7.3 Noise in Amplifiers 201Since the transistors are operated at very low current densities, the long chan-nel approximations are used for g and d, as discussed in Chapter 4, that is, g = 0.67 and d = 1.33.It can be noted that the above equation for the noise factor is valid for a common- source amplifier. However, this amplifier has matching components LS and LG and this affects the noise somewhat. In particular, since gain is no longer given by gm multiplied by RL but is determined by (7.38), this must be used to convert the drain channel noise into the equivalent input noise. As well, because of the gate inductance LG and because of impedance matching, the noise current into the gate node sees an impedance that can be shown to be approximately (1 + Q2)Rs where Q is given by ω LG/RS. The resulting equation for F and the resulting numerical value is 222222(1)14184.108.40.206 0.04 50(1 2.44 ) 5.210.67 0.04 4 5050285281 0.162 0.183 0.128 1.4731.68 dBgLGm smssTTrrg RQFgRRFFωδωγωω++æöæö= ++×+ç÷ç÷èøèø××+æöæö= ++×× ×+ç÷ç÷èøèø= +++=Þ Simulated noise figure, shown in Figure 7.25, is 1.6 dB, close to the predicted value. By examining the simulated transistor, small-signal parameters, and noise summary, it seems that the transistor is approaching subthreshold operation; thus, even smaller values for g and d could be used. It is also noted that when designing amplifiers with very low noise, even small noise contributions, for example, from the bias resistor and from the cascode transistor, can end up having a significant impact on noise.7.3.5 Relationship Between Noise Figure and Bias CurrentNoise due to the base resistance is in series with the input voltage so it sees the full amplifier gain. The output noise due to base resistance is given by: no,14brbmLvkTrg R»´ (7.71)Figure 7.25 Noise figure and NFmin versus bias current.