Aperture power density¶

Three quantities in this package share the words "power" and "density" and mean different things. Read this table first.

Quantity	Units	Where	What it is
Aperture heat flux	W/cm²	`heat_flux_w_per_cm2`	Dissipated power per unit array aperture area. Selects the cooling technology.
Radiated power density	W/cm²	`radiated_power_density_*_w_per_cm2`	Radiated power per unit aperture area, at the aperture face.
Far-field power density	W/m²	radar equation	Flux at a distant target, `S = P_t G_t / 4πR²`. Falls as 1/R².
PA power density	W/mm	`data/technologies.yaml`	Semiconductor power per unit gate periphery. A device property, not an array one.
Power-aperture product	W·m²	`power_aperture_product_w_m2`	Mission figure of merit. Dimensionally the inverse of a power density.

The clutter resolution_cell_m2 in the radar models is a patch of ground, not an array unit cell.

Geometry¶

ArrayConfig stores spacing in wavelengths and carries no frequency, so the physical scale comes from the scenario:

\[A_{cell} = d_x d_y \lambda^2, \qquad A_{ap} = N A_{cell} = (n_x d_x)(n_y d_y)\lambda^2\]

with dx, dy in wavelengths. The radiating aperture is N·d per axis, not the (N−1)·d tip-to-tip extent of the element centres: each element owns a full cell.

Why it earns a metric¶

At half-wave spacing \(A_{cell} = (\lambda/2)^2 = (c/2f)^2\), so at fixed per-element dissipation

\[q'' = \frac{P_{diss,elem}}{A_{cell}} \propto f^2\]

Doubling frequency quadruples aperture heat flux. Moving a design from X-band to Ka-band multiplies it by about nine with no other change. This is the whole reason the quantity is worth computing: nothing else in a system model tells you that the same T/R module, unchanged, is an air-cooled design at 10 GHz and a liquid-cooled one at 30 GHz.

The junction-temperature model is a per-device normalization:

\[T_j = T_{amb} + R_{th}\frac{P_{diss}}{N}\]

Dividing by element count answers "how hot is one device"; dividing by aperture area answers "can the cooling approach remove this flux". They are different questions, and the second is invisible to the first: packing elements tighter leaves junction dissipation unchanged while raising heat flux as \(1/d^2\).

Averaging convention¶

Heat flux is reported on average power. Cold-plate and coolant-loop time constants are seconds; a radar PRI is microseconds, so the plate sees the duty-cycle-averaged load.

The junction does not average that way. GaN junction thermal time constants are comparable to pulse widths, so within a pulse the junction rises above its pulse-averaged value, and the pulse-to-pulse swing drives thermo-mechanical fatigue. This package has no thermal transient model and makes no peak-junction claim. Radiated power density is reported at both peak and average because peak is what matters for field strength and average is what matters for heat.

Cooling feasibility¶

ReliabilityConfig.thermal_resistance_c_per_w is an assertion about a cooling solution. Setting Architecture.cooling checks it: the design's heat flux is compared against what the declared class can remove, from data/cooling.yaml.

Class	Gate (W/cm²)	Basis
`natural_convection`	0.05	judgment
`forced_air`	1.0	quoted (DARPA MACE target: 10 K rise at 1 W/cm²)
`liquid_cold_plate`	20	judgment, bounded below the DARPA ACM figure
`microchannel_two_phase`	100	judgment

These are order-of-magnitude regime gates, not cliffs. Every entry records whether its number was quoted from the primary source or is an engineering-judgment gate consistent with it; two are quoted verbatim from Bar-Cohen, Maurer & Felbinger (CS MANTECH 2013), and the entries relying on Mudawar's 2001 IEEE review are marked judgment because that PDF renders its numerals as embedded objects that text extractors drop. The catalog says so.

Crossing a boundary is not a smooth penalty. Going from forced air to a liquid cold plate adds pumps, a heat exchanger, plumbing, coolant mass, leak paths and a maintenance burden. That discreteness is what makes the metric useful in a trade study.

Power-aperture product¶

For volume search (Barton, Radar Equations for Modern Radar, 2013; Skolnik, Introduction to Radar Systems, 3rd ed.):

\[P_{avg} A_e = \frac{4\pi k T_s L (S/N) R^4 \Omega}{\sigma t_s}\]

Frequency and antenna gain do not appear. Search performance depends on the product of average power and effective aperture, not on how the aperture is partitioned into beams. Required power-aperture scales as \(R^4\) and as \(\Omega/t_s\): halving the revisit time doubles what the mission demands.

The two metrics pull in opposite directions, which is why the package computes both. Power-aperture says how much power and aperture the mission needs; heat flux constrains how tightly that power may be packaged. Optimizing either alone produces a design that is oversized or unbuildable.

What is not modeled¶

Die-level and junction-level heat flux (two to four orders of magnitude higher, governed by spreading resistance through the module) belong to MMIC and package design. RF exposure limits are a siting output, not a design driver, and a plane-wave power density cannot establish compliance in the reactive near field of a large array. Multipaction requires hard vacuum and applies to space missions only; air breakdown at the aperture face of a ground array is orders of magnitude away and binds inside high-power feed components instead.