Source Conversion

The current source appearing in the previous section is called an ideal source due to the absence of any internal resistance. In reality, all sources—whether they are voltage sources or current sources—have some internal resistance in the relative positions shown in [Fig. 1]. For the voltage source, if $Rs = 0Ω$, or if it is so small compared to any series resistors that it can be ignored, then we have an "ideal" voltage source for all practical purposes. For the current source, since the resistor $R_P$ is in parallel, if $R_P = \infty$, or if it is large enough compared to any parallel resistive elements that it can be ignored, then we have an ideal current source. Unfortunately, however, ideal sources cannot be converted from one type to another. That is, a voltage source cannot be converted to a current source, and vice versa—the internal resistance must be present. If the voltage source in [Fig. 1(a)] is to be equivalent to the source in [Fig. 1(b)], any load connected to the sources such as $R_L$ should receive the same current, voltage, and power from each configuration. In other words, if the source were enclosed in a container, the load $R_L$ would not know which source it was connected to. This type of equivalence is established using the equations appearing in [Fig. 2]. First note that the resistance is the same in each configuration—a nice advantage. For the voltage source equivalent, the voltage is determined by a simple application of Ohm's law to the current source: $E = I R_p$. For the current source equivalent, the current is again determined by applying Ohm's law to the voltage source: $I = E/R_s$. At first glance, it all seems too simple, but Example 1 verifies the results. The internal characteristics of each are quite different.