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Example 18 Design an op amp circuit such that vout 3v1 5v 2 4v3 . In this problem, we want to design a circuit having three inputs v1 , v 2 , and v 3 , and one output v out .The output must be related to the inputs by vout 3v1 5v 2 4v3 . This required circuit must multiply each input by a number and add the results. The polarity of the first two input voltages are reversed. As we know, one of the applications of operational amplifiers is to build circuits that perform mathematical operations. This is why it is called operational amplifier. So we can use op amps to design this circuit. A basic summing amplifier comes to my mind now. Let’s consider a 3 inputs summing amplifier circuit. R1 vin1 Rf R2 vin2 R3 _ vin3 vo + For a summing amplifier, the output should be a weighted sum of all the inputs. The weight for each input is simply the feedback resistance divided by the input resistance which is connected to the input. Rf Rf Rf Rf Rf Rf v o vin1 vin 2 vin 2 vin1 vin 2 vin 2 R1 R2 R2 R2 R2 R1 We might want to connect input v1 , v 2 to vin1 and v in 2 . Notice here, the polarity of each input is reversed by the summing amplifier. In the design specification, we don’t want to flip the polarity of v 3 . So we might use an inverting amplifier to reverse polarity of v 3 first and then sent it to the input of the summing circuit. Ro Rin vin _ vo + Firstly, let’s connect the first two inputs of the summing amplifier with v1 and v 2 . We can pick up a reasonable resistance value for the feedback resistor, which can be 15kΩ. To make Rf R1 3 , R1 should be Rf 3 15 5k 3 Similarly, the coefficient of v 2 is negative 5. To make Rf R2 5 , R 2 should be Rf 5 15 3k 5 Assume that we want the gain of the inverting amplifier to be negative 1, to make Rf R3 4 , R3 should be Rf 4 15 3.75 k . 4 This is not a commercial available component. We might have to use two resistors for this resistance. Let us make Rf R3 1 and let the inverting circuit to provide a gain of negative 4. Rf R3 1 which gives us R3 15k . Ro 4 . Rin So The two resistance of the inverting amplifier can be set as Rin 1k and Ro 4k Finally the output of the inverting amplifier is connected with the third input of the summing amplifier. 5 kΩ 4 kΩ v1 3 kΩ v2 1 kΩ v3 15 kΩ _ 15 kΩ _ vo + + .