RF calculations

Reference: Complex, RfCalculations, SmithFormatter, MarkerMeasurements.

Calculations without a chart

import { Complex, RfCalculations } from 'smithkit';

const gamma = RfCalculations.impedanceToReflection(Complex.from(75, 25), 50)!;
const reading = RfCalculations.readReflection(gamma, 50);
console.log(reading.impedanceOhms?.toVector()); // Approximately [75, 25].
console.log(reading.admittanceSiemens?.toVector());
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Comparison results contain frequencyDeltaHz, impedanceDeltaOhms, and phaseDeltaDegrees. Phase differences use B − A wrapped to [−180°, 180°): 179° → −179° gives +2°; an exact half turn gives −180°. Phase is undefined if either Γ is zero or non-finite. Impedance differences are undefined if either Z is singular or non-finite. Frequencies must be finite and non-negative. This is a point comparison, not sweep phase unwrapping or group delay.

Complex.from(re, im) constructs complex numbers. Read components through re and im. Arithmetic (add, sub, mul, div, pow) returns new values. The class also provides abs, arg (radians), and static methods such as Complex.conj, Complex.sqrt, Complex.exp, Complex.log, and trigonometric/hyperbolic functions and inverses. toVector() returns [real, imaginary]; toString(dp) formats a Cartesian value. See the exported declarations for all operations.

The SmithFormatter class provides static methods: SmithFormatter.number(value) (three significant digits and SI prefixes), SmithFormatter.complex(value, unit?, decimalPlaces?), and SmithFormatter.polar(value, unit?, decimalPlaces?) (phase in degrees). They work without a chart or DOM. Complex formatters default to three fractional digits. SmithFormatter.number includes spacing so you can append a unit, e.g. SmithFormatter.number(1e9) + 'Hz'.

RfCalculations.reactanceToComponent(reactanceOhms, frequencyHz) calculates an ideal equivalent series component without formatting or constructing a chart:

import { RfCalculations, SmithFormatter } from 'smithkit';

const component = RfCalculations.reactanceToComponent(-50, 1e9);
if (component?.kind === 'capacitor') {
  console.log(SmithFormatter.number(component.capacitanceFarads) + 'F'); // 3.18 pF
} else if (component?.kind === 'inductor') {
  console.log(SmithFormatter.number(component.inductanceHenries) + 'H');
}
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Use reading.impedanceOhms.im for the reactance when impedance is defined. Zero frequency, zero reactance, and unrepresentable results return undefined. Non-finite reactance or negative/non-finite frequency throws RangeError. This is a single-frequency equivalence, not a fitted circuit model.

Reference impedance and renormalization

chart.renormalize(referenceImpedanceOhms) changes the positive real reference impedance and transforms every loaded Γ to preserve physical Z. Trace/marker IDs, names, colors, visibility, frequencies, and selected sample indices are retained. Results for all traces are validated before any change; a singular/unrepresentable result rejects the operation without changing Z₀ or data. Active marker drags end, cursor indicators are cleared, and marker readings are queued with the new values. Changing to the current Z₀ has no effect. Mutations after destruction throw.

Two DOM-independent methods are available on RfCalculations:

• RfCalculations.renormalizeReflection(gamma, fromOhms, toOhms) returns the new complex Γ or undefined for a singular/unrepresentable result. Exact open and short limits remain Γ = +1 and −1. References must be positive, finite, real ohm values.
• RfCalculations.renormalizeSamples(samples, fromOhms, toOhms) returns a new sample array in the same order, preserving frequencies. Invalid samples or a singular result throw RangeError; the input is never modified.

For example, a matched 75 Ω load has Γ = 0 at 75 Ω and Γ = 0.2 at 50 Ω. Renormalization changes Γ, VSWR, and loss readings; physical impedance stays 75 Ω. Simply relabeling the same Γ with a new Z₀ would describe a different load.

The demo exposes chart Z₀ and explicitly renormalizes existing traces when applied. Import renormalization is enabled by a labeled checkbox. Disable it to reject files whose reference differs from the chart. Complex reference impedances and multiport renormalization are outside the supported scope.

Numerical limits

Complex uses JavaScript binary64 numbers. Multiplication and division scale intermediate products to avoid premature overflow and underflow; logarithms, square roots, and reciprocals also handle extreme finite components. Results still round to binary64: unrepresentable magnitudes become infinity and tiny results can underflow to signed zero. Division by zero and reciprocals at zero return [NaN, NaN]. These operations reject non-finite operands with NaN components. The principal logarithm of zero retains its -Infinity real limit, and signed zeros select the side of square-root and logarithm branch cuts. pow(z, 0) is one, including zero to the zeroth power; negative powers of zero are undefined.

RF helpers validate finite inputs and use undefined for unrepresentable complex readings, including an overflowing impedance difference between markers. These conventions do not imply arbitrary precision or numerical certification of every transcendental operation.