Convert one RF quantity into all the others for a reference impedance Z0: impedance Z ↔ normalized z ↔ admittance Y ↔ reflection coefficient Γ (S11), plus VSWR, return loss, mismatch loss, delivered power and Q. Give exactly ONE of: z, z_normalized, y, gamma, or vswr (+ optional gamma_angle_deg). With a frequency, also returns the equivalent series and parallel R + L/C element values. Use for: 'what is the VSWR of 75 Ω on 50 Ω?', 'convert S11 = 0.5∠30° to impedance', 'return loss of 25-j15 Ω'.

Input impedance of a (lossy or lossless) transmission line terminated in a load: Zin = Z0·(ZL + Z0·tanh γℓ)/(Z0 + ZL·tanh γℓ). Length can be electrical (λ, degrees) or physical (mm, m, mil) with eps_eff / velocity_factor. Also returns Γ at load and input, electrical/physical length, guided wavelength, and the distances from the load to the first voltage maximum and minimum. Use for coax/microstrip/λ/4/λ/2 line questions and 'where is the voltage minimum?' problems.

Analyze a cascaded RF circuit (load → components → source) the way a Smith chart does: returns the impedance, Γ and VSWR at every node, the final input impedance with return/mismatch loss, an optional frequency sweep (S11 in dB, VSWR vs. frequency), matched bandwidth for a VSWR limit, and Monte-Carlo-free tolerance corner analysis (± tolerance_pct on each component). Supported elements: inductor, capacitor, resistor (series or shunt, with Q/ESR/ESL), series/parallel RLC, custom impedance or Z(f) table, transmission line (lossy, εeff/velocity factor), open/short stubs (shunt or series), ideal transformer and coupled inductors. The load may be a constant Z, a Γ, a Z(f) table or a measured .s1p file (antenna). Use to verify a matching network, check an antenna tuner, or answer 'what impedance does the source see?'.

Synthesize every two-element lumped L-network (series/shunt L and C) that matches a load to a source at one frequency. Handles complex loads and complex sources (conjugate match). Returns 2–4 solutions with exact component values, low-pass/high-pass classification, DC-block/DC-feed behaviour, verified input impedance and VSWR, matched bandwidth, and optional rounding to standard E12/E24/E96 values. Elements are listed load → source and can be passed directly to analyze_circuit or render_smith_chart. Use for 'match 25-j15 Ω to 50 Ω at 2.4 GHz'.

Synthesize three-element Pi (shunt-series-shunt) or T (series-shunt-series) lumped matching networks for a chosen loaded Q, giving control over bandwidth/harmonic suppression that an L-network cannot. Q must exceed √(Rhigh/Rlow − 1). Returns all low-pass/high-pass/mixed variants with component values, virtual resistance, verification and bandwidth. Use for PA output networks, harmonic filtering, or 'match 10 Ω to 50 Ω with Q = 5'.

Single-stub tuner design (Pozar §5.2): find the distance d from the load along the main line and the length ℓ of an open- or short-circuited stub (shunt or series) that matches the load to Z0. Returns all solutions in wavelengths, degrees and — when frequency is given — physical length (with eps_eff / velocity_factor), plus verification and matched bandwidth. Components are returned load → source for analyze_circuit / render_smith_chart. Use for microstrip/coax stub tuners and textbook Smith chart stub problems.

Design a λ/4 impedance transformer Z1 = √(Z0·R). Real loads are matched directly; complex loads first get a section of Z0 line that rotates them to the nearest voltage maximum (R = Z0·VSWR) or minimum (R = Z0/VSWR) on the real axis. Returns the offset length, transformer impedance, physical lengths (if frequency is given), verification and matched bandwidth. Elements are listed load → source.

Read a Touchstone v1 S-parameter file (from a VNA, simulator or datasheet) and summarize it: port count, reference impedance, frequency range, per-frequency table (S11/S21/S12/S22 in dB and angle, VSWR, input impedance, and for 2-ports K, μ and MAG/MSG), resonance / best match for 1-ports, unconditionally stable ranges for 2-ports, and noise parameters if present. Supports MA/DB/RI formats and any frequency unit.

Rollett stability factor K, |Δ|, Edwards-Sinsky μ (load) and μ' (source), unconditional-stability verdict and the input (source-plane) and output (load-plane) stability circles with their stable side. With a Touchstone file and no frequency, returns a K/μ table over the whole file and the stable frequency ranges. Use before designing any amplifier matching network to know which source/load impedances are safe.

Constant-gain circles for amplifier design (Pozar ch. 12): 'available' (G_A, source plane, bilateral), 'operating' (G_P, load plane, bilateral), 'unilateral_source' (G_S) or 'unilateral_load' (G_L) for S12≈0 designs. Returns centre (Γ and Z), radius and whether each gain is achievable, plus the reference maximum gain (MAG/MSG or G_S,max/G_L,max). Omit gains_db to get a ladder of circles below the maximum. Pass the circles to render_smith_chart to plot them.

Constant noise-figure circles in the source (ΓS) plane from the noise parameters NFmin, Γopt and Rn — taken from a .s2p noise block (interpolated at frequency) or given explicitly. Optionally evaluates the noise figure for a proposed source impedance/Γ and, if S-parameters are available, the available gain at Γopt (gain/noise trade-off). Use for low-noise amplifier (LNA) input matching.

Simultaneous conjugate match of a two-port for maximum transducer gain: ΓS and ΓL (and the impedances ZS, ZL the matching networks must present to the device), GT,max (= MAG), MSG, unilateral figure of merit U and the unilateral gain error bounds. Requires K > 1 and |Δ| < 1. With design_networks=true it also synthesizes L-section input and output matching networks from the system Z0 (verified by recomputing ΓS/ΓL).

Draw a publication-quality Smith chart and return it as an image (PNG, via resvg) and/or SVG. Layers (all optional, combine freely): a circuit (load + components listed load → source) drawn as the classic constant-R / constant-G / transmission-line arcs with a node marker per component, plus an optional frequency-sweep trace of the input; impedance or Γ points; VSWR circles; constant-Q contours; arbitrary circles (e.g. from gain_circles / noise_circles / amplifier_stability, centre given as Γ); an S11/S22 locus from a Touchstone file; and amplifier overlays computed from a device (stability circles with the unstable side shaded, available/operating gain circles, noise-figure circles). Impedance, admittance or combined grid; light or dark theme; optional output_path to also save the file.

Report which version of smith-charts-mcp is running and what changed between versions. Without arguments: current version, release date and its release notes. version: notes of one specific release. since: every change released after that version (e.g. 'what changed since 0.1.0?'). all: the full history. Also reports runtime capabilities (PNG rendering, filesystem access).