Problem 4.33

Subject: 4. Operational Amplifiers

Problem

 Determine the output voltage, eqimages/Q5683_.png , of the noninverting averaging circuit shown in Fig. P4.33.
xxx
(Figure P4.33, page 159)

Hints

  1.  Ideal op-amp's model conditions eqimages/Q5683_2.png  and eqimages/Q5683_3.png .

Directions

  1.  Write node equations at the op-amp's input terminals. Use the ideal op-amp model conditions eqimages/Q5683_4.png  and eqimages/Q5683_5.png  to combine the two equations and eliminate the eqimages/Q5683_6.png  and eqimages/Q5683_7.png  terms.
    Rearrange to obtain the required result.
    eqimages/Q5683_8.png .

Detailed Solution

  1.  We are asked to determine the output voltage eqimages/Q5683_9.png  of the noninverting averaging circuit shown in Fig. P4.33a.
    xxx
    (Figure P4.33a)
  2.  Using the ideal op-amp model condition eqimages/Q5683_10.png , we write node equations at the op-amp's input terminals. The node equation at the noninverting terminal is
    eqimages/Q5683_11.png .
    At the inverting terminal KCL yields
    eqimages/Q5683_12.png .
  3.  Using the ideal op-amp model condition eqimages/Q5683_13.png , we combine the two equations to eliminate the eqimages/Q5683_14.png  and eqimages/Q5683_15.png  terms,
    eqimages/Q5683_16.png .
    Then, we write eqimages/Q5683_17.png  in terms of eqimages/Q5683_18.png , eqimages/Q5683_19.png  and eqimages/Q5683_20.png ,
    eqimages/Q5683_21.png .

Final Answer

  eqimages/Q5683_22.png