To: File

From: Jon Hagen

Date: Oct. 1, 2001

Subject: Input waveguide contribution to noise figure of 8-10 GHz receiver

We model the 8-10 GHz receiver as a 15 deg. LNA preceded first by 8 inches of circular aluminum waveguide (diam. 0.912") at a physical temperature of 15 deg. K and then by 3 inches of the same waveguide at 290 deg. K. Both waveguides act as attenuators; let their gains (less than unity) be designated by G1 and G2 . The cooled attenuator is modeled as a directional coupler whose terminations are at 15 deg. K. The noise figure looking into this "attenuator" is designated as NF1. Since the input attenuator is at the reference temperature, 290 deg. K, the overall noise figure is given by NF1/G2, where G2 is the gain of the input attenuator.

From inspection of the figure, we can write the expression for NF1:

The Mathcad calculations below show the overall receiver temperature as a function of

frequency.