input P1dB
RX-MIX
R1-LNA-outA1-IF
-6.0 dB-86.500000 → -92.50000081.500000Conditional CW screen; ≥10 dB below input P1dB
RX-DRV
A1-IFA1-ADC-in
30.0 dB-92.500000 → -62.50000082.500000Conditional CW screen; ≥10 dB below input P1dB
Individual wanted/blocker powers and stage conditions
Every tracked source at its own plane · on-time average dBm
Stage / conditionSource / input frequencyInput → output powerEvidence
RX-FE
Illustrative CW screen; nominal bias, 25 °C active devices, matched 50 Ω RF / 100 Ω differential A1. RX-FE and extra losses at 290 K. Flat RF 2430–2470 MHz / IF 80–120 MHz; LO 2350 MHz, adequate fixed drive assumed. IIP3 normalization: CW pair, 1 MHz spacing. Not measured or normative.
W · 2450.000 MHz-105.000000 → -106.500000 dBmConditional CW amplitude
RX-LNA
Illustrative CW screen; nominal bias, 25 °C active devices, matched 50 Ω RF / 100 Ω differential A1. RX-FE and extra losses at 290 K. Flat RF 2430–2470 MHz / IF 80–120 MHz; LO 2350 MHz, adequate fixed drive assumed. IIP3 normalization: CW pair, 1 MHz spacing. Not measured or normative.
W · 2450.000 MHz-106.500000 → -86.500000 dBmConditional CW amplitude
RX-MIX
Illustrative CW screen; nominal bias, 25 °C active devices, matched 50 Ω RF / 100 Ω differential A1. RX-FE and extra losses at 290 K. Flat RF 2430–2470 MHz / IF 80–120 MHz; LO 2350 MHz, adequate fixed drive assumed. IIP3 normalization: CW pair, 1 MHz spacing. Not measured or normative.
W · 2450.000 MHz-86.500000 → -92.500000 dBmConditional CW amplitude
RX-DRV
Illustrative CW screen; nominal bias, 25 °C active devices, matched 50 Ω RF / 100 Ω differential A1. RX-FE and extra losses at 290 K. Flat RF 2430–2470 MHz / IF 80–120 MHz; LO 2350 MHz, adequate fixed drive assumed. IIP3 normalization: CW pair, 1 MHz spacing. Not measured or normative.
W · 100.000 MHz-92.500000 → -62.500000 dBmConditional CW amplitude

IM origins at the wanted channel

No enumerated pairwise product overlaps the wanted ±10 kHz region at this time.

Constructive bound for supported coincident wanted-band contributions: unknown dBm at A1. This bound applies only to the listed supported contributions, not omitted or suppressed products. No random-phase power sum, IM-as-thermal-noise substitution, or interference acceptance threshold is assumed.

All pairwise IM2 / IM3 frequency geometry (0 rows)
Pairwise enumeration · IM2 amplitudes unknown without IIP2
OriginParents / productOrigin → A1 frequencyLocal / A1 contributionValidity

Enumerates fa+fb, |fa−fb|, 2fa±fb and 2fb±fa for each pair of active blockers. Omits self harmonics, wanted/blocker mixing, three-distinct-tone cubic products and higher orders. No complete spur-free claim.

Reciprocal mixing

All blockers off here: no reciprocal contribution. This explicit zero branch does not require an LO mask.

Independent noise-proxy degradation at R2: 0.000000 dB. Known noise sum: unknown dBm. Direct leakage, coherent IM, compression, blanking and ADC clipping stay separate.

Gain state and event trace

Blocker-free state references · same 20 kHz, Ts = 290 K, 8 dB SNR + 2 dB implementation
StateTotal gain / NFR2 sensitivityA1 physical noise
high42.500000 / 2.799879 dB-118.165008 dBm-85.665008 dBm
medium22.500000 / 2.799879 dB-118.165008 dBm-105.665008 dBm
low2.500000 / 2.799879 dB-118.165008 dBm-125.665008 dBm
Manually inspected AGC state versus timeTime zero to 2000 microseconds. High, medium and low are separate labelled rows. Dotted vertical line is the selected time. Shaded bands show blocker on intervals and switch blanking. Event table gives exact boundaries.highmediumlow0500100015002000Time [µs] · A1 average observer
Source bands show [start, stop); narrow red bands mark switch blanking. No animation or browser clock. State transitions move one adjacent step.
AGC transitions · exact integer-microsecond boundaries
TransitionTime → settledQualifying detectorCause

No supported automatic transition in this horizon. Manual selection holds its chosen state.

First-failure trace and remaining evidence

Quiet corner clears the supplied scalar screens. Power handling, waveform fidelity, converter noise and real hardware evidence remain outside this model.

Physical failures are listed in signal-flow order; timing events are chronological. Screen clearance never qualifies a real receiver. With an invalid predecessor, every downstream numerical level shown above is an explicitly uncompressed extrapolation.

Printable synthesis · operating-corner review

Three states, four threats, one causal record

All states retain nominal NF 2.799879362 dB and blocker-free R2 sensitivity −118.165007875 dBm under 290 K, 20 kHz detector ENBW, required SNR 8 dB and implementation loss 2 dB. Gain is 42.5/22.5/2.5 dB; quiet A1 wanted is −62.5/−82.5/−102.5 dBm. Fixed driver NF is a synthetic condition, not a hardware promise. The 13.5 kHz wanted support remains distinct from 20 kHz ENBW.

Reviewed four-corner × three-state operating table · first failure and downstream claim
Threat / timeHigh · 42.5 dBMedium · 22.5 dBLow · 2.5 dBRequired action / next waveform test
Quiet · any tNo supplied scalar failureAnalog NF unchanged; converter-noise allocation inspectAnalog NF unchanged; converter-noise allocation inspectR2→R3 quiet waveform sensitivity by gain state; A1 noise spectrum and actual ADC input model.
Strong · t=0…1999RX-LNA at R1-LNA-in: −3.5 dB marginSame first invalid LNA inputSame first invalid LNA inputRequire ≥9.5 dB added pre-LNA blocker attenuation for 6 dB reserve (wanted contribution also counted), or a conditioned input-P1dB allocation ≥−5.5 dBm. Recheck all later stages and wanted-plus-blocker recovery; post-mixer AGC cannot qualify the chain.
Pair −55 each · on intervalIM inspect: A1 origins −115.5/−105.5/−107.5 dBm; pair rail reserve 13.4691 dBSame upstream IM; A1 terms each 20 dB lowerSame upstream IM; A1 terms each 40 dB lowerNo interference limit supplied. Specify R3 wanted quality, parent filter transfer and IIP3 conditions. Test both tone slopes/spacing, then actual modulated coexistence. Digital fidelity is not established by intercept arithmetic.
Timed burst · [50,150) µsMixer first reserve failure at R1-LNA-out: 1.5 dB; A1 blocker +17.5 dBm, conditional rail screen failsSame mixer reserve; A1 blocker −2.5 dBm, generic peak +3.5 dBm clears rail reserveSame mixer reserve; A1 blocker −22.5 dBm; converter-noise trade inspectRequire ≥4.5 dB parent attenuation before mixer for 6 dB margin (total includes wanted). Verify actual mixer response and detector range, capture preamble/blanking overlap and waveform recovery. Gain changes cannot fix the upstream reserve.

Thresholds −12/−36 dBFS, 20/1000 µs holds and 5 µs blanking yield high→medium at 70, medium→low at 95 and low→medium at 1150 µs. Settled times are 75, 100 and 1155 µs. Packet or preamble exposure is an evidence request, never an invented packet-error result. If the amplitude model becomes invalid, defer the dependent timing result.

The synthesis may conclude inspect or defer. A useful record explains precisely what would falsify the current design: a measured coupling level, a waveform-dependent compression result, an LO mask outside assumed support, or a gain-settling capture. Give each request an owner using 05.1’s requirement grammar.

Next, turn the link around: the node’s transmitter must meet range and waveform goals without becoming another receiver’s blocker.

Ungraded review

Check your understanding

Answer each question in your own words, then reveal the model answer.

  1. 01Identify the first failure for the −10 dBm, +20 MHz corner and propose a useful filter change.
    Model answer

    At t=0, RX-FE gives −11.5 dBm at R1-LNA-in. Against −15 dBm input P1dB, margin is −3.5 dB and linear downstream fidelity/noise/timing claims are invalid. At least 9.5 dB pre-LNA rejection is needed for the local 6 dB reserve before accounting for wanted power; post-mixer rejection cannot repair this stage. Recheck every later input and test the actual wanted-plus-blocker waveform, bias, temperature, terminations and recovery.

  2. 02At −55 dBm each, which frequencies and IM origins require review?
    Model answer

    2451 and 2452 MHz give 2f1−f2=2450 MHz, exactly wanted. Per-tone stage outputs are −56.5/−36.5/−42.5/−12.5 dBm. In-band A1 contributions from LNA/mixer/driver are −115.5/−105.5/−107.5 dBm. Relative phases are unknown; the constructive bound is −99.012062399 dBm. A 1 dB joint parent rise gives 3 dB product rise only in the compatible guarded region. Ask for waveform-specific interference tolerance and test slopes and coupling.

  3. 03Explain the reciprocal anchor without an unexplained sideband factor.
    Model answer

    At mixer RF input, −35−120+10log10(20000)=−111.989700043 dBm. Subtract 18.5 dB preceding wanted gain for −130.489700043 dBm at R2. With the same 20 kHz baseline −128.165007875 dBm and declared independence, degradation is 2.001676806 dB. One CW blocker translates one relevant LO side; no extra factor 2. Measure the LO over all 990–1010 kHz offsets and keep spurs separate.

  4. 04Why does the −43 dBm-per-tone ADC corner fail reserve without clipping?
    Model answer

    The pair alone reaches +2.510299957 dBm average and +8.530899870 dBm worst peak at A1. Against the 10 dBm rail, reserve is 1.469100130 dB: less than the required 3 dB, still above zero. Valid upstream analog IM estimates remain available. Specify an actual waveform peak/CCDF and converter test before claiming digital fidelity or a clipping probability.

  5. 05Step the timed burst and name what automatic gain cannot recover.
    Model answer

    Source starts at 50; attack gives high→medium 70, settled 75; restarted attack gives medium→low 95, settled 100. Removal at 150 begins release; low→medium 1150, settled 1155. High is beyond the 2000 µs horizon. Mixer input remains −6.5 dBm while on, only 1.5 dB below IP1dB, failing the local reserve. Earlier clipped samples and [70,75), [95,100), [1150,1155) blanking cannot be undone. Capture waveform/preamble timing with detector and gain commands.

  6. 06Why is gain reduction not a complete receiver improvement?
    Model answer

    Moving only the final driver gain preserves this synthetic input-referred analog NF but lowers A1 signal and noise. Fixed converter noise then matters more; upstream blocker margins do not change. A real distributed gain table can also change device NF/intercepts. Require gain-state noise, linearity, settling and converter evidence at their named planes.

Sources and further study

Access checked 7 September 2026. All numerical gateway parameters, masks and event times are local illustrative/derived fixtures, not device specifications or conformance requirements. Model/fixture p05-m04-blocker-agc-v1; inherited noise p05-m03-receiver-ledger-v1; rules p05-m04-screen-rules-v1; serialization p05-m04-corner-json-v1; display p05-m04-display-v1. Full precision is retained; six decimal places for live dB results, three for MHz, integer µs; independent anchors show nine decimals. Numeric dB tolerance 10⁻⁶; event boundaries exact.

  1. Analog Devices, Use Selectivity to Improve Receiver Intercept Point, modified cascading derivation, equations 2–11 and Figures 2–3. Its in-phase worst-case contribution addition informs the disclosed constructive bound and parent/product filter distinction. No measured receiver curve imported.
  2. Haijiao Fan, How a High Dynamic Range RF Transceiver Solves the Blocking Challenge for Mission Critical Communications, 25 April 2022, “Receiver Blocking Tolerance” and “LO Phase Noise.” Used to organize linearity, dynamic-range, image and LO-noise evidence. Its named-standard levels and device performance examples are not adopted.
  3. Analog Devices UG-1828, ADRV9001 System Development User Guide, Rev. A, listed 12 August 2024 on the current ADRV9002 product page. “Receiver Gain Control,” “Gain Control Detectors” and “AGC Clock and Gain Block Timing” identify implementation evidence categories. Indexed first-party sections and revision listing were available; direct PDF rendering was unavailable during research. No device timer or gain coefficient is attributed to this fixture.
  4. W. F. Egan, Practical RF System Design, Wiley–IEEE, 2003: Chapters 4–6 on nonlinearity and linearity architectures, 7 on conversion, and 9 on phase noise. Publisher contents consulted; full chapter text unavailable. Derivations and independent Decimal fixtures supply the displayed numerical evidence.
  5. G. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design, 2nd ed., Prentice Hall, 1997 (CIR-1). Curriculum reading for conditional amplifier gain/noise/stability. Full text was not available for this implementation; no page-specific assertion or device parameter is attributed to it. Continue through the implemented LNA lesson.
  6. 04.6 Mixers & Frequency Conversion and 04.7 Oscillators & Phase-Locked Loops: inherited frequency-plane and SSB-mask discipline; ADI PLL Fundamentals is the curriculum’s first-party orientation. RF Fundamentals Noise supplies the existing matched Friis implementation, cross-checked against the RF Cascade Tool.