Asymptotic gain model G1 ref.

The gain of the system can be obtained as:

$$ \frac{V_{\mathrm{\ell}}}{V_{s}}=\frac{A_{r}\,g_{m}\,\left(R_{a}+R_{b}\right)}{R_{a}+R_{b}+A_{r}\,R_{b}\,g_{m}+R_{a}\,R_{b}\,g_{m}} $$

The asymptotic gain $A_{\infty G1}$ is found as:

$$ A_{\mathrm{{\infty}{G1}}}=\frac{A_{r}\,\left(R_{a}+R_{b}\right)}{R_{b}\,\left(A_{r}+R_{a}\right)} $$

The loop gain $L_{G1}$ is found as:

$$ L_{\mathrm{G1}}=-\frac{1.0\,R_{b}\,g_{m}\,\left(A_{r}+R_{a}\right)}{R_{a}+R_{b}} $$

The servo function $S_{G1}$ is found as:

$$ S_{\mathrm{G1}}=\frac{R_{b}\,g_{m}\,\left(A_{r}+R_{a}\right)}{R_{a}+R_{b}+A_{r}\,R_{b}\,g_{m}+R_{a}\,R_{b}\,g_{m}} $$

The direct transfer $\rho_{G1}$ is found as:

$$ \mathrm{\rho}_{\mathrm{G1}}=0 $$

If we calculate the gain $A_f$ from the asymptotic gain, the servo function and the direct transfer, we obtain:

$$ A_{f}=\frac{A_{r}\,g_{m}\,\left(R_{a}+R_{b}\right)}{R_{a}+R_{b}+A_{r}\,R_{b}\,g_{m}+R_{a}\,R_{b}\,g_{m}} $$

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