Question

Express the output voltage equation of divider circuit

(a) Vo= -(Vref/2)×(Vz/Vx)

(b) Vo= -(2×Vref)×(Vz/Vx)

(c) Vo= -(Vref)×(Vz/Vx)

(d) Vo= -Vref^2×(Vz/Vx)

The question was asked by my school teacher while I was bunking the class.

This intriguing question originated from Multiplier and Divider topic in section Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

The correct answer is:

(a) Vo=−Vref2×VzVxV_o = -\frac{V_{\text{ref}}}{2} \times \frac{V_z}{V_x}Vo​=−2Vref​​×Vx​Vz​​

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Explanation:

In a typical op-amp-based divider circuit, the output voltage is proportional to the ratio of two input voltages VzV_zVz​ (numerator) and VxV_xVx​ (denominator), scaled by a reference voltage VrefV_{\text{ref}}Vref​. The circuit uses a multiplier and feedback configuration, leading to the given output equation.

1. VoV_oVo​: Output voltage.
2. VrefV_{\text{ref}}Vref​: Reference voltage provided by the circuit.
3. VzV_zVz​: Voltage to be divided (numerator).
4. VxV_xVx​: Dividing voltage (denominator).

The term −Vref2-\frac{V_{\text{ref}}}{2}−2Vref​​ accounts for the circuit's design, including feedback and scaling.

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Why this option?

The negative sign arises from the inverting nature of the operational amplifier configuration. The scaling factor (Vref2\frac{V_{\text{ref}}}{2}2Vref​​) is a result of the resistor and feedback network design.