I am attempting to calculate an antenna's input impedance. I have been given this information:
A 50 Ω coaxial line is feeding an antenna with a signal frequency of 150 MHz. The coaxial line has a dielectric constant of 2.25, with an outer conductor of 40 mm. The antenna and coaxial cable are not matched, therefore have a standing wave ratio of 2.7. The first voltage minimum occurs 0.42 m from the antenna.
So far I have this, however it does not seem right, any clues??
\[ \lambda = \frac{c}{f\sqrt{\epsilon_r}}=\frac{3*10^8}{150*10^6\sqrt{2.25}}=\frac{4}{3}\approx 1.33m \]
\[ \beta = \frac{2\pi}{\lambda}=\frac{2\pi}{1.33}= \frac{3}{2}\pi\approx4.712 rad/m \]
\[ \theta_r = 2 \beta d_{min(n)} - (2n+1)\pi rad = 2 * \frac{3}{2}\pi * 0.42 - \pi = \frac{13}{50} \pi \approx 46.8^\circ \]
\[ |\Gamma|=\frac {VSWR-1}{VSWR+1} = \frac {2.7-1}{2.7+1}\approx 0.4594 \]
\[ Z_L = Z_0 \frac{1+|\Gamma|}{1-|\Gamma|}=50\frac{1+0.4594e^{j46.8^\circ}}{1-0.4594e^{j46.8^\circ}}=67.767+j57.54\Omega \]
A 50 Ω coaxial line is feeding an antenna with a signal frequency of 150 MHz. The coaxial line has a dielectric constant of 2.25, with an outer conductor of 40 mm. The antenna and coaxial cable are not matched, therefore have a standing wave ratio of 2.7. The first voltage minimum occurs 0.42 m from the antenna.
So far I have this, however it does not seem right, any clues??
\[ \lambda = \frac{c}{f\sqrt{\epsilon_r}}=\frac{3*10^8}{150*10^6\sqrt{2.25}}=\frac{4}{3}\approx 1.33m \]
\[ \beta = \frac{2\pi}{\lambda}=\frac{2\pi}{1.33}= \frac{3}{2}\pi\approx4.712 rad/m \]
\[ \theta_r = 2 \beta d_{min(n)} - (2n+1)\pi rad = 2 * \frac{3}{2}\pi * 0.42 - \pi = \frac{13}{50} \pi \approx 46.8^\circ \]
\[ |\Gamma|=\frac {VSWR-1}{VSWR+1} = \frac {2.7-1}{2.7+1}\approx 0.4594 \]
\[ Z_L = Z_0 \frac{1+|\Gamma|}{1-|\Gamma|}=50\frac{1+0.4594e^{j46.8^\circ}}{1-0.4594e^{j46.8^\circ}}=67.767+j57.54\Omega \]
