Derivation of Sinusoidal Steady State Analysis
Since , f=1/T
[Tex]\omega = 2\pi f = \frac{2\pi}{T} [/Tex]
[Tex]v(t)= Vm. \sin(\omega t + \phi) [/Tex]
The coefficient of Vm, Vm in the above equation represents the maximum amplitude of the sinusoidal voltage, as cosine is confined within the bounds of (+Vm,−Vm), encapsulating the amplitude range. The illustrated figure elucidates these characteristics. Meanwhile, the angle Φ is denoted as the phase angle of the sinusoidal voltage. The value is found as the square root of the mean value of the square function
–[Tex]\sqrt{\int_{t_0}^{t_0+T} V_{m} ^2\cos^2(\omega t + \phi) \, dt} [/Tex]
The above equation reduces
[Tex]\frac{V_m^2}{{2}}
[/Tex]
Now,
[Tex]V_{\text{rms}} = \frac{V_m}{\sqrt{2}} [/Tex]
Sinusoidal Steady State Analysis – Electric circuits
In steady state (the fully charged state of the cap), current through the capacitor becomes zero. The sinusoidal steady-state analysis is a key technique in electrical engineering, specifically used to investigate how electric circuits respond to sinusoidal AC (alternating current) signals. This method simplifies the intricate details involved in time-varying AC circuits by representing voltages and currents as phasors—complex quantities that succinctly convey both amplitude and phase information.
Table of Content
- Sinusoidal Steady State Analysis
- Sinusoidal Source
- Derivation
- V-I Relation for an Inductor
- V-I Relationship for a Capacitor
- Frequency Response
- Bode Plots
- Examples