RF Chain Budget

A receive chain stage by stage, each stage a System block with its own parameters - gain, noise figure, intercepts, compression, sensitivity and dynamic range in closed form, an N-way array included - and one action that writes the chain as test benches whose simulations put a number beside every one of them.

What it is

A chain budget is the spreadsheet every receiver starts as: an ordered list of stages, each with a gain, a noise figure and an intercept, and the cascade worked out stage by stage. The RF Chain Budget is that table, with two differences that matter here:

• Every stage is a part circuitRF already has. An amplifier stage is the System Amplifier with the Amplifier's own Gain, NF, IP3 and IP3Ref; a filter stage is the Filter with its own Response, Form, band and IL. The budget reads each part's numbers the way the part's model behaves.
• One action turns the chain into a simulation. Transfer to Schematic writes the chain as test benches of those same parts, with the analyses that check the budget already set up and the budget's numbers written beside the simulated ones. The cascade is closed-form arithmetic; the check is circuitRF's own S-parameter, harmonic-balance and envelope analyses.

Opening it

• Tools ▸ RF Chain Budget opens a new chain: an LNA, a filter and a second amplifier.
• A .cchain in the workspace tree opens on a double-click.
• File ▸ New ▸ Examples ▸ RF Chain Budget has a 2.45 GHz superhet, a four-element steered array and a front end with a canceller, each already transferred.

The window has three parts, and every edit recomputes all of them at once:

• The chain, input on the left, drawn two ways that share one selection:

  • Blocks: one idealised block per stage, drawn with its System block's own symbol, with its own gain, NF and intercept under it and the cascade at its output (Σ) under that. An array is drawn compactly: the branch's stages once, each marked "× N", into one combiner block drawn as its variant — a direct combiner one N:1 symbol, a tree its levels of 2:1 (a deep one as "× levels"), an amplifier after each when it is active. A filter's block shows its band form. Drag a block left or right to move its stage: a line shows where it will land. Delete removes the selected block's stage. Right-click for Insert Block ▸ a part, which inserts a stage of that part where you clicked (the left half of a block before it, the right half after it), Copy, which puts the whole lineup on the clipboard as a picture to paste into a slide or a document, and Remove Block, which removes the block you clicked.
  • Schematic: the schematic Transfer would write, drawn as every circuitRF schematic is, without the bench's sources, analyses and isolators: each stage is its own parts (a composed stage its composition, a tree its levels of Combiners), and in an array every element's branch is drawn into the combiner. Above each stage are four lines: its own gain and NF, its own intercept and compression point, and the cascade's gain, NF, IIP3 and SNR at its output. Scroll to zoom, drag with the middle button to pan. Z and a drag zoom to a box, and F, the Fit button or a double-click fits. Right-click ▸ Copy copies it as the schematic editor copies: a picture for a slide or a document, and parts and wires to paste into a schematic.

  Clicking a block, or a part in the schematic, selects its stage, and the selected stage is drawn selected in both.

• The stages, one row each: the name, the part, and the part's parameters. Selecting a stage in either view scrolls its row to the top of the list.

• The cascade, the levels and the canceller, three Data Display tabs: the cascade table, one row per stage; the levels at every node, the budget's lines with the transferred benches' simulated points once they have run, where a marker on a trace selects its node's stage in both views; and, for a chain with a canceller, its depth against its errors. The chain's totals are below them.

Drag the gap between two of the three parts to give one more height.

Undo and Redo (the toolbar, or Ctrl+Z and Ctrl+Shift+Z, ⌘ on a Mac) step through every edit: an input, a stage's name, part or parameter, and every stage added, removed or moved. A value typed into a box is one step. Undoing back to the chain as it was opened or last saved leaves it unchanged, with nothing to save.

A value the budget cannot use is never taken. While you type one, its box is outlined in red, the reason is under the chain's totals, and everything else keeps showing the last chain that worked; leave the box (or press Enter) with the value still refused and it goes back to the last one that worked. A choice from a list that the budget refuses, such as a tree combiner whose N is not a power of 2, is not made, and the reason is shown.

The system inputs

Transfer to Schematic's drop-down has include a modulated-signal demo, which adds the demo bench to what it writes.

The stages, and the parts a stage can be

A stage has a name (its instance name on the schematic), a part, and that part's parameters. Nine parts are System blocks — the splitter and the array combiner are the library's Combiner, an active combiner that block with an Amplifier after each — and the library has no phase shifter, limiter or canceller, so three more are composed of parts it does have. Transfer places exactly that composition. One more is data: an S-parameter data stage is a Touchstone file.

P1dB follows from the intercept for every part that compresses, because an ideal Amplifier and Mixer have one nonlinearity, a tanh limiter, whose 1 dB compression point is IIP3 − 8.9625 dB. The budget uses the part's own law, so the simulation it is checked against compresses where the budget says.

S-parameter data

An S-parameter data stage puts a measured or simulated part into the chain as its Touchstone file: a filter, an LNA, a cable, a board. Pick the file with … beside File; a file inside the workspace is written relative to it, so the chain and its benches move with the workspace. Choosing the part asks for the file at once.

The file is interpolated to the frequency the stage sees — the chain's, or after a mixer the IF — exactly as the SnP block interpolates it in a simulation, and renormalised to 50 Ω if it is referenced to another impedance. A file with more than two ports is read from In to Out, every other port terminated in 50 Ω.

NF stated replaces the file's figure and may not be below it. On the benches a stated NF above the file's own, or a stated IIP3, is an ideal Amplifier of 0 dB after the block that carries the extra noise and the intercept, so the simulation still checks the stage.

The budget does not extrapolate. It refuses the chain, naming the stage, when:

• no file is named, there is no file at the path, or the file is not Touchstone;
• In or Out is not one of the file's ports, or both are the same port;
• the stage's frequency is outside the file's frequencies, or outside its noise rows when the noise comes from them (state NF to use the file there);
• the file has gain and no noise data, and NF is blank;
• a relative path is given in a chain that has not been saved.

A blocker that reaches the stage outside the file's frequencies is carried at the file's nearest frequency, as the block holds it in a simulation, and the Notes say so.

What the cascade computes

Each row of the cascade is the chain up to and including that stage, referred to the chain's input. With G the available-power gains, T the noise temperatures and T0 = 290 K:

The intercept sum takes every stage's third-order products in phase, the worst case. For ideal blocks with real gains that is exactly what happens, and the two-tone simulation agrees to 2×10⁻⁴ dB. The compression sum is an approximation of the same form: when two stages compress at similar levels the cascade compresses a little later than it predicts (see agreement).

A mixer's noise figure is its single-sideband one, and an SSB figure is stated with the image sideband terminated at T0. The budget also takes the image as filtered of every earlier stage's noise, which is what a preselector is for.

Arrays: N elements into a combiner

A Combiner stage makes the chain an array. Every stage before it is one element's branch, repeated N times; the stages after it are the one receiver the elements are combined into. Every number is then referred to one element's input, and the input power is per element.

• Signal from the N branches arrives in phase and adds in amplitude: the combiner's signal gain is +10·log10 N − IL.
• Noise from the N branches is uncorrelated and adds in power: the combiner's noise gain is −IL only. The array's noise temperature is therefore one branch's Friis sum, with the combiner's excess loss as a pad, and its NF is one element's.
• SNR rises by 10·log10 N, the array gain: SNR = Pin + 10·log10 N − 10·log10(k·(Ts + Te)·B) − 30. The MDS and sensitivity per element fall by the same amount.
• Intercepts after the combiner see N times one element's power, so the intercept and compression points referred to one element fall by 10·log10 N for the stages after it, and the output-referred ones rise.

Steer is the phase step of the arriving wave between adjacent elements. Transfer draws the wave's extra path to element k as a line of (k − 1)·Steer in front of it, and sets element k's phase shifter to Phase + (N − k)·Steer, which brings every element to the combiner in phase. Without a phase shifter before the combiner a non-zero Steer misaligns the elements, and the budget says so: its coherent sum assumes they are aligned.

The combiner's four variants

A Combiner stage is one of four, chosen by two parameters:

Each variant's budget is the cascade of its own levels, and every number is referred to one element's input:

• The element paths first. With amplitudes a_k = 10^(−PathIL_k/20), N in-phase inputs of power P combine to (Σa_k)²·P/N and their uncorrelated noise to (Σa_k²/N)·n²; the weighting itself is a matched passive network at T0, adding T0·(N/Σa_k² − 1) of noise. With equal paths all three are N·P, n² and nothing.
• Then each level: a passive n-way level of loss L gains n·(1/L) in signal and 1/L in noise and adds T0·(L − 1) of noise; an active level's amplifier follows it with its own gain, noise figure and intercept.
• Signal and noise gains, noise temperatures and intercepts cascade through the levels exactly as they do through a chain: Friis with the noise gains, the intercept sum with the signal gains. The amplifiers of one level are in parallel, each fed by its own pair, and identical, so together they behave as one amplifier seeing the combined power.
• The array gain is the signal gain over the noise gain: (Σa_k)²/Σa_k², which is N for equal paths and less with a taper.

So a passive tree's loss accumulates level by level, and its noise figure is its whole loss; a direct combiner has one loss. An active combiner's noise figure is set by its first level, and its intercept by its last, which sees the most power: in the example's array, the active tree's IIP3 is 7 dB below the direct active combiner's.

The example's array, the same four elements into each variant (IL 0.5 dB, the amplifiers 10 dB, NF 2 dB, IIP3 10 dBm), at the combiner's output and per element:

Transfer to Schematic

Transfer to Schematic saves the chain and writes its test-bench cells beside the .cchain, named after it, each with a Data Display of the same name that Simulate opens on the bench's own result. Every chain gets 1-Tone, 2-Tone, Envelope and Levels; a chain with blockers a Blockers bench; a chain with a canceller a Canceller bench; an array whose branch has no mixer Steering (when the branch has a phase shifter) and Combiners; and, when asked, the Demo:

The chain's parts are placed as written. Three things are the bench's and not the chain's:

• the sources, the load and each mixer's LO, a P1Tone at Flo and Plo;
• an isolator in front of each mixer (a Circulator whose third port is terminated at the ambient). It terminates the mixer's image at T0, the termination its SSB noise figure is stated against. A filter in front of a mixer reflects the image instead, and the mixer's noise then differs: in the superhet example the harmonic-balance noise figure reads 0.28 dB higher without the isolator. Delete it to see what your own image termination does;
• in an array, the arriving wave's path: a TLIN of (k − 1)·Steer in front of element k (on the Steering and Combiners benches, the splitter's own path phases instead).

Every bench sets temp = 16.85, which puts every part at 290 K, the temperature a noise figure is stated at. Each row of its MEAS block reads one analysis, so circuitrf hb … -a SW1 evaluates the compression rows on its own. The envelope SNR is measured over the NR carrier's occupied bandwidth (the 15 kHz-spacing channel nearest the chain's bandwidth), and its prediction beside it is computed in that bandwidth.

An array's 1-Tone bench has N + 1 ports. Its gain is |Σₖ S(N+1, k)|², which is the budget's only if every phase shifter removes its element's steering, and its NF is one element's: F = 1 + (F₁ − 1)·|S(N+1, 1)|²/Σₖ|S(N+1, k)|², where F₁ is the noise factor from port 1 with the other elements' terminations noiseless — F = 1 + (F₁ − 1)/N for equal paths.

Steering the beam in simulation

The Steering bench is the array at the combiner, fed by a plane wave and steered from its own VAR block:

The wave is one Port into a Combiner used as a splitter, whose path k has the phase −(k − 1)·psi_in: element k receives the wave (k − 1) element spacings later. Each element's phase shifter advances it by (k − 1)·dphi (its line is (k − 1)·(360° − dphi) long, the same phase at the bench's frequency and never a negative length), and the taper sits on the combiner's paths. Because the splitter shares the wave's power equally and its own isolation network is noisy at T0, each element sees an equal share of the signal and its own, uncorrelated, thermal noise, as an element of a real array does from its own antenna.

Its display plots the pattern, the simulated gain over the budget's peak gain at the combiner, against theta_in for each steer angle, and beside it the closed-form array factor:

AF(θ_in) = | Σₖ a_k · e^(−j·(k − 1)·(ψ_in − ψ_steer)) | / Σₖ a_k,      ψ = 2π·(d/λ)·sin θ

with a_k each path's amplitude weight (its PathIL and the taper). Each peak sits at its steer angle, and there the table reads the gain, the NF from the wave's port and the array gain, 10·log10 N less what the NF says it costs over one element's own: 6.02 dB for four equal elements, at every steer angle, with the NF unmoved. With a taper the main lobe widens and the sidelobes fall, and both the pattern and the closed form lose the taper's coherent loss at the peak. Change d_over_lambda to 1 and the grating lobes appear at ±90°.

Edit a sweep's values, or delete the sweeps and set theta_in and theta_steer by hand: everything is an ordinary variable.

Levels at every node

The Levels tab and the Levels display follow the chain node by node: node 0 is the input and node k the output of stage k. At every node:

The simulated points come from three benches: the Levels bench (two tones each at the input power: the signal and the IM3), the Blockers bench (the blockers alone, an isolator after every stage so that each node's voltage is the wave going forward, not a reflection standing on a filter's stopband) and the 1-Tone bench (each stage's cumulative NF, from the noise run's own shares, and the noise floor that NF gives at the node through the budget's noise gain). In the window they appear once those benches have been simulated beside the .cchain; in the display they are its points, the budget its lines. The displays plot against a variable nodeix that each bench sweeps around a trivial DC solve, which is how one number per node becomes one curve.

Add a marker to a trace in the window's Levels plots and its node's stage is selected, in the stage list and in both views; move the marker and the selection follows.

The canceller

A Canceller stage subtracts a weighted copy of an interference from the main path: a reference path from the interference's own source, through an amplitude setting, a phase setting and a delay, into a directional coupler's isolated port, the main path being the coupler's through arm.

On the wanted signal it is the through arm, a loss L_t = 10^(IL/10)/(1 − c), and the noise the reference path injects. That path needs a gain G_ref with G_ref·P_ref·c = P_int·(1 − c); its output is at T0·F_ref·G_ref, coupled by c/(1 − c) against the through arm, so

F = L_t + (F_ref·G_ref − 1)·c/(1 − c)

A passive path (F_ref·G_ref = 1) adds nothing to the coupler's loss.

On the interference the residual is the fraction R the subtraction leaves. With an amplitude ratio a = 10^(AmpErr/20), a phase error φ and a delay mismatch τ, a carrier of bandwidth B and flat spectrum, centred ν from where the phase was set, leaves the band's average of |1 − a·e^(j(φ − 2πfτ))|²:

R = 1 + a² − 2a·cos(φ − 2πντ)·sinc(πBτ),      sinc x = sin x / x,      depth = −10·log10 R

33.5 dB at 0.1 dB and 1°; with 1 ns of delay mismatch alone, 40.8 dB over 5 MHz, 28.8 dB over 20 MHz and 22.8 dB over 40 MHz. The window's Canceller tab draws the depth against the phase error for five amplitude errors, and against the bandwidth for four delay mismatches. The levels carry the interference and its residual node by node.

The Canceller bench studies it with real signals. Two MOD_Sources, which the Signal Designer edits: the wanted signal, an NR 64-QAM carrier and a QPSK one, and the interference, three NR carriers of 10, 5 and 20 MHz, the first two under the wanted ones. The interference is split: one share leaks into the main path through a line of 1 ns, the other is the reference path — an Amp for the amplitude, one path of a 2-way Combiner for a flat phase, a line for the delay — into the coupler's isolated port. Its VAR block sets the errors, amp_err, phase_err and delay_err, and two switches, canc_on (the reference path) and sig_on (the wanted signal). Its envelope runs:

• the interference alone, uncancelled: the reference each depth is measured from;
• the depth against each error, swept, the others at their nominal values, at every interference carrier: beside it the closed form above at that carrier's bandwidth and offset, so the 20 MHz carrier shows how a delay mismatch costs a wider signal more;
• the wanted carriers with and without cancellation, their noise on: EVM, SNR, and each constellation both ways.

Open either source in the Signal Designer to change its modulation (LTE, NR, DBPSK, FSK, CSS and the rest it offers) or its bandwidth; the bench measures whatever it sends.

The modulated-signal demo

include a modulated-signal demo, in Transfer to Schematic's drop-down (or --demo, or "Demo": true in the .cchain), adds <chain> Demo: the chain demodulated end to end. Each element is fed an NR 64-QAM carrier and, from a second source beside it, a DBPSK carrier at twice the bandwidth's offset, joined by a 2-way Combiner, each at the input power and noisy at the source temperature. Each mixer's LO carries a phase-noise mask, which an envelope run plays as a random phase. An envelope run with Noise=yes and EvmSplit=yes is swept over the input power in seven steps, from 5 dB of SNR to 5 dB past the input P1dB. Its display:

• the 64-QAM constellation at the output, received points over the ideal ones, at the middle and the highest power;
• the EVM against the input power, 64-QAM and DBPSK, and beside it the budget's from its SNR, EVM ≈ 1/√SNR, which holds where noise dominates;
• the EVM's split into its noise and distortion parts: noise at low power, the LO's phase noise as a floor, distortion past compression;
• the SNR in the carrier's channel, simulated and the budget's.

How closely the simulation agrees

Measured on the example's superhet and array, the budget against the simulation of the benches it writes:

The same array at RF, with no mixer, runs its noise through the S-parameter analysis instead and reads 3×10⁻¹⁰ dB in gain and 10⁻¹¹ dB in NF. The envelope SNR is a measurement of one noise record: four seeds of the array read 29.17 to 29.42 dB against 29.37 dB predicted.

The superhet's Levels bench puts the signal on the budget to 2×10⁻⁵ dB at every node and the IM3 to 8×10⁻⁵ dB; its Blockers bench reads each blocker 0.001 to 0.003 dB below the budget, the blocker's own slight compression at −40 and −50 dBm into the LNA. The front end's 1-Tone bench reads the canceller's noise, its through arm and the reference path's coupled noise, on the formula to 10⁻⁶ dB.

The Canceller bench's depth, at each of the three interference carriers and every swept error, is the closed form's to within 1.4 % of the depth, 0.7 dB at 49.7 dB deep and under 0.3 dB everywhere shallower than 45 dB. With cancellation the 64-QAM carrier's EVM falls from 840 % to 3.2 % and the QPSK one's from 1036 % to 8.6 %.

The superhet's Demo bench reads the SNR 0.20 dB under the budget at its lowest power, where noise dominates, and the EVM's noise part 57.0 % against the budget's 1/√SNR of 56.2 %. Higher up, two floors the budget does not model take over: the LO's phase noise, 1.23 % of EVM in the distortion part, which is the mask integrated over the channel (−38.2 dBc), and a noise part that stops at about 1 % (40 dB of SNR), which the Canceller bench's NR carriers show as well. At 5 dB past the input P1dB the distortion part is 15.5 %.

The array's Steering bench puts its pattern on the closed-form array factor to 3×10⁻⁹ dB within 3 dB of each peak and to 10⁻⁶ dB down to −60 dB, and its gain, NF and array gain at each peak on the budget to 10⁻¹⁴ dB. The Combiners bench reads each variant's gain and NF to 10⁻¹⁴ dB; each variant's intercepts and compression point, transferred on its own, read as the table above does.

The .cchain file

A .cchain is JSON. The system inputs are numbers whose names carry their unit; a stage's parameters are text, exactly as the part's netlist line carries them.

{
  "FormatVersion": 1,
  "FrequencyHz": 2450000000,
  "BandwidthHz": 4500000,
  "InputPowerDbm": -70,
  "TemperatureK": 290,
  "RequiredSnrDb": 10,
  "Stages": [
    { "Name": "LNA", "Part": "Amp", "Parameters": { "Gain": "16", "NF": "1", "IP3": "15", "IP3Ref": "Output" } },
    { "Name": "RFBPF", "Part": "Filter", "Parameters": { "Response": "Butterworth", "F1": "2.35 GHz", "F2": "2.55 GHz", "IL": "1.5" } },
    { "Name": "MIX", "Part": "Mixer", "Parameters": { "ConvGain": "-7", "NF": "7", "IIP3": "10", "Plo": "7", "Flo": "2.1 GHz" } }
  ]
}

A chain has at most one Combiner. An SnP stage's File is a path; a relative one resolves from the workspace the .cchain belongs to, or its own folder when it belongs to none.

From the command line

circuitrf chain Superhet.cchain                      the cascade, as the window shows it
circuitrf chain Superhet.cchain -o budget.npy        the budget as a DataSet: per-stage cubes over a stage axis
circuitrf chain Superhet.cchain --to-schematic       the benches and their displays, beside the .cchain
circuitrf hb "Superhet 2-Tone/schematic/Superhet 2-Tone.csch"

--to-schematic [dir] writes into another folder, --name names the benches, --demo adds the demo bench, and an existing bench is a refusal unless --replace is given. circuitrf check reads a .cchain through the same budget and reports its refusals. Over the MCP server the verb is run analysis=chain.

See also: System Components · Simulations ▸ Noise · Measurements · Data Display.