Question

What is the disadvantage of log-antilog multiplier?

(a) Provides four quadrant multiplication only

(b) Provides one quadrant multiplication only

(c) Provides two and four quadrant multiplication only

(d) Provides one, two and four quadrant multiplication only

I got this question in homework.

This is a very interesting question from Multiplier and Divider topic in section Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

The correct answer is:

(b) Provides one quadrant multiplication only

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Explanation:

A log-antilog multiplier circuit works by converting the input signals to their logarithmic values, summing them, and then applying an antilogarithmic function to get the product. This approach has some inherent limitations:

1. One Quadrant Operation:

   • The circuit can only handle positive input voltages for VxV_xVx​ and VyV_yVy​ because logarithms are undefined for negative numbers or zero.
   • Therefore, it performs multiplication only in the first quadrant where both inputs are positive.

2. Quadrant Multiplication:

   • Four-quadrant multiplication requires handling both positive and negative input voltages. A log-antilog multiplier cannot achieve this due to the restriction of logarithmic operations.

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Why the Other Options Are Incorrect:

• (a) Provides four quadrant multiplication only:
  • Incorrect, as four-quadrant multiplication is not possible with this configuration.
• (c) Provides two and four quadrant multiplication only:
  • Incorrect, as the circuit is limited to one quadrant.
• (d) Provides one, two and four quadrant multiplication only:
  • Incorrect, as the circuit strictly operates in one quadrant.

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This limitation makes the log-antilog multiplier unsuitable for applications requiring negative input values or quadrants other than the first.