分抗在正弦电压源中的功率与电学性质研究

为得到分抗、分抗逼近电路在正弦电压源中的功率,从功率角度探究分抗的电学性质。给出了分抗在正弦电压源激励下的功率因数、有功功率等数学表达式;并与电阻、电容和电感比较,得到统一表达式。设计半阶感性与半阶容性Oldham分形链分抗逼近电路,计算并电路仿真验证阶频特征与F特征以及在正弦电压源激励下的有功功率。结果表明:容性分抗的功率因数、有功功率介于电阻与电容之间,感性分抗的功率因数、有功功率介于电阻与电感之间;电阻、电容、电感可看做分抗阶数延伸到整数阶的特殊情况。

The Power Consumption and Electrical Properties of Fractance in Sinusoidal Voltage Source

To achieve the power consumption of fractance and fractance approximation circuits in the sinusoidal voltage source, the electrical properties of fractance is explored from the perspective of power. The mathematical expressions of the power factor and active power of fractance driven by sinusoidal voltage source are provided, compared with the resistance, capacitance and inductance. As a result, the unified expression is obtained. Besides, the concrete semi order inductive and capacitive Oldham fractal chain fractance are designed and the theoretical analysis and experimental test are carried out for order-frequency characteristics and F characteristics. In addition, the consumption of active power sinusoidal alternating voltage is calculated and validated by conducting experiments. The results show that the power factor and active power of the capacitive fractance are between the resistance and capacitance, while those of the inductive fractance are between the resistance and inductance. Therefore, the resistance, capacitance, and inductance can be considered as special cases in which the fractional order is extended to the special condition of integer order.