Calculate a complete RF link budget using the Friis transmission equation.

Computes free-space path loss (FSPL), received power, and validates antenna gains against the physical gain limit. The hard bound is G_max = max((piD/lambda)^2, (ka)^2 + 2ka) with k = 2pi/lambda and a = D/2, i.e. the larger of the eta = 1 aperture value and Harrington's bound for an antenna enclosed in a sphere of diameter D (numerically the Harrington value, which converges to the aperture value for D >> lambda and matters for electrically small antennas, D < lambda); a claimed gain above it is rejected. A claimed gain above the typical-efficiency value eta*(pi*D/lambda)^2 (eta = 0.55 by default) but below the physical bound is accepted with a warning. Negative losses are rejected (conservation of energy).

Use this tool when you need to:

• Estimate received signal strength for a wireless link

• Validate whether a claimed link budget is physically achievable

• Check if antenna gain claims are consistent with antenna dimensions

• Compute free-space path loss at a given frequency and distance

Returns both human-readable summary and machine-readable JSON with all intermediate values. Returns a PhysicalViolationError dict if any input violates physics.

Calculate Shannon-Hartley channel capacity and validate throughput claims.

Computes the theoretical maximum data rate C = B * log2(1 + SNR) for an AWGN channel. If a claimed throughput is provided, validates it against this limit. Any claim exceeding the Shannon limit is a physical impossibility.

Use this tool when you need to:

• Calculate maximum achievable throughput for a given bandwidth and SNR

• Validate whether a throughput claim is physically possible

• Determine spectral efficiency limits

• Check if a modulation/coding scheme claim is realistic

Returns a PhysicalViolationError dict when a claim exceeds the Shannon limit.

Calculate thermal noise power (kTB), cascaded noise figure, and receiver sensitivity.

Computes the fundamental thermal noise floor N = k_B * T * B, which is -174 dBm/Hz at the IEEE standard temperature of 290K. Optionally cascades multiple amplifier/filter stages using the Friis noise figure formula F_total = F_1 + (F_2-1)/G_1 + (F_3-1)/(G_1G_2) + ..., the receiver's effective input noise temperature T_e = T_0(F-1) with T_0 = 290 K (the IEEE reference at which noise figure is defined, independent of temperature_k), and receiver sensitivity S_min = k_B*(T_A + T_e)BSNR_required, which reduces to N_floor + NF + SNR_required when temperature_k = 290 K.

Use this tool when you need to:

• Determine the thermal noise floor for a receiver bandwidth

• Cascade noise figures through a multi-stage receiver chain

• Calculate minimum detectable signal / receiver sensitivity

• Validate that a claimed noise figure is physically plausible

Returns a PhysicalViolationError dict if inputs violate thermodynamic limits.

Calculate maximum monostatic radar detection range and validate range claims.

Computes the radar range equation R_max = [P_t * G^2 * lambda^2 * sigma / ((4*pi)^3 * S_min * L)]^(1/4) for a monostatic radar (same antenna for transmit and receive). Validates that claimed detection ranges do not exceed the theoretical maximum. Catches the common fourth-root fallacy where LLMs incorrectly state that doubling transmit power doubles radar range (it only increases range by a factor of 2^(1/4) = 1.19x).

Use this tool when you need to:

• Calculate the maximum detection range of a radar system

• Validate whether a claimed radar detection range is physically achievable

• Determine minimum detectable signal power for a radar receiver

• Check if radar performance claims account for the R^4 path loss

• Verify that RCS assumptions are reasonable for the target class

Returns both human-readable summary and machine-readable JSON with all intermediate values. Returns a PhysicalViolationError dict if any input violates physics or the claimed range exceeds R_max.

Calculate antenna aperture gain limits, beamwidth, far-field distance; validate gain claims.

For a circular aperture of diameter D (or an aperture of area A, converted to the equivalent circular diameter D = sqrt(4A/pi)) computes the planar-aperture directivity D_0 = 4piA/lambda^2 = (piD/lambda)^2 (aperture efficiency eta = 1), Harrington's bound D_max = (ka)^2 + 2ka (k = 2pi/lambda, a = D/2) for any antenna enclosed in a sphere of diameter D, the hard physical gain limit max(D_0, D_max) (numerically D_max; equal to D_0 to within 0.1 dB for D >> lambda, but several dB higher for electrically small antennas D < lambda, e.g. a 2.15 dBi dipole in a 0.1 m footprint at 900 MHz is valid although D_0 = -0.5 dBi), and the typical gain G = etaD_0 at the given efficiency (default eta = 0.55, parabolic dish). The limiting_bound field reports 'harrington' for D < lambda and 'aperture' for D >= lambda. Also returns the effective aperture A_e = etaA, a half-power beamwidth estimate (HPBW ~ 70lambda/D degrees for a tapered reflector; 58.4lambda/D for a uniformly illuminated circular aperture) and the far-field (Fraunhofer) distance 2*D^2/lambda.

If claimed_gain_dbi is given it is validated: a claim above the physical limit is rejected as a physics violation; a claim between the typical gain and the physical limit is accepted with a warning and the implied planar-aperture efficiency eta = G_claim / D_0 is reported.

Use this tool when you need to:

• Check whether a quoted antenna gain is consistent with its size and frequency

• Estimate the gain, beamwidth or effective aperture of a dish of known diameter

• Find the minimum far-field range for antenna measurements or Friis validity

• Size an antenna for a required gain at a given frequency

Returns a PhysicalViolationError dict if any input violates physics or the claimed gain exceeds the aperture limit.

Calculate pulse-Doppler radar ambiguity limits and validate range/velocity claims.

Computes the maximum unambiguous range R_ua = c / (2 * PRF), the first blind speed lambda * PRF / 2, the unambiguous velocity v_ua = +/- lambda * PRF / 4 (Doppler within +/- PRF/2), the Doppler shift f_d = 2 * v_r / lambda of a target (closing velocity positive) and whether it aliases, and — when a pulse width is given — the duty cycle, eclipsing minimum range c * tau / 2 and the range resolution c * tau / 2 (or c / (2 B) when a compressed bandwidth is supplied). Reports the range-Doppler dilemma invariant R_ua * v_ua = c * lambda / 8, which no choice of PRF can beat (Skolnik, Introduction to Radar Systems, Ch. 2-3; Richards, Fundamentals of Radar Signal Processing, Ch. 1, 3, 5).

Use this tool when you need to:

• Find the unambiguous range and velocity coverage of a given PRF

• Check whether a claimed unambiguous range or velocity is possible at that PRF

• Check whether a claimed range resolution is possible for the pulse/bandwidth

• Determine whether a target's Doppler will alias or fall at a blind speed

• Expose claims that silently violate the range-Doppler dilemma

Returns both human-readable summary and machine-readable JSON with all intermediate values. Returns a PhysicalViolationError dict if any input violates physics (PRF <= 0, tau <= 0, duty cycle >= 1) or a claim exceeds its limit.