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Wednesday, July 1, 2020

INA formula chk



E1+(VXE1)·R2R6+R2=E2+(VRE2)·R5R7+R5
E1+(E2E1)·R1R1+R4+R3=V1E1V1R1=E1E2RΣ3
E2+(E1E2)·R4R1+R4+R3=V2V2E2R4=E1E2RΣ3
E1=R1R4(V2E2)+V1E2=R4R1(V1E1)+V2
E2E1+(E1E2)R4+(E1E2)R1RΣ3=V2V1

1R1+R4RΣ3=V2V1E2E1=V2V1E2R1R4(V2E2)V1=V2V1R4R1(V1E1)+V2E1
E2(1+R1R4)(V2R1R4+V1)=V2V11R1+R4RΣ3
 E1(1+R4R1)(V2+V1R4R1)=V2V11R1+R4RΣ3
E2=V2V11R1+R4RΣ3+V2R1R4+V11+R1R4=V2V11R1+R4RΣ3R4+V2R1+V1R4R1+R4
E1=V2V11R1+R4RΣ3+V2+V1R4R11+R4R1=V2V11R1+R4RΣ3R1+V2R1+V1R4R1+R4
. . .
VXR2R6+R2VRR5R7+R5=E2R7R7+R5E1R6R6+R2

IF : {R1=R4=RAR3=RDR6=R7=RFR2=R5=RG
E_1=\frac{\cancel{R_A}\left({V_2+V_1}\right)-\frac{V_2-V_1}{1-\frac{2R_A}{2R_A+R_D}}\cancel{R_A}}{2\ \cancel{R_A}}=\frac{V_2+V_1}2-\frac{V_2-V_1}2·\frac{2R_A+R_D}{R_D}
E_2=\frac{\cancel{R_A}\left({V_2+V_1}\right)+\frac{V_2-V_1}{1-\frac{2R_A}{2R_A+R_D}}\cancel{R_A}}{2\ \cancel{R_A}}=\frac{V_2+V_1}2+\frac{V_2-V_1}2·\frac{2R_A+R_D}{R_D}
.\ .\ .

\left({V_X-V_R}\right)\frac{R_G}{\cancel{R_F+R_G}}=\left[{\left({\cancel{\frac{V_2+V_1}2}+\frac{V_2-V_1}2·\frac{2R_A+R_D}{R_D}}\right)-\left({\cancel{\frac{V_2+V_1}2}-\frac{V_2-V_1}2·\frac{2R_A+R_D}{R_D}}\right)}\right]\frac{R_F}{\cancel{R_F+R_G}}
\boxed{\frac{V_X-V_R}{V_2-V_1}=\frac{R_F}{R_G}·\frac{2R_A+R_D}{R_D}=\frac{R_6}{R_2}·\frac{2R_1+R_3}{R_3}}

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