Independent Versus Dependent Controlled Sources

In the previous chapters, each source appearing in the analysis of dc or ac networks was an independent source, such as $E$ and $I$ (or $E$ and $I$) in [Fig. 1].

What is an independent source?

What is a dependent source?

Currently two symbols are used for controlled sources. One simply uses the independent symbol with an indication of the controlling element, as shown in [Fig .2]. In [Fig .2(a)], the magnitude and phase of the voltage are controlled by a voltage $V$ elsewhere in the system, with the magnitude further controlled by the constant $k_1$. In [Fig. 2(b)], the magnitude and phase of the current source are controlled by a current $I$ elsewhere in the system, with the magnitude further controlled by the constant $k_2$. To distinguish between the dependent and independent sources, the notation of [Fig. 3] was introduced. In recent years many respected publications on circuit analysis have accepted the notation of [Fig. 3], although a number of excellent publications in the area of electronics continue to use the symbol of [Fig. 2], especially in the circuit modeling for a variety of electronic devices such as the transistor and FET. This text will employ the symbols of [Fig. 3]. Possible combinations for controlled sources are indicated in [Fig. 4]. Note that the magnitude of current sources or voltage sources can be controlled by a voltage and a current, respectively. Unlike with the independent source, isolation such that $V$ or $I = 0$ in [Fig. 4(a)] will result in the short-circuit or open-circuit equivalent as indicated in [Fig. 4(b)]. Note that the type of representation under these conditions is controlled by whether it is a current source or a voltage source, not by the controlling agent ($V$ or $I$).