4/17/2005 Noise Figure of Passive Devices 1/4 Jim Stiles The Univ. of Kansas Dept. of EECS Noise Figure of Passive Devices Recall that passive devices are typically lossy. Thus, they have a “gain” that is less than one—we can define this in terms of device attenuation A: 1AG= where for a lossy, passive device 1G<, therefore 1A> . Q: What is the equivalent noise temperature eT or noise figure F of a passive device (i.e., not an amplifier) ? A: The equivalent noise temperature of a passive device can be shown to be approximately (trust me!): ()1eTAT=− where T is the physical temperature of the passive device. Typically we assume this physical temperature to be 290KD, so that: ()1290eTAK=−D4/17/2005 Noise Figure of Passive Devices 2/4 Jim Stiles The Univ. of Kansas Dept. of EECS Thus, we find that the output noise temperature of a passive device is: ()()1290290290out in ein eininTGT TTTAAKTAAKTKAA=++=−=+=− +DDD This result is very interesting, and makes sense physically. As attenuation A approaches the lossless case 1A=, we find that out inTT=. In other words the noise passes through the device unattneuated, and the device produces no internal noise! Æ Just like a length of lossless transmission line! On the other hand, as A gets very large, the input noise is completely absorbed by the device. The noise at the device output is entirely generated internally, with a noise temperature 290outTK=D equal to its physical temperature. inT ()()out in ein eTGT TTTA=+=+ A,Te4/17/2005 Noise Figure of Passive Devices 3/4 Jim Stiles The Univ. of Kansas Dept. of EECS Æ Just like the output of a resistor at physical temperature 290TK=D Q: So, what is the noise figure F of a passive device? Now, we determined earlier that the noise figure of a two-port device is related to its equivalent noise temperature as: 1290eoTFK=+ Therefore, the noise figure of a passive device is: ()()1290129011AKFKAA−=+=+ −=DD Thus, for a passive device, the noise figure is equal to its attenuation! 1FGA== So, for an active two-port device (e.g., an amplifier), we find that two important and independent device parameters are gain G and noise figure F—both values must be specified.4/17/2005 Noise Figure of Passive Devices 4/4 Jim Stiles The Univ. of Kansas Dept. of EECS However, for passive two-port devices (e.g., an attenuator), we find that attenuation A and noise figure F are not only completely dependent—they are in fact equal! Finally, we should not that the value A represents the attenuation (i.e., loss) of any passive device—not just an attenuator. For example, A would equal the insertion loss for a switch, filter, or coupler. Likewise, it would equal the conversion loss of a mixer. Thus, you should now be able to specify the noise figure and equivalent noise temperature of each and every two-port device that we have
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