Since the feedback and input resistances are constant, the gain variation is dependent solely on the source impedance. It then becomes apparent that maximum gain is achieved only when the source impedance is at a minimum value (assumed to be zero). Likewise, the minimum gain is reached when the source impedance is at a maximum value of 50 ohms. Using this information, the following equations are constructed: c. The designed circuit was simulated using Multisim. To determine the gain characteristics at the minimum and maximum source impedance settings, two sets of simulations were run. The first set was performed with a source impedance of 50 ohms and the second set shorted the said resistor. To more effectively capture the response of the circuit, a DC sweep was performed from 100 mV to 1V for each simulation. The results of the simulations can be seen below: Seeing these results, it can be said that the actual response of the circuit was above the lower limit for the gain. However, under certain conditions, it can be seen that the actual response of the circuit exceeds that of the theoretical upper boundary established. This difference is present due to the fact that the design took into consideration an ideal op-amp while Multisim uses a more complex model. Particularly, the finite input resistance and the presence of offset voltages may explain the variations from the design. The first set was performed with a source impedance of 50 ohms and the second set shorted the said resistor....

d. A basic op-amp may be used for this circuit. To reduce the effect of input resistance, a low offset JFET input op-amp such as the LF411 may be appropriate. The resistors for the circuit have the values shown in the circuit above.

2.

a. To analyze the given circuit, it is useful to treat the op-amp as an ideal device with infinite input impedance. Knowing this, it is easy to derive the output expression for the circuit. Using the principle of superposition, the effect of each source can be taken while the remaining sources are shorted to ground. For instance, the effect of v1 on the output can be treated separately while v2, v3, and v4 are connected to ground. Due to the infinite resistance of the op-amp, the following equation can be obtained:

Since the potential on the inverting and non-inverting inputs of an op-amp can be seen as equal the non-inverting input can be seen acting as a virtual ground. Knowing this, the previous equation can be transformed using Ohm's law to:

This equation can be subsequently transformed into:

Using a similar analysis, the remaining contributions to the output voltage are obtained:

Taking the sum results to the output voltage expression:

b. Assuming values of 1k, 2k, 3k, and 4k for R1, R2, R3, and R4 respectively and a value of 2k for the feedback resistor, the following output voltage is obtained:

c. The circuit was simulated on Multisim with the following circuit:

Using this schematic, a value of 799.979 mV was obtained at the output. Comparing this to the theoretical output voltage reveals that the circuit operates close to ideal. The remaining error can again be attributed to imperfections of the devices.

d. For a single
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