C2 · BJT

DC Bias: Settle the Spot Before Anything Swings

Before using it to amplify, you park the transistor at a point in the active region. Change the bias yourself and find where on the load line the operating point gives the signal the widest room to swing.

Move the operating point along the load line

The straight line is the load line. The collector current and Vce always sit together on it. Change the bias and the operating point Q slides along the line. The upper end is saturation, the lower end cutoff. Where is the spot with the widest room for the signal to swing?

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 almost at Vcc, so there is room to fall but almost none to rise.

At an edge · no swing

The load line, a promise of the collector loop

At the collector, the supply Vcc and a resistor Rc are in series with the transistor. Applying Kirchhoff’s voltage law to this loop gives Vcc = Ic Rc + Vce, that is, Vce = Vcc - Ic Rc. This is a straight line on the Ic-versus-Vce plane: the load line. One end is cutoff with Ic = 0 (Vce = Vcc), the other is saturation with Vce near 0 (Ic = Vcc/Rc). The transistor’s operating point must lie somewhere on this line.

The bias sets the operating point Q

Which point on the load line it sits at is set by the bias current fed into the base. Once the bias fixes Ib, the relation Ic = β Ib from C1 fixes the collector current, and where that Ic meets the load line is the operating point Q. Give too little bias and Q drops to cutoff and the transistor turns off; give too much and it climbs to saturation, where Vce sticks to the floor and can move no further.

The middle is best: room to swing

Later, when a signal is applied, Vce swings up and down about the operating point. If Q is too close to one end, the swing soon hits cutoff or saturation and is sliced off (clipping). At the center of the load line, where the room above and below is equal, Vce sits near half of Vcc and the signal can swing widest both ways. A good bias must also be stable, so Q does not move much when β or temperature changes; this stability is often gained with an emitter resistor.

ObserveVce = Vcc - Ic Rc

The load line is the KVL of the collector loop.

ChooseIc,sat = Vcc / ?

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

Fill inIc = β ?

The operating-point collector current is β times the biased Ib.

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 end near cutoff, with no room to swing up. With a lot it stuck to the upper end toward saturation, with no room to swing down. Only at the center of the load line did the room above and below become equal and the swing-headroom indicator fill the highest. The operating point always lies on the load line; what sets its place is the bias; and the best place is the very middle, where the signal can swing freely both ways. Now it is time to see how a small wobble is amplified from that spot.

To use a transistor you must first park the operating point (Q-point) in the active region with DC bias. The KVL of the collector loop sets the load line Vce = Vcc - Ic Rc, and the bias sets Ib (hence Ic = β Ib), choosing one point on that line. Put the Q-point at the center of the load line (Vce ≈ Vcc/2) and the signal swings maximally without hitting cutoff or saturation. A good bias must be stable against β and temperature changes.

What comes next

The transistor now sits stably at a point in the active region. The next unit peels off only the small wobble about that point. Forgetting the large DC for a moment, it views the transistor near the operating point as a linear device: the small-signal model. From there, the arithmetic of amplification begins, showing how a small input grows into a large output.