Load line (electronics)

Diode load line. The curve shows the diode response (I vs V_D) while the straight line shows the behaviour of the linear part of the circuit: I=(V_DD-V_D)/R. The point of intersection gives the actual current and voltage.

A load line is used in graphical analysis of nonlinear electronic circuits, representing the constraint other parts of the circuit place on a non-linear device, like a diode or transistor. It is usually drawn on a graph of the current vs the voltage in the nonlinear device, called the device's characteristic curve. A load line, usually a straight line, represents the response of the linear part of the circuit, connected to the nonlinear device in question. The points where the characteristic curve and the load line intersect are the possible operating point(s) (Q points) of the circuit; at these points the current and voltage parameters of both parts of the circuit match.^[1]

The example at right shows how a load line is used to determine the current and voltage in a simple diode circuit. The diode, a nonlinear device, is in series with a linear circuit consisting of a resistor, R and a voltage source, V_DD. The characteristic curve (curved line), representing the current I through the diode for any given voltage across the diode V_D, is an exponential curve. The load line (diagonal line) represents the relationship between current and voltage due to Kirchhoff's voltage law applied to the resistor and voltage source, is

$V_D = V_{DD} - I R \,$

Since the current going through the three elements in series must be the same, and the voltage at the terminals of the diode must be the same, the operating point of the circuit will be at the intersection of the curve with the load line.

In a BJT circuit, the BJT has a different current-voltage (I_C-V_CE) characteristic depending on the base current. Placing a series of these curves on the graph shows how the base current will affect the operating point of the circuit.

DC and AC load lines

Semiconductor circuits typically have both DC and AC currents in them, with a source of DC current to bias the nonlinear semiconductor to the correct operating point, and the AC signal superimposed on the DC. Load lines can be used separately for both DC and AC analysis. The DC load line is the load line of the DC equivalent circuit, defined by reducing the reactive components to zero (replacing capacitors by open circuits and inductors by short circuits). It is used to determine the correct DC operating point, often called the Q point.

Once a DC operating point is defined by the DC load line, an AC load line can be drawn through the Q point. The AC load line is a straight line with a slope equal to the AC impedance facing the nonlinear device, which is in general different from the DC resistance. The ratio of AC voltage to current in the device is defined by this line. Because the impedance of the reactive components will vary with frequency, the slope of the AC load line depends on the frequency of the applied signal. So there are many AC load lines, that vary from the DC load line (at low frequency) to a limiting AC load line, all having a common intersection at the DC operating point. This limiting load line, generally referred to as the AC load line, is the load line of the circuit at "infinite frequency", and can be found by replacing capacitors with short circuits, and inductors with open circuits.

Load lines for common configurations

Transistor load line

Common emitter transistor load line.

Note: This section confuses the load's open circuit voltage, the load's short circuit current, the transistor's cutoff current, the transistor's saturation current, and the transistor's active region. The suggested operating point is at the saturation boundary. See BJT and File:Current-Voltage relationship of BJT.png. The selected load line is also poor for linearity; compare with figure 92, page 105, Basic Theory and Application of Transistors, Dover, 1963.

The load line diagram at right is for a transistor connected in a common emitter circuit. It shows the collector current in the transistor I_C versus collector voltage V_CE for different values of base current I_base. The load line represents a particular value of collector load resistor (R_C). The intersections of the load line with the transistor characteristic curve represent the different values of I_C and V_CE at different base currents.

The point on the load line where it intersects the collector current axis is referred to as saturation point.^[2] At this point, the transistor current is maximum and voltage across collector is minimum, for a given load. For this circuit, I_C-SAT= V_CC/R_C.^[3]

The cutoff point is the point where the load line intersects with the collector voltage axis. Here the transistor current is minimum (approximately zero) and emitter is grounded. Hence V_CE-CUTOFF=V_cc.

The operating point of the circuit in this configuration is generally designed to be in the active region, approximately in the middle of the load line and close to the saturation point. In this region, the collector current is proportional to the base current, and hence useful for amplifier applications. A load line is normally drawn on I_c-V_ce characteristics curves for the transistor used in amplifier circuit.

References

• Vias.org

1. Adel Sedra, Kenneth Smith. Microelectronic Circuits, 5th ed.
2. Assuming an ideal transistor.
3. Assuming Vce = 0 for an ideal transistor, so for the ideal transistor the voltage over R_C equals V_CC at this point on the load line.