Practical Current Source Equivalent Circuit

A practical current source is a real-world device that provides a constant current to a load, similar to how a battery provides a constant voltage. Unlike an ideal current source, a practical current source has internal limitations.

An ideal current source is theorized to deliver a constant current regardless of the voltage across its terminals or the load connected to it. This implies that an ideal current source has infinite internal resistance, meaning no current is diverted internally.

In reality, no current source is perfectly ideal. A practical current source can be represented by an equivalent circuit model. This model helps us understand and analyze its behavior when connected to a load.

The equivalent circuit of a practical current source consists of:

• An ideal current source.
• An internal impedance (or admittance) connected in parallel (shunt) with the ideal current source.

For DC circuits or at a specific frequency where only resistance is considered, this internal impedance is represented by an internal resistance, often denoted as $R_s$. Since this resistance is in parallel with the current source, some of the current generated by the ideal source will flow through this internal resistance rather than reaching the load.

For a practical current source to behave as closely as possible to an ideal current source, the internal resistance should be very high. A very high parallel resistance means that most of the current from the ideal source flows into the external circuit (load) and very little is diverted internally.

Conductance ($G$) is the reciprocal of resistance ($R$). The relationship is given by: $$G = \frac{1}{R}$$ $$R = \frac{1}{G}$$ The unit of resistance is Ohms ($\Omega$), and the unit of conductance is Siemens (S).

If a practical current source has a very high internal resistance ($R_s \to \infty$), then its internal conductance ($G_s = 1/R_s$) will be very low ($G_s \to 0$). Conversely, if the internal resistance is finite, the internal conductance will be non-zero.

Since a practical current source is modeled with an internal resistance in parallel, and for it to be "practical" (i.e., relatively good at being a current source), this internal parallel resistance should be high. Therefore, the equivalent circuit includes an internal parallel element which represents this non-ideal behavior.

Considering the options provided in terms of conductance:

• "Shunt low resistance": This implies high conductance, which is not desired for a good current source.
• "Low resistance": This implies high conductance, also not desired.
• "High conductance": Directly states high conductance, not desired.
• "Low conductance": This implies high resistance ($R_s = 1/G_s$, if $G_s$ is low, $R_s$ is high). This is consistent with the requirement for a practical current source to have a high internal parallel resistance.

Thus, a practical current source is equivalent to an ideal current source in parallel with a low conductance, which corresponds to a high internal resistance.