The op-amp in the amplifier in Fig. P4.19 operates with ±15...

The op-amp in the amplifier in Fig. P4.19 operates with $\pm 15 \mathrm{V}$ supplies and can output no more than $200 \mathrm{mA}$ What is the maximum gain allowable for the amplifier if the maximum value of $V_{s}$ is $1 \mathrm{V} ?$
$$R_{1}+R_{2}=10 \mathrm{k} \Omega$$

Key Concepts

Output Current Limitation

Op-amps have a maximum current they can safely supply at the output. Exceeding this current limit can lead to performance issues or damage. When designing an amplifier, the load or connected external circuitry (such as a resistor network) must be considered to ensure that the output current does not exceed this limit, particularly when the output voltage approaches its maximum level.

Operational Amplifier Supply Voltage Limitations

An op-amp’s output is bounded by its supply voltages. In designing amplifiers, it is crucial to recognize that the maximum permissible output voltage is limited by the supply rails, meaning that even if the theoretical gain would drive the output higher, the op-amp will saturate at or near its supply limits. This understanding ensures that amplifier designs remain within practical, linear operating ranges.

Amplifier Voltage Gain

Amplifier gain is defined as the ratio of the output voltage to the input voltage. In designing an amplifier, one must account for how much the input signal is amplified, while ensuring that the resulting output does not exceed the op-amp’s voltage or current limits. This concept is key to determining the maximum allowable gain when given specific input limitations.

Feedback Resistor Network

Most amplifier configurations use a resistor network to set the gain and provide feedback. The total resistance in the network influences both the amplifier’s gain and the current drawn from the output. A proper selection of resistor values is essential to achieving the desired gain while ensuring that the output current remains within safe limits. This concept is fundamental in ensuring stability and linearity in amplifier design.

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