RF Journey

01 / 10

Failure: a clean block diagram hides a collision

The wanted carrier reaches the chosen IF. What else reaches it?

The fictional gateway from 05.1 tunes across 2.400–2.500 GHz. In normal mode it selects a QPSK channel at 2.450 GHz: 10 ksymbol/s, 20 kbit/s with uncoded/no-overhead mapping, and ideal raised-cosine support of 13.5 kHz, or ±6.75 kHz. Tuning coverage is not simultaneous instantaneous bandwidth. This is an Illustrative engineering case, not a named radio standard or a hardware selection.

Think about itLO 2350 MHz puts RF 2450 MHz at IF 100 MHz. Which second RF frequency has the same destination?

Answer

RF 2250 MHz. Its signed difference is −100 MHz while wanted is +100 MHz. A real mixer produces conjugate pairs, so both contribute at positive 100 MHz. A filter placed after this superposition cannot identify their origins. Suppression must act before the mixer, or the architecture must separate the complex branches.

Derived opening failure · independent arithmetic at the real mixer
Origin / entry	Signed RF−LO	Positive real IF / decision
WANTED · R2 · 2450 MHz; [2449.99325, 2450.00675] MHz	2450−2350 = +100 MHz	[99.99325,100.00675] MHz; slope +1
B-IMAGE · R2 · 2250 MHz; CW; −35 dBm metadata	2250−2350 = −100 MHz	100 MHz, strictly inside wanted. RF preselection required.
Unprotected post-mixer proposal	One physical IF with two origins	Reject under the local no-overlap screen. Actual degradation still needs level, gain and wanted-quality evidence.

The model stores blocker powers as metadata at their entry planes. It does not borrow a conversion-loss proxy from the preceding mixer lesson to manufacture system-level spur amplitudes. The narrow selected channel here also differs deliberately from 04.6’s 100 MHz observation-span example; carry the definitions forward, not the old bandwidth.

Common misconceptionA no-collision frequency plan proves adequate spur margin.

It proves only the bounded geometry screen. Missing sources, nonlinear amplitudes, noise skirts, compression, converter limits and calibration can still change the receiver decision.

To make the hidden collision visible, replace each symbolic block with an explicit frequency transformation and selection boundary.

02 / 10

Architecture is a chain of spectral transformations

What must remain attached to a signal as it moves from antenna feed to complex samples?

Record its entire support, representation and orientation at a named plane. A center-frequency arrow alone conceals image superposition and boundary crossing. Our directed graph has a fixed sequence; it is not a general circuit editor. Analog sum branches remain visible until a declared filter region conditionally excludes them.

Graph contract · local nodes mapped to portfolio reference planes
Edge / plane	Transformation and representation	Selection / evidence obligation
R2 → R1	Real absolute RF; R2 available blocker power at nominal matched 50 Ω	RF-PRE output; pass 2400–2500 MHz, transition 2300–2400 / 2500–2600 MHz; stop beyond. Attenuation and front-end gain unknown.
R1 → M1	Local mixer output; signed precursor then positive real IF, or complex signed f−LO	Retain difference/sum/conjugate provenance. Conversion amplitudes and LO drive unknown.
M1 → F1 → M2 (HIF only)	Local first IF filter, then second real mixer LO 350 MHz	450 MHz first IF selection prevents second-stage image superposition; no inferred stage gain.
M1/M2 → A1F → A1	A1F local analog IF/baseband filter output; A1 ADC input	A1 coupled clock enters after the filters. A1 impedance, voltage scaling, driver, noise and amplitude unknown.
A1 → A0	Uniform ideal sampling; one real ADC or two real I/Q ADC branches	Record input Nyquist zone and each signed wrap/fold segment. Analog bandwidth and clock performance unverified.
A0 → D3	Select alias, translate to complex zero, correct orientation, filter and decimate	Ideal selected-channel boundary, 80 kcomplex-sample/s; no voltage/full-scale assumption. Acquisition correction must precede narrowing.

\begin{aligned}u &= I + j Q \\ s_{\mathrm{RF}} &= \operatorname{Re}{u \exp (+j 2\pi f_c t)} \\ f' &= f - f_{\mathrm{LO}}\end{aligned}

Definition · f and fLO in Hz; signed complex translation has derivative +1 with respect to input frequency. Absolute value is a subsequent real-branch representation.

A geometric filter has three disjoint region types: the closed pass interval, transitions excluding the pass edges, and stops strictly beyond the outer transition edges. “Requires stopband attenuation” is an evidence request. The conditional comparison may assume complete rejection of a wholly stopped source, but retains the source, location and missing attenuation. A source partly in transition stays unresolved.

Go deeperWhy a complex image can be separated

A real cosine contains positive and negative spectral components tied by conjugation. Complex I/Q retains independent signed offsets: +Δ and −Δ need not carry the same information. Ideal quadrature conversion can therefore select one side. Gain/phase mismatch introduces a conjugate term, often written v = a u + b u*, where b is the leakage coefficient. Geometry identifies the mirror location; no image-rejection ratio follows until a and b are characterized.

This boundary record lets us compare architectures by the work performed at each plane.

03 / 10

Direct conversion: integration with DC and I/Q costs

If the wanted channel lands at zero, where do DC errors land?

Zero IF translates the selected carrier directly to a complex envelope. Here LO 2450 MHz places wanted support at ±6.75 kHz. Two real ADC branches run at 1.280 MS/s each, represented together as 1.280 Mcomplex-sample/s. The downstream 80 ksample/s D3 rate is a separate ideal processing boundary.

ZIF impairment allocation · locations derived; all amplitudes unknown
Mechanism / origin	Spectral consequence	Required boundary / evidence
LO leakage and self-mixing	LO energy coupling back to an RF input may mix with itself to DC	Characterize coupling paths, LO isolation and DC change across tuning, gain and temperature.
DC and flicker noise	Near-zero impairment overlaps the center of the wanted complex channel	Baseband offset/noise and detector tolerance; a high-pass remedy may remove wanted low-frequency information.
Even-order effects	A strong blocker can produce low-frequency difference/envelope content	IIP2/modulated-blocker evidence, front-end balance and calibration operating range.
Quadrature gain/phase error	Conjugate leakage reflects complex offset +Δ to −Δ	IQ image rejection versus offset, tuning, gain and temperature; residual after calibration.
Calibration and settling	Correction changes with operating conditions and may interrupt acquisition	Startup time, tracking range, drift, DC steps and usable-data timing.

TI SBAA328 §2.1 identifies DC, IQ mismatch and second-order effects as zero-IF concerns. The local allocation above asks which measurements would constrain this gateway; no typical vendor figure is substituted for those missing results.

Committed geometry · ZIF channelgeometry clears

Wanted A0: signed 0 MHz → selected 0 MHz; local slope 1. Required LO range [2400, 2500] MHz.

Frequency-error expansion ±0 Hz. Programmed LO error 0 Hz. H=4; 0 signed RF/LO coefficient lineages evaluated. Higher orders, cross-source products and unlisted emissions omitted.

Conditional comparison assumes declared stop regions reject whole source supports; attenuation remains unverified. Geometry clears never establishes spur margin or receiver performance.

ZIF channel wanted graph; sum branches and filter requirements included · Derived / Illustrative · MHz, not level spectra
Source / edge	Support / center / orientation	Representation / zone / selection	Level evidence / lineage
WANTED · R2 → R2	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. no filter yet.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1)
WANTED · R2 → R1	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes
WANTED · R1 → M1	[-0.00675, 0.00675] MHz Center 0 MHz Slope +1 Signed precursor: [-0.00675, 0.00675] MHz	complex; signed offset from LO. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1)
WANTED · M1 → A1F	[-0.00675, 0.00675] MHz Center 0 MHz Slope +1 Signed precursor: [-0.00675, 0.00675] MHz	complex; signed offset from LO. continuous. BB: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1) → BB passes
WANTED · A1F → A1	[-0.00675, 0.00675] MHz Center 0 MHz Slope +1 Signed precursor: [-0.00675, 0.00675] MHz	complex; signed offset from LO. continuous. BB: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1) → BB passes
WANTED · A1 → A0	[-0.00675, 0] MHz Center -0.003375 MHz Slope +1 Signed precursor: [-0.00675, 0] MHz	complex; signed complex sample frequency. zone 1. BB: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1) → BB passes → signed wrap at 1.28 MS/s
WANTED · A1 → A0	[0, 0.00675] MHz Center 0.003375 MHz Slope +1 Signed precursor: [0, 0.00675] MHz	complex; signed complex sample frequency. zone 1. BB: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1) → BB passes → signed wrap at 1.28 MS/s
WANTED · A0 → D3	[-0.00675, 0] MHz Center -0.003375 MHz Slope +1 Signed precursor: [-0.00675, 0] MHz	complex; signed offset from selected digital channel. ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required. Ideal downstream channel selection: retained; overlapping origins cannot be removed.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1) → BB passes → signed wrap at 1.28 MS/s → select 0 MHz; digital translate
WANTED · A0 → D3	[0, 0.00675] MHz Center 0.003375 MHz Slope +1 Signed precursor: [0, 0.00675] MHz	complex; signed offset from selected digital channel. ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required. Ideal downstream channel selection: retained; overlapping origins cannot be removed.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → complex f−2450 MHz (slope +1) → BB passes → signed wrap at 1.28 MS/s → select 0 MHz; digital translate

Common misconceptionZero IF has no image problem.

Ideal quadrature selection removes the ordinary real-mixer ambiguity, but real IQ imbalance leaks the conjugate image. In addition, DC/flicker problems sit inside the wanted band. “Ideal complex” is a model assumption, not a calibration guarantee.

Moving the channel away from DC changes those allocations. It also creates a new image-selection problem.

04 / 10

Low IF: move DC, inherit image rejection

How much separation from DC is useful, and what does it cost in image rejection?

“Low IF” is a relative architecture label. The curriculum’s IF100 example is 100 MHz absolute IF, small relative to 2.45 GHz but enormous relative to a 13.5 kHz channel. It uses a real mixer and real ADC. A different near-baseband low-IF receiver might use analog I/Q and a complex filter that distinguishes positive and negative offsets; that is a different physical boundary, not a free change of sample-rate label.

IF100 low-side · selection before sampling
Source / support at M1	IF100 region at A1F	Consequence
Wanted 99.99325–100.00675 MHz	Pass 99.980–100.020 MHz	13.25 kHz to each pass edge in nominal mode. This is not an ENBW specification.
B-IMAGE 2250 →100 MHz	Same pass interval as wanted	IF filter cannot separate it. RF-PRE must suppress 2250 MHz before M1.
B-ALIAS 2430 →80 MHz; B-HALF 2400 →50 MHz (fundamentals)	Both in required stop regions	Conditional exclusion requires actual analog IF attenuation; harmonic products are checked separately.
CLK-IF 100 MHz at A1, after A1F	Filter was already traversed	A1F cannot suppress an injected source downstream of itself.

\begin{aligned}&100 \mathrm{MHz} \pm 6.75 \mathrm{kHz} \subset 100 \mathrm{MHz} \pm 20 \mathrm{kHz} \\ 20 - 6.75 &= 13.25 \mathrm{kHz} \text{pass-edge margin}\end{aligned}

Derived / IF100, nominal mode. Closed signal support; pass edges are a geometric allocation, with no realized attenuation/order guarantee.

Residual DC still consumes converter headroom and may affect later processing even if it is outside the selected IF. A complex filter can reject an opposite signed image only while that information remains separate. Once a real mixing or sampling boundary makes supports overlap, later I/Q processing cannot recover the lost origin.

Go deeperPass width, transition width and noise bandwidth differ

The pinned IF pass interval is 40 kHz wide, transitions extend 80 kHz on each side, and the wanted ideal RC support is 13.5 kHz. None determines the integral of |H(f)|² that defines noise-equivalent bandwidth. In 05.3, a stated 20 kHz ENBW would be a separate noise-budget assumption, not this ±20 kHz pass half-width.

A larger first IF increases the RF image spacing. The next comparison exposes the extra stage it needs.

05 / 10

High IF and superheterodyne: separation for more stages

Does moving the image farther away eliminate the image problem, or move it to another filter?

With LO 2000 MHz, wanted 2450 MHz becomes positive 450 MHz. Its first RF image is 1550 MHz: both are 450 MHz from the LO. The 900 MHz RF spacing may ease the first preselection requirement compared with the 200 MHz spacing of IF100. This does not establish a realizable filter or a better receiver without attenuation, loss and blocker evidence.

HIF two-stage lineage · all frequencies MHz, Derived / Illustrative
Boundary	Wanted and image	Required selection before superposition
R1 → M1; LO 1=2000	2450→+450; 1550→−450→positive 450. Sum wanted 4450.	Reject 1550 MHz at RF; first-IF filter rejects unwanted sum/other products.
M1 → F1	Wanted 449.99325–450.00675	Pass 449.980–450.020; transitions 449.900–449.980 and 450.020–450.100; stop beyond.
F1 → M2; LO 2=350	450→+100; 250→−100→positive 100	First-IF filter must suppress 250 MHz before the second mixer. Once at 100 MHz, IF100 cannot separate it.
M2 → A1F → A1 → A0	Wanted 100→signed +20 / positive 20 at 80 MS/s	Pinned IF100 selection then analog input/clock evidence at A1. Two LOs bring additional coupling and spur requests.

Think about itAt the second mixer, which first-IF frequency imitates 450 MHz when LO 2 = 350 MHz?

Answer

250 MHz: |250−350|=100 MHz. This is a first-IF image, so the 450 MHz filter must act before M2. A clean first-stage RF image plan does not settle the second-stage image.

Common misconceptionAn architecture with fewer blocks is automatically lower power and lower risk.

Power depends on the actual converters, filters, buffers, clock generation and digital workload at the required performance. Extra stages add evidence burden; removing them can demand much more from the ADC or calibration. Compare operating modes and measured allocations, not block count.

RF sampling removes analog frequency translation entirely. Sampling itself then becomes the first many-to-one mapping to audit.

06 / 10

RF sampling: alias zones do not remove the analog front end

How can an 80 MS/s converter return 30 MHz for two different RF sources?

Think about itDo 2450 MHz and 2430 MHz remain separable after one real 80 MS/s ADC?

Answer

No. 2450−31×80=−30 MHz; 2430−30×80=+30 MHz. Real sampling represents the conjugate pair at positive 30 MHz. The local slopes are opposite: wanted decreases toward 29 MHz for a +1 MHz RF marker, while the 2430 MHz source increases toward 31 MHz. At their centers the supports overlap exactly.

\begin{aligned}\operatorname{wrap}(f,f_{s}) &= f - f_{s} \operatorname{floor}[\frac{f + \frac{f_{s}}{2}}{f_{s}}] \\ \mathrm{fpositive} &= |\operatorname{wrap}(f,f_{s})|\end{aligned}

Definition · exact wrapping to [−fs/2,+fs/2); f,fs in Hz. Complex sampling retains the sign. Real one-sided display uses absolute value and implies conjugate negative support.

Independent real-ADC anchors · fs=80 MS/s
Analog input / input zone	Signed alias / positive alias	Local positive-frequency slope
100 MHz; zone 3 (80,120) MHz	+20 /20 MHz	+1; 101→21 MHz
2450 MHz; zone 62 (2440, 2480) MHz	−30 /30 MHz	−1; 2451→29 MHz
2430 MHz; zone 61 (2400, 2440) MHz	+30 /30 MHz	+1; 2431→31 MHz
Exactly 2400, 2440 or 2480 MHz	0,−40, 0 signed respectively	Zone boundary; no unique local orientation across the boundary

Each lane uses its own linear MHz scale. Markers show support, never amplitude. Thin channels have a center diamond; exact widths and all branches are in the table. W = wanted; B = RF source; C = coupled source. Dashed support = conditional stop exclusion.

A0 · nonnegative real alias; conjugate negative support implied · MHz. Scroll this lane horizontally if needed.

The full tuning band is 100 MHz wide, but a real 80 MS/s converter offers a 40 MHz nonredundant interval. Full-band simultaneous capture fails the geometry bound even without blockers. A selected 13.5 kHz band can fit, but a broad RF passband also admits the exact alias pair. Analog anti-alias selection must exclude unwanted origins before sampling.

ADI MT-002 distinguishes undersampling from ADC input-bandwidth limits. A low sample rate does not make a 2.45 GHz input behave like a 30 MHz analog input. The converter, driver and clock must still handle the RF frequency.

RF-sampling evidence request · amplitude model deliberately absent
Boundary	Required actual evidence	Why geometry is insufficient
A1 converter/driver	Input bandwidth, input impedance/matching, SFDR and full-scale/headroom at 2.45 GHz over required conditions	A passing alias plan cannot prevent analog overload or establish settling.
Sampling clock	Permitted sample-rate range, clock drive/slew, aperture jitter and discrete coupled spurs	Random timing error depends on analog input frequency; coupled clock tones have their own entry paths.
RF preselector	Attenuation at every folded origin and noise-folding region; insertion loss, tuning and acquisition support	The downstream digital filter cannot undo prior superposition or overload.

Go deeperSplit support where the mapping changes branch

At 80 MS/s, real input [39, 41] MHz splits at 40 MHz. The two pieces both map into [39, 40] MHz, with slopes +1 and −1: wanted self-overlap. Complex sampling instead gives [39, 40) and [−40,−39] MHz. The apparent gap is a wrap discontinuity; never join the outer endpoints through the middle. The exact point 40 MHz wraps to −40 MHz. Signed support and open limiting endpoints must remain explicit.

Common misconceptionSampling above twice channel bandwidth always makes RF sampling safe.

It does not check band placement, conjugate overlap, other admitted sources, input bandwidth or filtering. Conversely, intentional undersampling is not categorically destructive: a properly selected band can retain its information when replicas remain separate.

Sampling can invert the selected real branch just as injection side can. Track both effects before assigning the output I/Q convention.

07 / 10

Injection side and orientation at every plane

Where does a marker 1 MHz above the RF carrier land after every selection?

Think about itDoes high-side complex mixing itself have a negative frequency slope?

Answer

No. f′=f−fLO always has slope +1. With LO 2550 MHz, 2450→−100 and 2451→−99 MHz. The inversion appears when the negative branch is represented at positive real IF: 100 and 99 MHz. That is a slope −1 mapping of the RF marker.

Orientation ledger · independent +1 MHz RF marker; marker is a probe, outside the 13.5 kHz channel
Plan	RF → signed mixer → selected real/complex branch	A0 selection → translated marker → D3 convention
IF100 low-side	2450/2451 → +100/+101 →100/101 MHz	20/21 →0/+1 MHz; preserve orientation
IF100 high-side	2450/2451 → −100/−99 →100/99 MHz	20/19 →0/−1 MHz; conjugate to 0/+1 MHz
ZIF	2450/2451 →0/+1 MHz complex	At 1.280 Mcomplex-sample/s the distant 1 MHz probe wraps to −0.280 MHz; local narrow-channel slope remains +1. The probe is outside the analog passband.
RF 80	2450/2451 → direct RF, no mixer	−30/−29 signed →30/29 positive →0/−1 MHz; conjugate if this conditional selected-band plan is revisited
HIF	2450/2451 →450/451 →100/101 MHz	20/21 →0/+1 MHz; two low-side positive branches preserve the sign

Use the local marker to establish slope; do not treat a 1 MHz probe as a passed waveform component through a 40 kHz IF pass interval. For the actual selected support, IF100 high-side maps upper RF offsets to lower IF offsets. Conjugation after digital translation changes Q’s sign and restores positive complex offset above the RF carrier.

\begin{aligned}\text{overall orientation} &= \text{mixer selection slope} \times \text{sampling fold slope} \\ \text{high-side IF100}: (-1) \times (+1) &= -1 \\ \text{after conjugation}: (-1) \times (-1) &= +1\end{aligned}

Derived sign bookkeeping for the selected IF100 branch, away from DC/Nyquist boundaries. Each multiplication refers to the stated representation, not a mixer’s gain.

Common misconceptionHigh- and low-side injection preserve identical orientation.

The signed translation slopes match, but selecting their positive real IF branches gives different RF orientation. Record the conjugation decision in the interface contract so downstream demodulation sees the agreed I/Q sign.

Now keep that same source and branch discipline for products that originate outside the wanted signal chain.

08 / 10

LO harmonics, clocks, digital emissions, and half-IF threats

Which source creates the interference, and which filter does it actually pass through?

A spur plan is a system record. Start with a physical source and entry plane, then allow products only at declared nonlinear stages. The bounded mixer family here uses signed integer coefficients, m≠0, and 1≤|m|+|n|≤H. H defaults to 4 and is limited to 6. Equal frequency geometries are grouped, but all distinct source/coefficient/signed-branch lineages remain attached. An omitted coefficient is not evidence that its product is absent in hardware.

\begin{aligned}q &= m f_{\mathrm{in}} + n f_{\mathrm{LO}} \\ 2 \times 2400 - 2 \times 2350 &= 100 \mathrm{MHz} \\ |m| + |n| &= 2 + 2 = 4\end{aligned}

Derived candidate location, not amplitude. m,n are signed integers; H is total order. n=0 denotes a source harmonic at the explicit nonlinear stage; m=0 LO feedthrough/harmonics are separately named sources.

Think about itWhy can the same 100 MHz collision demand two completely different fixes?

Answer

B-HALF enters at RF 2400 MHz and may form the order 4 product at M1; suppress its RF input or establish the mixer’s conversion susceptibility. CLK-IF enters directly at A1 after the filters; RF preselection cannot reach that path. Both can reach the wanted 20 MHz sampled alias, but their amplitudes and mitigation locations differ.

Four frozen interference lineages · IF100 low-side; levels are metadata only
ID / source / entry	Frequency path	Selection and unresolved evidence
B-IMAGE · 2250 MHz CW · −35 dBm at R2	2250−2350=−100 → real 100 → sampled +20 → wanted	RF-PRE stop; conditional suppression requires RF attenuation. IF100 passes the collision if it survives.
B-ALIAS · 2430 MHz CW · −25 dBm at R2	Real IF 80 → sampled 0; direct RF variant 2430→+30	IF100 rejects the 80 MHz fundamental conditionally. RF 80 admits the exact 30 MHz alias pair.
B-HALF · 2400 MHz CW · −30 dBm at R2	B-HALF → (m=2,n=−2) →100 MHz IF →+20 MHz A0 → wanted digital channel	Order 4 candidate absent at H=3. At H=4, request nonlinear spur evidence under actual LO drive and source level.
CLK-IF · 100 MHz · unknown coupled amplitude at A1	A1 injection 100 →+20 MHz A0 → wanted digital channel	After RF-PRE and A1F; change coupling/clock/entry filtering or allocate amplitude. Candidate collision, not proved hardware failure.

A finite-width variant must declare support. For example, a 10 kHz-wide source centered at 2400 MHz has RF support [2399.995, 2400.005] MHz. Under the m=2 term its candidate IF support becomes [99.990,100.010] MHz before sampling; this geometry does not simulate a modulated nonlinear waveform or assign its power. A CW marker has zero width and is still a collision when it lies strictly inside the wanted interval.

Include oscillator harmonics, digital clocks, supply-related lines and emission coupling only with an explicit origin. Do not mix arbitrary intermediate graph nodes with each other or recursively feed every generated product into another unspecified nonlinearity. Cross-source intermodulation, phase-noise skirts and amplitude budgets remain separate work.

Common misconceptionA spur chart is only a mixer data-sheet task.

A downstream clock can bypass every RF filter. A data sheet describes a characterized component under its conditions; the system planner must still locate the source, coupling path and conversion/sampling chain.

The comparison now has enough structure to ask what tuning, acquisition and implementation evidence would change the choice.

09 / 10

Compare filters, tuning, settling, calibration, cost, and power

Does a spectrally separated nominal plan still acquire the incoming packet at the clock-tolerance corners?

Tuning and acquisition ledger · Derived bounds; not phase-noise simulation
Requirement / plan	Checked range or support	Consequence
IF100 low-side across 2400–2500 MHz	LO 2300–2400 MHz	Tune LO with RF carrier; image sweeps 2200–2300 MHz. RF filter attenuation must be checked over that range.
IF100 high-side across 2400–2500 MHz	LO 2500–2600 MHz	Image sweeps 2600–2700 MHz; preserve orientation correction.
ZIF across 2400–2500 MHz	LO 2400–2500 MHz	Select one channel at a time; IQ/DC calibration and tracking remain required.
One ±20 ppm reference at 2450 MHz	±49 kHz; expanded support ±55.75 kHz	Exceeds IF100 ±20 kHz pass and D3 ±40 kHz interval if uncorrected.
Two independently bounded ±20 ppm radios	±98 kHz worst relative bound; support ±104.75 kHz	Worst signed extremes add; this is not RSS. Acquire/correct at a wider upstream boundary before narrow filtering/decimation.

\begin{aligned}20 \times 10^{-6} \times 2.450 \times 10^{9} &= 49,000 \mathrm{Hz} \\ 49,000 + 49,000 &= 98,000 \mathrm{Hz} \\ 98,000 + 6,750 &= 104,750 \mathrm{Hz} > 40,000 \mathrm{Hz}\end{aligned}

Derived deterministic tolerance bound. Relative error maximum occurs at opposite signed radio errors; no probability distribution or independence-based RSS is assumed.

The nominal IF100 plan therefore cannot simply be reused in acquisition mode. Its narrow analog IF pass region must be widened, switched or preceded by an acquisition/tuning correction strategy. ZIF’s illustrative ±200 kHz baseband pass region contains the ±104.75 kHz bound at A0’s 1.280 Mcomplex-sample/s rate, but immediate uncorrected narrowing to 80 ksample/s still loses coverage. Changing the sample rate alone does not repair an earlier narrow analog filter.

Go deeperTracking selection is different from 100 MHz simultaneous capture

A tracking RF preselector can move its passband with the selected carrier, while a broad front-end may deliberately cover the tuning band and rely on a later IF filter. For either choice, acquisition support and credible blockers must be included. Do not require a fixed 40 kHz passband centered at 2450 MHz to pass every carrier from 2400 to 2500 MHz at once. State the filter tuning law, tolerances, transient behavior and stopband evidence instead.

Five complete named candidates · p05-m02-frequency-graph-v1
Candidate / analog plan	A0 → D3 selection	Required condition / decision
ZIF channel · complex LO 2450 MHz; I+jQ at zero	Two real 1.280 MS/s ADC branches = 1.280 Mcomplex-sample/s; ideal filter/decimation to 80 ksample/s complex	One channel plausible. DC, flicker, even-order effects, IQ mismatch, LO leakage and calibration amplitudes unknown.
IF100 low-side · real LO 2350 MHz; +100 MHz branch	One real 80 MS/s ADC; signed +20 / positive 20 MHz; digital translation; D3 80 ksample/s	Conditional image preselection at RF; 99.980–100.020 MHz analog IF passband. Half-IF and CLK-IF require amplitude evidence.
IF100 high-side · real LO 2550 MHz; signed −100 → positive 100 MHz	Same 80 MS/s / 20 MHz selection; conjugate after translation to restore portfolio orientation	RF image at 2650 MHz; +1 MHz RF marker → 99 MHz IF. No universal power/cost winner.
RF 80 unprotected · RF 2450 MHz straight to ADC; RF pass 2400–2500 MHz	One real 80 MS/s ADC; wanted −30 signed → positive 30 MHz; B-ALIAS 2430 → +30	Reject: passed CW is strictly inside wanted alias. Full 100 MHz cannot fit 40 MHz real interval. Narrow tracking preselection may reopen review.
HIF comparison · LO 2000 →450 MHz; LO 350 →100 MHz	450 MHz first IF filtered before second mixer; 100 MHz IF filter before 80 MS/s ADC; select 20 MHz	RF image 1550 MHz; second-stage image 250 MHz. Two IF filters and two LO evidence sets; additional spurs/gain/power remain unallocated.

Requirement-conditioned trade · no invented power, cost or performance scores
Condition	Architecture question	Next evidence that could reverse the choice
Single channel; strong out-of-band image	Can IF preselection suppress the relevant image before mixing without excessive receive loss?	Filter attenuation/loss and blocker susceptibility over tuning, temperature and manufacturing variation.
Fast retuning or short wake interval	Do PLL, analog filter, ADC and calibration all produce usable samples before the required window?	Spectral settling and calibration sequence, not a lock flag alone. See 04.7.
Strict converter/digital power budget	Does RF sampling or dual-IQ processing meet the actual boundary workload and mode duty?	Part-specific active/sleep/startup power, clock/driver requirements and digital throughput in 05.6.
Cost and size pressure	Does integration remove external burden or transfer it to calibration/filter specifications?	Bill of materials, test/calibration cost, layout and risk evidence; no automatic winner.

TI ADC32RF45 Rev.C §§8.3.1–8.3.2 and 9.1.3 makes the needed distinctions concrete: analog input response depends on the interface; aperture jitter depends on clock drive; SNR must be evaluated at the analog input frequency. This data sheet is an evidence-reading example, not the device behind the synthetic 80 MS/s plans.

Use the canvas to make one change that repairs a geometric failure, and record the evidence it still needs.

10 / 10

Create the gateway frequency plan

Which plan can you reject now, and which plan can you defend conditionally?

Predict the 2250 MHz image, then load IF100 low-side and inspect M1/A0.
Load IF100 high-side; compare the signed precursor and local slope, then disable orientation correction.
Load RF 80 unprotected. Trace WANTED and B-ALIAS at A0; both occupy 30 MHz.
Return to IF100 low-side. Set H=3 then 4; locate the B-HALF coefficient lineage and the independent CLK-IF path.
For RF 80, change RF-PRE pass edges to 2449.980/2450.020 MHz and outer transition edges to 2449.900/2450.100 MHz. Apply the conditional stop assumption. The alias source now requires analog stopband attenuation.
Enable two-radio acquisition. Explain why the nominal narrow filter and uncorrected D3 rate need a new allocation. Copy the committed record with all missing evidence.

Class 1 · frequency-only teaching model

Architecture Frequency-Plan Canvas

Follow a source across physical boundaries. Select a named plan, predict its image or alias, then change the analog selection that determines whether the plan can proceed.

p05-m02-frequency-graph-v1 · p05-m02-geometry-rules-v1 · integer Hz internally; MHz displayed to 1 Hz. Source powers are input metadata, never spur estimates. No data leaves this page.

Architecture / complete presetChanging preset restores every defining input. Changing a view below does not edit the plan.

Wanted signal, tuning and acquisition

Tuning lower endpoint (GHz)0.1–6 GHz; step 0.000001.

Tuning upper endpoint (GHz)0.1–6 GHz; step 0.000001.

Selected RF carrier (GHz)0.1–6 GHz; step 0.000001.

Selected total signal width (MHz)0.001–100 MHz; step 0.001. The exact 0.0135 MHz preset is retained; edits accept integer Hz without quantizing the fixture.

Requested captureTuning coverage is not simultaneous bandwidth. Fixed D3 is the selected channel only.

Frequency-error support expansionWorst bounded offset, not random RSS or phase noise. At 2450 MHz: ±49 / ±98 kHz.

Physical conversion and sampling boundary

First IF magnitude (MHz)0–1000 MHz; step 0.001.

Programmed first LO (GHz)0.1–6 GHz; step 0.000001. Use the derive button after changing carrier/IF; a manual LO keeps its programmed error.

A0 sample rate (MS/s)0.08–5000 MS/s; step 0.001. One physical real ADC. D3 remains 0.080 Mcomplex-sample/s.

Total harmonic order H (integer)1–6 integer; step 1.

First-mixer injection sideThen derive LO. HIF retains its second real mixer at LO 350 MHz.

Digital orientation correctionPreserves u=I+jQ after positive-frequency selection.

Analog filters · edit selection regions and evidence

Analog selection · fixed physical filter locations

Stop-region evidence assumptionNo attenuation value or realized filter order is supplied. Transition remains unresolved. Pass is closed; outer stop edges belong to transition.

RF-PRE · R1

Lower transition edge (MHz)

Lower pass edge (MHz)

Upper pass edge (MHz)

Upper transition edge (MHz)

Ordered edges in MHz; −6000…6000 only for signed ZIF offsets, otherwise 0…6000; step 0.001. Stop regions lie beyond the outer edges; transitions exclude the closed pass interval.

IF100 · A1F (before A1 clock injection)

Lower transition edge (MHz)

Lower pass edge (MHz)

Upper pass edge (MHz)

Upper transition edge (MHz)

Ordered edges in MHz; −6000…6000 only for signed ZIF offsets, otherwise 0…6000; step 0.001. Stop regions lie beyond the outer edges; transitions exclude the closed pass interval.

Interference sources · edit supports and entry planes

Interference sources · CW or declared finite support

Three RF rows and two coupled rows maximum. Width 0 means a CW point, not an empty field. RF input levels refer to available power at nominal matched 50 Ω R2; no 50 Ω or voltage scaling is implied at digital planes.

B-IMAGE · RF source

Source frequency (MHz) · B-IMAGE0…6000 MHz, step 0.001. Required.

Total support width (MHz) · B-IMAGE0…100 MHz, step 0.001; 0 = CW. Required.

Optional input level (dBm) · B-IMAGE−180…+30 dBm, step 0.1; blank = unknown. Metadata only.

Entry plane · B-IMAGEInjection at a node bypasses preceding filters. Frequency is interpreted at that plane.

Include · B-IMAGE

B-ALIAS · RF source

Source frequency (MHz) · B-ALIAS0…6000 MHz, step 0.001. Required.

Total support width (MHz) · B-ALIAS0…100 MHz, step 0.001; 0 = CW. Required.

Optional input level (dBm) · B-ALIAS−180…+30 dBm, step 0.1; blank = unknown. Metadata only.

Entry plane · B-ALIASInjection at a node bypasses preceding filters. Frequency is interpreted at that plane.

Include · B-ALIAS

B-HALF · RF source

Source frequency (MHz) · B-HALF0…6000 MHz, step 0.001. Required.

Total support width (MHz) · B-HALF0…100 MHz, step 0.001; 0 = CW. Required.

Optional input level (dBm) · B-HALF−180…+30 dBm, step 0.1; blank = unknown. Metadata only.

Entry plane · B-HALFInjection at a node bypasses preceding filters. Frequency is interpreted at that plane.

Include · B-HALF

CLK-IF · coupled source

Source frequency (MHz) · CLK-IF0…6000 MHz, step 0.001. Required.

Total support width (MHz) · CLK-IF0…100 MHz, step 0.001; 0 = CW. Required.

Optional input level (dBm) · CLK-IF−180…+30 dBm, step 0.1; blank = unknown. Metadata only.

Entry plane · CLK-IFInjection at a node bypasses preceding filters. Frequency is interpreted at that plane.

Include · CLK-IF

Committed geometry · IF100 low-sideinspect—candidate collision

Wanted A0: signed 20 MHz → selected 20 MHz; local slope 1. Required LO range [2300, 2400] MHz.

Frequency-error expansion ±0 Hz. Programmed LO error 0 Hz. H=4; 128 signed RF/LO coefficient lineages evaluated. Higher orders, cross-source products and unlisted emissions omitted.

Conditional comparison assumes declared stop regions reject whole source supports; attenuation remains unverified. Geometry clears never establishes spur margin or receiver performance.

Committed filter and clock boundary

RF-PRE @ R1: closed pass [2400, 2500] MHz; transitions from 2300 to 2400 and 2500 to 2600 MHz, excluding pass edges. Stops beyond outer edges. Illustrative geometric regions; realized attenuation unknown.

IF100 @ A1F: closed pass [99.98, 100.02] MHz; transitions from 99.9 to 99.98 and 100.02 to 100.1 MHz, excluding pass edges. Stops beyond outer edges. Illustrative geometric regions; realized attenuation unknown.

A0 80 MS/s, one real ADC. D3 80 kcomplex-sample/s after ideal selection/filtering and acquisition correction. Converter input bandwidth and permissible sample-clock range still require a real data sheet.

Inspect physical plane

A0 · nonnegative real alias; conjugate negative support implied · MHz. Scroll this lane horizontally if needed.

Table rows 1–6 of 6 at A0. The lane shows the first eight rows on this table page; no hidden row changes the decision.

Complete per-plane boundary record · Derived / Illustrative · MHz, not level spectra
Source / edge	Support / center / orientation	Representation / zone / selection	Level evidence / lineage
WANTED · A1 → A0	[19.99325, 20.00675] MHz Center 20 MHz Slope +1 Signed precursor: [19.99325, 20.00675] MHz	real; nonnegative real alias; conjugate negative support implied. zone 3. IF100: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes → signed wrap, then positive fold at 80 MS/s
CLK-IF · A1 → A0	20 MHz (CW) Center 20 MHz Slope +1 Signed precursor: 20 MHz (CW)	real; nonnegative real alias; conjugate negative support implied. zone 3. no filter yet.	Unknown amplitude. CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s
CLK-IF×2 · A1 → A0	40 MHz (CW) Center 40 MHz Slope 0 (boundary) Signed precursor: -40 MHz (CW)	real; nonnegative real alias; conjugate negative support implied. boundary; no unique orientation. no filter yet.	Unknown amplitude. CLK-IF×2 @ A1 (CLK-IF harmonic 2 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s
CLK-IF×3 · A1 → A0	20 MHz (CW) Center 20 MHz Slope -1 Signed precursor: -20 MHz (CW)	real; nonnegative real alias; conjugate negative support implied. zone 8. no filter yet.	Unknown amplitude. CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s
CLK-IF×4 · A1 → A0	0 MHz (CW) Center 0 MHz Slope 0 (boundary) Signed precursor: 0 MHz (CW)	real; nonnegative real alias; conjugate negative support implied. boundary; no unique orientation. no filter yet.	Unknown amplitude. CLK-IF×4 @ A1 (CLK-IF harmonic 4 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s
B-HALF product · A1 → A0	20 MHz (CW) Center 20 MHz Slope +2 Signed precursor: 20 MHz (CW)	real; nonnegative real alias. zone 3. Nonlinear candidate; no amplitude model.	Unknown nonlinear amplitude; input dBm is metadata only. B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel

Collision and constraint record · sorted by physical stage, severity, frequency, source
Plane / source	Decision / exact geometry	Causal lineage / action
A0 · B-HALF	inspect—candidate collision · 20 MHz. Possible nonlinear product; collision. Geometry does not predict its level. H=4; gain/conversion/spur-table evidence missing.	B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel
A0 · CLK-IF	inspect—candidate collision · 20 MHz. collision: CLK-IF 20 MHz (CW) and wanted [19.99325, 20.00675] MHz; 0 Hz positive-width overlap. Change analog selection before this ADC; digital filtering cannot separate overlapping origins. Amplitude/headroom evidence unknown.	CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s
A0 · CLK-IF×3	inspect—candidate collision · 20 MHz. collision: CLK-IF×3 20 MHz (CW) and wanted [19.99325, 20.00675] MHz; 0 Hz positive-width overlap. Change analog selection before this ADC; digital filtering cannot separate overlapping origins. Amplitude/headroom evidence unknown.	CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s
D3 · CLK-IF	inspect—candidate collision · 0 MHz. collision: CLK-IF 0 MHz (CW) and wanted [-0.00675, 0.00675] MHz; 0 Hz positive-width overlap. Filter before the first superposition. Amplitude/headroom evidence unknown.	CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate
D3 · CLK-IF×3	inspect—candidate collision · 0 MHz. collision: CLK-IF×3 0 MHz (CW) and wanted [-0.00675, 0.00675] MHz; 0 Hz positive-width overlap. Filter before the first superposition. Amplitude/headroom evidence unknown.	CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate

A0 support relationships and available spectral separation
Source / support	Nearest wanted support relation	Meaning / location of selection
CLK-IF; 20 MHz (CW)	collision; available gap 0 Hz; overlap width 0 Hz	An overlapping origin requires selection before superposition or source-specific amplitude/coupling evidence.
CLK-IF×2; 40 MHz (CW)	separated; available gap 19993250 Hz; overlap width 0 Hz	Gap is geometric room for a subsequent transition, not attenuation. Analog overload still needs upstream evidence.
CLK-IF×3; 20 MHz (CW)	collision; available gap 0 Hz; overlap width 0 Hz	An overlapping origin requires selection before superposition or source-specific amplitude/coupling evidence.
CLK-IF×4; 0 MHz (CW)	separated; available gap 19993250 Hz; overlap width 0 Hz	Gap is geometric room for a subsequent transition, not attenuation. Analog overload still needs upstream evidence.
B-HALF product; 20 MHz (CW)	collision; available gap 0 Hz; overlap width 0 Hz	An overlapping origin requires selection before superposition or source-specific amplitude/coupling evidence.

Trace one diagnostic

Collision and constraint record · sorted by physical stage, severity, frequency, source
Plane / source	Decision / exact geometry	Causal lineage / action
A0 · B-HALF	inspect—candidate collision · 20 MHz. Possible nonlinear product; collision. Geometry does not predict its level. H=4; gain/conversion/spur-table evidence missing.	B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel

Committed JSON record · local copy fallback

{
  "versions": {
    "model": "p05-m02-frequency-graph-v1",
    "fixture": "p05-m02-frequency-graph-v1",
    "rules": "p05-m02-geometry-rules-v1",
    "serialization": "p05-m02-plan-json-v1",
    "display": "p05-m02-hz-display-v1",
    "convention": "u=I+jQ; sRF=Re{u exp(+j2πfct)}; positive offset is above carrier",
    "evidence": "Derived / Illustrative; gain, attenuation and coupled amplitudes unknown"
  },
  "input": {
    "preset": "if-low",
    "topology": "if",
    "low": 2400000000,
    "high": 2500000000,
    "carrier": 2450000000,
    "width": 13500,
    "capture": "channel",
    "ifHz": 100000000,
    "injection": "low",
    "lo": 2350000000,
    "fs": 80000000,
    "order": 4,
    "acquisition": 0,
    "correct": true,
    "assumeStop": true,
    "filters": [
      {
        "id": "RF-PRE",
        "plane": "R1",
        "edges": [
          2300000000,
          2400000000,
          2500000000,
          2600000000
        ],
        "evidence": "Illustrative geometric regions; realized attenuation unknown"
      },
      {
        "id": "IF100",
        "plane": "A1F",
        "edges": [
          99900000,
          99980000,
          100020000,
          100100000
        ],
        "evidence": "Illustrative geometric regions; realized attenuation unknown"
      }
    ],
    "sources": [
      {
        "id": "B-IMAGE",
        "kind": "rf",
        "hz": 2250000000,
        "width": 0,
        "dbm": -35,
        "entry": "R2",
        "enabled": true,
        "evidence": "p05-m02-frequency-graph-v1"
      },
      {
        "id": "B-ALIAS",
        "kind": "rf",
        "hz": 2430000000,
        "width": 0,
        "dbm": -25,
        "entry": "R2",
        "enabled": true,
        "evidence": "p05-m02-frequency-graph-v1"
      },
      {
        "id": "B-HALF",
        "kind": "rf",
        "hz": 2400000000,
        "width": 0,
        "dbm": -30,
        "entry": "R2",
        "enabled": true,
        "evidence": "p05-m02-frequency-graph-v1"
      },
      {
        "id": "CLK-IF",
        "kind": "clock",
        "hz": 100000000,
        "width": 0,
        "dbm": null,
        "entry": "A1",
        "enabled": true,
        "evidence": "p05-m02-frequency-graph-v1"
      }
    ]
  },
  "rows": [
    {
      "id": "WANTED",
      "source": "WANTED",
      "from": "R2",
      "plane": "R2",
      "support": [
        2449993250,
        2450006750
      ],
      "signed": [
        2449993250,
        2450006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1)",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "B-IMAGE",
      "source": "B-IMAGE",
      "from": "R2",
      "plane": "R2",
      "support": [
        2250000000,
        2250000000
      ],
      "signed": [
        2250000000,
        2250000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-IMAGE @ R2 (p05-m02-frequency-graph-v1)",
      "level": "-35 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-ALIAS",
      "source": "B-ALIAS",
      "from": "R2",
      "plane": "R2",
      "support": [
        2430000000,
        2430000000
      ],
      "signed": [
        2430000000,
        2430000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-ALIAS @ R2 (p05-m02-frequency-graph-v1)",
      "level": "-25 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-HALF",
      "source": "B-HALF",
      "from": "R2",
      "plane": "R2",
      "support": [
        2400000000,
        2400000000
      ],
      "signed": [
        2400000000,
        2400000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-HALF @ R2 (p05-m02-frequency-graph-v1)",
      "level": "-30 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "WANTED\u003eR1",
      "source": "WANTED",
      "from": "R2",
      "plane": "R1",
      "support": [
        2449993250,
        2450006750
      ],
      "signed": [
        2449993250,
        2450006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "B-IMAGE\u003eR1",
      "source": "B-IMAGE",
      "from": "R2",
      "plane": "R1",
      "support": [
        2250000000,
        2250000000
      ],
      "signed": [
        2250000000,
        2250000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "RF-PRE: requires stopband attenuation; conditionally excluded, attenuation unverified",
      "excluded": true,
      "uncertain": false,
      "lineage": "B-IMAGE @ R2 (p05-m02-frequency-graph-v1) → RF-PRE requires stopband attenuation",
      "level": "-35 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-ALIAS\u003eR1",
      "source": "B-ALIAS",
      "from": "R2",
      "plane": "R1",
      "support": [
        2430000000,
        2430000000
      ],
      "signed": [
        2430000000,
        2430000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-ALIAS @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes",
      "level": "-25 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-HALF\u003eR1",
      "source": "B-HALF",
      "from": "R2",
      "plane": "R1",
      "support": [
        2400000000,
        2400000000
      ],
      "signed": [
        2400000000,
        2400000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "absolute RF",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-HALF @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes",
      "level": "-30 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "WANTED\u003eR1\u003eM1:difference:0",
      "source": "WANTED",
      "from": "R1",
      "plane": "M1",
      "support": [
        99993250,
        100006750
      ],
      "signed": [
        99993250,
        100006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "WANTED\u003eR1\u003eM1:sum:1",
      "source": "WANTED",
      "from": "R1",
      "plane": "M1",
      "support": [
        4799993250,
        4800006750
      ],
      "signed": [
        4799993250,
        4800006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed [4799.99325, 4800.00675] MHz → positive branch",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "B-ALIAS\u003eR1\u003eM1:difference:0",
      "source": "B-ALIAS",
      "from": "R1",
      "plane": "M1",
      "support": [
        80000000,
        80000000
      ],
      "signed": [
        80000000,
        80000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-ALIAS @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed 80 MHz (CW) → positive branch",
      "level": "-25 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-ALIAS\u003eR1\u003eM1:sum:1",
      "source": "B-ALIAS",
      "from": "R1",
      "plane": "M1",
      "support": [
        4780000000,
        4780000000
      ],
      "signed": [
        4780000000,
        4780000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-ALIAS @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed 4780 MHz (CW) → positive branch",
      "level": "-25 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-HALF\u003eR1\u003eM1:difference:0",
      "source": "B-HALF",
      "from": "R1",
      "plane": "M1",
      "support": [
        50000000,
        50000000
      ],
      "signed": [
        50000000,
        50000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-HALF @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed 50 MHz (CW) → positive branch",
      "level": "-30 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-HALF\u003eR1\u003eM1:sum:1",
      "source": "B-HALF",
      "from": "R1",
      "plane": "M1",
      "support": [
        4750000000,
        4750000000
      ],
      "signed": [
        4750000000,
        4750000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "RF-PRE: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "B-HALF @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed 4750 MHz (CW) → positive branch",
      "level": "-30 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "product:B-HALF:100000000",
      "source": "B-HALF product",
      "from": "R1",
      "plane": "M1",
      "support": [
        100000000,
        100000000
      ],
      "signed": [
        -100000000,
        -100000000
      ],
      "orientation": 2,
      "representation": "real",
      "axis": "nonnegative real IF; signed coefficient lineage retained",
      "zone": "continuous",
      "filter": "Nonlinear candidate; no amplitude model",
      "excluded": false,
      "uncertain": true,
      "lineage": "B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel",
      "level": "Unknown nonlinear amplitude; input dBm is metadata only",
      "candidate": true
    },
    {
      "id": "WANTED\u003eR1\u003eM1:difference:0\u003eA1F",
      "source": "WANTED",
      "from": "M1",
      "plane": "A1F",
      "support": [
        99993250,
        100006750
      ],
      "signed": [
        99993250,
        100006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "WANTED\u003eR1\u003eM1:sum:1\u003eA1F",
      "source": "WANTED",
      "from": "M1",
      "plane": "A1F",
      "support": [
        4799993250,
        4800006750
      ],
      "signed": [
        4799993250,
        4800006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: requires stopband attenuation; conditionally excluded, attenuation unverified",
      "excluded": true,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed [4799.99325, 4800.00675] MHz → positive branch → IF100 requires stopband attenuation",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "B-ALIAS\u003eR1\u003eM1:difference:0\u003eA1F",
      "source": "B-ALIAS",
      "from": "M1",
      "plane": "A1F",
      "support": [
        80000000,
        80000000
      ],
      "signed": [
        80000000,
        80000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: requires stopband attenuation; conditionally excluded, attenuation unverified",
      "excluded": true,
      "uncertain": false,
      "lineage": "B-ALIAS @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed 80 MHz (CW) → positive branch → IF100 requires stopband attenuation",
      "level": "-25 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-ALIAS\u003eR1\u003eM1:sum:1\u003eA1F",
      "source": "B-ALIAS",
      "from": "M1",
      "plane": "A1F",
      "support": [
        4780000000,
        4780000000
      ],
      "signed": [
        4780000000,
        4780000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: requires stopband attenuation; conditionally excluded, attenuation unverified",
      "excluded": true,
      "uncertain": false,
      "lineage": "B-ALIAS @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed 4780 MHz (CW) → positive branch → IF100 requires stopband attenuation",
      "level": "-25 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-HALF\u003eR1\u003eM1:difference:0\u003eA1F",
      "source": "B-HALF",
      "from": "M1",
      "plane": "A1F",
      "support": [
        50000000,
        50000000
      ],
      "signed": [
        50000000,
        50000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: requires stopband attenuation; conditionally excluded, attenuation unverified",
      "excluded": true,
      "uncertain": false,
      "lineage": "B-HALF @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed 50 MHz (CW) → positive branch → IF100 requires stopband attenuation",
      "level": "-30 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "B-HALF\u003eR1\u003eM1:sum:1\u003eA1F",
      "source": "B-HALF",
      "from": "M1",
      "plane": "A1F",
      "support": [
        4750000000,
        4750000000
      ],
      "signed": [
        4750000000,
        4750000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: requires stopband attenuation; conditionally excluded, attenuation unverified",
      "excluded": true,
      "uncertain": false,
      "lineage": "B-HALF @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed 4750 MHz (CW) → positive branch → IF100 requires stopband attenuation",
      "level": "-30 dBm input metadata only; no propagated level",
      "candidate": false
    },
    {
      "id": "WANTED\u003eR1\u003eM1:difference:0\u003eA1F\u003eA1",
      "source": "WANTED",
      "from": "A1F",
      "plane": "A1",
      "support": [
        99993250,
        100006750
      ],
      "signed": [
        99993250,
        100006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real IF; conjugate negative support implied",
      "zone": "continuous",
      "filter": "IF100: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "CLK-IF",
      "source": "CLK-IF",
      "from": "A1",
      "plane": "A1",
      "support": [
        100000000,
        100000000
      ],
      "signed": [
        100000000,
        100000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "frequency at entry plane",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF @ A1 (p05-m02-frequency-graph-v1)",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×2",
      "source": "CLK-IF×2",
      "from": "A1",
      "plane": "A1",
      "support": [
        200000000,
        200000000
      ],
      "signed": [
        200000000,
        200000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "frequency at entry plane",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×2 @ A1 (CLK-IF harmonic 2 at explicit A1 coupling origin; amplitude unknown)",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×3",
      "source": "CLK-IF×3",
      "from": "A1",
      "plane": "A1",
      "support": [
        300000000,
        300000000
      ],
      "signed": [
        300000000,
        300000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "frequency at entry plane",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown)",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×4",
      "source": "CLK-IF×4",
      "from": "A1",
      "plane": "A1",
      "support": [
        400000000,
        400000000
      ],
      "signed": [
        400000000,
        400000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "frequency at entry plane",
      "zone": "continuous",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×4 @ A1 (CLK-IF harmonic 4 at explicit A1 coupling origin; amplitude unknown)",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "product:B-HALF:100000000:A1",
      "source": "B-HALF product",
      "from": "A1F",
      "plane": "A1",
      "support": [
        100000000,
        100000000
      ],
      "signed": [
        100000000,
        100000000
      ],
      "orientation": 2,
      "representation": "real",
      "axis": "nonnegative real IF; signed coefficient lineage retained",
      "zone": "continuous",
      "filter": "IF100: passes; attenuation unknown",
      "excluded": false,
      "uncertain": true,
      "lineage": "B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel",
      "level": "Unknown nonlinear amplitude; input dBm is metadata only",
      "candidate": true
    },
    {
      "id": "WANTED\u003eR1\u003eM1:difference:0\u003eA1F\u003eA1\u003eA0:0",
      "source": "WANTED",
      "from": "A1",
      "plane": "A0",
      "support": [
        19993250,
        20006750
      ],
      "signed": [
        19993250,
        20006750
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real alias; conjugate negative support implied",
      "zone": "zone 3",
      "filter": "IF100: passes",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes → signed wrap, then positive fold at 80 MS/s",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "CLK-IF\u003eA0:0",
      "source": "CLK-IF",
      "from": "A1",
      "plane": "A0",
      "support": [
        20000000,
        20000000
      ],
      "signed": [
        20000000,
        20000000
      ],
      "orientation": 1,
      "representation": "real",
      "axis": "nonnegative real alias; conjugate negative support implied",
      "zone": "zone 3",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×2\u003eA0:0",
      "source": "CLK-IF×2",
      "from": "A1",
      "plane": "A0",
      "support": [
        40000000,
        40000000
      ],
      "signed": [
        -40000000,
        -40000000
      ],
      "orientation": 0,
      "representation": "real",
      "axis": "nonnegative real alias; conjugate negative support implied",
      "zone": "boundary; no unique orientation",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×2 @ A1 (CLK-IF harmonic 2 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×3\u003eA0:0",
      "source": "CLK-IF×3",
      "from": "A1",
      "plane": "A0",
      "support": [
        20000000,
        20000000
      ],
      "signed": [
        -20000000,
        -20000000
      ],
      "orientation": -1,
      "representation": "real",
      "axis": "nonnegative real alias; conjugate negative support implied",
      "zone": "zone 8",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×4\u003eA0:0",
      "source": "CLK-IF×4",
      "from": "A1",
      "plane": "A0",
      "support": [
        0,
        0
      ],
      "signed": [
        0,
        0
      ],
      "orientation": 0,
      "representation": "real",
      "axis": "nonnegative real alias; conjugate negative support implied",
      "zone": "boundary; no unique orientation",
      "filter": "no filter yet",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×4 @ A1 (CLK-IF harmonic 4 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "product:B-HALF:100000000:A0",
      "source": "B-HALF product",
      "from": "A1",
      "plane": "A0",
      "support": [
        20000000,
        20000000
      ],
      "signed": [
        20000000,
        20000000
      ],
      "orientation": 2,
      "representation": "real",
      "axis": "nonnegative real alias",
      "zone": "zone 3",
      "filter": "Nonlinear candidate; no amplitude model",
      "excluded": false,
      "uncertain": true,
      "lineage": "B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel",
      "level": "Unknown nonlinear amplitude; input dBm is metadata only",
      "candidate": true
    },
    {
      "id": "WANTED\u003eR1\u003eM1:difference:0\u003eA1F\u003eA1\u003eA0:0\u003eD3",
      "source": "WANTED",
      "from": "A0",
      "plane": "D3",
      "support": [
        -6750,
        6750
      ],
      "signed": [
        -6750,
        6750
      ],
      "orientation": 1,
      "representation": "complex",
      "axis": "signed offset from selected digital channel",
      "zone": "ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required",
      "filter": "Ideal downstream channel selection: retained; overlapping origins cannot be removed",
      "excluded": false,
      "uncertain": false,
      "lineage": "WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "level": "Unknown amplitude",
      "candidate": false
    },
    {
      "id": "CLK-IF\u003eA0:0\u003eD3",
      "source": "CLK-IF",
      "from": "A0",
      "plane": "D3",
      "support": [
        0,
        0
      ],
      "signed": [
        0,
        0
      ],
      "orientation": 1,
      "representation": "complex",
      "axis": "signed offset from selected digital channel",
      "zone": "ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required",
      "filter": "Ideal downstream channel selection: retained; overlapping origins cannot be removed",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×2\u003eA0:0\u003eD3",
      "source": "CLK-IF×2",
      "from": "A0",
      "plane": "D3",
      "support": [
        20000000,
        20000000
      ],
      "signed": [
        20000000,
        20000000
      ],
      "orientation": 0,
      "representation": "complex",
      "axis": "signed offset from selected digital channel",
      "zone": "ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required",
      "filter": "Ideal downstream channel selection: outside selected support",
      "excluded": true,
      "uncertain": false,
      "lineage": "CLK-IF×2 @ A1 (CLK-IF harmonic 2 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×3\u003eA0:0\u003eD3",
      "source": "CLK-IF×3",
      "from": "A0",
      "plane": "D3",
      "support": [
        0,
        0
      ],
      "signed": [
        0,
        0
      ],
      "orientation": -1,
      "representation": "complex",
      "axis": "signed offset from selected digital channel",
      "zone": "ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required",
      "filter": "Ideal downstream channel selection: retained; overlapping origins cannot be removed",
      "excluded": false,
      "uncertain": false,
      "lineage": "CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "CLK-IF×4\u003eA0:0\u003eD3",
      "source": "CLK-IF×4",
      "from": "A0",
      "plane": "D3",
      "support": [
        -20000000,
        -20000000
      ],
      "signed": [
        -20000000,
        -20000000
      ],
      "orientation": 0,
      "representation": "complex",
      "axis": "signed offset from selected digital channel",
      "zone": "ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required",
      "filter": "Ideal downstream channel selection: outside selected support",
      "excluded": true,
      "uncertain": false,
      "lineage": "CLK-IF×4 @ A1 (CLK-IF harmonic 4 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "level": "Unknown amplitude",
      "candidate": true
    },
    {
      "id": "product:B-HALF:100000000:D3",
      "source": "B-HALF product",
      "from": "A0",
      "plane": "D3",
      "support": [
        0,
        0
      ],
      "signed": [
        0,
        0
      ],
      "orientation": 2,
      "representation": "complex",
      "axis": "signed offset from selected digital channel",
      "zone": "continuous",
      "filter": "Nonlinear candidate; no amplitude model",
      "excluded": false,
      "uncertain": true,
      "lineage": "B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel",
      "level": "Unknown nonlinear amplitude; input dBm is metadata only",
      "candidate": true
    }
  ],
  "diagnostics": [
    {
      "plane": "A0",
      "source": "B-HALF",
      "severity": "inspect—candidate collision",
      "frequency": 20000000,
      "reason": "Possible nonlinear product; collision. Geometry does not predict its level. H=4; gain/conversion/spur-table evidence missing.",
      "lineage": "B-HALF → (m=-2,n=2; order 4); B-HALF → (m=2,n=-2; order 4) → 100 MHz (CW) M1 → 100 MHz (CW) A1 → 20 MHz (CW) A0 → wanted digital channel",
      "relation": {
        "state": "collision",
        "overlapHz": 0,
        "gapHz": 0
      }
    },
    {
      "plane": "A0",
      "source": "CLK-IF",
      "severity": "inspect—candidate collision",
      "frequency": 20000000,
      "reason": "collision: CLK-IF 20 MHz (CW) and wanted [19.99325, 20.00675] MHz; 0 Hz positive-width overlap. Change analog selection before this ADC; digital filtering cannot separate overlapping origins. Amplitude/headroom evidence unknown.",
      "lineage": "CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s",
      "relation": {
        "state": "collision",
        "overlapHz": 0,
        "gapHz": 0
      }
    },
    {
      "plane": "A0",
      "source": "CLK-IF×3",
      "severity": "inspect—candidate collision",
      "frequency": 20000000,
      "reason": "collision: CLK-IF×3 20 MHz (CW) and wanted [19.99325, 20.00675] MHz; 0 Hz positive-width overlap. Change analog selection before this ADC; digital filtering cannot separate overlapping origins. Amplitude/headroom evidence unknown.",
      "lineage": "CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s",
      "relation": {
        "state": "collision",
        "overlapHz": 0,
        "gapHz": 0
      }
    },
    {
      "plane": "D3",
      "source": "CLK-IF",
      "severity": "inspect—candidate collision",
      "frequency": 0,
      "reason": "collision: CLK-IF 0 MHz (CW) and wanted [-0.00675, 0.00675] MHz; 0 Hz positive-width overlap. Filter before the first superposition. Amplitude/headroom evidence unknown.",
      "lineage": "CLK-IF @ A1 (p05-m02-frequency-graph-v1) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "relation": {
        "state": "collision",
        "overlapHz": 0,
        "gapHz": 0
      }
    },
    {
      "plane": "D3",
      "source": "CLK-IF×3",
      "severity": "inspect—candidate collision",
      "frequency": 0,
      "reason": "collision: CLK-IF×3 0 MHz (CW) and wanted [-0.00675, 0.00675] MHz; 0 Hz positive-width overlap. Filter before the first superposition. Amplitude/headroom evidence unknown.",
      "lineage": "CLK-IF×3 @ A1 (CLK-IF harmonic 3 at explicit A1 coupling origin; amplitude unknown) → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate",
      "relation": {
        "state": "collision",
        "overlapHz": 0,
        "gapHz": 0
      }
    }
  ],
  "status": "inspect—candidate collision",
  "errors": {},
  "loRange": [
    2300000000,
    2400000000
  ],
  "errorHz": 0,
  "offsetBound": 0,
  "alias": 20000000,
  "signedAlias": 20000000,
  "orientation": 1,
  "enumerated": 128,
  "products": [
    {
      "frequency": 100000000,
      "support": [
        99993250,
        100006750
      ],
      "lineages": [
        {
          "source": "WANTED",
          "m": -1,
          "n": 1,
          "signed": [
            -100006750,
            -99993250
          ],
          "order": 2
        },
        {
          "source": "WANTED",
          "m": 1,
          "n": -1,
          "signed": [
            99993250,
            100006750
          ],
          "order": 2
        }
      ]
    },
    {
      "frequency": 200000000,
      "support": [
        199986500,
        200013500
      ],
      "lineages": [
        {
          "source": "WANTED",
          "m": -2,
          "n": 2,
          "signed": [
            -200013500,
            -199986500
          ],
          "order": 4
        },
        {
          "source": "WANTED",
          "m": 2,
          "n": -2,
          "signed": [
            199986500,
            200013500
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 2250000000,
      "support": [
        2249993250,
        2250006750
      ],
      "lineages": [
        {
          "source": "WANTED",
          "m": -1,
          "n": 2,
          "signed": [
            2249993250,
            2250006750
          ],
          "order": 3
        },
        {
          "source": "WANTED",
          "m": 1,
          "n": -2,
          "signed": [
            -2250006750,
            -2249993250
          ],
          "order": 3
        }
      ]
    },
    {
      "frequency": 2450000000,
      "support": [
        2449993250,
        2450006750
      ],
      "lineages": [
        {
          "source": "WANTED",
          "m": -1,
          "n": 0,
          "signed": [
            -2450006750,
            -2449993250
          ],
          "order": 1
        },
        {
          "source": "WANTED",
          "m": 1,
          "n": 0,
          "signed": [
            2449993250,
            2450006750
          ],
          "order": 1
        }
      ]
    },
    {
      "frequency": 2550000000,
      "support": [
        2549986500,
        2550013500
      ],
      "lineages": [
        {
          "source": "WANTED",
          "m": -2,
          "n": 1,
          "signed": [
            -2550013500,
            -2549986500
          ],
          "order": 3
        },
        {
          "source": "WANTED",
          "m": 2,
          "n": -1,
          "signed": [
            2549986500,
            2550013500
          ],
          "order": 3
        }
      ]
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            -50000000,
            -50000000
          ],
          "order": 2
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": -1,
          "signed": [
            50000000,
            50000000
          ],
          "order": 2
        }
      ]
    },
    {
      "frequency": 100000000,
      "support": [
        100000000,
        100000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -2,
          "n": 2,
          "signed": [
            -100000000,
            -100000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 2,
          "n": -2,
          "signed": [
            100000000,
            100000000
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 2300000000,
      "support": [
        2300000000,
        2300000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -1,
          "n": 2,
          "signed": [
            2300000000,
            2300000000
          ],
          "order": 3
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": -2,
          "signed": [
            -2300000000,
            -2300000000
          ],
          "order": 3
        }
      ]
    },
    {
      "frequency": 2400000000,
      "support": [
        2400000000,
        2400000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -1,
          "n": 0,
          "signed": [
            -2400000000,
            -2400000000
          ],
          "order": 1
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": 0,
          "signed": [
            2400000000,
            2400000000
          ],
          "order": 1
        }
      ]
    },
    {
      "frequency": 2450000000,
      "support": [
        2450000000,
        2450000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -2,
          "n": 1,
          "signed": [
            -2450000000,
            -2450000000
          ],
          "order": 3
        },
        {
          "source": "B-HALF",
          "m": 2,
          "n": -1,
          "signed": [
            2450000000,
            2450000000
          ],
          "order": 3
        }
      ]
    },
    {
      "frequency": 4650000000,
      "support": [
        4650000000,
        4650000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -1,
          "n": 3,
          "signed": [
            4650000000,
            4650000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": -3,
          "signed": [
            -4650000000,
            -4650000000
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 4750000000,
      "support": [
        4750000000,
        4750000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -1,
          "n": -1,
          "signed": [
            -4750000000,
            -4750000000
          ],
          "order": 2
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": 1,
          "signed": [
            4750000000,
            4750000000
          ],
          "order": 2
        }
      ]
    },
    {
      "frequency": 4800000000,
      "support": [
        4800000000,
        4800000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -2,
          "n": 0,
          "signed": [
            -4800000000,
            -4800000000
          ],
          "order": 2
        },
        {
          "source": "B-HALF",
          "m": 2,
          "n": 0,
          "signed": [
            4800000000,
            4800000000
          ],
          "order": 2
        }
      ]
    },
    {
      "frequency": 4850000000,
      "support": [
        4850000000,
        4850000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -3,
          "n": 1,
          "signed": [
            -4850000000,
            -4850000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 3,
          "n": -1,
          "signed": [
            4850000000,
            4850000000
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 7100000000,
      "support": [
        7100000000,
        7100000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -1,
          "n": -2,
          "signed": [
            -7100000000,
            -7100000000
          ],
          "order": 3
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": 2,
          "signed": [
            7100000000,
            7100000000
          ],
          "order": 3
        }
      ]
    },
    {
      "frequency": 7150000000,
      "support": [
        7150000000,
        7150000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -2,
          "n": -1,
          "signed": [
            -7150000000,
            -7150000000
          ],
          "order": 3
        },
        {
          "source": "B-HALF",
          "m": 2,
          "n": 1,
          "signed": [
            7150000000,
            7150000000
          ],
          "order": 3
        }
      ]
    },
    {
      "frequency": 7200000000,
      "support": [
        7200000000,
        7200000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -3,
          "n": 0,
          "signed": [
            -7200000000,
            -7200000000
          ],
          "order": 3
        },
        {
          "source": "B-HALF",
          "m": 3,
          "n": 0,
          "signed": [
            7200000000,
            7200000000
          ],
          "order": 3
        }
      ]
    },
    {
      "frequency": 9450000000,
      "support": [
        9450000000,
        9450000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -1,
          "n": -3,
          "signed": [
            -9450000000,
            -9450000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 1,
          "n": 3,
          "signed": [
            9450000000,
            9450000000
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 9500000000,
      "support": [
        9500000000,
        9500000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -2,
          "n": -2,
          "signed": [
            -9500000000,
            -9500000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 2,
          "n": 2,
          "signed": [
            9500000000,
            9500000000
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 9550000000,
      "support": [
        9550000000,
        9550000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -3,
          "n": -1,
          "signed": [
            -9550000000,
            -9550000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 3,
          "n": 1,
          "signed": [
            9550000000,
            9550000000
          ],
          "order": 4
        }
      ]
    },
    {
      "frequency": 9600000000,
      "support": [
        9600000000,
        9600000000
      ],
      "lineages": [
        {
          "source": "B-HALF",
          "m": -4,
          "n": 0,
          "signed": [
            -9600000000,
            -9600000000
          ],
          "order": 4
        },
        {
          "source": "B-HALF",
          "m": 4,
          "n": 0,
          "signed": [
            9600000000,
            9600000000
          ],
          "order": 4
        }
      ]
    }
  ],
  "limitations": [
    "Filter stop exclusion is conditional and unverified.",
    "No nonlinear amplitude, ADC overload, input bandwidth, PLL purity, power/cost or compliance prediction.",
    "D3 filtering/decimation is an ideal boundary; correct acquisition upstream.",
    "Cross-source products, phase-noise skirts, higher orders and unlisted emissions are omitted."
  ]
}

Interactive editing needs JavaScript. All five candidate comparisons, canonical IF100/ZIF graphs, interference paths, independent arithmetic, model answers and reviewed plans are provided in the lesson below.

Printable synthesis · two reviewed plans

Plan A · reject RF 80 unprotected

Mode: nominal, selected 13.5 kHz channel at 2450 MHz within 2400–2500 MHz tuning coverage. R2→R1 real RF pass 2400–2500 MHz; no analog mixer; A1 real RF ADC input, A0 one 80 MS/s stream. WANTED signed alias −30 MHz has positive 30 MHz support [29.99325, 30.00675] MHz and slope −1. B-ALIAS 2430 MHz, −25 dBm R2 metadata, maps to +30 MHz with slope +1 and lies strictly inside it. Reject—geometry. No digital 20/30 MHz selection can separate the superposed origins. Requested simultaneous 100 MHz capture also exceeds the 40 MHz real interval by 60 MHz.

Specific reconsideration boundary: place a tracking RF selection before A1 with nominal pass 2449.980–2450.020 MHz and transitions 2449.900–2449.980 /2450.020–2450.100 MHz, rejecting 2430 MHz and every other folded origin. These regions are Illustrative; required attenuation, order, loss and tuning accuracy remain unknown. At 2450 MHz the CW at 2430 MHz is 19.99325 MHz from the nearest wanted edge. This is available spectral separation, not verified attenuation. Track the passband with carrier and widen/switch it for acquisition.

Remaining boundary contract: real RF input at A1 needs bandwidth, full-scale, SFDR, jitter and permitted sample-clock evidence at 2.45 GHz; no converter is selected. Conjugate the selected positive 30 MHz envelope after digital translation to preserve I+jQ. D3 remains 80 kcomplex-sample/s after upstream frequency acquisition/correction. No gain, spur amplitude, cost or power is approved.

Committed geometry · RF80 unprotectedreject—geometry

Wanted A0: signed -30 MHz → selected 30 MHz; local slope -1. Required LO range [2400, 2500] MHz (no analog LO in this topology).

Frequency-error expansion ±0 Hz. Programmed LO error 0 Hz. H=4; 0 signed RF/LO coefficient lineages evaluated. Higher orders, cross-source products and unlisted emissions omitted.

Conditional comparison assumes declared stop regions reject whole source supports; attenuation remains unverified. Geometry clears never establishes spur margin or receiver performance.

RF80 unprotected wanted graph; sum branches and filter requirements included · Derived / Illustrative · MHz, not level spectra
Source / edge	Support / center / orientation	Representation / zone / selection	Level evidence / lineage
WANTED · R2 → R2	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. no filter yet.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1)
WANTED · R2 → R1	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes
WANTED · R1 → A1	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes
WANTED · A1 → A0	[29.99325, 30.00675] MHz Center 30 MHz Slope -1 Signed precursor: [-30.00675, -29.99325] MHz	real; nonnegative real alias; conjugate negative support implied. zone 62. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → signed wrap, then positive fold at 80 MS/s
WANTED · A0 → D3	[-0.00675, 0.00675] MHz Center 0 MHz Slope +1 Signed precursor: [-0.00675, 0.00675] MHz	complex; signed offset from selected digital channel. ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required. Ideal downstream channel selection: retained; overlapping origins cannot be removed.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → signed wrap, then positive fold at 80 MS/s → select 30 MHz; digital translate; conjugate to portfolio convention

Plan B · conditional IF100 low-side

Mode: nominal selected channel. LO tunes 2300–2400 MHz for RF 2400–2500 MHz and is 2350 MHz at the default carrier. R2/R1 are real absolute RF; RF-PRE provides the image-selection boundary. M1 retains wanted signed +100 MHz and its 4.800 GHz sum branch; the IF filter conditionally excludes the sum. A1F’s pass 99.980–100.020 MHz contains wanted 99.99325–100.00675 MHz; transitions extend to 99.900/100.100 MHz. A1 is real 100 MHz IF; A0 at 80 MS/s selects positive 20 MHz, slope +1. Digital translation and ideal channel filtering/decimation produce D3’s signed ±6.75 kHz support at 80 kcomplex-sample/s.

Conditional choice: proceed to gain/noise and blocker allocation because nominal desired support fits and the known RF image has an earlier selection boundary. B-IMAGE 2250 MHz requires RF-PRE attenuation. B-ALIAS 2430 MHz’s 80 MHz IF fundamental requires IF100 attenuation. B-HALF 2400 MHz can produce order 4 IF 100 MHz and sampled 20 MHz; CLK-IF 100 MHz at A1 reaches the same channel after bypassing the filters. Both remain inspect—candidate collision pending amplitude/susceptibility evidence. The low-side plan is not a verified receiver.

Acquisition exception: one/two-radio tolerance expands support to ±55.75/±104.75 kHz. The pinned ±20 kHz IF pass region cannot support that acquisition strategy unchanged. Assign a wider acquisition filter or upstream correction, then reduce to the nominal channel. Specify filter and synthesizer settling before accepting usable-data timing.

Committed geometry · IF100 low-sideinspect—candidate collision

Wanted A0: signed 20 MHz → selected 20 MHz; local slope 1. Required LO range [2300, 2400] MHz.

Frequency-error expansion ±0 Hz. Programmed LO error 0 Hz. H=4; 128 signed RF/LO coefficient lineages evaluated. Higher orders, cross-source products and unlisted emissions omitted.

Conditional comparison assumes declared stop regions reject whole source supports; attenuation remains unverified. Geometry clears never establishes spur margin or receiver performance.

IF100 low-side wanted graph; sum branches and filter requirements included · Derived / Illustrative · MHz, not level spectra
Source / edge	Support / center / orientation	Representation / zone / selection	Level evidence / lineage
WANTED · R2 → R2	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. no filter yet.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1)
WANTED · R2 → R1	[2449.99325, 2450.00675] MHz Center 2450 MHz Slope +1 Signed precursor: [2449.99325, 2450.00675] MHz	real; absolute RF. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes
WANTED · R1 → M1	[99.99325, 100.00675] MHz Center 100 MHz Slope +1 Signed precursor: [99.99325, 100.00675] MHz	real; nonnegative real IF; conjugate negative support implied. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch
WANTED · R1 → M1	[4799.99325, 4800.00675] MHz Center 4800 MHz Slope +1 Signed precursor: [4799.99325, 4800.00675] MHz	real; nonnegative real IF; conjugate negative support implied. continuous. RF-PRE: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed [4799.99325, 4800.00675] MHz → positive branch
WANTED · M1 → A1F	[99.99325, 100.00675] MHz Center 100 MHz Slope +1 Signed precursor: [99.99325, 100.00675] MHz	real; nonnegative real IF; conjugate negative support implied. continuous. IF100: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes
WANTED · M1 → A1F	[4799.99325, 4800.00675] MHz Center 4800 MHz Slope +1 Signed precursor: [4799.99325, 4800.00675] MHz	real; nonnegative real IF; conjugate negative support implied. continuous. IF100: requires stopband attenuation; conditionally excluded, attenuation unverified. Conditionally excluded; attenuation unverified.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → sum LO 2350 MHz; signed [4799.99325, 4800.00675] MHz → positive branch → IF100 requires stopband attenuation
WANTED · A1F → A1	[99.99325, 100.00675] MHz Center 100 MHz Slope +1 Signed precursor: [99.99325, 100.00675] MHz	real; nonnegative real IF; conjugate negative support implied. continuous. IF100: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes
WANTED · A1 → A0	[19.99325, 20.00675] MHz Center 20 MHz Slope +1 Signed precursor: [19.99325, 20.00675] MHz	real; nonnegative real alias; conjugate negative support implied. zone 3. IF100: passes.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes → signed wrap, then positive fold at 80 MS/s
WANTED · A0 → D3	[-0.00675, 0.00675] MHz Center 0 MHz Slope +1 Signed precursor: [-0.00675, 0.00675] MHz	complex; signed offset from selected digital channel. ideal downstream 80 kcomplex-sample/s boundary; upstream acquisition correction required. Ideal downstream channel selection: retained; overlapping origins cannot be removed.	Unknown amplitude. WANTED @ R2 (p05-m02-frequency-graph-v1) → RF-PRE passes → difference LO 2350 MHz; signed [99.99325, 100.00675] MHz → positive branch → IF100 passes → signed wrap, then positive fold at 80 MS/s → select 20 MHz; digital translate

Frequency-plan handoff · request evidence, do not fill unknowns with typical values
Owner / destination	Record to preserve	Next data-sheet or measurement request
Receiver systems · 05.3	R2→A1 gain/loss, wanted pass definition and selected mode; all gains unknown	Front-end/filter/LNA/mixer loss and NF, bandwidth/ENBW, temperature and uncertainty; reconcile a weak-signal budget.
Coexistence/linearity · 05.4	B-IMAGE/B-ALIAS/B-HALF input levels, support, entry and nonlinear order; coupled CLK-IF amplitude unknown	Actual stopband attenuation, compression and relevant spur conversion under the stated source/LO conditions; coupled clock spectrum at A1.
RF synthesis / 04.7 and 05.6	LO range 2300–2400 MHz, programmed/ppm errors, clock 80 MS/s and D3’s separate 80 ksample/s	Tuning resolution and usable settling, phase-noise/spur spectra, acquisition/calibration limits; converter rate/clock-drive range and jitter.
Converter/driver · 05.6	A1 real 100 MHz input, A0 real 80 MS/s, positive 20 MHz digital selection	Input-bandwidth and SFDR/SNR curves at 100 MHz under actual driver/clock/full-scale conditions; data-rate and power allocations.
Validation · Path 08	Every conditional filter and amplitude claim; exact reference planes and modes	Plan discriminating measurements with calibration/uncertainty. Detailed instrument procedures remain in Path 08.

For your synthesis, deliver both decisions with the complete graph, tuning/clock ranges, filter regions, signed orientation, source lineage and unresolved amplitudes. Explain what evidence could reverse Plan B. Named channel plans belong to Path 07, antenna/channel behavior to Path 06, and conformity/physical implementation to Paths 09–10.

Ungraded review

Check your understanding

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

01Derive both IF100 images and the +1 MHz marker orientation.
Model answer
Low-side LO 2350: wanted 2450→+100, image 2250→−100; real branch 100, marker 2451→101 MHz. High-side LO 2550: wanted 2450→−100, image 2650→+100; real branch 100, marker 2451→99 MHz. Complex translation slope is +1 in both; positive real-branch selection causes high-side inversion.
02Why does RF 80 fail despite fs being far above twice 13.5 kHz?
Model answer
2450→signed −30 / positive 30 and 2430→signed +30 / positive 30 MHz. The passed CW is strictly inside wanted support. Digital filtering cannot distinguish the origins. Full 100 MHz simultaneous capture also exceeds 40 MHz real represented width.
03Trace the half-IF and clock collision, including the filtering location.
Model answer
B-HALF 2400 at R2 →(m=2,n=−2), H=4 →100 MHz M1 →+20 MHz A0 →wanted. CLK-IF 100 enters at A1 after RF/IF filters →+20 MHz A0. Both amplitudes remain unknown; H=3 omits the half-IF product. Fix the source-specific path.
04What happens when support crosses a Nyquist boundary?
Model answer
At 80 MS/s, real [39,41] MHz splits into [39,40] with slopes +1 and −1 and self-overlaps. Complex [39,41] wraps into [39,40) plus [−40,−39], preserving signed slope +1. Exact 40 maps to −40; do not connect only the outer endpoints.
05Can two ±20 ppm radios acquire directly through the nominal IF100 filter and 80 ksample/s D3?
Model answer
Worst relative offset is ±98 kHz; include ±6.75 kHz wanted support for ±104.75 kHz acquisition extent. This exceeds the ±20 kHz IF pass and ±40 kHz D3 interval. Acquire/correct upstream with suitable analog support before narrowing/decimation.
06Defend one architecture without claiming a hardware pass.
Model answer
IF100 low-side has contained nominal wanted support and a defined RF image-selection boundary, but needs verified image/IF attenuation, half-IF and clock amplitudes, gain/NF/headroom, converter 100 MHz input performance and acquisition handling. ZIF is another conditional one-channel choice if IQ/DC/flicker/calibration risks and acquisition processing are allocated.

Sources and model provenance

Access checked 7 September 2026. All diagrams, frequency values and filter regions are local Derived/Illustrative geometry from p05-m02-frequency-graph-v1. No Measured or Normative claim is made. Model/rules/serialization/display: p05-m02-frequency-graph-v1 / p05-m02-geometry-rules-v1 / p05-m02-plan-json-v1 / p05-m02-hz-display-v1. Integer-Hz input fixtures; half-width edges retain full precision; display to 1 Hz. Exact equality uses at most 1 Hz computational tolerance, never assumed filter rejection.

Texas Instruments, SBAA328, RF Sampling for Multi-band Radios, April 2019, §§2.1–2.4 and 5–6: architecture/impairment and converter-boundary context. The consulted report still carries the 2019 revision; its specific cellular-device comparisons are not imported as gateway guarantees.
Walt Kester, Analog Devices MT-002, Rev.A, October 2008, pp.4–10: Nyquist zones, undersampling and anti-alias selection. The local signed-wrap equation and split-interval arithmetic are independently derived under the portfolio convention.
TI ADC32RF45 data sheet, SBAS747C, May 2016, revised December 2016 (official currently served Rev.C). §§8.3.1–8.3.2: differential analog/clock interfaces, input bandwidth and clock-amplitude dependence; §9.1.3: input-frequency/jitter dependence. Figure 68 uses 1/2 GHz inputs and 3 GSPS. This device is not selected for the fictional 80 MS/s boundary; no typical numbers are copied into amplitude rows.
Analog Devices, Phase-Locked Loop Fundamentals, current unnumbered web edition; integer/fractional-N and spur discussion read. Frequency plans must retain PLL spur/settling evidence at the actual tuning conditions. RF Signal Chain Discourse Part 2: Essential Building Blocks, current unnumbered web edition, mixer/image-reject discussion: phase cancellation and practical implementation context.
MIT OpenCourseWare Unified Engineering Signals and Systems, Fall 2005–Spring 2006, sampling/modulation resource index and prescribed Oppenheim, Willsky and Nawab, Signals and Systems, second edition. Sampling convention cross-check and further study; the full textbook was not available for this review.
W.F.Egan, Practical RF System Design, Wiley–IEEE, 2003, Chapter 7 “Frequency Conversion”: publisher catalog/abstract context for architecture and frequency conversion. Full paywalled chapter not consulted; all numerical anchors here are independent local derivations, not attributed to an unseen chapter.
Repository portfolio conventions v1.0; source-backed 04.6 mixer and 04.7 LO lessons. This module deliberately uses total harmonic order H rather than 04.6’s maximum coefficient N, and a 13.5 kHz selected channel rather than its 100 MHz observation fixture. Source entry, pass/transition/stop regions and acquisition support are explicit local additions.

Receiver Architectures& Frequency Planning

Failure: a clean block diagram hides a collision

Architecture is a chain of spectral transformations

Direct conversion: integration with DC and I/Q costs

Low IF: move DC, inherit image rejection

High IF and superheterodyne: separation for more stages

RF sampling: alias zones do not remove the analog front end

Injection side and orientation at every plane

LO harmonics, clocks, digital emissions, and half-IF threats

Compare filters, tuning, settling, calibration, cost, and power

Create the gateway frequency plan

Plan A · reject RF 80 unprotected

Plan B · conditional IF100 low-side

Check your understanding

Sources and model provenance

Receiver Architectures
& Frequency Planning