Alan0354
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This is a homework problem. The question is to find VSWR of lossless dipole antenna connected to a 50Ω lossless tx line. The length of antenna is l=λ/4, λ/2,3λ/4, λ. Assuming the antenna resonates are the given length.
For lossless dipole,\[Z_{in}=R_{in}+jX_{in}\] where \[X_{in}=-jZ_{ant}\cot(\frac{kl}{2})\] and \[\Gamma =\frac{Z_{in}-Z_0}{Z_{in}+Z_0}\]
Obviously, \[Z_{in} \]is complex except length l=nΠ/2 where \[X_{in}=0\]. But the answer from the solution manual claimed \[\Gamma =\frac{R_{in}-Z_0}{R_{in}+Z_0}\] for all cases.
I can agree with l=λ/2 and l=λ where \[X_{in}=0\]. But not for λ/4 and 3λ/4. Please help.
For lossless dipole,\[Z_{in}=R_{in}+jX_{in}\] where \[X_{in}=-jZ_{ant}\cot(\frac{kl}{2})\] and \[\Gamma =\frac{Z_{in}-Z_0}{Z_{in}+Z_0}\]
Obviously, \[Z_{in} \]is complex except length l=nΠ/2 where \[X_{in}=0\]. But the answer from the solution manual claimed \[\Gamma =\frac{R_{in}-Z_0}{R_{in}+Z_0}\] for all cases.
I can agree with l=λ/2 and l=λ where \[X_{in}=0\]. But not for λ/4 and 3λ/4. Please help.