Question 6.12: Consider a FET with gm = 0.152 S. Find the series and parall......
Consider a FET with \text{g}_m=0.152\text{ S}. Find the series and parallel feedback resistances needed to obtain S_{21 f}=15\text{ dB} at low frequency with matching on R_0=50 \; \Omega.
Without feedback we have S_{21}=-2 R_0 \text{g}_m=-15.2. The required \left.S_{21 f}\right|_{\text{dB} }=15 dB corresponds, in natural units, to \left|S_{21 f}(0)\right|=10^{15 / 20}=5.623. Since the relation \left|S_{21}\right| \geq 2\left(1+\left|S_{21 f}(0)\right|\right) here corresponds to the values 15.2 > 2(1 + 5.623), the design is possible and:
R_p=R_0\left(1+\left|S_{21 f}(0)\right|\right)=331.17 \; \Omega .
The transconductance must satisfy the relation:
\text{g}_m=0.152>\frac{R_p}{R_0^2}=0.132\text{ S};
since \text{g}_m is larger than the minimum theoretical value required we must introduce a series feedback resistor of value:
R_s=\frac{R_0^2}{R_p}-\frac{1}{g_m}=0.970 \; \Omega .