The correct answer is:
(c) Vx<10V;Vy<10VV_x < 10V; V_y < 10VVx<10V;Vy<10V
Explanation:
In an operational amplifier (op-amp) based multiplier or divider circuit, the output voltage depends on the product or division of the input voltages VxV_xVx and VyV_yVy, and the reference voltage (VrefV_{\text{ref}}Vref). To prevent saturation of the output, the input voltages must be controlled so that the resulting output voltage stays within the permissible range defined by the op-amp's supply voltage.
- Saturation Condition: Saturation occurs when the output voltage exceeds the maximum or minimum voltage that the op-amp can output, which is usually close to the supply voltage (VccV_{\text{cc}}Vcc).
- Non-Saturation Condition: To prevent saturation, the output voltage needs to remain within the linear operating range of the op-amp. This is often ensured by keeping the input voltages within a certain limit, so that their product or quotient doesn’t drive the output beyond the op-amp's output swing.
In this case, the condition Vx<10VV_x < 10VVx<10V and Vy<10VV_y < 10VVy<10V ensures that the multiplication or division result of the input voltages will produce an output within the linear range of the op-amp, avoiding saturation.
Why the Other Options Are Incorrect:
- (a) Vx>10V;Vy>10VV_x > 10V; V_y > 10VVx>10V;Vy>10V: This condition is more likely to cause the output to saturate, as both input voltages are large.
- (b) Vx<10V;Vy>10VV_x < 10V; V_y > 10VVx<10V;Vy>10V: This might lead to saturation depending on the specific circuit design and reference voltage.
- (d) Vx>10V;Vy<10VV_x > 10V; V_y < 10VVx>10V;Vy<10V: Similar to (a), this condition could cause the output to exceed the linear range of the op-amp and result in saturation.
Thus, (c) provides the safe condition where the output will not saturate, as both input voltages are kept low.