10/26/2006 System Equivalent Noise Temperature 1/6 Jim Stiles The Univ. of Kansas Dept. of EECS System Equivalent Noise Temperature Say we cascade three microwave devices, each with a different gain and equivalent noise temperature: These three devices together can be thought of as one new microwave device. Q: What is the equivalent noise temperature eT of this overall device? A: First of all, we must define this temperature as the value eT such that: ()out in eTGT T=+ or specifically: inT 22eG,T 33eG,T outT eG,T 11eG,T10/26/2006 System Equivalent Noise Temperature 2/6 Jim Stiles The Univ. of Kansas Dept. of EECS outeinTTTG=− Q: Yikes! What is the value of G ? A: The value G is the total system gain; in other words, the overall gain of the three cascaded devices. This gain is particularly easy to determine, as is it simply the product of the three gains: 123GGGG= Now for the hard part! To determine the value of outT, we must use our equivalent noise model that we studied earlier: + G * eT inT ()out in eTGT T=+ Amplifier Ideal Noiseless Amplifier w/ gain G Noise Source w/ noise temperature Te10/26/2006 System Equivalent Noise Temperature 3/6 Jim Stiles The Univ. of Kansas Dept. of EECS Thus, we cascade three models, one for each amplifier: We can observe our model and note three things: ()11 1out in eTGT T=+ ()21 1 1out out eTGT T=+ ()31 2 1out out eTGT T=+ Combining these three equations, we find: ()()()3123 1 232 33out in e e eTGGGT T GGT GT=+++ a result that is likewise evident from the model. + * 1eT inT + * 2eT 1outT + * 3eT 2outT G1 G2 G3 3out outTT=10/26/2006 System Equivalent Noise Temperature 4/6 Jim Stiles The Univ. of Kansas Dept. of EECS Now, since 3out outTT= , we can determine the overall (i.e., system) equivalent noise temperature eT: ()()()123 1 23 2 3 3123231112outeinin e e eineeeTTTGGGGT T GGT GTTGGGTTTGGG=−++ +=−=+ + Moreover, we will find if we cascade an N number of devices, the overall noise equivalent temperature will be: 23 41112123 123 1ee e eNeeNTTT TTTGGGGGG GGGG−=+ + + ++"" I assume that you can use the above equation to get the correct answer—but I want to know if you understand why your answer is correct! Make sure you understand where this expression comes from, and what it means. Look closely at the above expression, for it tells us something very profound about the noise in a complex microwave system (like a receiver!).10/26/2006 System Equivalent Noise Temperature 5/6 Jim Stiles The Univ. of Kansas Dept. of EECS Recall that we want the equivalent noise temperature to be as small as possible. Now, look at the equation above, which terms in this summation are likely to be the largest? * Assuming this system has large gain G, we will find that the first few terms of this summation will typically dominate the answer. * Thus, it is evident that to make eT as small as possible, we should start by making the first term as small as possible. Our only option is to simply make 1eT as small as we can. * To make the second term small, we could likewise make 2eT small, but we have another option! Æ We could likewise make gain 1G large! Note that making 1G large has additional benefits, as it likewise helps minimize all the other terms in the series! Thus, good receiver designers are particularly careful about placing the proper component at the beginning of a receiver. They covet a device that has high gain but low equivalent noise temperature (or noise figure). Æ The ideal first device for a receiver is a low-noise amplifier! G Æ Big Te Æ Small10/26/2006 System Equivalent Noise Temperature 6/6 Jim Stiles The Univ. of Kansas Dept. of EECS Q: Why don’t the devices at the end of the system make much of a difference when it comes to noise? A: Recall that each microwave device adds more noise to the system, As a result, noise will generally steadily increase as it moves through the system. * By the time it reaches the end, the noise power is typically so large that the additional noise generated by the devices there are insignificant and make little increase in the overall noise level. * Conversely, the noise generated by the first device is amplified by every device in the overall system—this first device thus typically has the greatest impact on system noise temperature and system noise
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