# Why for a dipole antenna half wave length is optimum size?

For a dipole antenna, half wave length is optimum size. Why is this so? What I understand is that radiation resistance of antenna is around 50 ohms at this size, which matches with the characteristic resistance of transmission line and hence less reflection loss. Is this reasoning correct? If yes, then why transmission line cannot have lower resistance? If no, what is the reason?

• I have cleaned up some of the comments on this post. As a reminder to all, please be courteous to others.
– user22021
Dec 26 '16 at 22:30
• Perhaps a good starting point is to understand the radiation pattern of the antenna: antenna-theory.com/antennas/halfwave.php Dec 27 '16 at 15:46
• Peter - excellent link! Feb 6 '19 at 23:22
• Portions of this question might be a dup of : electronics.stackexchange.com/questions/400665/… Oct 31 '20 at 15:44

A couple things. First, a center fed dipole antenna that is slightly shorter than half wave length is in resonance, which means its impedance is purely resistive. Typically, its impedance is about 70 ohms.

I think by transmission line resistance you mean impedance. You can make transmission lines with impedances lower than 50 ohms, but these are not common. Most coaxial cable is either 50 of 75 ohms, with 75 ohm being less lossy for a given diameter.

The characteristic impedance of a transmission line is proportional to (the square root of) the ratio of inductance to capacitance (per unit length). So, to make a much lower inductance transmission line, you might need to make the wires thicker than the distance between their centers, which is very hard to do at reasonable costs and geometries.