C2 · BJT

DC Bias: Settle the Spot Before Anything Swings

To use a transistor for amplification, you must first settle it at a point in the active region. In this unit you change the bias yourself and find where on the load line the operating point should sit for the signal to swing as widely as possible.

Move the operating point along the load line

The slanted straight line is the load line, and the collector current and collector-emitter voltage always lie on it together. Change the bias and the operating point slides along the line: the upper-left end is saturation and the lower-right end is cutoff. Find the spot where the signal can swing the widest.

Bias base current IbIb = 8 μA

Operating point Q

Vce = 9.2 V   Ic = 0.8 mA

The operating point is near cutoff. Vce is filled almost up to Vcc, so there is plenty of room to fall but hardly any to rise.

At an edge · no swing

The load line, a promise of the collector loop

On the collector side, the supply Vcc and the resistor Rc are in series with the transistor. Writing Kirchhoff's voltage law around this loop gives Vcc = Ic Rc + Vce, that is, Vce = Vcc - Ic Rc, which is a straight line on the plane of Ic and Vce plotted against each other: the load line. One end is cutoff, where Ic is 0 (Vce = Vcc), and the other is saturation, where Vce is nearly 0 (Ic = Vcc/Rc). The transistor's operating point always lies somewhere on this line.

The bias sets the operating point Q

Which point on the load line it settles at is decided by the bias current fed into the base. Once the bias sets Ib, the relation from C1, Ic = β Ib, sets the collector current, and where that Ic meets the load line is the operating point Q. Too little bias drops Q toward cutoff and the transistor turns off; too much raises it toward saturation, where Vce sticks to the bottom and can move no further.

The middle is best: room to swing

Later, when a signal is applied, Vce swings up and down around the operating point. If Q is too close to one end, the swing soon hits cutoff or saturation and is cut off (clipping). At the very center of the load line, where the room above and below is equal, that is, when Vce is about half of Vcc, the signal can swing the widest in both directions. A good bias must also keep Q from moving much when β or temperature changes, and a resistor in the emitter is the usual way to get that stability.

ObserveVce = Vcc - Ic Rc

The load line is KVL written for the collector circuit.

ChooseIc,sat = Vcc / ?

At the saturation end Vce=0, so Ic is Vcc over Rc.

Fill inIc = β ?

The collector current at the operating point is β times the Ib set by the bias.

On your ownVce,Q ≈ ?

Maximum swing is when Vce is half of Vcc.

Back to the first screen

With little bias, the operating point hung at the lower-right end near cutoff, with no room to swing upward. With a lot of bias, it stuck to the upper-left end near saturation and the room to swing downward disappeared. Only at the center of the load line did the room above and below become equal. The operating point always lies on the load line, its position is set by the bias, and the best place is the center, where the signal can swing freely both ways. Next comes seeing how a small swing grows at that spot.

To use a transistor, you must first settle its operating point (Q point) in the active region with DC bias. KVL for the collector circuit sets the load line Vce = Vcc - Ic Rc, and the bias sets Ib (and hence Ic = β Ib), picking one point on that line. Placing the Q point at the center of the load line (Vce ≈ Vcc/2) lets the signal swing the most without hitting cutoff or saturation. A good bias must also be stable against changes in β and temperature.

What comes next

The transistor now sits stably at one point in the active region. The next unit separates out just the small swings around that point: setting the large DC aside for a moment, it treats the transistor near the operating point as a linear element, the small-signal model. That is where the arithmetic of amplification begins, showing how a small input grows into a large output.