# Phasors and Imaginary and Real help

• th3plan
In summary, a circuit that falls on the imaginary axis is considered unstable and is rarely found in real life. However, if the feedback reduces the instability, then the circuit is considered stable.
th3plan
Ok so i just want to clear up something about phasors and just circuit input functions in general. So based on the imaginary and real graph, where imaginary is like the y-axis and the real is the x axis, when let's say a circuit falls on the imaginary axis is it considered a stable circuit? Do these exist in real life ? If it falls on the right side of the imaginary axis i know this means there very unstable , and that they rarely exist and the circuits operates to bring them back to the left side of the imaginary axis to make them stable again.

Please tell me if me if my thinking is right, and that part about the imaginary axis, if there is solution right on it

Thanks

Could you clarify your questions? Are you talking about a voltage function or current function? The only thing that I know about an input function's phasors deviating from the real axis (∠0°,∠180°,∠-180° ) or imaginary axis (∠90°,∠270°,∠-90°) is due to the characteristics of the circuit's impedance. Is it purely resistive, does it have inductive reactance, or capacitive reactance?

th3...your question appears inconsistent..first you say input functions then you reference a circuit.
usually you characterize a circuit via an input function, a transform representing the circuit characteristics, and an output...you seem to have the first two mixed.

There can be unstable circuits to be sure and these will be characterized by certain feedback characteristics. If the feedback reduces such instability by appropriately altering the input signal control is achieved..

See http://en.wikipedia.org/wiki/Feedback#In_electronic_engineering

and possibly Nyquist stability criterion :
Stability of the closed-loop control system may be determined directly by computing the poles of the closed-loop transfer function

## What are phasors?

Phasors are mathematical representations of a complex sinusoidal signal, which consist of a magnitude and a phase. They are commonly used in electrical engineering to analyze and understand AC circuits.

## What is the difference between imaginary and real numbers?

Imaginary numbers are numbers that, when squared, result in a negative number. They are represented by the letter "i". Real numbers, on the other hand, are all numbers that can be plotted on a number line and include positive and negative numbers as well as zero.

## How are phasors used in circuit analysis?

Phasors are used to simplify the analysis of AC circuits. By converting the time-domain signals into phasors, calculations become easier and more efficient, as they can be treated as simple vectors in the complex plane.

## What is the relationship between phasors and impedance?

Phasors can be used to represent impedance in AC circuits. The magnitude of the phasor represents the magnitude of the impedance, while the phase angle represents the phase shift between the voltage and current in the circuit.

## How can I convert a phasor into a time-domain signal?

To convert a phasor into a time-domain signal, you can use the inverse Fourier transform. This will give you a complex sinusoidal signal in the time-domain, which can then be converted into a real-valued signal by taking the real part of the result.

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