Demo — Quarter-Wave RAM

Demo — Quarter-Wave RAM#

A Salisbury screen makes one clean promise: at its design frequency the echo cancels. This demo models that screen as a shorted transmission-line stub, plots its reflection across 2–18 GHz, and lets you watch the \(-10\) dB notch snap to a single band — then double the spacer and see it hand \(X\)-band right back. The lesson is not the null; it is how little of the spectrum any single null covers.

The model#

An air spacer of depth \(d\) over the metal skin behaves as a shorted stub with input impedance \(Z_\text{spacer} = j Z_0 \tan(\beta d)\), where \(\beta = 2\pi f/c\). The matched resistive sheet \(R_s\) sits in parallel with that stub, so the surface impedance seen by an incoming wave is

\[ Z_\text{in} = \frac{R_s \cdot j Z_0 \tan(\beta d)}{R_s + j Z_0 \tan(\beta d)}, \qquad \text{reflect}_{\text{dB}}(d) = 20\log_{10}\left|\frac{Z_\text{in} - Z_0}{Z_\text{in} + Z_0}\right|. \]

With \(Z_0 = R_s = 377\ \Omega\), the reflection drops toward \(-\infty\) wherever \(\tan(\beta d)\) blows up — at the quarter-wave frequency and its odd harmonics. The two cases are \(d_1 = c/(4\times 10\ \text{GHz}) = 7.5\) mm (quarter-wave at \(X\)-band) and \(d_2 = 2 d_1 = 15\) mm.

Interactive demo#

Open in full screen

Walkthrough#

  1. Read the reflection curve. The vertical axis is reflection in dB; lower is better. The horizontal dashed line sits at \(-10\) dB — the 90%-absorbed threshold. Anywhere the curve dips below it, the screen is doing its job.

  2. Find the 7.5 mm notch. The \(d = 7.5\) mm curve plunges to a deep null at 10 GHz and holds \(-10\) dB from about 6.3 to 13.7 GHz — one slice of the band.

  3. Double the spacer to 15 mm. The single \(X\)-band null splits into two, at 5 and 15 GHz (the odd harmonics), with \(-10\) dB coverage running roughly 3.1–6.9 and 13.1–16.9 GHz.

  4. Compare the covered fraction. Either design protects about 47% of 2–18 GHz and leaves the other 53% wide open. Doubling \(d\) buys the low band but silently gives back \(X\)-band — exactly where fire-control threats live.

  5. Open the “Intercept asymmetry” tab. A reused L11 view: the radar pays \(1/R^4\) to see you while your RWR pays \(1/R^2\) to hear it — the detect-before-detected band RAM and shaping are buying into.

Key observations#

  • The null is a promise kept at one frequency. Between the harmonics the phase geometry drifts and the echo returns; \(-10\) dB coverage is only about \(\pm37\%\) of \(f_0\).

  • Broader is not free. Doubling the spacer moves the protection, it does not add it — coverage stays near 47%, and the depth (and weight) doubled to get it.

  • No single resonant layer defends VHF-to-\(K_u\). That is why real LO skins go layered (Jaumann), magnetic (iron-loaded), and structural — buying bandwidth with thickness, weight, and maintenance hours.

Source#

MATLAB bundle · L27_QuarterWaveRAM.m↓

The companion script sweeps \(f\) from 2 to 18 GHz, builds the parallel-stub impedance for both spacer depths, plots the two reflection curves against a \(-10\) dB reference line, and prints the null frequencies and covered bands so the class can compare the 47% either design protects against the 53% it leaves open.

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