Final answer:
To scale an input voltage range of [-3, 7] volts to [5, 12] volts using an op-amp circuit, calculate the gain using the formula A = 1 + (Rf/Ri) and determine the appropriate resistor values for Rf and Ri to maintain the desired proportionality, including a voltage offset if necessary.
Step-by-step explanation:
To design an operational amplifier (op-amp) circuit that scales an input voltage range of [-3, 7] volts to an output range of [5, 12] volts, you can use a non-inverting amplifier configuration. The gain (A) of the amplifier is calculated by considering the required input and output voltage ranges. The formula for gain in a non-inverting amplifier is A = 1 + (Rf/Ri), where Rf is the feedback resistor and Ri is the input resistor. You'll need to find appropriate values for Rf and Ri that satisfy the gain necessary to map the input range to the output range proportionally.
Once the gain is determined, you can calculate Rf and Ri, taking into account the op-amp's power supply limits and ensuring that the resistor values are practical and standard. A voltage offset can be applied as well to align the scaled voltage properly with the desired output range. It's vital to calculate the correct values so that the circuit operates within the specifications and the input-output proportionality is maintained.