Objective: Design a summing amplifier to produce a specified output signal. Specifications: The output signal generated from an ideal amplifier circuit is $v_{O1} = 1.2 − 0.5 \sin ω t (V)$ . Design a summing amplifier to be connected to the am-plifier circuit such that the output signal is $v_{O} = 2 \sin ω t (V)$ .
Choices: Standard precision resistors with tolerances of ±1 percent are to be used in the final design. Assume an ideal op-amp is available

Question

Objective: Design a summing amplifier to produce a specified output signal. Specifications: The output signal generated from an ideal amplifier circuit is [latex]v_{O1} = 1.2 − 0.5 \sin ω t (V)[/latex]. Design a summing amplifier to be connected to the am-plifier circuit such that the output signal is [latex]v_{O} = 2 \sin ω t (V)[/latex].
Choices: Standard precision resistors with tolerances of ±1 percent are to be used in the final design. Assume an ideal op-amp is available

Accepted Answer

In this case, we need only two inputs to the summing amplifier, as shown in Figure 9.14. One input to the summing amplifier is the output of the ideal amplifier circuit and the second input should be a dc voltage to cancel the +1.2 V signal from the amplifier circuit. If the voltage gains of each input to the summing amplifier are equal, then an input of −1.2 V at the second input will cancel the +1.2 V from the amplifier circuit.
For a −0.5 V sinusoidal input signal and a desired 2 V sinusoidal output signal, the summing amplifier gain must be
[latex]A_{v} = \frac{−R_{F}}{R_{1}} = \frac{2}{−0.5} = −4[/latex]
If we choose the input resistances to be [latex]R_{1} = R_{2} = 30 k\Omega[/latex], then the feedback resistance must be [latex]R_{F} = 120 k \Omega[/latex].
Trade-offs: From Appendix C, we can choose precision resistor values of
[latex]R_{F} = 124 k\Omega[/latex] and [latex]R_{1} = R_{2} = 30.9 k\Omega[/latex]. The ratio of the ideal resistors is 4.013. Considering the ±1 percent tolerance values, the output of the summing amplifier is
[latex]v_{O} = \frac{−R_{F} (1 ± 0.01)}{R_{1}(1 ± 0.01)} \cdot (1.2 − 0.5 \sin ωt) − \frac{R_{F} (1 ± 0.01)}{R_{2}(1 ± 0.01)} \cdot (−1.2) [/latex]
The dc output voltage is in the range [latex]−0.1926 ≤ v_{O} (dc) ≤ 0.1926 V [/latex] and the peak ac output voltage is in the range [latex]1.967 ≤ v_{O} (ac) ≤ 2.047 V[/latex].
Comment: In this example, we have used a summing amplifier to amplify a time-varying signal and eliminate a dc voltage (ideally).

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