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KU EECS 622 - Noise Figure and SNR

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10/26/2006 Noise Figure and SNR 1/9 Jim Stiles The Univ. of Kansas Dept. of EECS Noise Figure and SNR Of course, in addition to noise, the input to an amplifier in a receiver will typically include our desired signal. Say the power of this input signal is insP. The output of the amplifier will therefore include both a signal with power outsP, and noise with power outnP: where: out inssPGP= and: ()outnin ein ePNGkTBGk T TB=+=+ In order to accurately demodulate the signal, it is important that signal power be large in comparison to the noise power. Thus, a fundamental and important measure in radio systems is the Signal-to-Noise Ratio (SNR): snPSNRP G insinP,N out outsnP,P10/26/2006 Noise Figure and SNR 2/9 Jim Stiles The Univ. of Kansas Dept. of EECS The larger the SNR, the better! At the output of the amplifier, the SNR is: ()()outsoutoutninsin einsin ePSNRPGPGk T T BPkT T B==+=+ Moreover, we can define an input noise power as the total noise power across the bandwidth of the amplifier: innin inPNBkTB== And thus the input SNR as: in inssininninPPSNRPkTB== Now, let’s take the ratio of the input SNR to the output SNR: ()1inin ein sinout in sin eineinkT T BSNR PSNR kT B PTTTTT+⎛⎞=⎜⎟⎝⎠+==+10/26/2006 Noise Figure and SNR 3/9 Jim Stiles The Univ. of Kansas Dept. of EECS Since 0eT> , it is evident that: 11in eout inSNR TSNR T=+> In other words, the SNR at the output of the amplifier will be less than the SNR at the input. Æ This is very bad news! This result means that the SNR will always be degraded as the signal passes through any microwave component! As a result, the SNR at the input of a receiver will be the largest value it will ever be within the receiver. As the signal passes through each component of the receiver, the SNR will get steadily worse! Q: Why is that? After all, if we have several amplifiers in our receiver, the signal power will significantly increase? A: True! But remember, this gain will likewise increase the receiver input noise by the same amount. Moreover, each component will add even more noise—the internal noise produced by each receiver component.10/26/2006 Noise Figure and SNR 4/9 Jim Stiles The Univ. of Kansas Dept. of EECS Thus, the power of a signal traveling through a receiver increases—but the noise power increases even more! Note that the ratioin outSNR SNR essentially quantifies the degradation of SNR by an amplifier—a ratio of one is ideal, a large ratio is very bad. So, let’s go back and look again at ratio in outSNR SNR: 1in eout inSNR TSNR T=+ Note what this ratio depends on, and what it does not. This ratio depends on: 1. eT (a device parameter) 2. inT (not a device parameter) This ratio does not depend on: 1. The amplifier gain G. 2. The amplifier bandwidth B. We thus might be tempted to use the ratio in outSNR SNR as another device parameter for describing the noise performance of an amplifier. After all, in outSNR SNR depends10/26/2006 Noise Figure and SNR 5/9 Jim Stiles The Univ. of Kansas Dept. of EECS on eT, but does not depend on other device parameters such as G or B. Moreover, SNR is a value that can generally be easily measured! But the problem is the input noise temperature inT. This can be any value—it is independent of the amplifier itself. For example, it is event that as the input noise increases to infinity: 11in inin eTTout inSNR Tlim limSNR T→∞ →∞⎛⎞=+=⎜⎟⎝⎠ In other words, if the input noise is large enough, the internally generated amplifier noise will become insignificant, and thus will degrade the SNR very little! Q: Degrade the SNR very little! This meansout inSNR SNR=! Isn’t this desirable? A: Not in this instance. Note that if inT increases to infinity, then: 0in ininsinTTinPlim SNR limkT B→∞ →∞⎛⎞==⎜⎟⎝⎠ In other words, the SNR does is not degraded by the amplifier only because the SNR is already as bad (i.e.,0SNR=) as it can possibly get!10/26/2006 Noise Figure and SNR 6/9 Jim Stiles The Univ. of Kansas Dept. of EECS Conversely, as the input noise temperature decreases toward zero, we find: 001in inin eTTout inSNR Tlim limSNR T→→⎛⎞=+=∞⎜⎟⎝⎠ Q: Yikes! The amplifier degrades the SNR by an infinite percentage! Isn’t this undesirable? A: Not in this instance. Note that if inT decreases to zero, then: 00in ininsinTTinPlim SNR limkT B→→⎛⎞==∞⎜⎟⎝⎠ Note this is the perfect SNR, and thus the ratio in outSNR SNRwill likewise be infinity, regardless of the amplifier. Anyway, the point here is that although the degradation of SNR by the amplifier does depend on the amplifier noise characteristics (i.e., eT), it also on the noise input to the amplifier (i.e., inT). This input noise is a variable that is unrelated to amplifier performace Q: So there is no way to use in outSNR SNRas a device parameter?10/26/2006 Noise Figure and SNR 7/9 Jim Stiles The Univ. of Kansas Dept. of EECS A: Actually there is! In fact, it is the most prevalent parameter for specifying microwave device noise performance. This measure is called noise figure. The noise figure of a device is simply the measured ratio in outSNR SNR exhibited by a device, for a specific input noise temperature inT. I repeat: Æ “for a specific input noise temperature inT.” This specific noise temperature is almost always taken as the standard “room temperature” of 290oTK=D. Note this was likewise the standard antenna noise temperature assumption. Thus, the Noise Figure (F ) of a device is defined as: 29029011290inininoutTKeinTKeSNRFSNRTTTK==⎛⎞=+⎜⎟⎝⎠=+DDD10/26/2006 Noise Figure and SNR 8/9 Jim Stiles The Univ. of Kansas Dept. of EECS It is critically important that you understand the definition of noise figure. A common mistake is to assume that: inoutSNRSNRF= Å This is not generally true! Note this would only be true if 290inTK=D, but this is almost never the case (i.e., 290inTK≠D generally speaking). Thus, an incorrect (but widely repeated) statement would be: “ The noise figure specifies the degradation of SNR.” Whereas, a correct statement is: “ The noise figure specifies the degradation of SNR, for the specific condition when 290inTK=D, and for that specific condition only” The one exception to this is when an antenna is connected to the input of an amplifier. For this case, it is evident that the input


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