10. Worked Examples and Things to Try

10.1 Compute the gain of a 1 m dish at 10 GHz

$\lambda = c/f = 3 \times 10^8 / 10^{10} = 0.03$ m. Physical area $A_{phys} = \pi(0.5)^2 = 0.785$ m². Aperture efficiency (typical) 60%, so $A_e = 0.471$ m². Gain $G = 4\pi A_e / \lambda^2 = 4\pi (0.471) / (0.03)^2 = 6577$, or 38.2 dBi. HPBW $\approx 70(0.03)/1 = 2.1°$, a pencil beam.

10.2 Friis link budget for a UHF link

A 5 W transmitter at 433 MHz feeds a 6 dBi Yagi. The receiver, 1 km away, has a 3 dBi whip. What is the received power?

$P_t = 37$ dBm. $G_t = 6$ dB. $G_r = 3$ dB. Path loss = $20\log(1000) + 20\log(4.33 \times 10^8) - 147.55 = 60 + 172.7 - 147.55 = 85.2$ dB. $P_r = 37 + 6 + 3 - 85.2 = -39.2$ dBm. A typical 433 MHz receiver needs about –110 dBm, so 70 dB of margin: more than enough.

10.3 Compute the array factor of an 8-element ULA

Use the Python snippet in section 5.6. Vary delta from 0 to $-\pi$ to scan the beam from broadside to end-fire. Plot in dB and observe how the side lobe levels stay around –13 dB for uniform amplitudes; apply a Hamming taper across the elements and watch them drop to about –42 dB at the cost of a slightly wider main beam.

10.4 Build a simple 433 MHz Yagi

Cut a half-wave dipole driven element of about 32 cm. Add a reflector 5% longer (~34 cm) about 8 cm behind; add 2 directors 5% shorter (~30 cm) at 8 cm spacing in front. The result is a ~10 dBi Yagi for the 433 MHz ISM band. Mount on a wooden boom with copper-wire elements. Use it to receive cheap weather sensors, key fobs, and tire-pressure monitors. (This is a fully legal exercise as long as you only receive, not transmit.)

10.5 Simulate a half-wave dipole in 4nec2 or NEC2

Free antenna simulators based on the NEC2 method-of-moments engine let you model wires, plot patterns, and compute impedance. Build a half-wave dipole at any frequency, sweep it, observe the 73 Ω resistance and zero reactance at resonance, and verify the doughnut pattern.

10.6 Watch a TEMPEST demonstration

There are public demonstrations of recovering display content via Van Eck phreaking, and academic videos showing AES key recovery via near-field probes. The barrier to entry is depressingly low: a software-defined radio (~$300), a high-gain antenna, and a few weekends of DSP. It is sobering to see how unassuming the setup is, and it is the best motivation to take Faraday-shielding seriously in security-critical environments.