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b. The requirements for the circuit specify a negative voltage gain. To achieve such a gain, an op-amp may be used as an inverting amplifier. With such a design, the gain can then simply be computed as:
However, it should be noted that the transducer itself has variable impedance.
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.
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