186 LNA Design(Note the exact expression from the same equation would have resulted in 16.5, so the approximate expression is sufficient.) Thus, the gain has been reduced from 26 dB to 24.4 dB. From the source, the gain is reduced much more since the input impedance is much reduced so there is a lot of attenuation. The gain from the source, instead of from vi, can be shown to be just over 15 dB.Thus, gain is reduced from 23.8 dB to about 15 dB by feedback. in500 100500 (196244)28.161.9820fLfm LRRZR Zjjg Rπ++æö»=-=-ç÷èø outip50053.634.9611 0.2 (41.224.27)fmRZjg Zj»==+++´- where Zip = Rs½½Rf½½Zs = 50½½500½½(196 - j244) = 41.22 - j4.27.We note that at low frequency without feedback, Zin would have been 500W due to rp, while with feedback, it can be shown to be 27W (assuming the feedback capacitor is large enough so that feedback is still being applied), so the impedance is much more steady across frequency.In Section 7.9, we will conclude the chapter with a major example of a broad-band amplifier design, including considerations of noise and linearity. Noise and linearity are topics that will be discussed in some of the following sections.7.3 Noise in AmplifiersWhen the signal is first received by the radio, it can be quite weak and can be in the presence of a great deal of interference. The LNA is the first part of the radio to process the signal and it is therefore essential that it amplify the signal while add-ing a minimal amount of additional noise to it. Thus, one of the most important considerations when designing an LNA is the amount of noise present in the circuit. The following sections discuss this important topic.7.3.1 Input Referred Noise Model of the Bipolar TransistorNote that the following two sections contain many equations, which may be tedious to some readers. Reader discretion is advised. Those who find equations disturbing can choose to go directly to Section 7.3.4. In Chapter 2, we made use of an idealized model for an amplifier with two noise sources at the input. If the model is to be applied to an actual LNA, then all the noise sources, as discussed in Chapter 4, must be written in terms of these two input- referred noise sources, as shown in Figure 7.12. Starting with the model shown in Figure 7.12(a) and assuming that the emitter is grounded with base input and col-lector output, the model may be determined with some analysis.