7.3 Noise in Amplifiers 191will be shown in the CMOS design example; however, it can be noted that the results are not that different. It can also be noted that in practice at low gigahertz frequencies, the gate induced noise term, the last term in (7.66), can often be left out to simplify the calculations.7.3.4 Input Matching of LNAs for Low NoiseSince the LNA is the first component in the receiver chain, the input must be matched to be driven by 50W. Many methods for matching the input using passive circuit elements are possible with varying bandwidths and degrees of complexity, many of which have already been discussed; however, one of the most elegant is described in . This method requires two inductors to provide the impedance and noise match for the LNA as shown in Figure 7.14.Starting with (7.39), and using the component names for the bipolar transistor, the input impedance for this transistor (assuming that the Miller effect is not impor-tant and that rp is not significant at the frequency of interest) is: inm eebjg LZj Lj LCCππωωω-=+++ (7.67)Note that to be matched, the real part of the input impedance must be equal to the source resistance Rs so that: m esg LRCπ= (7.68)Therefore: ssemTR CRLgπω== (7.69)Note that Cm has been ignored. If it were considered, the value of the capaci-tance would be larger than Cp , and therefore a larger inductor would be required to perform the match. Figure 7.14 LNA driver transistor with two inductors to provide power and noise matching: (a) with bipolar transistor and (b) with MOS transistor.