the case for :
\[\cases{signal\ :\ U_S=U_1\\ reference\ :\ U_R=U_0\\ gain\ :\ R_G=R_0\\ feedback\ :\ R_F=R_1\\ output\ :\ U_O=U_X}\]
\[U_R=U_\overline{IN}=U_S+\left({U_O-U_S}\right)·\frac{R_G}{R_G+R_F}\]
\[U_S-U_R=-\left({U_O-U_R+U_R-U_S}\right)·\frac{R_G}{R_G+R_F}\]
\[\frac{U_O-U_R}{U_S-U_R}-1=A_V-1=-1-\frac{R_F}{R_G}\]
\[\boxed{A_V=-\frac{R_F}{R_G}}\]
\[\begin{align*}\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \\ \hline \end{align*}\]
\[\cases{signal\ :\ U_S=U_0\\ reference\ :\ U_R=U_1}\]
\[U_S=U_\overline{IN}=U_R+\left({U_O-U_R}\right)·\frac{R_G}{R_G+R_F}\]
\[U_S-U_R=\left({U_O-U_R}\right)·\frac{R_G}{R_G+R_F}\]
\[\frac{U_O-U_R}{U_S-U_R}=\boxed{A_V=1+\frac{R_F}{R_G}}\]
\[\frac{U_Y}{U_1}=\frac{R_0+R_1}{R_0}\qquad \frac{U_X-U_0}{U_Y-U_0}=-\frac{R_3}{R_2}\\ {\ }\]
\[\boxed{U_X=}\ U_0\left({\frac{R_2+R_3}{R_2}}\right)-\frac{R_3}{R_2}U_1\left({\frac{R_0+R_1}{R_0}}\right)\ {^?= {}_?}\ \mathbf{...}\ =\left({U_0-U_1}\right)\frac{R_2+R_3}{R_2}\ \boxed{=\Delta U_{IN}\left({1+\mathbf{M}}\right)}\\ {\ }\]
\[?\qquad \frac{R_2+R_3}{R_2}=\frac{R_3R_0+R_3R_1}{R_0R_0}\ {^?= {}_?}\ ...\ =\frac{R_3\frac{R_0}{R_1}+R_3}{\frac{R_0}{R_1}R_2}=\frac{R_3\frac{R_3}{R_2}+R_3}{\frac{R_3}{R_2}R_2}=\frac{R_2+R_3}{R_2}\\ {\ }\]
\[R_0=\frac{R_3\left({R_0+R_1}\right)}{R_3+R_2}\\ {\ }\]
\[\cases{\underline{R_0R_3}+R_0R_2=\underline{R_0R_3}+R_1R_3\\ {\ }\\ \boxed{R_0R_2=R_1R_3}}\qquad \frac{R_3}{R_2}=\frac{sR_0}{sR_1}=\mathbf{M}\qquad \mathbf{...} \uparrow\]
some tests :
MAX input impedance test :
Max. frequency TEST :
[Eop]
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