Tensão de Thevenin

Thevenin Voltage

The Thevenin voltage e used in Thevenin's Theorem is an ideal voltage source equal to the open circuit voltage at the terminals. In the example below, the resistance R₂does not affect this voltage and the resistances R₁ and R₃ form a voltage divider, giving

Thevenin resistance

Numerical example

Norton equivalent

Thevenin's Theorem

Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short circuited.

Thevenin voltage

Thevenin resistance

Numerical example

Norton equivalent

to AC Version

Application in Digital to Analog Converter

Teorema de Norton

Norton's Theorem

Any collection of batteries and resistances with two terminals is electrically equivalent to an ideal current source i in parallel with a single resistor r. The value of r is the same as that in the Thevenin equivalent and the current i can be found by dividing the open circuit voltage by r.

Norton current

Norton resistance

Numerical example

Thevenin equivalent

Fontes de Corrente e Tensão

Voltage and Current Sources

Real voltage sources can be represented as ideal voltage sources in series with a resistance r, the ideal voltage source having zero resistance. Real current sources can be represented as ideal current sources in parallel with a resistance r, the ideal current source having infinite resistance.

Such ideal voltage and current sources are used in modeling real circuits withThevenin's theorem and Norton's theorem.

Teorema de Thevenin CA

AC Thevenin's Theorem

Any combination of sinusoidal AC sources and impedances with two terminals can be replaced by a single voltage source e and a single series impedance z. The value of e is the open circuit voltage at the terminals, and the value of z is e divided by the current with the terminals short circuited. In this case, that impedance evaluation involves a series-parallel combination.

Thevenin voltage

Thevenin resistance

Numerical example

Norton equivalent

to DC Version

Combinação Série - Paralelo

Series-Parallel Combination

Most networks in AC circuits can be broken into blocks no more complicated than the one below. The complex impedance approach provides the tool necessary to reduce such a combination to an equivalent impedance. This kind of combination may be encountered in the development of an AC Thevenin equivalent for the analysis of an AC circuit.

Calculation

The parallel part of the impedance can be put in the form

which can be rationalized by the operation :

,

and when terms are collected the results can be added to Z₁ , giving the equivalent 

Circuito RLC Paralelo

RLC Parallel Circuit

Finding the impedance of a parallel RLC circuit is considerably more difficult than finding the series RLC impedance. This is because each branch has a phase angle and they cannot be combined in a simple way. The impedance of the parallel branches combine in the same way that parallel resistors combine:

But although the branch impedance magnitudes can be calculated from and RL Circuit RC Circuit

they cannot be directly combined as suggested by the expression above because they are different in phase - like vectors in different directions cannot be added directly. This dilemma is most easily solved by the complex impedance method.