Question

Determine output voltage of analog multiplier provided with two input signal Vx and Vy.

(a) Vo = (Vx ×Vx) / Vy

(b) Vo = (Vx ×Vy / Vref

(c) Vo = (Vy ×Vy) / Vx

(d) Vo = (Vx ×Vy) / Vref^2

The question was asked in my homework.

I'm obligated to ask this question of Multiplier and Divider topic in chapter Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

The correct answer is:

(b) Vo=Vx×VyVrefV_o = \frac{V_x \times V_y}{V_{\text{ref}}}Vo​=Vref​Vx​×Vy​​

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Explanation:

An analog multiplier is a circuit that provides an output voltage proportional to the product of two input voltages, scaled by a reference voltage (VrefV_{\text{ref}}Vref​) for proper dimensionality and normalization.

Output Voltage Equation:

Vo=Vx×VyVrefV_o = \frac{V_x \times V_y}{V_{\text{ref}}}Vo​=Vref​Vx​×Vy​​

Here:

• VoV_oVo​: Output voltage.
• VxV_xVx​: First input voltage.
• VyV_yVy​: Second input voltage.
• VrefV_{\text{ref}}Vref​: Reference voltage (used to normalize the product and ensure correct scaling).

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Why This Formula?

1. Working Principle:

   • The analog multiplier multiplies VxV_xVx​ and VyV_yVy​ to compute their product.
   • The result is divided by VrefV_{\text{ref}}Vref​, which acts as a scaling factor and ensures the units of VoV_oVo​ match the system's requirements.

2. Applications:

   • Used in amplitude modulation (AM), frequency mixing, and other signal processing tasks.
   • Essential in circuits for generating product signals.

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Incorrect Options:

• (a) and (c) suggest the square of one input, which does not match the operation of an analog multiplier.
• (d) divides the product by Vref2V_{\text{ref}}^2Vref2​, which is incorrect; only a single VrefV_{\text{ref}}Vref​ is used for scaling.