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A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
Ideal diode with a series voltage source and resistor. The I-V characteristic of the final circuit looks like this: I-V characteristic of an ideal diode with a series voltage source and resistor. The real diode now can be replaced with the combined ideal diode, voltage source and resistor and the circuit then is modelled using just linear elements.
The logarithmic scale used for the bottom plot is useful for expressing the equation's exponential relationship. The Shockley diode equation , or the diode law , named after transistor co-inventor William Shockley of Bell Labs , models the exponential current–voltage (I–V) relationship of semiconductor diodes in moderate constant current ...
A logarithmic resistor ladder is an electronic circuit, composed of a series of resistors and switches, designed to create an attenuation from an input to an output signal, where the logarithm of the attenuation ratio is proportional to a binary number that represents the state of the switches.
The binary weighted configuration uses power of two multiples of a base resistor value. However, as the ratios of resistor values increases, the ability to trim the resistors to accurate ratio tolerances becomes diminished. More accurate ratios can be obtained by using similar values, as is used in R–2R ladder.
Since some values of the E24 series do not exist in the E48, E96, or E192 series, some resistor manufacturers have added missing E24 values into some of their 1%, 0.5%, 0.25%, 0.1% tolerance resistor families. This allows easier purchasing migration between various tolerances.
Since the exponential function equals its derivative, this implies that the exponential function is monotonically increasing. Extension of exponentiation to positive real bases: Let b be a positive real number. The exponential function and the natural logarithm being the inverse each of the other, one has = ().
A log amplifier's elements can be rearranged to produce exponential output, the logarithm's inverse function. Such an amplifier may be called an exponentiator, an antilogarithm amplifier, or abbreviated like antilog amp. [3]