Bipolar junction transistors: physics and characteristics

The bipolar junction transistor, or BJT, was the device that made modern electronics possible. Invented at Bell Laboratories in the late 1940s, it replaced vacuum tubes in radios, computers and hearing aids, and although MOSFETs now dominate integrated circuits, BJTs remain everywhere in discrete and analog design: in precise amplifiers, current sources, voltage references, radio-frequency circuits, LED and relay drivers and power-supply controllers. A BJT is two pn junctions back to back, sharing a very thin middle layer, and its essential trick is that a small current into that middle layer controls a much larger current through the device.

Amara's LED current sink from lesson 5 needs a transistor, and so do the relay drivers that switch the cabinet's flash transfer relays and the input stage of the microphone amplifier. Daniel standardizes on a general-purpose small-signal npn transistor in the 2N3904 class for low-current work: rated about 40 V and 200 mA, with a current gain of roughly 100 to 300.

Structure and symbols

An npn transistor has an n-type emitter, a thin p-type base and an n-type collector. The emitter is very heavily doped, the base is lightly doped and extremely thin, often well under a micrometer in a modern device, and the collector is moderately doped and large. A pnp transistor reverses all three. The circuit symbol has an arrow on the emitter showing the direction of conventional current through the base–emitter junction when it is forward biased: out of the emitter for npn (Not Pointing iN), into the emitter for pnp.

How the transistor works

In normal amplifier use, the active mode, the base–emitter junction is forward biased and the base–collector junction is reverse biased. The forward-biased emitter junction injects a flood of electrons from the heavily doped emitter into the base. Because the base is thin and lightly doped, very few of these electrons find a hole to recombine with before they diffuse to the edge of the collector junction. There, the strong field of the reverse-biased junction sweeps them into the collector. The collector current is therefore set by how many electrons the emitter injects, which depends exponentially on v_BE, exactly as in a diode:

The base current has two small parts: holes injected from the base back into the emitter, which is small because the emitter is so much more heavily doped, and holes needed to replace those lost to recombination in the base. Both are proportional to the collector current, so their ratio is fixed. This ratio is the common-emitter current gain β, also written h_FE on datasheets:

With β = 100, the base current is 1 percent of the collector current and α = 0.99: 99 percent of the electrons leaving the emitter reach the collector. That is the source of current gain. It is important to see what controls what. Physically, v_BE controls i_C exponentially, and the base current is a by-product. In circuit design it is often convenient to think of the base current controlling the collector current through β, but β is a poorly controlled parameter, and good designs never depend on its exact value.

The four operating modes

Each junction can be forward or reverse biased, which gives four modes. Analog amplifiers use the active mode. Digital and switching circuits use cutoff, where both junctions are reverse biased and the transistor is off, and saturation, where both are forward biased and the transistor acts as a closed switch with a small voltage V_CE(sat) of about 0.1 to 0.3 V. The reverse active mode, with the roles of emitter and collector swapped, works but with very low gain and is rarely used deliberately.

A quick test for an npn transistor in a circuit: if v_BE is about 0.7 V and v_CE is more than about 0.3 V, it is active; if v_CE is down near 0.2 V, it is saturated; if v_BE is well below 0.5 V, it is cut off.

Characteristic curves

The input characteristic, i_B against v_BE, is simply a diode curve: almost nothing below 0.5 V and a steep rise near 0.6 to 0.7 V. Like any junction, v_BE falls about 2 mV per °C at constant current. The output characteristics plot i_C against v_CE for several fixed base currents. Each curve rises steeply from the origin through the saturation region, bends sharply at about v_CE = 0.2 to 0.3 V, and then runs almost flat across the active region, where the collector current depends on the base current and hardly at all on v_CE.

The Early effect

The active-region curves are not perfectly flat; they slope gently upward. As v_CE rises, the collector junction's depletion region widens and eats into the base, so the effective base gets thinner, fewer electrons are lost, and i_C rises a little. This is the Early effect, after James Early who explained it. Extended backward, the curves all meet the voltage axis near a single point, −V_A, where V_A is the Early voltage, typically 50 to 150 V for small-signal transistors. The effect is modeled by

The output resistance r_o is the inverse slope of the curve. At I_C = 1 mA and V_A = 100 V, r_o = 100 kΩ. It is large but not infinite, and it limits the gain of amplifiers in lesson 11 and the quality of current sources.

Current gain is not a constant

Datasheets give β as a range, often three to one or wider between units of the same type: a 2N3904-class part might list h_FE from 100 to 300 at 10 mA. β also rises with temperature, roughly 0.5 to 1 percent per °C, and varies with collector current, falling at very low currents and again at high currents. A design that works only for one value of β will not survive production. Lesson 7 shows bias circuits whose operating point depends very little on β, which is the central idea of good BJT design.

import math
VT, Is, VA = 0.0257, 2e-15, 100.0
# Output characteristics: iC versus vCE for several base currents (beta = 150)
beta = 150
print(" vCE(V) " + "".join(f"  iB={ib:2d}uA" for ib in (10, 20, 30, 40)))
for vce in (0.5, 2, 4, 6, 8, 10, 12):
    row = []
    for ib in (10, 20, 30, 40):
        ic = beta * ib * 1e-6 * (1 + vce / VA)   # active region with Early effect
        row.append(f"{ic*1000:9.3f}mA")
    print(f"{vce:7.1f} " + " ".join(row))
# Small-signal output resistance at 1 mA
print(f"ro at IC = 1 mA: {VA / 1e-3 / 1000:.0f} kOhm")
# vBE needed for 1 mA, and its temperature drift (about -2 mV per degree C)
vbe = VT * math.log(1e-3 / Is)
print(f"vBE at 1 mA, 25 C: {vbe:.3f} V; at 75 C about {vbe - 0.002 * 50:.3f} V")

 vCE(V)   iB=10uA  iB=20uA  iB=30uA  iB=40uA
    0.5     1.507mA     3.015mA     4.522mA     6.030mA
    2.0     1.530mA     3.060mA     4.590mA     6.120mA
    4.0     1.560mA     3.120mA     4.680mA     6.240mA
    6.0     1.590mA     3.180mA     4.770mA     6.360mA
    8.0     1.620mA     3.240mA     4.860mA     6.480mA
   10.0     1.650mA     3.300mA     4.950mA     6.600mA
   12.0     1.680mA     3.360mA     5.040mA     6.720mA
ro at IC = 1 mA: 100 kOhm
vBE at 1 mA, 25 C: 0.692 V; at 75 C about 0.592 V

The load line and the Q-point

A transistor in a circuit must also obey the external circuit. For the common arrangement with a collector resistor R_C from a supply V_CC, Kirchhoff's voltage law gives v_CE = V_CC − i_C R_C, a straight line on the output characteristics running from (V_CC, 0) to (0, V_CC/R_C). The transistor's operating point lies on this load line, at the intersection with the curve for the actual base current. For an amplifier, the Q-point is placed near the middle of the line's active section, so the collector voltage can swing both up and down. For a switch, the transistor is driven between cutoff at one end of the line and saturation at the other.

Limits and ratings

Every transistor has a safe operating area bounded by maximum collector current, maximum collector–emitter voltage V_CEO (with the base open), maximum power dissipation and, for power transistors, a second-breakdown limit at high voltage and current together. Power dissipation in the active mode is P = V_CE I_C + V_BE I_B ≈ V_CE I_C, and it heats the junction above ambient by P times the thermal resistance θ_JA, often about 200 °C/W for a small plastic package with no heatsink. A 2N3904-class part in free air can therefore dissipate only about 0.6 W at 25 °C ambient, and less in a hot cabinet. Because β and leakage rise with temperature, a transistor that heats up conducts more and heats further; without a bias design that resists it, this thermal runaway can destroy the part.

The pnp transistor

A pnp transistor works the same way with every polarity reversed: the emitter injects holes, the base is n-type, currents flow out of the base and collector and into the emitter, and in active mode the emitter is the most positive terminal, with v_EB ≈ 0.7 V. Holes are slower than electrons, so pnp transistors are somewhat slower and weaker than npn of the same size, but they are indispensable as high-side switches, in current mirrors and in complementary push-pull output stages. Daniel's flash relay driver, for example, uses a pnp to switch the 24 V side of the relay coil.