5. The BJT: Three Layers of Magic

Now we get to the bipolar junction transistor. Start with one pn junction (the diode), and now sandwich a third layer to make either an NPN structure or PNP structure. The middle layer is called the base; the outer layers are the emitter and collector.

The transistor has two pn junctions: the base-emitter junction and the base-collector junction.

     N (collector)
       |
     P (base)  ← thin, lightly doped
       |
     N (emitter) ← heavily doped

(For PNP, swap N and P throughout.)

5.1 How an NPN works: the elevator-pitch version

In normal "active" mode operation:

• The base-emitter junction is forward-biased (about 0.7 V across it).
• The base-collector junction is reverse-biased (the collector is at a much higher potential than the base).

The base is thin (typically a fraction of a micron) and lightly doped. The emitter is heavily doped — far more electrons than the base has holes.

Because the base-emitter junction is forward-biased, electrons flood from the heavily-doped emitter into the lightly-doped base — just like in a diode. But here is the trick: the base is so thin and so lightly doped that almost none of those electrons recombine with holes in the base. They diffuse across the base in a fraction of a nanosecond. By the time they reach the other side of the base, they encounter the strong reverse field of the base-collector junction, which immediately sweeps them up into the collector.

So a small base-emitter forward bias causes a huge emitter-to-collector electron flow. The base "controls" the much larger collector current. A small base current controls a large collector current — current amplification.

Water-faucet analogy. The collector-emitter circuit is like a fire hose with a heavy faucet between them. The faucet handle is the base. Apply a small twist to the handle (small base current) and the hose blasts water (large collector current). The twist is the input; the blast is the amplified output. The handle barely moves while the water flows hundreds of times the volume.

The currents:

• $I_E$ (emitter): the total current entering the emitter — almost all electrons.
• $I_C$ (collector): the part that makes it across the base and out the collector. Almost all of the emitter current.
• $I_B$ (base): the small current that recombines in the base or supplies holes to support hole-injection back into the emitter.

By Kirchhoff's current law, $I_E = I_C + I_B$.

5.2 The two famous gain parameters

Define:

• $\alpha = I_C / I_E$ — common-base current gain. Typically 0.99 or higher.
• $\beta = I_C / I_B$ — common-emitter current gain. Typically 50 to 300 for general-purpose transistors, up to 1000 for "Darlington" pairs.

These are related by:

$\beta = \frac{\alpha}{1 - \alpha}$

If $\alpha = 0.99$, $\beta = 99$. If $\alpha = 0.999$, $\beta = 999$.

Datasheets quote $\beta$ (often called $h_{FE}$, the same thing in slightly different notation). Important to know: $\beta$ varies wildly from device to device, even between two transistors from the same batch — by a factor of two or three is common. It also varies with temperature and current. You should never rely on a specific value of $\beta$ in a circuit design. We will see why this matters when we discuss biasing.

5.3 The four operating regions of a BJT

A BJT can be in one of four states, depending on whether each junction is forward or reverse biased:

For analog amplifier circuits, we keep the transistor in the active region. For digital circuits, we use only cutoff (off) and saturation (on); the transistor acts as a switch.

5.4 The output characteristics: the curves you must memorize

Plot $I_C$ on the vertical axis vs $V_{CE}$ on the horizontal, for various values of $I_B$:

   I_C
    |
    |___________________ I_B = 30 µA
    |___________________ I_B = 20 µA
    |___________________ I_B = 10 µA
   /|saturation| active region
  / |__________|________________________ V_CE
   0

For a fixed $I_B$, the collector current is approximately constant ($= \beta I_B$) once $V_{CE}$ exceeds the saturation knee (about 0.2 V). This is the active region: the transistor behaves like a current source whose value is set by $I_B$.

At very low $V_{CE}$ (less than ~0.2 V), the transistor is in saturation: $I_C$ falls off because the base-collector junction is now also forward-biased and is competing with the base-emitter junction for the available carriers.

5.5 The Ebers-Moll model: full physics

For SPICE simulators, the BJT is usually described by the Ebers-Moll equations:

$I_C = I_S\left(e^{V_{BE}/V_T} - 1\right) - \frac{I_S}{\alpha_R}\left(e^{V_{BC}/V_T} - 1\right)$

(plus a similar equation for $I_E$). Here $I_S$ is the saturation current, $V_T = kT/q \approx 26$ mV, and $\alpha_R$ is the reverse common-base gain (small, often ~0.1).

For the active region ($V_{BC}$ very negative), the second term collapses and we get the simple result:

$I_C \approx I_S e^{V_{BE}/V_T}$

So the collector current depends exponentially on $V_{BE}$. A 60 mV change in $V_{BE}$ gives a 10× change in $I_C$. This sensitivity is at the heart of why we cannot drive a BJT with a fixed voltage source — see "biasing" below.

Two important consequences:

• The transistor is a transconductance device. Small change in $V_{BE}$ → exponentially big change in $I_C$. The slope at the operating point is the transconductance $g_m = I_C / V_T$ — a quantity you will use constantly. At 1 mA, $g_m = 1/26 = 38$ mS, often quoted as $g_m \approx 40 \cdot I_C$ in mA-to-mS.
• $V_{BE}$ varies only slightly with current. Over a decade of collector current (say 1 mA to 10 mA), $V_{BE}$ rises by only $\ln(10) \cdot V_T \approx 60$ mV. So in many circuit calculations we approximate $V_{BE} = 0.7$ V regardless of current, and that approximation is good to within tens of millivolts.

5.6 The three configurations: CB, CE, CC

A transistor has three terminals, and depending on which one is "common" (shared between input and output), we get three classic single-stage amplifier topologies:

(CC is also called the emitter follower.)

These three configurations have very different gain, impedance, and frequency-response characteristics. The CE is by far the most common, used as the basic gain stage in audio amplifiers and many other circuits. The CC (emitter follower) is used as a buffer — high input impedance, low output impedance, gain ≈ 1. The CB has very low input impedance and is used in RF circuits where its high frequency response matters.

We will analyze them properly with small-signal models in section 9.

5.7 Photo-transistor and other variants

A photo-transistor is a BJT where the base is exposed to light. Photons absorbed in the base region create electron-hole pairs that flow into the base, supplying the base current. So $I_B \propto$ light intensity, and $I_C = \beta I_B \propto$ amplified light intensity. Used in:

• TV remote-control receivers.
• Optical encoders (rotary position sensing on motors).
• Optoisolators (a packaged LED + phototransistor pair providing electrical isolation between two circuits).

Other BJT variants worth knowing: the Darlington pair (two BJTs cascaded for $\beta = \beta_1 \beta_2$, giving 10,000+ effective gain — used in audio output stages and motor drivers), and the photo-Darlington (for very low light levels).