Topic: Microwave Engineering
Design a single section, quarter wave impedance transformer at 5 GHz from $3.75~cm\times 2$ cm guide to $3.75~cm\times 1$ cm guide. Assume air filled wave guide with transformer section having same width as that of the input and output sections.
- A. Height=1.414 cm, Length=3 cm
- B. Height=1.5 cm, Length=2.5 cm
- C. Height = 1.414 cm, Length=2.5 cm
- D. Height=1.5 cm, Length=3 cm
Answer: C. Height = 1.414 cm, Length=2.5 cm
Explanation: The cutoff frequency for the $TE_{10}$ mode is $f_c = \frac{c}{2a} = \frac{3 \times 10^{10}}{2 \times 3.75} = 4$ GHz. The guide wavelength at 5 GHz is $\lambda_g = \frac{c/f}{\sqrt{1 - (f_c/f)^2}} = \frac{6}{\sqrt{1 - 0.64}} = \frac{6}{0.6} = 10$ cm. The length of the quarter-wave transformer is $L = \lambda_g / 4 = 10 / 4 = 2.5$ cm. For matching waveguide heights (which is proportional to characteristic impedance), the transformer height is the geometric mean $H = \sqrt{b_1 b_2} = \sqrt{2 \times 1} = \sqrt{2} \approx 1.414$ cm.