Math Analysis

Mathematical Analysis

In this section we provide the DC load line analysis.

The dc collector current path for this circuit consists of the transistor in series with the collector resistor across the supply. Since the transistor's current equals the resistor's current, and teh transistor's voltage is the supply minus the resistor's voltage, the range of possible transistor voltages and currents is given by a linear equation:

Ic = V_Rc/Rc = (Vcc - Vc) / Rc

This indicates that there is a straight line on the V vs. I graph which represents all possible combinations of voltage and current for the transistor. Voltage and current combinations which do not lie on the line are not possible.

This line called the dc or static load line, can be readily positioned by its end points, which represent the extreme conditions of the transistor's condition, i.e. fully on (saturated) or fully off (cutoff).

If the transistor's base current is zero, the collector current is likewise zero (assuming no leakage), and no voltage will be dropped across the collector resistor. Hence, the resistor's collector voltage will equal the supply voltage when Ic is zero. This determines the cutoff end of the load line.

If the transistor is fed enough base current to cause saturation, only a few tenths of a volt appear from collector to emitter, and almost the full supply voltage appears across Rc. The transistor acts very much like a short circuit in this case, and the collector current is found by

Ic = Vcc / Rc

This saturation collector current with near zero collector volatage determines the second end point of the static load line. All possible circuit consitons lie on the straight line from saturation to cutoff.

Movement up and down the load line is caused by changes in transistor base current. notice that as higher input voltages case larger base current, the collector output voltage decreases. The amplifier, therefore, gives an output signal which is inverted from the input signal. This inversion is often termed a 180 ^ophase shift, since for a symmetrical signal like a sine, square, or triangle wave, the effect is the same.