For the noninverting amplifier circuit shown in Figure 9 pro

For the non-inverting amplifier circuit shown in Figure 9, prove that for an ideal operational amplifier the virtual short concept is valid, i.e. V^+ = V^- rightarrow v_d = 0.

Solution

Ans)

Problem 6) a) We have for an op-amp V_out=Ao V_d

and for ideal op-amp gain Ao=infinity

For non- inverting amplifier V⁺=V_in as shown in figure given

and V^-=V_out*R₁/(R₁+R_F) --(Voltage division rule and for ideal op-amp input currents =0)

Vd=V⁺-V^-=V_in-V_out*R₁/(R₁+R_F)

as we know V_out=AoV_d=Ao(V_in-V_out*R₁/(R₁+R_F))

Rearranging the terms

V_out(1+AoR₁/(R₁+R_F))=AoV_in

V_out=AoV_in/((1+AoR₁/(R₁+R_F))) dividing numerator and denominator by Ao

V_out=V_in/((1/(Ao)+R₁/(R₁+R_F)))

as For Ideal op-amp Ao=infinity so 1/Ao=0

Vout=V_in*(R₁+R_F)/R₁=V_in*(1+R_F/R₁)

Now using above result we can prove Vd=0

as Vd=V⁺-V^-=V_in-V_out*R₁/(R₁+R_F) substituting Vout from above results we find that

Vd=Vin-Vin=0

So it proves that Virtual short between V+ and V-