Right way to calculate reflector and active-phased-array antenna system noise temperature taking into account antenna mismatch

In calculating the antenna system temperature the question always arises as to how to account for the antenna mismatch - should it be treated as completely ohmic, nonohmic or something else. In this paper it is shown that the antenna mismatch should be treated neither as ohmic nor nonohmic. Its effect instead is to introduce another term into the antenna system temperature equation. This term accounts for the increase in system temperature due to the reflection of the noise coming out of the receiver in the direction of the antenna that is reflected back into the receiver towards its signal output port. For a single port reflector antenna system this term is equal to the temperature T_Γ of the noise coming out of the receiver towards the antenna times the antenna power reflection coefficient |Γ|. This is usually included in the radiometer field but not by those in the radar and antenna power reflection coefficient communication fields. For an active phased array the question that arises is: What reflection coefficient to use? It is shown that for an active phased array the reflection coefficient to use for this incoherent noise is the same one used for a coherent signal transmitted in the direction of the main beam. This result is new for those in the radiometer, radar and communication fields. Sometimes system engineers in calculating the antenna mismatch assume the antenna mismatch has no effect on the system temperature, it being argued to be nonohmic. Doing this can yield a large underestimate of the system temperature at large scan angles, 1.2 to 2.5 dB for the examples cases considered here. Finally, if on the other hand the mismatch is taken to be completely ohmic the off-broadside antenna system temperature at large scan angles can be overestimated by a large amount, by 1.7 dB. We will first analyze single port dish and lens antennas which use a single low noise amplifier (LNA) for the sum channel and then cover active electronically scanned arrays (transmit/receive and receive only).