Analysis circuits with memory
1) u-1(t):
It is the defined unitary step like 
,
it appropiatamente describes the physical behavior of the switch,
unless in the circuits where they are present inducers and therefore
it is necessary the derivative of the current, but u-1(t) does not admit derived in the
origin in how much batch processing line.
2) u-1,and(t):
in such a way the function unitary step that is batch
processing line in the origin comes defined like limit for and ® 0 of one
class of continuous functions 
.
3) Ulterior definition of unitary step u-1,and(t):
4)u0(t):
It is the function unitary impulse or d of Dirac 
, in
the theory of the distributions is the derivative of unitary step u-1(t).
5) u0,and(t):
deriving uthe -1(and,t) 
for it is obtained in fact has 
,
enough to observe that the function is worth 1/and for 0<t<and but if the limit is used for and®0 various values to second
are had that the limit is outside or within to this last integral.
6) Ulterior definition of unitary impulse u0,and(t):
It is observed that it coincides with the function that describes the discharge of a condenser.
7) Property of the d of Dirac:
8) Usefullness of the theory of the distributions:
Theory of functions is valid from step u-1(t) in poi u-2(t) = rampa , u-3(t) = rampa parabolica which can to obtain integrating repeatedly, when but there are functions like the step that they have of the discontinuities, in order to derive them is necessary to use the theory of the distributions.
9) Fasore:
The fasore is a carrier associated to marks them
sinusoidali isofrequenziali, is characterized solo from amplitude and
phase and wheel in the complex plan with a speed that is equal to the
pulsation of marks them 
.
10) Like passing from the expression in the time to the fasore:
It is necessary to characterize the amplitude that it is that one that multiplies the cosine and the phase that is the term that to the inside of the argument of the cosine is not multiplied for t, such phase is the argument of the complex exponential .
11) Like passing from the fasore to the expression in the time:
From the fasore it is necessary to determine the module and the phase by means of the customary formulas, dopodichè the module goes to multiply the cosine whose argument is the pulsation (that it must famous a priori) be multiplied for the time and be added to the phase.
12) Relation between the fasore and the e(t):
The sinusoidale largeness e(t) is equal to the projection
on the real axis of the associated rotary 
carrier to
the fasore of the largeness stessa 
, an other
interpretation sees the fasore and its conjugated complex to ruotare
in opposite sense and their sum moment for moment gives place to the
e(t), is obtained expressing the cosine like semisum of esponenziali.
13) Order of a system of equations differentiates associated them to a circuit with memory:
The order is equal to the sum of the condensers and the present inductances in the circuit.
14) Interpretation of the time constant:
The time constant is the intersection with the tangent in the origin to the curve that describes the largeness that stà observing itself and the axis of the times. It coincides with the interval of necessary time so that the largeness is reduced to 1/e of the its maximum value.
15) Analysis in the dominion of the time:
This type of analysis is based on the formulation of a series of relative equations is to the circuit that to the present members in it, dopodichè must be made in way of ridurle to an only integral equation - one incognito differentiates according to them, such equation must be resolved with the relative methods you to the equations differentiates them, and in it the conditions must be replaced begin them.
16) transformed Definition of of Laplace:
The transformed one of Laplace is defined from the
following limit 
, where s it is a complex number
that has like measure unit the inverse one of a time.
17) Definition of transformed of Laplace in distribuzionale within:
It is necessary to consider also 0- in how much otherwise for a function like the impulse, the informative contribution is neglected that is had in the origin.
18) Transformed in the dominion of Laplace of the independent generator of tension and its unit of measure:
The value of the generator in the dominion of s is the transformed one of the function that describes the generator in the dominion of the time, the measure joined one is [ V][s ].
19) Transformed in the dominion of Laplace of the independent generator of current and its unit of measure:
The value of the generator in the dominion of s is the transformed one of the function that describes the generator in the dominion of the time, the measure joined one is [ A][s ].
20) Stiffness:
When the law of Ohm in the dominion of s can be written, in linear way, the constant of proportionality between tension and current are called stiffness and are the equivalent of the resistance in the real case.
21) Admittance:
When the law of Ohm in the dominion of s can be written, in linear way, the constant of proportionality between current and tension are called admittance and are the equivalent of the conductance in the real case.
22) constituent Relation of the condenser in the dominion of s:
It is obtained applying transformed of Laplace to 
the obtaining 
the , one looks at
therefore as in the equivalent circuit in the dominion of s a
generator that it simulates the presence of the conditions begins
them, in this case must be added is a generator of current added in
parallel to the ability to 
value while if the
equation in the shape is written 
, where pu² to
acknowledge a conductance multiplied for a potential difference the
series of one them, in the equivalent circuit is had ability to value and a generator of tension of 
value.
23) constituent Relation of the inducer in the dominion of s:
It is obtained applying the transformed ones of Laplace to 
the obtaining 
. It is
interesting to see that the associate circuit sees an inductance of
value sL with in series a generator of tension of Li(0 value-) that antitransformed it corresponds
to a impulsive generator of Li(0 value-)u0(t).
Collecting sL a generator of current of value is also
possible to associate a circuit with an inductance of value sL having
in parallel 
that antitransformed corresponds to a
generator to step of value i(0-)u-1(t).
24) Method of the conditions begins them for the resolution of the circuits:
When the antitransformation is not simple, its equivalent circuit having of the impulsive generators can be worked directly in the dominion of the time replacing to the member or to step in place of the generators of conditions it begins them that they are had in the dominion of Laplace.
25) Calcolo of the transformed one of Laplace of marks them sinusoidale:
It marks them 
possesses
transformed 
.
