Resistive Terminated LNA

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Well suited topology for broadband LNA design. Schematic of the LNA with resistive termination is shown in Figure 1(a). The resistive termination(R_I) at the input provides broadband impedance matching over a wide frequency band.

The equivalent circuit of resistive termination LNA is shown in Figure 1c.

Figure 1. LNA with Resistive termination

Figure 1. LNA with Resistive termination

 

Gain of LNA,

(1)   \begin{equation*} G= |G_i|^2= \left( i_o i_o^* \over i_s i_s*\right) = \left|{ g_m \over {1\over R_s}+{1\over R_I}+j\omega C_{gs}}\right|^2 \end{equation*}

Noise Factor of LNA is given by

(2)   \begin{equation*} F = 1 + {N_A \over G N_i}\end{equation*}

where,
N_i = \frac{4kT}{R_s} \rightarrow noise power at the input of LNA due to the source
N_A \rightarrow noise power added by the LNA referred to the output

(3)   \begin{equation*} N_A = G. {4kT \over R_I} + 4kT\gamma g_{d0} \end{equation*}

From Eq.(2),

(4)   \begin{eqnarray*} F &=& 1 + {G \frac{4kT}{R_I} + 4kT\gamma g_{do}\over G \frac{4kT}{R_s}} \\ &=& 1 + {R_s \over R_I}+{\gamma g_{do} R_s \over G} \\ &=& 1 + {R_s \over R_I} + {\gamma g_{do} \over g_m^2} R_s \left(\left({1\over R_s}+ {1\over R_I}\right)^2 + (\omega C_{gs})^2 \right)\\ &=& 1 + {R_s \over R_I} + {\gamma g_{do} \over g_m^2} R_s \left({1\over R_s}+ {1\over R_I}\right)^2 + \gamma g_{do}R_s {\left(\omega \over \omega_T\right)^2 } \end{eqnarray*}

where, \omega_T = {g_m \over C_{gs}}. When R_s = R_I, then noise factor is

(5)   \begin{equation*} F = 2 + {4\gamma \over \alpha g_m R_s} + \gamma g_{do} R_s ({\omega \over \omega_T})^2 \end{equation*}

Therefore the noise figure of Resistive terminated LNA is > 3dB.

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