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How to calculate phasor manually in circuit analysis is like 2∠45+ 1∞.
Angle is a special angle calculated by hand:

For example: 2 ∠ 45+2 ∠ 60 = 2× (∠ 2/2+j ∠ 2/2)+2× (1/2+j ∠ 3/2) = ∠ 2+j. ......

The parallelogram rule should be adopted in phasor addition and subtraction analysis. Special angles are easy to calculate, and non-special angles can be converted into complex numbers and then calculated.

The phasor multiplication and division method is simple. Multiplication: modular multiplication, angular addition, coexistence of initial modules, angular subtraction.

But if it is not a special angle, if manual calculation is needed, I'm afraid I have to use trigonometric function table (that is, the table commonly used by students in middle schools for mathematics). Otherwise, you can't get the sine and cosine of the general angle, and you still have to use a calculator.

Extended data:

In operation, it should be noted that phasor complex numbers are expressed in capital letters with dots on their heads. Phasor in analysis generally refers to effective phasor.

Phasor means sine, which means that they are corresponding, not equal. Because sine is a function of time, and phasor is only a complex number corresponding to the magnitude of sine and the initial phase.

An analysis method of sinusoidal steady-state circuit. 1893 was first put forward by German steinmetz. This method uses a complex number called phasor to represent sine quantity, and transforms the differential (integral) equation describing sinusoidal steady-state circuit into a complex algebraic equation, thus simplifying the analysis and calculation of the circuit to a great extent. At present, this method is almost always used when analyzing the sinusoidal steady state of circuits.

Baidu encyclopedia-phasor method