Sources

Figure 3.1: A DC source (Ideal Voltage Source) with a circuit element

Ideal voltage source: Whatever amount of current is drawn from it the voltage at the terminals is always same. Whenever the terminals are short circuited (resistance of $0\; \Omega$ between the terminals) the infinite amount of current flows to maintain voltage. This is hypothetical condition, why?

Figure 3.2: Ideal Current Source

Ideal current source: Whatever load or network of elements is connected to source, the current pumped by the source into the load always remains same. Whenever the terminals are open circuits (Terminals are not connected to any thing) the voltage across the terminals becomes $\infty$ to maintain the same amount of current through terminals. This is also hypothetical condition, why?

Can I leave a current source as shown in figure 3.3?

Figure 3.3: Current Source left open

In this case, voltage across the terminals will be $\infty$.

Non Ideal Voltage Source: See the circuit in figure 3.4. A non ideal voltage source is modeled with an internal resistance of source $R_{int}$. Thus battery terminal voltage changes with the load current.

Figure 3.4: Non Ideal Voltage Source

Under no load, i.e. for zero current, $V_{ab}=V$. When a load current $i$ flows, $V_{ab}=V-iR_{int}$. For a new battery, generally, $R_{int}$ is negligible, and it increases as the battery gets discharged. $V$ is a function of electrolyte and terminal materials.

Non Ideal Current Source: See the circuit in figure 3.5.

Figure 3.5: Non-ideal Current Source

A non ideal current source is modeled by an internal conductance $G_{int}$ in parallel with the source. $G_{int}=\frac{1}{R_{int}}$.
From the figure, we see that: $I-G_{int}V_{ab}=I_{AB}$. Ideal current source has $G_{int}=0$, i.e., $R_{int}=\infty$.

Non-ideal voltage source and current source analysis: The source is non-ideal, hence v is not constant. If it is linear circuit, $V_{ab}$ and $i$ are linearly related. $v$ is cause, and $i$ is effect. Thus we get:

Figure 3.6: Battery

$$dv=m\;di$$ (3.1)

$$v=mi+c$$ (3.2)

Figure 3.7: Model

This equation is equivalent to fig.3.7. Thus a battery can be represented by 3.8:

Figure 3.8: Battery Model

Similarly, for a nonideal current source (fig.3.9), if it is linear,

$$dv=m\;di$$ (3.3)

$$i=\frac{1}{m}v+c$$ (3.4)

For ideal current source, $di=0$ always. Thus $\frac{1}{m}=0$.

Figure 3.9: Current Source

Figure 3.10: Current Source Model

In the above, the sources are modelled using ideal voltage (current) sources whose voltage (current) remains constant.

We can also have source whose output can be controlled. These can be used to model certain real life devices (e.g., transistor) We will study transistor later during the course.