# Dragon Notes

UNDER CONSTRUCTION
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## TERMINAL IMPEDANCE

Optimal power transmission is achieved when:

CURRENT: VOLTAGE:
Input Impedance: high Input Impedance: low
Output Impedance: low Output Impedance: high

Consider the simple case of a power supply with internal impedance and a load; [asm.] resistive impedance:

The voltage transmission relation from input to output is $\s{V_{\text{out}}=\left[ \frac{R_{\text{L}}}{R_{\text{L}}+R_{\text{int}}}\right],}$ where $$\s{R_{\text{int}}=}$$ source internal resistance. As the relation implies, to deliver a voltage to the load as close to rated value as possible, $$\s{R_L}$$ must be $$\s{\gg R_{\text{int}}}$$. Then, $$\s{V_{\text{out}}\approx V_{\text{in}}}$$ – or, alternatively, $$\s{V_{\text{delivered}} \approx V_{\text{rated}}}$$. This can be attained either via a high load resistance or low internal resistance.

➢ The main advantage to having a low $$\s{R_{\text{int}}}$$ is a larger range of $$\s{R_L}$$ for effective power transmission; that is, $$\s{R_L\gg R_{\text{int}}}$$ is met for more values of $$\s{R_{\text{L}}}$$.

[In other words, from the point of view of the load, low source internal resistance is desirable as it allows for a greater range of $$\s{R_L}$$ values for which voltage is delivered as intended. From the point of view of the source, high load resistance is desireable as it allows to meet required $$\s{R_{\text{int}}}$$ easier].

For the case of current, consider the same circuit; the current source is formed by the $$\s{V_{\text{in}}}$$ & $$\s{R_{\text{int}}}$$ configuration. The current transmission relation from input to output is $\s{I=\frac{V_{\text{in}}}{R_{\text{L}}+R_{\text{int}}}.}$ To meet $$\s{I_{\text{delivered}} \approx I_{\text{rated}}}$$, we need $$\s{R_{\text{int}} \gg R_L}$$. The source delivers exactly the rated current at $$\s{R_{\text{total}}=R_{\text{int}}}$$. Hence, if a current source is rated at, say, 5A – then to supply 5A instead of 10A or 1A, $$\s{R_L}$$ must be insignificant in comparison with $$\s{R_{\text{int}}}$$ – that is, for I to not vary much with $$\s{R_L}$$, $$\s{R_{\text{int}}}$$ must be $$\s{\gg R_L}$$. Like with voltage sources, this also constitutes the main advantage of a higher $$\s{R_{\text{int}}}$$.