RF Journey

01 / 10

Failure: when a 20 dB coupler lies

A gateway reports steady forward power while its antenna load changes. The amplifier drive has not moved. A nominal 20 dB coupler is being treated as a perfect observer, although its forward sample also contains a small contribution from the reflected wave.

This is the illustrative 2.450 GHz node/gateway from 04.1: Real Components, Models & Operating Regions. We will add a T/R switch, protection, a test pad, and an observation path. First, decide what the coupler reading actually means.

Illustrative port boundary diagram · forward sample 1 → 2. Solid arrows a: into the network; dashed arrows b: out. All boundaries are real 50 Ω at R1; no extra line length. Physical port numbers stay fixed.

Think about itWith +10.000 dBm incident at P1 and 20.000 dB coupling, what should a perfect forward sample read?

Answer

−10.000 dBm, or 0.100000 mW, at matched P3. Dividing that sample power by 0.01 indicates 10.000 mW at P1. This first check fixes incident power; the full ledger later fixes source available power, which is a different boundary condition.

\begin{aligned}|\Gamma| &= \frac{\mathrm{VSWR} - 1}{\mathrm{VSWR} + 1} = \frac{1}{11} \\ |\Gamma|^{2} &= 0.0082644628\end{aligned}

Derived, one load reflection at the named 50 Ω load plane; VSWR = 1.200.

The load reflects 0.826446% of the wave power arriving there and accepts 99.173554%, or −0.036041 dB relative to incident. That small reflected power has a 9.090909% wave amplitude. A directional sampler responds to amplitudes and phase before the detector squares them.

\frac{P_{\mathrm{ind}}}{P_{\mathrm{incident}}} = |1 + (\frac{1}{11})10^{-\frac{20}{20}}e^{j\psi}|^{2}

Derived local two-wave sanity model: through amplitude t = 1, directivity D = 20 dB. ψ is the reverse-leakage contribution phase relative to the forward sample.

Derived analytic sanity cases · +10 dBm fixed incident · t = 1 · matched observation
Relative phase ψ	Indication error	Meaning
0°	0.078606 dB	Reverse contamination adds coherently.
180°	-0.079324 dB	Reverse contamination subtracts coherently.
Ideal directivity	0.000000 dB	Reverse leakage amplitude is exactly zero.

Common misconceptionA coupled-port reading equals forward power regardless of mismatch and directivity.

The detector measures the squared magnitude of the total sample wave. It cannot distinguish two coherent contributions simply because one was intended and one was leakage.

The sign changes when reflection phase rotates. A scalar calibration at one load phase does not remove that dependence. Before improving the detector, we need a network model that keeps every reflected wave.

02 / 10

Passive multiports and conservation constraints

Draw the component boundary first. At every physical port, a travels into the network and b travels out. All examples use real Zref = 50 Ω, the e^+jωt convention, and R1 component-terminal reference planes. There are no undisclosed transmission-line lengths.

\begin{aligned}a &= \frac{V + Z_{\mathrm{ref}} I}{2\sqrt{Z_{\mathrm{ref}}}} \\ b &= \frac{V - Z_{\mathrm{ref}} I}{2\sqrt{Z_{\mathrm{ref}}}} \\ b_{i} &= \sum _{j} S_{\mathrm{ij}}a_{j}\end{aligned}

Definition: normalized power waves a,b in √W; V and I are RMS phasors, with I into the network. These simple formulas require real Zref.

Sᵢⱼ describes outgoing port i for excitation at port j, with the other incident waves zero. It is a dimensionless complex ratio, including phase. With real equal normalization, net power entering port i is |aᵢ|² − |bᵢ|² watts. For a load outside the network, that sign reverses: absorbed power is |bᵢ|² − |aᵢ|².

Definitions · separate network properties at one declared condition
Property	Test	What it does not establish
Matched port i	Sii = 0 with other ports matched	A mismatched remote termination can still reflect back to i.
Reciprocal	S = Sᵀ at compatible normalization	Equal reflection at different ports, or geometric symmetry.
Symmetric under a named exchange	S = P S Pᵀ; disclose port permutation P	Symmetry under every possible port exchange.
Lossless	SᴴS = I	Useful isolation, or zero power in external loads.
Passive	SᴴS ⪯ I; equivalently σmax ≤ 1	Linearity, survivability, or passivity outside this condition.
Isolated path j → i	Small \|Sij\| under the declared terminations	No route through other ports, control feedthrough, or immunity to high drive.

Think about itEvery entry of a 2 × 2 matrix is 0.8. Is that enough to call the matrix passive?

Answer

No. Equal in-phase inputs produce an amplitude gain of 1.6 in the common mode; σmax is 1.6. Each individual entry can be below one while a coherent combination creates more outgoing than incident power.

Common misconceptionChecking every |Sij| below one proves matrix passivity.

Passivity constrains every simultaneous excitation. Test the largest singular value, or the full Hermitian power inequality, rather than isolated entries.

\begin{aligned}a&=a_G+\Gamma b\\(I-\Gamma S)a&=a_G\\P_{\mathrm{avs}}&=\frac{|a_G|^2}{1-|\Gamma_{\mathrm S}|^2}\end{aligned}

Derived steady-state boundary solve; Γ is a diagonal matrix of source/load reflections, not an S-parameter matrix.

At an undriven termination aG = 0. Match is Γ = 0, open is +1, and short is −1 exactly. At a source, aG is the launched source wave before feedback; the last equation assumes a passive source reflection with |ΓS| < 1. The drive phase reference is the first driven port. Moving any plane requires the corresponding propagation phase, including the reflection round trip.

Model acceptance uses σmax ≤ 1 + 10⁻¹⁰. The full complex feedback condition κ₂(I − ΓS) is inspected above 10⁹ and rejected at or above 10¹². Conservation must hold within max(10⁻¹² W, 10⁻⁹ × total net source delivery). Rejected solves suppress waves; the model never rescales a matrix to make it pass.

Go deeperWhy the power inequality is the right test

The network dissipates aᴴa − bᴴb = aᴴ(I − SᴴS)a. This quadratic form must be nonnegative for every vector a. A lossless network makes it zero for every vector; a Wilkinson may make it zero for the common mode and positive for the differential mode. The test says nothing about an unmodeled nonlinear operating region.

Keep the Path 03 S-parameter conventions with the component record. We can now compare passive blocks without changing what a watt or a port means.

03 / 10

Attenuators: match traded for irreversible loss

A test receiver sees a poorly controlled load. A resistive pad can reduce the reflection returning to the preceding block, but it uses signal power to do so. Its purpose is a trade among match, receiver headroom, sensitivity, and resistor heating.

Informative resistive topology orientation · real resistors at the design condition
Topology	Physical arrangement	Orientation decision
Symmetric T	Two equal series arms; center shunt to return	Interchangeable input/output for equal impedances; unequal arm dissipation is still possible under mismatch.
Symmetric π	Shunt at each end; a series resistor between	Same matched attenuation can have different resistor stresses and parasitics from a T.
Asymmetric T or π	Unequal arms, possibly unequal design impedances	Preserve input/output impedance labels and ratings; reciprocity does not make the two reflections equal.

\begin{aligned}S&=\begin{bmatrix}0&g\\g&0\end{bmatrix}\\g&=10^{-A/20},\quad L_A=10^{A/10}\\\Gamma_{\mathrm{in}}&=g^2\Gamma_{\mathrm L}\end{aligned}

Derived symmetric matched pad at one frequency. A is positive attenuation in dB; g is wave transmission, LA is available power loss.

A 3.000 dB pad between matched ports transmits 5.011872 mW from 10.000000 mW and dissipates 4.988128 mW. It is slightly different from an exact half-power split, whose ratio is 3.010300 dB. With VSWR 1.2 at the load, the same pad reduces the returned reflection amplitude from 0.090909091 to 0.045562476 at its input plane.

Think about itIf a pad improves return loss by 6 dB, has it recovered any signal energy?

Answer

No. A matched 3 dB pad attenuates a reflection on both the outward and return trip. The improved input match accompanies useful signal loss and heat. Its full source/load result must be compared at the same planes and source available power.

\begin{aligned}F &= 1 + \frac{(L_{\mathrm{A}} - 1)T_{\mathrm{p}}}{T_{0}} \\ T_{\mathrm{p}} &= T_{0} = 290 K \Rightarrow F = L_{\mathrm{A}}\qquad \mathrm{NF} = A \mathrm{dB}\end{aligned}

Derived available-noise relation for a passive matched attenuator in thermal equilibrium. Tp is pad temperature and T0 is the noise-factor reference temperature.

The ledger exposes the numeric identity only in its separate matched 290 K noise subfixture. The 25 °C matrix metadata is not silently substituted for 290 K. Under mismatch, a scalar insertion loss is insufficient for a general noise calculation. A pad ahead of the first receiver gain also spends sensitivity; later receiver allocation belongs to Path 05.

Common misconceptionAdding a pad is free because it improves match.

Loss reduces both wanted signal and large unwanted inputs. That can improve following-stage headroom, but resistor voltage, pulse energy, average heating, and the pad’s own nonlinear behavior still need evidence.

The VAT-3+ example [3] supplies a real connectorized 3 dB reference. Its headline power rating does not distribute power among individual resistors or qualify an arbitrary pulse. Choose the pad after recording the load-power cost, then check whether division is actually required.

Go deeperA 50 Ω resistive design check

For K = 10^(A/20), a symmetric T uses series arms Z0(K − 1)/(K + 1) and a shunt arm 2Z0K/(K² − 1). The π dual uses shunt arms Z0(K + 1)/(K − 1) and series arm Z0(K² − 1)/(2K). These are ideal resistive design-frequency equations. The zero-loss limit contains an open shunt and a zero series path; do not evaluate it as a finite resistor network by dividing by zero.

04 / 10

Splitters and combiners need phase and termination discipline

A two-way divider makes two copies available at different ports. Its useful behavior depends on what returns from those ports. An ideal-frequency Wilkinson separates common and differential excitation: common-mode power reaches the common port, while differential power reaches an internal resistor.

S=\begin{bmatrix}0&-j/\sqrt2&-j/\sqrt2\\-j/\sqrt2&0&0\\-j/\sqrt2&0&0\end{bmatrix}

Illustrative p04-m02-wilkinson-v1, 2.450 GHz, real 50 Ω, P1 common; P2/P3 branches. Ideal zero excess-loss case.

With only P1 driven and both branches matched, b2 = b3 = −ja1/√2. Each branch gets half the power, not half the voltage-wave amplitude. At +10 dBm total available from a matched source, each load receives 5.000000 mW; the ideal resistor dissipates zero.

Common misconceptionA splitter divides voltage and power in the same way under any termination.

The √2 amplitude ratio implies a factor of two in power only for the stated normalization and matched boundaries. Reflections feed back into the complete multiport solution.

Think about itTwo equal sources provide 5 mW each at P2 and P3. Where does their 10 mW go at 0° and 180° relative phase?

Answer

At 0°, 10 mW reaches matched P1. At 180°, P1 receives exactly zero and the ideal internal isolation resistor dissipates 10 mW. Total input power stays fixed between the comparisons.

\begin{aligned}P_{\mathrm{common}} &= \frac{|a_{2} + a_{3}|^{2}}{2} \\ P_{\mathrm{resistor}} &= \frac{|a_{2} - a_{3}|^{2}}{2} \\ \eta &= \frac{1 + r^{2} + 2r \cos \phi}{[2(1 + r^{2})]}\end{aligned}

Derived matched ideal combine case. a2 and a3 are complex incident waves, not dBm values.

Here r = |a3|/|a2| and φ is source 3 phase relative to source 2 at their branch planes. For equal amplitudes η = cos²(φ/2): 90° sends half to the load and half to the resistor. At 180°, unequal inputs leave a residual common output. Excess loss in the teaching fixture further attenuates its common mode; differential resistor loss remains a separate ledger entry.

Common misconceptionTwo equal signals always combine to +3 dB.

Equal coherent signals can add or cancel. The in-phase result is 3.010300 dB above either individual 5 mW source, and 0 dB above their combined 10 mW input. State the comparison baseline.

Common misconceptionUnused ports do not matter.

An open or short branch returns its wave with a specific phase. The reflected energy can reach the source, other loads, or the resistor. The termination’s power rating is part of the network.

The ZFSC-2-2500+ [4] is a real splitter/combiner comparison, not a claim that its internal construction equals this Wilkinson. Record its vendor SUM-port numbering separately. Choose a divider only when two simultaneous paths justify its power allocation.

05 / 10

Directional couplers: coupling, isolation, and directivity

Forward sampling keeps most power on a through path while observing a small fraction. For the physical orientation P1 input → P2 through, P3 is forward-coupled and P4 is isolated. Reverse excitation from P2 couples to P4 and isolates P3. The device has not become nonreciprocal: S31 = S13 can hold while S31 and S41 differ.

\begin{aligned}C_{\mathrm{forward}} &= -20 \log _{10}|S_{31}| \\ I_{\mathrm{forward}} &= -20 \log _{10}|S_{41}| \\ D_{\mathrm{forward}} &= I_{\mathrm{forward}} - C_{\mathrm{forward}} \\ &C_{\mathrm{reverse}} \mathrm{uses} S_{42}\qquad I_{\mathrm{reverse}} \mathrm{uses} S_{32}\end{aligned}

Definitions with unused ports matched, identical frequency, real Zref, drive, temperature and R1 planes.

Common misconceptionIsolation is merely negative gain.

The logarithm alone does not identify the physical path, state, or termination. A leakage specification needs all three. It cannot substitute for a complete power-routing or protection claim.

The frozen coupler uses t = 10^(−0.5/20) = 0.9440608762859234, k = 0.1, and l = 0.01. Its intended coupling and reverse leakage both have −j phase. Therefore the composite phase ψ equals load-reflection phase in this fixture with matched auxiliary ports and no added line.

S=\begin{bmatrix}0&t&-jk&-jl\\t&0&-jl&-jk\\-jk&-jl&0&t\\-jl&-jk&t&0\end{bmatrix}

Exact illustrative matrix definition · p04-m02-coupler-v1 · 2.450 GHz · 25 °C · matched native ports · no bias; linear mathematical drive scale.

With both auxiliaries matched, a2 = ΓL t a1 and b3 = −jk a1 − jl a2. The indicated power is |b3|²/|S31|²; truth is |a1|². Their ratio is |1 + (l/k)tΓL|². This retains the fixture’s actual through attenuation.

Derived phase anchors · one-pass sanity model versus full matched-auxiliary fixture
Case	ψ = 0° error · dB	ψ = 180° error · dB
t = 1 analytic sanity	0.078606	-0.079324
Full fixture t = 10^(−0.5/20)	0.074227	-0.074867

The full default uses +10 dBm available source power and ΓS = ΓL = +1/11. Feedback makes actual P1 incident power 10.065082 mW. Its ideal sample would be 0.100651 mW; the finite sample is 0.102386 mW and indicates 10.238588 mW. Source delivery is 9.999008 mW. None of those quantities should be relabeled as another.

A single-channel scalar correction can remove a fixed scale error at one condition. It cannot separate an unknown changing reverse phasor. A calibrated vector reflectometer with separate forward and reverse observations can estimate the waves, subject to residual directivity, match, drift, and plane errors. See the manufacturer discussion [5]; calibration procedures remain in Path 08.

Go deeperDefault solution without a general matrix solver

For matched P3/P4, let d = 1 − ΓSΓLt². Then a1 = aG/d, a2 = ΓLt a1, b1 = t a2, b2 = t a1, b3 = −j(k a1 + l a2), and b4 = −j(l a1 + k a2). The independent checks use these complex closed forms and separately sum all outgoing powers. The two singular-value branches are √[t² + (k + l)²] and √[t² + (k − l)²], each repeated twice.

Written default decision: accept this local static observation model with matched P3/P4 and the declared R1 planes. σmax = 0.950447756657 is passive; the +0.074227 dB indication error is within this lesson’s ±0.25 dB teaching criterion. That criterion is not a product accuracy or protection specification. Hardware selection remains conditional on the evidence pack.

One decision model · Class 1

Passive Multiport Power Ledger

Change one condition, predict where the wave goes, then apply. Every port stays in the power account.

The canonical result, diagrams, equations and tables below are available without JavaScript. Changing conditions and copying with the button require JavaScript; the copyable text record remains available.

Predict the ideal −10 dBm coupled sanity case.
Apply load phase 180°; compare its sign with 0°.
Open or short P4. Then open P3 and read the rejected measurement claim.
Select Wilkinson, combine, matched sources/load; compare 0° and 180°.
Select the pad and compare its no-pad record. Match both ports to reveal the separate 290 K noise row.

Topology and operating state

BlockChanging block restores its named defaults. Apply to commit the result.

Operating modePhysical port numbers and matrix indexing stay fixed; source/load and observation roles remap.

Through insertion loss · dBThis is a positive attenuation magnitude. Range 0 to 6; step 0.1.

Coupling · dBCoupling is derived with the active orientation's Sij indices. Range 3 to 40; step 0.1.

Directivity modelIdeal is an exact limit, not an 80 dB approximation.

Finite directivity · dBIsolation = coupling + directivity in this orientation. Range 10 to 80; step 0.1.

Sources, load and phase at R1

Source available power · dBmAvailable source power; not necessarily incident or net delivered. Range -30 to 40; step 0.1.

Source VSWRApplies to source port 1. Range 1 to 5; step 0.01.

Source reflection phase · °ΓS at the driven plane; no added propagation. Stored phase is retained at match. Range -180 to 180; step 1.

Load VSWRAt intended load P2. Range 1 to 5; step 0.01.

Load reflection phase · °ΓL at the load plane; ψ equals this phase for the matched-auxiliary coupler fixture. Range -180 to 180; step 1.

Every auxiliary boundary

P3 · Forward sample termination

P3 termination stateIndependent boundary at physical P3. An observation port must be matched for the coupler estimate.

P4 · Reverse sample termination

P4 termination stateIndependent boundary at physical P4. An observation port must be matched for the coupler estimate.

Displayed result: committed Directional coupler.

accept—forward sample 1 → 2; stated terminations and phase pass local matrix/conservation rules. Matched observation supports the bounded indication estimate.

External rating, compression, thermal, calibration and measurement evidence remain required. This matrix does not predict hot switching, protection, recovery, harmonics, PIM or broadband behavior.

Canonical conventions and committed input record
Condition	Value
Model / fixture	p04-m02-multiport-ledger-v1 · p04-m02-coupler-v1 · p04-m02-fixtures/1.0.0
Evidence / domain	Illustrative / Simulated · Linear, single-frequency, settled state. Drive is a mathematical scale, not a component rating.
Frequency / temperature	2.450 GHz only · 25 °C (matrix)
Normalization and planes	50 Ω real, all ports; R1 component-terminal planes P1…Pn; no added propagation
Waves and indexing	e^(+jωt); b = Sa; Sij is outgoing port i / incident port j; a,b in √W
Topology / settled state	Directional coupler · forward sample 1 → 2
Bias / control	No bias; passive linear teaching fixture.
Source available / loss	10.0 dBm total; 0.5 dB path attenuation
Source / load Γ	VSWR 1.2 ∠0° / 1.2 ∠0° at their physical ports; phase N/A for VSWR = 1
Coupler condition	20 dB coupling; 20 dB directivity
Relative branch drive	N/A
SPDT isolation / use	N/A
Display / export	Display: waves 9 decimals √W; powers 6 decimals mW; dB 6 decimals. Export: full binary64 precision; no rescaling.

Illustrative complex S · p04-m02-coupler-v1 · row i outgoing / column j incident
Sij	a1	a2	a3	a4
b1	0.0000000000 + j0.0000000000	0.9440608763 + j0.0000000000	0.0000000000 − j0.1000000000	0.0000000000 − j0.0100000000
b2	0.9440608763 + j0.0000000000	0.0000000000 + j0.0000000000	0.0000000000 − j0.0100000000	0.0000000000 − j0.1000000000
b3	0.0000000000 − j0.1000000000	0.0000000000 − j0.0100000000	0.0000000000 + j0.0000000000	0.9440608763 + j0.0000000000
b4	0.0000000000 − j0.0100000000	0.0000000000 − j0.1000000000	0.9440608763 + j0.0000000000	0.0000000000 + j0.0000000000

Matrix properties · pointwise, with disclosed residuals
Property	Result / rule
Passivity	Pass: σmax = 0.950447756657; σmax − 1 = -4.9552e-2; ≤ 1e−10
Reciprocity	Pass: max\|Sij − Sji\| = 0.0000e+0; tolerance 1e−10
Port-exchange symmetry	Pass: permutation [2, 1, 4, 3]; max\|S − PSPᵀ\| = 0.0000e+0; tolerance 1e−10
Losslessness	Fail: max element \|SᴴS − I\| = 9.8649e-2; tolerance 1e−10
Feedback condition	κ₂(I − ΓS) = 1.188343854; inspect > 1e9; reject ≥ 1e12

Boundary and source records · Γ at each named R1 port
Port	Termination	Γ	aG · √W	Available · mW
P1	source ΓS; VSWR 1.2; 0°	0.090909091 + j0.000000000	0.099585920 + j0.000000000	10.000000
P2	load ΓL; VSWR 1.2; 0°	0.090909091 + j0.000000000	0.000000000 + j0.000000000	N/A
P3	matched; Γ at P3	0.000000000 + j0.000000000	0.000000000 + j0.000000000	N/A
P4	matched; Γ at P4	0.000000000 + j0.000000000	0.000000000 + j0.000000000	N/A

Simulated complete port ledger · waves √W; powers mW; positive net is into network
Port	Role	a · √W	b · √W	\|a\|² · mW	\|b\|² · mW	Net · mW
P1 · Input end	Driven source	0.100324884 + j0.000000000	0.008128604 + j0.000000000	10.065082	0.066074	9.999008
P2 · Through end	Intended load	0.008610254 + j0.000000000	0.094712797 + j0.000000000	0.074136	8.970514	-8.896378
P3 · Forward sample	Auxiliary termination	0.000000000 + j0.000000000	0.000000000 − j0.010118591	0.000000	0.102386	-0.102386
P4 · Reverse sample	Auxiliary termination	0.000000000 + j0.000000000	0.000000000 − j0.001864274	0.000000	0.003476	-0.003476

At a source, |a|² is incident power, |b|² returns toward the source, and net is delivered by that source. At a load, |b|² arrives, |a|² is reflected, and −net is accepted by the termination. Network loss is recorded separately.

Conservation and topology result · full precision before rounding
Quantity	Value
Net source delivery	9.999008 mW
External termination absorption	9.002239 mW
Internal network dissipation	0.996769 mW
Conservation residual / tolerance	6.5052e-19 W / 9.9990e-12 W
Auxiliary change from matched case	N/A · no changed supported auxiliary decision plane
Available noise factor	N/A: numeric noise relation requires the matched passive pad subfixture at Tp = T0 = 290 K.

Coupler observation · C: S31; I: S41; through: S21
Quantity / plane	Value
Coupling / isolation / directivity	20.000000 / 40.000000 / 20.000000 dB
True incident at driven port	10.065082 mW
Ideal coupling of that same incident wave	0.100651 mW
Finite coupled observation	0.102386 mW
Nominally calibrated indicated power	10.238588 mW
Indication error versus incident truth	0.074227 dB; local teaching limit ±0.25 dB

Derived phase sweep · selected 0° · all other committed controls fixed; auxiliary ports matched. No measured uncertainty is implied.

Phase sweep: selected and worst cases at the driven-port plane
Phase	Error · dB
Selected 0°	0.074227
0° · constructive maximum	0.074227
±180° · destructive minimum	-0.074867

Copyable routing-observation record · full precision

{
  "model": "p04-m02-multiport-ledger-v1",
  "fixtures": "p04-m02-fixtures/1.0.0",
  "evidence": "Illustrative / Simulated",
  "frequency": "2.450 GHz only",
  "zref": "50 Ω real, all ports",
  "temperature": "25 °C (matrix)",
  "planes": "R1 component-terminal planes P1…Pn; no added propagation",
  "waves": "e^(+jωt); b = Sa; Sij is outgoing port i / incident port j; a,b in √W",
  "domain": "Linear, single-frequency, settled state. Drive is a mathematical scale, not a component rating.",
  "rounding": "Display: waves 9 decimals √W; powers 6 decimals mW; dB 6 decimals. Export: full binary64 precision; no rescaling.",
  "warnings": "External rating, compression, thermal, calibration and measurement evidence remain required. This matrix does not predict hot switching, protection, recovery, harmonics, PIM or broadband behavior.",
  "tolerances": {
    "passivity": 1e-10,
    "inspectCondition": 1000000000,
    "rejectCondition": 1000000000000,
    "absolutePower": 1e-12,
    "relativePower": 1e-9,
    "decisionDb": 0.25
  },
  "status": "accept",
  "decision": "accept—forward sample 1 → 2; stated terminations and phase pass local matrix/conservation rules. Matched observation supports the bounded indication estimate.",
  "errors": {},
  "inputs": {
    "block": "coupler",
    "mode": "forward sample 1 → 2",
    "power": 10,
    "loss": 0.5,
    "coupling": 20,
    "directivity": 20,
    "directivityModel": "finite",
    "isolation": 40,
    "sourceVswr": 1.2,
    "loadVswr": 1.2,
    "sourcePhase": 0,
    "loadPhase": 0,
    "amplitude": 0,
    "phase": 0,
    "condition": "settled",
    "auxiliary": [
      {
        "kind": "matched",
        "magnitude": 0,
        "phase": 0
      },
      {
        "kind": "matched",
        "magnitude": 0,
        "phase": 0
      },
      {
        "kind": "matched",
        "magnitude": 0,
        "phase": 0
      },
      {
        "kind": "matched",
        "magnitude": 0,
        "phase": 0
      }
    ]
  },
  "fixture": "p04-m02-coupler-v1",
  "matrix": [
    [
      {
        "re": 0,
        "im": 0
      },
      {
        "re": 0.9440608762859234,
        "im": 0
      },
      {
        "re": 0,
        "im": -0.1
      },
      {
        "re": 0,
        "im": -0.01
      }
    ],
    [
      {
        "re": 0.9440608762859234,
        "im": 0
      },
      {
        "re": 0,
        "im": 0
      },
      {
        "re": 0,
        "im": -0.01
      },
      {
        "re": 0,
        "im": -0.1
      }
    ],
    [
      {
        "re": 0,
        "im": -0.1
      },
      {
        "re": 0,
        "im": -0.01
      },
      {
        "re": 0,
        "im": 0
      },
      {
        "re": 0.9440608762859234,
        "im": 0
      }
    ],
    [
      {
        "re": 0,
        "im": -0.01
      },
      {
        "re": 0,
        "im": -0.1
      },
      {
        "re": 0.9440608762859234,
        "im": 0
      },
      {
        "re": 0,
        "im": 0
      }
    ]
  ],
  "checks": {
    "maximumSingularValue": 0.9504477566566958,
    "passivityResidual": -0.049552243343304214,
    "passive": true,
    "reciprocity": 0,
    "symmetry": 0,
    "lossless": 0.09864906186625444,
    "permutation": [
      2,
      1,
      4,
      3
    ]
  },
  "rows": [
    {
      "port": 1,
      "name": "Input end",
      "role": "Driven source",
      "termination": "source ΓS; VSWR 1.2; 0°",
      "gamma": {
        "re": 0.09090909090909088,
        "im": 0
      },
      "drive": {
        "re": 0.09958591954639384,
        "im": 0
      },
      "available": 0.01,
      "a": {
        "re": 0.10032488356786506,
        "im": 0
      },
      "b": {
        "re": 0.008128604236183503,
        "im": 0
      },
      "incident": 0.010065082262905681,
      "outgoing": 0.00006607420682850039,
      "net": 0.009999008056077181,
      "absorbed": null,
      "delivered": 0.009999008056077181
    },
    {
      "port": 2,
      "name": "Through end",
      "role": "Intended load",
      "termination": "load ΓL; VSWR 1.2; 0°",
      "gamma": {
        "re": 0.09090909090909088,
        "im": 0
      },
      "drive": {
        "re": 0,
        "im": 0
      },
      "available": 0,
      "a": {
        "re": 0.008610254317669265,
        "im": 0
      },
      "b": {
        "re": 0.09471279749436193,
        "im": 0
      },
      "incident": 0.00007413647941494223,
      "outgoing": 0.008970514009208012,
      "net": -0.00889637752979307,
      "absorbed": 0.00889637752979307,
      "delivered": null
    },
    {
      "port": 3,
      "name": "Forward sample",
      "role": "Auxiliary termination",
      "termination": "matched; Γ at P3",
      "gamma": {
        "re": 0,
        "im": 0
      },
      "drive": {
        "re": 0,
        "im": 0
      },
      "available": 0,
      "a": {
        "re": 0,
        "im": 0
      },
      "b": {
        "re": 0,
        "im": -0.0101185908999632
      },
      "incident": 0,
      "outgoing": 0.00010238588180081808,
      "net": -0.00010238588180081808,
      "absorbed": 0.00010238588180081808,
      "delivered": null
    },
    {
      "port": 4,
      "name": "Reverse sample",
      "role": "Auxiliary termination",
      "termination": "matched; Γ at P4",
      "gamma": {
        "re": 0,
        "im": 0
      },
      "drive": {
        "re": 0,
        "im": 0
      },
      "available": 0,
      "a": {
        "re": 0,
        "im": 0
      },
      "b": {
        "re": 0,
        "im": -0.0018642742674455772
      },
      "incident": 0,
      "outgoing": 0.0000034755185442597434,
      "net": -0.0000034755185442597434,
      "absorbed": 0.0000034755185442597434,
      "delivered": null
    }
  ],
  "kappa": 1.1883438540275064,
  "delivered": 0.009999008056077181,
  "absorbed": 0.009002238930138146,
  "internal": 0.0009967691259390344,
  "isolationResistor": null,
  "excessLoss": null,
  "residual": 6.505213034913027e-19,
  "tolerance": 9.999008056077182e-12,
  "efficiency": null,
  "efficiencyReason": "N/A for this topology or rejected result.",
  "indication": {
    "coupling": 20,
    "isolation": 40,
    "directivity": 20,
    "truth": 0.010065082262905681,
    "idealCoupled": 0.00010065082262905683,
    "coupled": 0.00010238588180081808,
    "indicated": 0.010238588180081805,
    "error": 0.07422746241069444,
    "indices": "C: S31; I: S41; through: S21"
  },
  "noise": null,
  "auxiliaryDelta": null,
  "displayRows": [
    [
      "P1 · Input end",
      "Driven source",
      "0.100324884 + j0.000000000",
      "0.008128604 + j0.000000000",
      "10.065082",
      "0.066074",
      "9.999008"
    ],
    [
      "P2 · Through end",
      "Intended load",
      "0.008610254 + j0.000000000",
      "0.094712797 + j0.000000000",
      "0.074136",
      "8.970514",
      "-8.896378"
    ],
    [
      "P3 · Forward sample",
      "Auxiliary termination",
      "0.000000000 + j0.000000000",
      "0.000000000 − j0.010118591",
      "0.000000",
      "0.102386",
      "-0.102386"
    ],
    [
      "P4 · Reverse sample",
      "Auxiliary termination",
      "0.000000000 + j0.000000000",
      "0.000000000 − j0.001864274",
      "0.000000",
      "0.003476",
      "-0.003476"
    ]
  ]
}

Derived canonical matched cases · 10 mW total available · 50 Ω · 2.450 GHz · 25 °C · fixtures v1
Case	P1 load mW	P2 load mW	P3 load mW	Internal mW	Decision
3 dB matched pad	Driven / absent	5.011872	Driven / absent	4.988128	accept
Ideal two-way split	Driven / absent	5.000000	5.000000	0.000000	accept
Equal combine · 0°	10.000000	Driven / absent	Driven / absent	0.000000	accept
Equal combine · 180°	0.000000	Driven / absent	Driven / absent	10.000000	accept
settled RFC → RF1	Driven / absent	7.943282	0.001000	2.055718	accept
settled RFC → RF2	Driven / absent	0.001000	7.943282	2.055718	accept
settled all-off	Driven / absent	0.001000	0.001000	9.998000	accept

The fixed cases above remain available without JavaScript. They use matched source/load boundaries: a 3 dB pad; ideal zero-excess-loss Wilkinson; and SPDT endpoints with 1 dB selected-path loss and 40 dB off-path isolation. All use 10 mW total source available power.

06 / 10

RF switches are state-dependent networks

The gateway’s T/R switch must connect the correct path before RF arrives and settle before the receiver measurement is trusted. Treat RFC → RF1, RFC → RF2, and all-off as three different networks. Reflective and absorptive off states need different terminations; neither description means that every incident threat is harmless.

Illustrative SPDT endpoint contract · P1 RFC, P2 RF1, P3 RF2 · real 50 Ω
State	Nonzero upper-triangle entries	Where power can go
RFC → RF1	S12 = u; S13 = −jq; S23 = 0	RF1, leakage into RF2, and internal loss.
RFC → RF2	S12 = −jq; S13 = u; S23 = 0	RF2, leakage into RF1, and internal loss.
All-off	S12 = S13 = −jq; S23 = 0	Both terminated branches and internal dissipation.

All diagonal entries are zero; Sji = Sij, u = 10^(−IL/20), and q = 10^(−Ioff/20). These are matched, reciprocal, absorptive teaching endpoints. A selected-path state need not be symmetric under RF1/RF2 exchange. The 1 dB / 40 dB matched case sends 7.943282 mW to the selected path and 0.001000 mW to the other, while 2.055718 mW is internal loss. The all-off case absorbs 9.998000 mW internally.

Think about itDoes 40 dB off-state isolation guarantee that a receiver behind RF2 survives a transmit event?

Answer

No. The endpoint ratio omits transition leakage, compression, control feedthrough, peak voltage under mismatch, off-port load absorption, and the receiver’s time-dependent damage limit.

Common misconceptionA switch’s off-state isolation proves the receiver is protected.

Compare an actual transient at the receiver plane with a qualified threat envelope. The small-signal isolation row supplies only one condition in that comparison.

ADRF5020 Rev. B [7] distinguishes hot-switch and other power conditions. Hot switching means RF is present while the switch changes state; cold switching removes RF during the transition. Switching time and RF settling time must be attached to their respective definitions and thresholds. Control transitions can inject a transient even when the nominal RF input is quiet.

Insertion loss, return loss, isolation direction, compression, harmonics, intermodulation, control levels, and supply sequencing all belong in the state record. AN-2558 [8] reinforces why arbitrary load phase can change a switch decision. The ledger rejects a hot-switch request and retains static endpoint examples; interpolating between S-matrices would not create a transient model.

For this case, require a settled-state interlock and qualified RF-mute timing before accepting the switch arrangement. Next, specify what the receiver protection must absorb, reflect, or clamp.

07 / 10

Limiters, ESD, and protection trade survival for parasitics

A protection element can add capacitance and leakage at low level, then become strongly nonlinear during a threat. ESD clamping and RF limiting address different stimuli. Their names do not define the pulse waveform, current return, source impedance, or recovery requirement.

\begin{aligned}Y_{\mathrm{cap}} &= j\omega C\qquad |X_{\mathrm{cap}}| = \frac{1}{2\pi f C} \\ &\text{At} 2.450 \mathrm{GHz}, 0.2 \mathrm{pF} \Rightarrow |X_{\mathrm{cap}}| \approx 325 \Omega\end{aligned}

Derived parasitic orientation only: ideal shunt capacitance. It does not model turn-on, breakdown, stored charge, or survival.

That reactance is large compared with 50 Ω but not infinite. Package inductance and the actual return route can change its effect. Low capacitance helps the quiet-state RF path; it does not specify clamp voltage at the protected die or how soon the receiver can measure after a pulse.

Informative protection evidence request · record at the protected receiver plane
Region	Required conditions	Decision evidence
Quiet RF	Band, bias, temperature, source/load match and board planes	S-data, capacitance/leakage, insertion and return loss.
Threat onset	Waveform, rise time, polarity, peak voltage/power, source impedance and return path	Turn-on delay, spike leakage and protected-plane voltage/current.
Pulse train / CW	Pulse width, repetition, duty, average heating and cooldown	Qualified energy/power envelope with stated derating.
Recovery	Post-threat level, reference threshold and measurement bandwidth	Time to the required gain/loss or sensitivity condition.

Think about itA limiter has a small-signal capacitance curve. Can it establish receiver survival for a 1 µs incident pulse?

Answer

No. A capacitance curve describes an incremental condition. Survival needs the pulse amplitude and source impedance, energy/thermal conditions, fixture, turn-on response, and the protected device’s limits.

Common misconceptionA limiter’s small-signal capacitance proves its transient survival behavior.

Use separate quiet-state and threat-state evidence. A linear model cannot infer a clamp transient or recovery from its small-signal slope.

CLA4606 documentation [9] gives a concrete PIN-limiter example with a 2.6 GHz fixture, at 25 °C, and a recovery definition tied to return within 3 dB of quiescent insertion loss. Its reported 5 ns typical recovery is conditional on that setup. Board and connector loss are not de-embedded.

Inspect the threat record: footnote 2 of document 203235C lists a 1 µs pulse, 10 kHz repetition, and 0.1% duty. Width × repetition gives 1%, so those conditions need manufacturer clarification before using the pulse ratings. This lesson makes no survival calculation from that inconsistent tuple.

The PIN limiter note [10] explains a further routing consequence: a conducting shunt limiter can reflect much of the incident threat. The return path must tolerate it. Put the protection boundary ahead of vulnerable receiver circuitry, then assess switch exposure separately; a downstream limiter cannot retroactively protect an upstream switch.

08 / 10

Circulators, isolators, and reciprocity exceptions

A circulator uses nonreciprocal routing, commonly associated with a magnetically biased ferrite structure. For the orientation 1 → 2 → 3 → 1, a wave from the transmitter at P1 goes to P2. A reflection entering P2 travels toward P3.

S=\begin{bmatrix}0&0&e^{j\theta_3}\\e^{j\theta_1}&0&0\\0&e^{j\theta_2}&0\end{bmatrix}

Illustrative ideal lossless circulator; equal real 50 Ω reference impedances and declared cyclic orientation. Not a ledger preset or a vendor model.

Each unit-magnitude route carries power to one other port, so the ideal matrix is unitary, passive, and nonreciprocal. Real insertion loss and finite isolation add heat and leakage. Reversing a package or changing its bias orientation can reverse the useful route; follow the actual port arrows.

Derived reflected-energy route · ideal 1 → 2 → 3 → 1 circulator
Event	Destination	Boundary consequence
Forward wave entering P1	P2 load	Useful output; actual insertion loss adds internal heat.
Load reflection entering P2	P3 termination	A matched dump absorbs it; its rating belongs in the design.
P3 left open	Reflection returns at P3 and exits P1	The transmitter can receive the returned energy.

Think about itAt an ideal isolator’s output plane, 1 W arrives at a load with VSWR 2. What must its dump handle?

Answer

|Γ| = 1/3, so 1/9 W ≈ 111.111 mW returns toward the isolator and reaches the matched dump. That is a local one-reflection example; real loss, pulse peaks, and repeated events change the thermal request.

Common misconceptionAn isolator makes reflected energy disappear.

An isolator typically embeds the circulator’s third-port termination. Energy is absorbed there, dissipated internally, leaked elsewhere, or reflected again if the termination is imperfect.

The Smiths L-band family [11] illustrates a physical input, output, and load arrangement. Its cited 1.57–1.62 GHz example is outside this lesson’s 2.450 GHz case and is not a candidate substitution. An appropriate in-band family would still need its reverse-power, temperature, mounting, and magnetic-environment evidence.

Use an isolator only when the added loss, volume, bias environment, and dump-power obligation are justified. Even a fully passive energy path can introduce nonlinear contamination.

09 / 10

Passive intermodulation is still nonlinear

The gateway may pass a single-tone insertion-loss check and still create unwanted products with two strong transmitters nearby. Nonlinear contacts, corrosion, unsuitable materials, and high-current regions can mix tones without a powered amplifier.

\begin{aligned}f_{\mathrm{IM3,low}}&=2f_1-f_2\\f_{\mathrm{IM3,high}}&=2f_2-f_1\\f_1&=2.440\,\mathrm{GHz},\quad f_2=2.450\,\mathrm{GHz}\\&\Rightarrow2.430\text{ and }2.460\,\mathrm{GHz}\end{aligned}

Derived frequency bookkeeping for third-order products; frequencies alone predict neither amplitude nor compliance.

A product can land in a receive band even when both carriers are outside it. Connector torque and condition, material interfaces, mounting stress, and current density can change the response. A low-level linear S-matrix has no mechanism for generating a new frequency.

Common misconceptionPassive parts cannot compress, generate harmonics, or create intermodulation.

Passive means no net energy generation in the stated accounting. A passive nonlinear element can redistribute energy among frequencies and change behavior with drive, temperature, or mechanical state.

Think about itIs a PIM result of −120 dBc enough to compare two assemblies?

Answer

No. Record carrier frequencies and powers, which carrier defines dBc, absolute product power, forward or reverse observation, reference planes, residual system PIM, termination, temperature, and mechanical condition. A different test can produce a different comparison.

Anritsu’s PIM discussion [12] supplies practical mechanisms and test context. For the node/gateway evidence pack, flag the antenna connector, switch-to-protection interconnect, and high-current dump path for inspection. Request a discriminating two-tone measurement if a product can enter the wanted band. Do not assign a universal PIM level to a material or calculate a reliability conclusion from this linear ledger.

10 / 10

Build the routing and observation network

The routing decision is now a set of conditional paths. Choose an observation plane deliberately, name every unused-port termination, and keep protection and thermal requirements alongside the useful signal route.

Illustrative routing proposal · not a simulated cascade

Transmit: transmitter output → coupler P1 → coupler P2 → switch RF1 → switch RFC → antenna.
Observe: matched coupler P3 → calibrated observation receiver. Coupler P4 → explicitly rated 50 Ω termination. The inferred forward power belongs at coupler P1, before the T/R switch.
Receive: antenna → switch RFC → switch RF2 → receiver protection → receiver input. The switch needs its own antenna-threat qualification.
Test: an isolated test mode inserts a qualified pad before the test instrument. Require termination and RF-mute sequencing while reconnecting.
Optional division: add a divider only for a demonstrated two-path requirement; terminate every output and rate its isolation resistor. Coherent combining requires phase control at both branch planes.

In transmit, the receiver path is off but remains a physical load; in receive, the transmit branch has its own off-state boundary. A protection element placed at the antenna could protect more of the chain, but would also see normal transmit power and add loss to both directions. That alternative needs a compatible threat/linearity record before selection.

Illustrative routing and observation evidence pack · case revision 04.2 / 1
Decision	Retained evidence and bound	Next discriminating request
Coupler observation: accept locally	p04-m02-coupler-v1; 2.450 GHz, 25 °C, 50 Ω R1 P1…P4; +10 dBm available; VSWR 1.2 at 0°; auxiliaries matched; error +0.074227 dB	Vector forward/reverse check at the actual coupler planes across intended mismatch and temperature.
T/R switch: inspect	Named RFC/RF1/RF2 maps; settled matrices only; drive scale is not a rating; off port terminated	Compression and hot/cold qualification at peak drive and worst load phase; verify mute and settling timing.
Receiver protection: inspect	Quiet-state loss/capacitance separately from threat pulse; protected receiver plane and return path named	Resolve limiter pulse-condition inconsistency; obtain a qualified spike/recovery record for the actual threat.
Test pad: conditional	3 dB matched fixture spends 4.988128 mW per 10 mW incident; noise equality only at matched 290 K	Check sensitivity/headroom budget and resistor pulse/thermal limits in the intended test path.
Divider/combiner: defer unless needed	Matched equal split is 5 + 5 mW; ideal 180° combine puts all 10 mW in the internal resistor	Declare simultaneous-path need and phase control; rate imbalance and fault dissipation.
Auxiliary and dump loads: required	Physical port, Γ(f), power, pulse, temperature, mounting and evidence class retained	Check connector/termination state and absorbed power under normal and reflected-wave cases.

Reject these arrangements: an open observation port used as a calibrated detector; an unqualified hot-switch transition inferred from endpoints; a downstream limiter claimed to protect an upstream switch; or a coupler before an unknown-loss switch claimed to measure antenna accepted power. Each loses a necessary termination, time condition, protection boundary, or power plane.

The single-block ledger compares disclosed fixtures; it does not cascade this proposed network. A combined model would require compatible planes, interconnects, state-dependent matrices, and separate nonlinear evidence. Preserve the model cards from 04.1 and request the missing evidence before turning a local accept into hardware approval.

Go deeperWhat moves into the next module

04.3 will own resonator and filter response, technology, loss, delay, and tolerance. LNA, PA, mixer, and PLL choices remain in 04.4–04.7; receiver and transmitter allocation in Path 05; measurement procedures in Path 08; detailed interconnect and production practice in Path 10.

Ungraded review

Check your understanding

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

01Why are +10 dBm available and +10 dBm incident different in the default coupler?
Model answer
Source available power fixes |aG|²/(1−|ΓS|²). Reflections alter the incident wave a1. The default has 10.065082 mW incident and 9.999008 mW net source delivery; its sample must be compared with the incident truth at P1.
02Which indices define coupling and isolation after reversing the coupler drive?
Model answer
Drive physical P2, through P1: coupling uses S42 and isolation S32. P4 becomes the intended matched observation; P3 becomes the isolated auxiliary. All physical numbers and reference planes remain fixed.
03Why can a reciprocal Wilkinson be lossy?
Model answer
Reciprocity is S = Sᵀ. Losslessness is SᴴS = I. Equal in-phase branch excitation reaches the common port without ideal resistor loss, while equal opposite-phase excitation dissipates in the internal resistor.
04When is a 3 dB passive pad also a 3 dB noise figure?
Model answer
For the stated matched available-power noise definition at pad temperature Tp = reference T0 = 290 K. It then has F = LA. Different temperature or mismatch requires additional noise and termination reasoning.
05What would reject an otherwise attractive switch/protection pair?
Model answer
Missing hot-switch or worst-load evidence, an unknown transient at the receiver plane, incompatible normal transmit drive, or an unresolved threat waveform. Neither off-state isolation nor small-signal capacitance proves survival.
06Where can power go when an observation or dump port is open?
Model answer
The outgoing wave returns with Γ = +1 and coherently re-enters the network. It can alter source delivery, other-port powers, and internal loss. At an ideal circulator dump it can route back to the transmitter; at the intended coupler observation it invalidates the matched detector estimate.

Sources and further study

Accessed 6 September 2026. Definitions and derived checks are separate from illustrative fixtures. Vendor examples below orient evidence requests; none supplies the ledger’s S-matrix. Missing test-plane or stimulus information is recorded as missing.

MW-1 · D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012. Publisher contents and edition record: chapters 4, 7, 9 and 10 identify the network, divider/coupler, ferrite and noise foundations. Edition/contents checked; the full text was not available for fresh page-by-page verification. The equations here are independently derived and tested.
CIR-2 · Analog Devices. RF Signal-Chain Discourse, Part 2: Essential Building Blocks, Analog Dialogue, 2021. Informative block roles and practical signal-chain orientation; not a component rating or network fixture.
Mini-Circuits VAT-3+. Official datasheet, Rev. H, stamp 200520, inspected through the indexed official document. 3 dB, 50 Ω, DC–6 GHz, 1 W rating; operating −45 to +100 °C. SMA male/female connector ends are the physical interfaces; no bias. A specific characterization drive, temperature, and de-embedding plane are not established by the inspected rating row. Obtain those before using it as a model card.
Mini-Circuits ZFSC-2-2500+. Official datasheet, Rev. E, stamp 151021, indexed document inspected. 10–2500 MHz, 50 Ω; input splitter rating 1 W, internal dissipation rating 0.125 W; operating −55 to +100 °C. Vendor SUM port 3 maps to lesson common P1; vendor ports 1/2 map to lesson branches P2/P3. No bias. Characterization drive and de-embedding planes require confirmation. This is a splitter comparison, not a verified Wilkinson construction.
Mini-Circuits application note. Directional Couplers: Their Operation and Application, current official web version, no revision identifier verified. Informative direction, termination, and directivity/mismatch context; individual products require their own conditions.
Mini-Circuits ZCDC20-263+. Official datasheet, Rev. OR, ECO-024734, stamp 250314; indexed official text inspected. 0.5–26.5 GHz, nominal 20 dB coupling, real 50 Ω, electrical table at +25 °C; 20 W absolute maximum input, case −55 to +100 °C. SMA female input/output/coupled interfaces and an included isolated termination; no bias. Preserve the functional diagram’s orientation. Test stimulus and exact calibration planes are not specified in the inspected table. Mainline loss includes coupling loss; absolute maximum is not a recommended operating level.
Analog Devices ADRF5020. Datasheet Rev. B, April 2020. Nonreflective 50 Ω SPDT, 100 MHz–30 GHz; RFC/RF1/RF2 and control/enable states are explicit. Specifications use Tcase = 25 °C unless stated, positive/negative supplies and stated control levels. Consult separate compression, hot-switch, through and terminated-path power conditions; connector-to-die de-embedding must not be assumed. The local reciprocal endpoint fixtures do not reproduce this part.
Analog Devices switch application material. AN-2558: RF Switch Performance with Arbitrary Loads, current web note, 2023; and MEMS Switch Technology FAQs, current official documentation. Used for load-dependent behavior and hot/cold terminology. MEMS lifetime statements are technology-specific and are not transferred to the semiconductor switch.
Skyworks CLA4606 family. PIN limiter datasheet 203235C, 10 July 2017. Conditions include 25 °C, 2.6 GHz, 50 Ω, −10 dBm quiet-state loss test, and a shunt diode/choke/DC-block fixture. Board/connector loss is not de-embedded; recovery uses its stated 3 dB criterion. Package pin maps and pulse footnotes must stay attached. The inconsistent pulse-width/repetition/duty tuple is unresolved; no survival rating is inferred here.
Skyworks. PIN Limiter Diodes in Receiver Protectors, 200480 Rev. C, 15 August 2008. Informative shunt-limiter operation, reflected threat power, charge and recovery context. Actual clamp/recovery qualification requires the device and external circuit conditions.
Smiths Interconnect L-band isolator family. Official family sheet, version 1.0, copyright 2021. Example band 1.57–1.62 GHz, input stripline P1, output TNC P2, integral 50 Ω load. The isolator table lists 162 W CW average and 1000 W peak full-reflection qualification; temperature ranges are −25 to +95 °C qualification and −20 to +90 °C acceptance. Exact characterization stimulus, magnetic bias and de-embedding planes need a part-specific record. Outside 2.450 GHz: orientation study only, with no transferred power rating.
Anritsu. Understanding PIM, current official web material; no revision/date verified. Informative nonlinear contact/material mechanisms and two-tone test context. Record carrier powers/frequencies, residual system response, observation direction, planes, load and mechanical/thermal state for any measured claim.

Passive Routing,Sampling & Control

Failure: when a 20 dB coupler lies

Passive multiports and conservation constraints

Attenuators: match traded for irreversible loss

Splitters and combiners need phase and termination discipline

Directional couplers: coupling, isolation, and directivity

RF switches are state-dependent networks

Limiters, ESD, and protection trade survival for parasitics

Circulators, isolators, and reciprocity exceptions

Passive intermodulation is still nonlinear

Build the routing and observation network

Check your understanding

Sources and further study

Passive Routing,
Sampling & Control