Search results
Results From The WOW.Com Content Network
Time-varying phasors are used in dynamic analysis of a large power system. [1] [5] The phasor representation of sinusoidal voltages and currents is generalized to arbitrary waveforms. [2] This mathematical transformation eliminates the 60 Hertz (Hz) carrier which is the only time-varying element in the stationary case. [3]
Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (, ) or the complex number + =, according to Euler's formula with =, both of which have magnitudes of 1.
One of the main reasons for using a frequency-domain representation of a problem is to simplify the mathematical analysis. For mathematical systems governed by linear differential equations, a very important class of systems with many real-world applications, converting the description of the system from the time domain to a frequency domain converts the differential equations to algebraic ...
The frequency domain variables can be taken as the Laplace transform or Fourier transform of the time domain variables or they can be taken to be phasors. The resulting frequency domain equations are ordinary differential equations of distance. An advantage of the frequency domain approach is that differential operators in the time domain ...
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function:
The term alternating current applies to a voltage vs. time function that is sinusoidal with a frequency f. When it is applied to a typical (linear time-invariant) circuit or device, it causes a current that is also sinusoidal. In general there is a constant phase difference φ between any two sinusoids. The input sinusoidal voltage is usually ...
As long as the manipulated function has no negative frequency components (that is, it is still analytic), the conversion from complex back to real is just a matter of discarding the imaginary part. The analytic representation is a generalization of the phasor concept: [ 2 ] while the phasor is restricted to time-invariant amplitude, phase, and ...
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.