Thevenin-Norton
equivalencies
Since Thevenin's and Norton's Theorems are
two equally valid methods of reducing a complex network down
to something simpler to analyze, there must be some way to
convert a Thevenin equivalent circuit to a Norton equivalent
circuit, and visa-versa (just what you were dying to know,
right?). Well, the procedure is very simple.
You may have noticed that the procedure for
calculating Thevenin resistance is identical to the
procedure for calculating Norton resistance: remove all
power sources and determine resistance between the open load
connection points. As such, Thevenin and Norton resistances
for the same original network must be equal. Using the
example circuits from the last two sections, we can see that
the two resistances are indeed equal:
Considering the fact that both Thevenin and
Norton equivalent circuits are intended to behave the same
as the original network in suppling voltage and current to
the load resistor (as seen from the perspective of the load
connection points), these two equivalent circuits, having
been derived from the same original network should behave
identically.
This means that both Thevenin and Norton
equivalent circuits should produce the same voltage across
the load terminals with no load resistor attached. With the
Thevenin equivalent, the open-circuited voltage would be
equal to the Thevenin source voltage (no circuit current
present to drop voltage across the series resistor), which
is 11.2 volts in this case. With the Norton equivalent
circuit, all 14 amps from the Norton current source would
have to flow through the 0.8 Ω Norton resistance, producing
the exact same voltage, 11.2 volts (E=IR). Thus, we can say
that the Thevenin voltage is equal to the Norton current
times the Norton resistance:
So, if we wanted to convert a Norton
equivalent circuit to a Thevenin equivalent circuit, we
could use the same resistance and calculate the Thevenin
voltage with Ohm's Law.
Conversely, both Thevenin and Norton
equivalent circuits should generate the same amount of
current through a short circuit across the load terminals.
With the Norton equivalent, the short-circuit current would
be exactly equal to the Norton source current, which is 14
amps in this case. With the Thevenin equivalent, all 11.2
volts would be applied across the 0.8 Ω Thevenin resistance,
producing the exact same current through the short, 14 amps
(I=E/R). Thus, we can say that the Norton current is equal
to the Thevenin voltage divided by the Thevenin resistance:
This equivalence between Thevenin and Norton
circuits can be a useful tool in itself, as we shall see in
the next section.
-
REVIEW:
-
Thevenin and Norton resistances are equal.
-
Thevenin voltage is equal to Norton
current times Norton resistance.
-
Norton current is equal to Thevenin
voltage divided by Thevenin resistance.
|
