Page 59 - Mechanical Engineers' Handbook (Volume 2)

48 Input and Output Characteristics

effort decreases slightly from operating point 2, then the source will be starved compared to
the demand of the load at that effort level, so the effort will fall until point 3 is reached.

4.3 Input and Output Impedance at the Operating Point
Lines of constant power are hyperbolas in the power plane, with increasing values of the
power at increasing distance from the origin. The usual sign conventions imply that sources
deliver power in the first and third quadrants while loads absorb power in those quadrants.
Conversely, sources absorb power in the second and fourth quadrants and loads return it.
The output impedance of a source is defined as minus the slope of the output characteristic.
For nonlinear characteristics, the output impedance at any point is defined as minus the slope
at that point. For loads, the input impedance is defined as the slope of the load line, but for
nonlinear characteristics there are two possibilities of importance: the slope of the line at a
point (the incremental or local input impedance) and the slope of the chord to the point from
the origin (the chordal impedance). Figure 8 summarizes these features of the power plane.

4.4 Operating Point and Load for Maximum Transfer of Power

Consider a battery with the voltage–current characteristic shown in Fig. 9. The maximum
unloaded terminal voltage (open circuit) of the battery is V volts and the short-circuit current
oc
is i amperes. The equation of the line shown is
sc
V V Ri
t oc ob
or

Figure 8 Definitions in the power plane.