Common Gate LNA

A common gate configuration LNA is shown in Figure 1(a). The equivalent circuit is shown if Figure 1(c).

Figure 1. LNA in common gate configuration

Figure 1. LNA in common gate configuration

The gain of LNA is,

(1)   \begin{equation*} G_m = {i_o \over v_s} = {g_m v_{gs} \over v_s} = g_m {Z_i \over R_s + Z_i} ={g_m \over {1 + R_s(g_m+j\omega C_{gs})}}\end{equation*}

(2)   \begin{equation*} G = |G_m|^2 = { i_o i_o^* \over v_s v_s^*} = {g_m \over (1+g_m R_s)^2 + (\omega R_s C_{gs})^2 } \end{equation*}

Noise factor

MOSFET channel noise only considered here for NF calculation.

Noise power added by the circuit referred to the output is , N_A = 4kT\gamma g_{do}

Noise power at input N_i = 4kTR_s

Noise factor of the circuit is

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

When g_m = 1/R_s, noise factor is

(4)   \begin{equation*}F = 1 + 4\gamma + \gamma \left( {\omega \over \omega_T}\right)^2\end{equation*}

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