Circuits

A sinusiods is a signal that has the form of the sine or cosine function .


A general expression for the sinusiods,


V(t)=Vm cos(t+ 0)


where,


Vm = the amplitude of the sinuiods


Ѡ = the angular frequency in radians


ɸ= phase


PHASOR


A phasor is a complex number that represent the amplitude and phase of a sinusiods.


It can be represented in one of the ff. three forms:


a) Rectangular : z = x + jy = r(cosɸ +sinɸ)


b) Polar : z = r <ɸ


c) Exponential : re















How to solve by using the four standard operations (addition< subtraction< multiplication and division).


We can subtract or add when it is in rectangular form, just simply add or subtract the real number to real number and imaginary number to imaginary number.


We can multiply or divide when it is in polar form, just multiply or divide the real number but in angle we should add when it is multiplication and subtract when it is division.


































Impedance


impedance is just like a resistance in DC analysis which is in AC analysis it express in phasor form.





Complex Impedance
Complex impedance describes the relationship between the voltage across an element (expressed as a phasor) and the current through the element (expressed as a phasor).
Impedance is a complex number.
Impedance depends on frequency.
Phasors and complex impedance allow us to use Ohm’s law with complex numbers to compute current from voltage and voltage from current.


A phasor is a complex number that represents the magnitude and phase of a sinusoid:


Click the image to enlarge:


Time domain


The time domain is described by graphs of power, voltage and current that depend upon time. The “Time domain” is simply another way of saying that our circuits change with time, and that the major variable used to describe the system is time. Another name is “Temporal”.


Frequency domain


The frequency domains are graphs of power, voltage and/or current that depend upon frequency such as Bode plots. Variable frequencies in wireless communication can represent changing channels or data on a channel. Another name is the “Fourier domain”. Other domains that an engineer might encounter are the “Laplace domain” (or the “s domain” or “complex frequency domain”), and the “Z domain”. When combined with the time, it is called a “Spectral” or “Waterfall.”


Sample:


solve the equivalent impedances of a-b:





















I learned that it is useful in solving of differents loads (resistance, inductance and capacitance) because it can be convert into same form and we can now simplify by connecting in series or parallel. It makes the circuit small amoount of loads.