Introduction to the circuits to concentrated constants

1) Law of Kirchoff of the currents:

The current that altogether exits from a surface sluice is equal to that it enters to you.

 

2) Law of Kirchoff of the tensions:

The algebrica of the tensions that meet in a circuit moving itself along a line sluice and ended sum is 0. The tensions are from considering themselves positive if it agrees with the movement.

 

3) Door :

Given 2 clips, the current entering in one is equal and opposite to the current entering in the other.

 

4)    constituent Relation of the resistore :

the current is from considering itself positive if it slides from to -.

 

5)    constituent Relation of the condenser :

 

6) constituent Relation of the inducer :

 

7) constituent Relation of the independent generator of tension :

v(t) = v₀(t) where v₀(t) are one function of the assigned time

 

8) constituent Relation of the independent generator of current :

i(t) =_{the 0}(t) where_{the 0}(t) is one function of the assigned time

 

9) real Generator of tension:

It is constituted from an ideal generator of tension with in series one resistance R_v , is had that the tension to the heads of the total generator of the resistance is .

 

10) real Generator of current:

It is constituted from an ideal generator of current with in parallel a resistance R_I , is had that the current distributed from the total generator of the resistance is .

 

11) Condition of equivalence between the real generator of tension and the real generator of current :

They are equivalents on condition that the resistances are equal, the result is obtained designing is for the current generator that for the tension generator the straight one that the characteristic characterizes tension-current characterizing for ognuna the value to the intersection with the aces and uguagliando between of they these amounts.

 

12) Power distributed from a real and ideal generator of tension :

Replacing in the P = YOU the equation of the generator of real tension obtains an expression that for R_v= 0 it is one straight one passing for the origin while for R_v ¹0 is one parabola that has the maximum for_{the CC}/2.

 

13) Considerations on power and rendering in a real generator of tension :

The rendering is given from the relationship between the supplied power to the cargo and the generated power, in order to estimate it considers the real generator closed on one cargo stiffness R₀. It is had . For the applications in which it is demanded a high rendering like for the transfer of tensions at a distance must be increased the cargo resistance while for the applications in which the maximum transfer of power is demanded the cargo resistance must be equal to the inner resistance of the generator.

 

14) constituent Relation of the generator of tension controlled in current :

In fact if in door 1 _{the 1} slides, us it cannot have fallen of upgrades them, in how much is introduced like a short circuit, the control parameter is a resistance therefore is spoken about transimpedenza.

 

15) constituent Relation of the generator of tension controlled in tension :

In fact if to door 1 ₁ is appliedv it is like if an open circuit were had and therefore does not slide current.

 

16) constituent Relation of the generator of current controlled in tension :

the control parameter is in this case an admittance therefore is spoken about transammettenza.

 

17) constituent Relation of the generator of current controlled in current :

 

18) constituent Relation of the nullatore :

Draft of a bipole the whose tension to the heads is worth 0 and cos¬ also current that crosses it, its symbol â?"o -- .

 

19) constituent Relation of the noratore :

Draft of a bipole whose tension to the heads and the current that crosses it can assume both a value whichever, its symbol is â?"oo -- .

 

20) constituent Relation of the nullore :

A gain in limited tension is demanded while the gain in current and power is demanded is infinite. The conditions for placing to the net 2-doors are:

while i₂ and v₂ can assume values whichever.

These relations derive from the fact that it is a circuit to 2 doors with a nullatore like bipole of income and a noratore like bipole of escape. It must be observed that nullatore and noratore they do not have some sense if considers you singularly.

 

21) constituent Relations of the coupled inductances :

 

22) Meant of the dot in the inductances coupled :

If the two currents that slide in the inducers are both entering or outgoing from the dots, the two falls of tension in the single relation are with the same sign, otherwise have various signs.

 

23) constituent Relation of the ideal transformer :

They have the two following relazioni

where is the transformation relationship, otherwise it can be observed that in writing the relations the tension has the various pedici while the current has the homogenous pedici that is , less for the currents has had like considers_{the 2} . The power absorbed from the ideal transformer is 0 and in order to demonstrate it enough to replace its constituent equations in P(t) = V₁I₁ V₂I₂ .

 

24) Utilizzo of the ideal transformer like stiffness transformer :

Images that the resistance on the secondary one is R_out and the R resistance is estimated_in that it is looked at on the head physician, replacing the constituent equations of the ideal transformer finds therefore can make that the circuit on which we close the head physician sees one various resistance from that effectively connected to the secondary one.

 

25) Value of the coefficient of mutual inductance :

It is obtained calculating the energy and demanding that it is positive imposing in such a way the passivity of the member, collecting an equation of 2° degree is obtained of which the coefficient of the term of 2° degree it is a positive relationship of inductances therefore therefore enough to impose that not there are intersections with the abscissas that is that the determining one is smaller of 0, is obtained .

 

26) Coefficient of connection :

 

27) Cut :

Draft of a line sluice that not more intersects every element than once and in correspondence to a solo finishes characterizing them therefore with of coppers such that their elimination renders the graph turning out not connected.

 

28) Mesh :

It is a line sluice that intersects every element in correspondence to both finishes them.

 

29) Tree :

With it is connected of coppers that comprise all the nodes of the graph without to form covered sluices. The n° of coppers he is equal to the n° of the nodes of graph less one.

 

30) Co-tree :

Draft of with of coppers of the graph not pertaining to the tree.

 

31) fundamental Mesh associated the tree :

Draft of the mesh that is obtained adding to the tree a single branch of the Co-tree.

 

32) fundamental Cut :

It is obtained considering a single branch of the tree and coppers of the connected Co-tree to it.

 

33) relative Equations of equilibrium to the cuts and the fundamental meshes :

where pedice c indicates i coppers of the coalbero while the pedice to indicates coppers of the tree.

 

34) Relation between the relative matrix [ To ] to the cuts and the matrix [ relative B ] to the meshes :

 

35) Principle of conservation of the instantaneous power :

It asserts that summary of the powers along R the coppers of a circuit it is 0, . It is demonstrated by means of the ; ; . is had in fact

 

36) Theorem of Tallegen :

If 2 circuits having same graph oriented but with members are considered distinguished, it is had that the sum of the mutual powers that is the product to scale between the carrier of the currents of the circuit the 1 and carrier of the tensions of circuit 2 is worth 0.