2.7 The Load Line

Another way to gain understanding in diode circuits is given by the concept of a load line. Consider the figure below that contains a voltage source, a resistor and an unknown component. So, for that unknown component, the relation between current and voltage is not known. However, these cannot be changed independently from each other, since the component is connected to other components in a loop.

diode_loadline_circuit

Figure 2.18 This circuit contains an unknown component. However, it’s voltage and current cannot change independently, due to VS and R.

So, the question is: “What is known about the relationship between the current IL and the voltage VL without knowing what the load is?” Before answering this question, note that the circuit above represents a very generic case. Remember from Thévenin’s theorem that any linear circuit can be replaced by one voltage source (the Thévenin voltage) and one resistor (the Thévenin resistance). The answer to the above question is given by Kirchhoff’s voltage law:

VS – R.IL – VL = 0 V

This equation allows the voltage to be calculated from the current:

VL = VS – R.IL

or the current from the voltage:

IL = (VS – VL) / RL

Graphically, these equations represent a straight line in the VS – IL plane (Figure 2.19). This line is called a load line, and can be defined as a graphical representation of the relationship between the voltage across and the current through a component, only taking the surrounding components into account. So, the current-voltage characteristic of that component is not taken into account.

diode_loadline_blank

Figure 2.19 The load line dictates which pairs of IL and VL are allowed, and connects the short circuit current with the open circuit voltage.

Two points on the load line have a special meaning.  The open circuit voltage and the short circuit current. The open circuit voltage VOC is the voltage across the load, if this would be an open circuit (nothing).  In that case, the current will be zero, and there is no voltage drop across the resistor. As a result, the voltage VOC equals the source voltage:

VOC = VS

The shortcut current ISC is the current through the load, if this would be a short circuit (an ideal conductor).  Since the voltage across the short circuit would be 0 V, the resistor gets the entire source voltage, and the current through the loop is:

ISC = VS / R

So, without knowing what the load is, one knows that the operating point – the point in the plane that corresponds to the voltage across and the current through the component – will be on the load line. By combining the information of the load line with the current-voltage characteristic of the component, the operating point is found. Very simple: it corresponds to the intersection of both graphs. Applied on a diode, the result shown in Figure 2.20 is obtained.

 diode_loadline_diodecurve

Figure 2.20 The load line and the diode characteristic.  The operating point corresponds to the intersection of both lines.

Diodes - Level 8

This quiz contains some questions related to the concept of the load line. Try to use “graphical” reasoning to find the correct answer.

Go to 2.8 Rectifiers

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