To the fundamental of electrician Cheng, most person is early foregone talk (or once knew) , and the article will introduce further to the fundamental of electrician Cheng, try to comb an a few new understanding, the attempt adds a few new things in discuss.

 

Jacobi is mensurable (Jacobi””s Law)

 

Most engineer is familiar most high-power transmits theorem (also call Jacobi law) . Graph 1 showed source of a resistor and block sex load, its purpose is from resistor power the source transmits load. This principle can elaborate so: “ is equal to laden resistor when the internal resistance of resistor source, transfers power is the greatest, exterior resistor can be changed, but internal resistance is constant. ”(graph 1) .

 

Graph 1 circuit graph shows the resistor cause that receives block sex load repeatedly.

 

When RL = RS, the power that transmits load is the greatest. An obligation that often is ignored is hypothesis source resistor (RS) is fixed, do not get control, otherwise, meeting choice RS = 0 serves as the optimal value that gains the greatest transmission power from resistor source.

 

Graph 2 show how the power that transmits load changes along with RL / RS. The power that transmits RL depends on the electricity that carries load and load the voltage of two end. RL value changes to be able to increase tension greatly (VL) , but make electric current (IL) decreases, similar, RL is worth decrescent to be able to increase load current, but can reduce laden tension. Apply knowledge of a bit calculus to be able to see, most when high-power happens in RL = RS.

 

The relation curve of graph 2 PL and RL / RS shows, the power when the load when RL / RS = 1 is the greatest

 

Answer impedance

 

Consideration impedance is plural AC circumstance now, if pursue,3 are shown. Source impedance is ZS = RS + JXS, laden impedance is ZL = RL + JXL, become ZL is ZS answer when conjugate, generation most high-power is transmitted. That is to say, RL = RS and XL = -XS, this is called sometimes answer conjugate matchs, of expect of no less than in that way, if XS = 0, return the case that returns block sex again.

 

Graph 3 circuit graph shows conjoint load and power source have answer impedance

 

With phasic about

 

Interesting is, when XL = -XS, voltage source VS but regard as pure resistor (RS + RL) , the electricity that this indication voltage source exports and voltage are inphase. This is not coincidence, between voltage and voltaic weaveform phasic main effect is having in laden average power. Look in light of answer the time domain of the instantaneous voltage of impedance, electric current and power expresses.

 

Instantaneous power by formula (1) gives out:

 

P(t) = V(t)i(t) (1)

 

Hypothesis V(t) and I(t) are sinusoid:

 

 

Among them Φ is the phasic difference between voltage and voltaic weaveform.

 

Graph 4 showed the V(t) of time domain weaveform when Φ=45° , I(t) and P(t) .

 

The V(t) when graph 4 Φ=45, I(t) and P(t) weaveform pursue

 

Apply trigonometric function identity:

 

 

P(t) expression by constant (1/2VSILcosΦ) and the double cosine function at primitive frequency is comprised. We are interested in the average power in weaveform only normally, this can pass through a cycle in weaveform to go up to beg integral to get to P(t) . Double frequency cosine will is on average 0, leave constant only, accordingly average power is:

 

PAVERAGE = 1/2VSILcosΦ

 

Graph 4 medium P(t) curves explain, instantaneous power changes with sine means, turn into inside partial cycle even negative worth. Want Φ to differ only Yu Ling, produce this kind of situation likely. Still can see from inside the graph, the average of P(t) is, this states power was transmitted laden.

 

Electric power engineer can be used real power and inspect in power (the concept of Apparent Power) will quantify phasic the influence to power. Real power represents the power that transmits actually, include the phasic effect between V and I, with watt (W) is measured for the unit. Inspect in power be more simplifying concept, it is original electric current is multiplied only with voltage, with volt-ampere (VA) is measured for the unit, in order to distinguish Yu Zhen real power.

 

Electric power engineer also uses power factor (the concept of PF) :

 

 

Undee to sine, power element is equal to the Yu Xian of the photo corner between voltage and voltaic weaveform:

 

PF = Cosφ

 

Power factor is to quantify how many is inspect in power changeover is useful (true) the simple and instinctive means of power. If Φ=0, criterion PTRUE = PAPPARENT, PF=1; is become when Φ=±90° , PTRUE drops 0, PF=0. The case that the graph shows 4 times is Φ=45° , power element =0.707, 70% what explain PTRUE is equal to PAPPARENT.

 

Summary

 

The article reviewed most the importance of the ABC that high-power transmits and phasic relation, and its and power factor, will true and inspect in the electric power such as power project idea is united in wedlock. The oversight discussion to transmission line, will reflect these power to transmit concept and normally transmission line concept (for example loss of standing wave comparing, echo and reflection coefficient) a lot of collective place between.