The BJT

The bipolar junction transistor was the workhorse of electronics for three decades before CMOS took over digital circuits. It remains indispensable in analog design: operational amplifiers, voltage references, bandgap circuits, high-speed ECL logic, and RF front-ends all rely on BJTs.

Where the MOSFET is a voltage-controlled switch, the BJT is a current-controlled current amplifier. A small current into the base produces a much larger current between collector and emitter, with a gain () that is remarkably well-controlled by the fabrication process.

Two flavors

NPN: Current flows from collector to emitter, controlled by base current. The emitter arrow points out of the device. This is the more common type.

PNP: Current flows from emitter to collector, controlled by base current. The emitter arrow points in. Complementary to NPN, like PMOS is to NMOS.

The BJT has three terminals: base (B), collector (C), and emitter (E). Unlike the MOSFET, the control terminal (base) draws significant current -- this is the fundamental difference between field-effect and bipolar devices.

The exponential law

The BJT's collector current follows an exponential relationship with base-emitter voltage:

where is the saturation current (typically to A) and mV at room temperature.

This exponential relationship is extraordinarily precise -- it holds over many decades of current. It gives the BJT its transconductance:

At mA, mS. Compare this to a MOSFET, where achieving the same requires much more current or a very wide device. This intrinsic transconductance advantage is why BJTs dominate in precision analog circuits.

The four operating regions

Forward active is the amplification region -- where the collector current is times the base current. Saturation (not the same meaning as MOSFET saturation) is where the BJT is used as a switch in the "on" state.

The Gummel-Poon Model

The Gummel-Poon model (1970) is to the BJT what BSIM3 is to the MOSFET: the standard model that every SPICE simulator implements.

The transport current

At the heart of the model is the transport current:

where:

This is the Ebers-Moll transport equation. In forward active operation (, ), the second exponential is negligible and .

Forward and reverse beta

The base current is the sum of forward and reverse components:

where is the ideal maximum forward beta (typically 100) and is the reverse beta (typically 1).

Base charge modulation

The Gummel-Poon model's key innovation is the normalized base charge , which modulates the transport current:

The base charge factor is:

where:

The term captures the Early effect: as increases, the base width narrows, decreases, and increases. The term captures high-injection effects: at large currents, gain rolls off.

Gummel plot

The Gummel plot shows and on a log scale vs. . It reveals the three regimes of beta: low-current recombination, the ideal region, and high-injection rolloff.

The parallel slopes on the log scale (both lines are straight with the same slope) confirm the exponential relationship. The vertical separation is the current gain .

How the BJT stamps into MNA

The linearized BJT becomes a companion model for Newton-Raphson with key conductances:

• -- transconductance
• -- output conductance (Early effect)
• -- input conductance
• -- reverse feedback

These stamp into the MNA matrix at the (collector, emitter), (base, emitter), and (base, collector) positions, along with equivalent current sources.

The exponential nonlinearity of the BJT makes Newton-Raphson convergence more challenging than for MOSFETs. A 26 mV change in changes by a factor of . The simulator must use voltage limiting and careful initial-guess strategies to converge reliably.

The Early Effect

In the ideal BJT, collector current depends only on . But real BJTs show a slight increase of with . This is the Early effect.

The physical picture

The collector-base junction has a depletion region. When increases, this depletion region widens, eating into the neutral base. A shorter effective base width means more carriers reach the collector, so increases slightly.

The Early voltage

If you extrapolate the vs. curves backward, they converge at a single point on the negative axis. This intercept is the forward Early voltage :

Output resistance

The Early effect gives the BJT a finite output resistance:

For a BJT biased at mA with V:

The intrinsic gain is -- nearly 4000. This is one reason BJTs excel in precision analog circuits. A MOSFET at the same current achieves an intrinsic gain of perhaps 20-50.

Parasitics

A real BJT has parasitic elements that affect its high-frequency behavior: series resistances, junction capacitances, and transit times.

Series resistances

Base resistance (RB) is the most important parasitic. It creates a voltage drop between the external base and the intrinsic junction, causing effective to decrease at high currents.

Junction capacitances

Each PN junction has a depletion capacitance:

The base-collector capacitance creates the Miller effect: the effective input capacitance is multiplied by the voltage gain:

This Miller multiplication is the dominant bandwidth limitation in common-emitter amplifiers.

Transit times

When carriers traverse the base, a diffusion capacitance arises:

where is the forward transit time (parameter TF). This determines the transition frequency :

Typical values range from 1 GHz (standard process) to 300+ GHz (SiGe HBTs).

Amplifier Circuits

The BJT's high transconductance and well-controlled current gain make it the natural choice for analog amplifier design. The common-emitter configuration is the most widely used topology.

The common-emitter amplifier

This is the simplest form: a single NPN transistor with a collector resistor. The input voltage drives the base; the output is taken at the collector.

DC operating point

With = V, SPICE computes:

The negative gain means the output is inverted relative to the input. A small increase in causes a large increase in , which pulls down.

The three BJT amplifier topologies

Each topology has the same BJT, the same Gummel-Poon model, the same MNA stamps. What changes is the circuit around it -- which terminal is the input, which is the output, which is the AC ground. SPICE does not know or care about the topology; it simply solves the matrix.

Biased common-emitter amplifier

The simple circuit above has a serious problem: the DC operating point is extremely sensitive to . A 10 mV change changes by about 50%. Practical amplifiers use feedback biasing with a voltage divider and emitter resistor:

The voltage divider (R1, R2) sets the base voltage. The emitter resistor RE provides negative feedback: if increases, the voltage across RE increases, reducing , which reduces back down. The price is reduced gain:

For AC amplification, RE is often bypassed with a capacitor to restore the full gain at signal frequencies while keeping the DC stabilization.

In spice-rs

The BJT device model lives in device/bjt.rs. It implements the Gummel-Poon model including transport current with forward and reverse components, base charge modulation (Early effect + high-injection), junction capacitances (depletion + diffusion), series resistances (RB, RE, RC), and transit times (TF, TR).

The BJT model is simpler than BSIM3/4 in parameter count but has its own subtleties, particularly in the treatment of base charge and the smooth transitions between operating regions.