So I am solving receiver figure of merit. I have gain in dB and noise temperature in K.

I know

[G/T] = [G] - [T] dB/K

Here should I need to take T in dB or just as K?


The relationship [G/T] = [G]-[T] when given in dB/K is with both the gain and the temperature in dB. T typically refers to the noise temperature of the terminal including the LNA, but is referenced to the input of the LNA (so basically the receiver gain after that is not included, but all cascaded noise contributions are, as referenced to the LNA input).

Example: Antenna Gain (up to LNA so including all antenna losses; ohmic, pointing, etc)= 30 dB. Noise temperature = 200K

For this G/K would be $30 - 10log10(200) = 7 dB/K

Reason being is convenience if a link budget when dealing with antenna effects specifically:

$C/N_o = EIRP - P_L + G/T - K$


$C/No$: Received Carrier to Noise ratio normalized to bandwidth (dB/Hz)

$EIRP$: Equivalent Isotropic Radiated Power (dBW)

$P_L$: Total Path Loss between Tx and Rx (dB)

$G/T$: Receiver terminal figure of merit in $dB/10Log_{10}(K)$

$K = 10 log_{10}(k)$

$k$: Boltzmann constant $\approx 1.38E-23$


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