BJTs#

The bipolar junction transistor is a current-controlled device. A small base current controls a much larger collector current — that’s the fundamental gain mechanism. BJTs were the first practical transistors and they’re still everywhere: discrete amplifiers, current mirrors, references, and inside most analog ICs.

Operating Regions#

A BJT has three operating regions, and knowing which one the device is in is the key to understanding what the circuit is doing.

Active (Forward Active)#

  • Base-emitter junction is forward biased (V_BE ~ 0.6-0.7 V)
  • Base-collector junction is reverse biased
  • I_C = β × I_B (collector current is proportional to base current)
  • This is the amplification region. The transistor is doing useful analog work

Saturation#

  • Both junctions are forward biased
  • V_CE drops to V_CE(sat), typically 0.1-0.3 V
  • The transistor is fully “on” — acting as a closed switch
  • I_C is no longer controlled by I_B; it’s limited by the external circuit
  • Beta is much lower in saturation than in active mode

Cutoff#

  • Both junctions are reverse biased (or V_BE below the turn-on threshold)
  • The transistor is fully “off” — no collector current (except leakage)
  • Acts as an open switch

What Happens at the Boundaries#

The transitions between regions are not sharp walls — they’re gradual. A transistor “near saturation” has reduced gain and increased distortion. A transistor “near cutoff” clips the signal. Understanding where the operating point sits relative to these boundaries determines how much signal swing is available before distortion.

Current Control and Beta#

The fundamental relationship: I_C = β × I_B

Beta (h_FE) is the current gain. Typical values range from 50 to 500, depending on the device and operating conditions.

The critical thing about beta: don’t design around it. Beta varies:

  • From device to device (even same part number): 2:1 spread is common
  • With temperature: beta increases with temperature
  • With collector current: peaks at a medium current, drops at very low and very high currents
  • With V_CE: slight increase with higher V_CE (Early effect)

Good analog design makes the circuit behavior depend on resistor ratios and V_BE, not on beta. If a circuit only works with β = 200, it will fail when a device with β = 80 is installed.

Biasing Fundamentals#

Setting the DC operating point so the BJT stays in the active region with enough headroom for the signal to swing without clipping.

The basic problem: Setting I_C to a known value despite beta variations. The classic topologies:

  • Fixed bias (resistor from VCC to base) — Simple but terrible. I_C depends directly on beta. Don’t use this for anything that needs to work reliably
  • Collector feedback bias — Resistor from collector to base. Provides negative feedback: if I_C increases, V_C drops, reducing base current. Better stability, but gain is reduced
  • Voltage divider bias (self-bias) — The standard approach. A voltage divider sets V_B, and an emitter resistor sets I_E ≈ (V_B - V_BE) / R_E. Nearly independent of beta if the divider is stiff enough. This is the workhorse biasing topology

V_BE is approximately 0.6-0.7 V for silicon at room temperature, decreasing about 2 mV/°C. Biasing circuits must account for this temperature variation or accept the resulting drift.

Small-Signal vs. Large-Signal Behavior#

Large-signal analysis sets the DC operating point — the bias. It uses the full nonlinear device equations (or simplified models like V_BE = 0.7 V, I_C = β × I_B).

Small-signal analysis describes how the transistor responds to small AC signals around that operating point. The device is linearized at the Q-point, producing a small-signal model with:

  • g_m (transconductance) = I_C / V_T, where V_T ≈ 26 mV at room temperature. This is the gain parameter — how much collector current changes per volt of base-emitter voltage change
  • r_π (input resistance) = β / g_m. The resistance seen looking into the base
  • r_o (output resistance) = V_A / I_C, where V_A is the Early voltage. Usually large enough to ignore in simple circuits

The small-signal model is a linear circuit that can be analyzed with all the standard techniques (superposition, Thevenin, KVL/KCL). This is where the Fundamentals section connects directly to analog design.

The key insight: the DC bias sets the small-signal parameters. Change the bias point, and g_m, r_π, and r_o all change. This is why biasing matters so much — it determines the amplifier’s gain, impedance, and linearity.

Tips#

  • Design biasing around resistor ratios and V_BE, not around a specific beta value
  • Use voltage divider biasing for stable, predictable operating points
  • Calculate g_m from the bias current to predict small-signal gain: g_m = I_C / 26 mV

Caveats#

  • Beta is not a design parameter — Design for the minimum beta specified in the datasheet, and verify the circuit works across the full beta range
  • V_BE is not exactly 0.7 V — It depends on current, temperature, and device type. For precision work, measure it. For design, use 0.6-0.7 V as an estimate and rely on feedback to handle the variation
  • Thermal runaway — BJTs have a positive temperature coefficient for collector current at a fixed V_BE (hotter = more current = hotter). In power applications, this requires thermal feedback or emitter degeneration resistors
  • Storage time in saturation — A saturated BJT has excess charge in the base region that must be removed before it can turn off. This limits switching speed. Schottky-clamped BJTs (like 74LS logic) prevent deep saturation to avoid this
  • Base current is not zero — Unlike MOSFETs, BJTs draw continuous base current. This loads the driving circuit. High-impedance sources may not be able to supply enough base current for the desired collector current
  • Second breakdown — At high voltage and high current simultaneously, localized heating can cause destructive current focusing. This is a safe operating area (SOA) limit, not a simple power limit

In Practice#

  • A BJT that shows V_CE near V_CC with no collector current is in cutoff — check the base drive circuit
  • A BJT that shows V_CE near 0.1-0.3 V regardless of base current is saturated — check if the load is drawing more current than the bias allows
  • Gain that varies significantly between devices of the same type indicates a circuit that depends on beta rather than using proper biasing
  • A transistor that runs hot in a linear application may be biased near its power dissipation limit — verify the operating point
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