The current that changes sinusoidally with time is called sinusoidal alternating current. There are generally three ways to express sinusoidal alternating current:
1. Analytical method
2. The sine curve method
3. Rotating phasor method
The representation method of sinusoidal alternating current1. Analytical method
Analytical method is a method that uses mathematical formulas to express the relationship between sinusoidal alternating current and changes in practice. The formula is as follows:
e=Emsin(ωt+Φe)
u=Umsin(ωt+Φu)
i=Imsin(ωt+Φi)
It can express the maximum value, initial phase angle and period of the sine. It can be seen from the above formula that as long as the maximum value of a sine quantity, initial phase angle and frequency are known, a sine quantity is completely determined. Therefore: usually: the maximum value, initial phase angle, and angular frequency are called the three elements of sinusoidal alternating current.
Second, the sine curve method
According to the analytical formula, the sine curve drawn in the Cartesian coordinate system is called the sine curve method. The ordinate represents the instantaneous value of the sine quantity, and the abscissa represents the electrical angle ωt. In the sinusoidal waveform diagram, the three elements of sinusoidal alternating current can also be obtained, that is, the maximum value of the instantaneous value is the maximum value; the time of one cycle of the curve is a cycle T, and the angular frequency ω=2π/T can be obtained; sine half wave The angle between the starting point and the origin O is the initial phase.
3. Rotating phasor method
To express the three elements of a sine quantity by rotating phasor method, the following requirements must be made:
The maximum value of the sine is the length of the rotating phasor;
The initial phase of the sine is the angle between the rotating phasor and the positive direction of the horizontal axis;
The angular frequency of the sine is the angular velocity at which the rotating phasor rotates counterclockwise with time t.
Then at any instant, the projection of the rotating phasor on the vertical axis is equal to the instantaneous value of the sine, as shown in the following figure:
Generally, only its starting position is drawn in the phasor diagram, but it should be understood that it rotates counterclockwise continuously at the angular frequency ω, and its position is related to time. After the elapsed time, it turns to the dotted line position. So, say it Is the time phasor.
In the same circuit, each sine quantity rotates at the same frequency, and the relative position (that is, the phase difference) between them remains unchanged. Therefore, as long as the initial position of the rotating phasor is used to express the sine quantity, we call this method of expressing the sine quantity the phasor method. The sine quantity is expressed as a phasor as a phasor diagram. If the length of the phasor line segment is equal to the effective value of the sine, it is called the effective value of the sine phasor, but the projection of the phasor on the vertical axis is not an instantaneous value.
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