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curriculum/Microwave Engineering
section 16 of 173 min read

16. Things to Try

  1. Compute the cutoff frequency of WR-90 (a = 22.86 mm). fc(10)=c/(2a)=3×108/0.0457=6.56f_c^{(10)} = c/(2a) = 3 \times 10^8 / 0.0457 = 6.56 GHz. The next mode (TE20_{20}) cuts on at c/a=13.12c/a = 13.12 GHz, and TE01_{01} at c/(2b)=14.76c/(2b) = 14.76 GHz with b=10.16b = 10.16 mm. So WR-90 is single-mode from 6.56 GHz to 13.12 GHz; the standard X-band operating range of 8.2–12.4 GHz fits inside with margin.

  2. Compute the guide wavelength in WR-90 at 10 GHz. λ0=30\lambda_0 = 30 mm. λg=30/1−(6.56/10)2=30/1−0.43=30/0.752≈39.9\lambda_g = 30/\sqrt{1 - (6.56/10)^2} = 30/\sqrt{1 - 0.43} = 30/0.752 \approx 39.9 mm.

  3. Design a 50 Ω microstrip on FR-4 (h = 1.6 mm, εr=4.4\varepsilon_r = 4.4). Using the Hammerstad formula, W≈3W \approx 3 mm gives Z0≈50Z_0 \approx 50 Ω, εeff≈3.32\varepsilon_{eff} \approx 3.32, propagation velocity c/3.32≈1.65×108c/\sqrt{3.32} \approx 1.65 \times 10^8 m/s, and λg\lambda_g at 1 GHz of 16.5 cm.

  4. Cavity resonance. For a rectangular cavity 22.86 mm × 10.16 mm × 50 mm (a WR-90 section closed at both ends), the lowest-frequency mode TE101_{101} resonates at f101=c/2⋅(1/0.02286)2+(1/0.05)2=1.5×108⋅1916+400 Hz=1.5×108⋅48.1=7.21f_{101} = c/2 \cdot \sqrt{(1/0.02286)^2 + (1/0.05)^2} = 1.5 \times 10^8 \cdot \sqrt{1916 + 400}\ \text{Hz} = 1.5 \times 10^8 \cdot 48.1 = 7.21 GHz.

  5. Klystron bunching parameter. For X=1.84X = 1.84 (optimal), V0=5V_0 = 5 kV, and β=1\beta = 1, θ0=2π\theta_0 = 2\pi (one cycle transit), the required RF amplitude is V1=2V0X/θ0=2×5000×1.84/(2π)≈2900V_1 = 2 V_0 X / \theta_0 = 2 \times 5000 \times 1.84 / (2\pi) \approx 2900 V. This is the buncher gap voltage swing needed for full bunching. Substantial; klystrons are not low-input-power devices.

  6. Open up a (unplugged!) microwave oven and identify the magnetron, the WR-340-like waveguide section, the mode stirrer fan, and the door's perforated mesh. Notice how thick the magnetron's permanent magnets are; that is the axial field that bends the electron paths.

  7. Get a $30 SDR (RTL-SDR or HackRF) and tune to 2.4 GHz. You can see the spectrum of nearby Wi-Fi traffic, a microwave oven leak (0.2 dB-level emissions), and Bluetooth devices. Cheap, instructive, and a gateway drug to RF.

  8. Simulate a microstrip patch antenna in OpenEMS or sonnet (free editions exist). Tune for 2.4 GHz and verify the resonant frequency, S11S_{11} bandwidth, and radiation pattern.

  9. Read a real Touchstone file in scikit-rf. Many manufacturers post sample S2P files for components on their websites. Plot ∣S21∣|S_{21}| in dB and see what a real amplifier's gain curve looks like.