generalised branch

 

 

 

 

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 For calculation of electric circuit by numerical methods the equations of the generalised electric branch are used which is presented on fig.1 1 (also known under other names : branch Kirhgoff, a primitive branch, is elementary a branch, etc.).

 

 

 

 

Fig 1: The circuit and the equation of the generalised branch

It is possible to present the equation of the generalised branch in two forms:

E= z(i+Ieq),  where Ieq = (I - e/z)

E + eeq = zi, where  eeq= e z I

 

Except the generalised branch it is possible to use primitive branches. For the analysis by methods of nodes potentials use a node branch. For the analysis by mesh-current method uses a contour branch

primitive node branch  I = YE

primitive contour branch  e = z i

 

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Electrical models for the ODE in the form of generalized branch


Equivalent circuit of linear capacitance

Euler's method of 1-st order

backward differential formula

method a trapeze

 

 

Iterative equivalent circuit of nonlinear capacity
implicit method of 2-nd order and method of direct iterations

 

                     

 

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Electrical models for the PDE



Approximation by central differences

where   B-=B(x-h,t);  B=B(x,t);  B+=B(x+h,t);  ΔB=B(x,t+Δt) - B(x,t).

 

equivalent circuit of the differential equation
 

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Change date : 22.05.2014