Multipliers are based on fundamental logarithmic relationship that states that the product of two terms is equals the sum of the logarithms of each term. The relation is shown by the following formula ln (a»b) =ln a+ ln b. This formula shows that two signal voltages are effectively multiplied if the logarithms of the signal voltages are added.
2.By Summing the outputs of the two log amplifiers, you get the logarithm of the product of the two original input signals.
The Block diagram shows how the functions are connected to multiply two input voltages. Constant terms are omitted for simplicity.
The Log and Antilog Amplifiers are non-linear circuits in which the output voltage is proportional to the logarithm (or exponent) of the input. It is well known that some processes such as multiplication and division, can be performed by addition and subtraction of logs.
Most logarithmic amplifiers are based on the inherent logarithmic relationship between the collector current, Ic, and the base-emitter voltage, vbe, in silicon bipolar transistors.
The input voltage is converted by R1 into a. current, which then flows through the transistor's collector modulating the base-emitter voltage according to the input voltage. The opamp forces the collector voltage to that at the noninverting input, 0 V.
Four-Quadrant Multiplier is a device with two inputs and a output.
Typically, k=0.1 to reduce the possibility of overload. It is called a four-Quadrant since inputs and outputs can be positive or negative. An example is a Motorola MC1494, powered by +15 or -15V power supply.