Complex gain
Overview
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
to describe the effect circuitry has on the amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
and phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of a sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...
signal. The term "complex" is used because mathematically this effect can be expressed as a complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
.
Suppose a circuit has an input voltage described by the equation
where ω equals 2π×100Hz, i.e.
Quotations
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Vinnie: [After finding out that the two girls he and Crazy picked up in a bar are prostitutes.] Well, listen, Ms. Movie star - Vinnie doesn't pay for it. OK? Vinnie NEVER pays for it.
Eva: [Watching Vinnie and Crazy fight each other.] Here I am right in the middle of it - defiant youth in action!