Source transformation is simplifying a circuit solution,
especially with mixed sources, by transforming a voltage into a current source, and vice versa. Finding a solution to a circuit can be
difficult without using methods such as this to make the circuit appear
simpler. Source transformation is an application of Thévenin's theorem and Norton's theorem.
Performing a source transformation consists of
using Ohm's law to
take an existing voltage source in series with
a resistance,
and replace it with a current source in parallel with
the same resistance. Remember that Ohm's law states that a voltage on a
material is equal to the material's resistance times the amount of current
through it (V=IR). Since source transformations are bilateral, one can be
derived from the other. [2] Source
transformations are not limited to resistive circuits however. They can be
performed on a circuit involving capacitors and inductors,
as long as the circuit is first put into the frequency
domain. In general, the concept of source transformation is an
application of Thévenin's theorem to a current
source, or Norton's
theorem to avoltage
source.
Specifically, source transformations are used to
exploit the equivalence of a real current source and a real voltage source,
such as a battery. Application of Thévenin's theorem
and Norton's theorem gives the quantities associated with the equivalence.
Specifically, suppose we have a real current source I, which is an ideal
current source in parallel with an impedance. If the ideal current source is
rated at I amperes, and the parallel resistor has an impedance Z, then applying
a source transformation gives an equivalent real voltage source, which is
ideal, and in series with the impedance. This new voltage
source V, has a value equal to the ideal current source's value times the
resistance contained in the real current source. The impedance
component of the real voltage source retains its real current source value.
In general, source transformations can be
summarized by keeping two things in mind:
· Impedance's remain the same
Overview and Insights
Source
transformations are easy to perform as long as there is a familiarity with Ohm's law. If
there is a voltage source in series with
an impedance, it is possible to find the value of the
equivalent current
source in parallel with
the impedance by dividing the value of the voltage source by the value of the
impedance. The converse also applies here: if a current source in parallel with
an impedance is present, multiplying the value of the current source with the
value of the impedance will result in the equivalent voltage source in series
with the impedance.
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