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Figure 10.1 illustrates an inverting summer op-amp:
(a) Find the expression for the output voltage Vo of the inverting summer, assumming the inverting op-amp is ideal.
(b) What mathematical operation does the inverting summer of figure 10.1 perform if R1 = R2 = R3 = 3RF?
The strings:
S7P5A51 (change - physical).
The math:
Pj Problem of Interest is of type change (physical - change).
(a) Consider figure 10.1. If the inverting op-amp is an ideal op-amp then Vd = 0 approximately, and AOL is infinitely large.
So, inverting node is a virtual ground.
So, the current in each of the resistors are independent.
So, using the principle of superposition we have:
Vo1 = -(RF/R1)Vs1
Vo2 = -(RF/R2)Vs2
Vo3 = -(RF/R3)Vs3
And Vo = Vo1 + Vo2 + Vo3
So, Vo = -RF(Vs1/R1 + Vs2/R2 + Vs3/R3)------(1)
(b) Substituting given resistor values into eq(1) we have:
Vo = -RF(Vs1/3RF + Vs2/3RF + Vs3/3RF)
So, Vo = -(Vs1 + Vs2 + Vs3)/3
So, for the given values, the circuit gives the negative of the instantaneous average value.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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