Antennas are nearly always reciprocal two port devices. Port one is connected to the transmitter or receiver, and port two is connected to free space. The only exception to this rule is if the (passive) antenna contains ferrite, or if the antenna is described as a unit which contains power combiners or isolators made of ferrite, or if the antenna is an active antenna and is considered as containing an amplifier.
If an antenna is a lossless reciprocal two-port network, then s12 = s21, and by the rules for lossless two-ports (see the notes on scattering parameters ) then the size of s11 is the same as the size of s22.
Moreover if the antenna is matched to the transmitter source, there is no reflected wave back into the transmitter and so the size of s11 must be zero.
It follows that the size of s22 must be zero also, and therefore there is no reflected power from the antenna/receiver combination when external power is incident on the antenna. We assume that the wave incident on the receiver impedance is all absorbed, as this impedance is matched to the feeder impedance. There is thus no reflected wave from the receiver to pass back through the antenna and be re-radiated.
It follows that the electromagnetic cross section (ECS) of a correctly matched antenna is precisely zero, no matter how large the antenna structure may be.
If the antenna is mismatched, there will be some reflected power as s11 = s22 is no longer zero. Note that the antenna can only be matched over a limited bandwidth.
Of course, we must remark here that the illumination on the antenna structure needs to be a time reversed replica of the signal it would emit in transmit mode. So in practice, if the antenna structure is illuminated by a plane wave or an expanding wave, having a totally different structure and originating from a remote radar, it is quite unlikely that these conditions will be met, and there will be scattering from the structure.
Tom W wrote:
Hi,
Your website says that
quote
It follows that the radar cross section (RCS) of a correctly matched
antenna is precisely zero, no matter how large the antenna structure may be.
unquote
This is in contradiction to texts on the subject that state that a dipole is an example of a minimum re-radiative antenna, and that 1/2 of the incident energy on a dipole is delivered to the load (max) and 1/2 is re-radiated as scattering. Not so?
Tom W.
Normally the device looking at the dipole is not mimicing the outgoing field distribution.
If you could suddenly change the sign of time so that the outgoing wave returned exactly as it went out, but in the opposite direction, the dipole would receive all the radiation and deliver it to the matched load without any re-radiation.
This is the principle of detailed balance. If it were not so, you could construct a perpetual motion machine and violate the second law of thermodynamics.
In this case the cross section is zero.
The usual arguments are misguided. If you take a transmission line of impedance Zo, and terminate it with a resistance R=Zo, the resistance has a voltage generated across it by the incident wave from the generator, and yet we know it produces no reflected wave.
The usual argument is that because a voltage exists across the antenna impedance, then it must reradiate.
It is far deeper a question than most people think it is at first meeting.
D.
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