BJT Bias Stability

A BJT amplifier is useless if its operating point drifts with temperature. BJT bias stability describes how well the collector current IC stays fixed when temperature changes, and it is measured numerically by the stability factor S.

Core Concept

Three transistor parameters change with temperature: reverse saturation current ICBO doubles every 10°C, the forward voltage VBE drops by about 2 mV per °C, and beta increases roughly 0.5% per °C. All three push IC upward as temperature rises. Without a stabilizing feedback, the transistor can enter thermal runaway and be destroyed.

The stability factor S is defined as S = dIC/dICBO, the rate of change of collector current with reverse leakage. A perfect circuit has S = 1. Fixed bias has S = beta + 1, which can be over 100. Voltage divider bias can achieve S of 1 to 3 because RE provides negative feedback.

When IC rises, the emitter current IE also rises, increasing the voltage drop across RE. This raises VE, which reduces VBE = VB - VE, which reduces IB, which pulls IC back down. This automatic correction is called emitter degeneration. A 2N3904 biased with RE = 1kΩ in a 12V circuit can maintain IC within 10% from 25°C to 85°C.

Key Equations

General stability factor: S = (1 + beta) / (1 + beta * RE / (RB + RE)) where RB is the Thevenin equivalent base resistance.

For fixed bias (RE = 0): S = 1 + beta. For beta = 100, S = 101, meaning IC increases 101 mA for every 1 mA increase in ICBO.

For voltage divider bias with large RE: S → 1 as RE increases. Practically S = 2 to 5 is achievable.

VBE stability coefficient: dIC/dVBE = -beta / RB. A large RB makes this worse; RE compensates.

Given:
  Circuit: Voltage divider bias with 2N3904
  VCC = 12V, R1 = 47kΩ, R2 = 10kΩ
  RE = 1kΩ, RC = 3.3kΩ, beta = 100

Why this formula:
  Find Thevenin base resistance RB = R1||R2,
  then apply stability factor formula.

Formula:
  S = (1 + beta) / (1 + beta * RE / (RB + RE))

Substitution:
  RB = (47000 * 10000) / (47000 + 10000)
     = 470000000 / 57000
     = 8245.6 Ω ≈ 8.25 kΩ

  S = (1 + 100) / (1 + 100 * 1000 / (8250 + 1000))
    = 101 / (1 + 100000 / 9250)
    = 101 / (1 + 10.81)
    = 101 / 11.81

Calculation:
  S = 101 / 11.81
  S ≈ 8.55

Final Answer:
  S ≈ 8.55
  This is far better than fixed bias (S=101) but can be improved
  further by increasing RE or lowering RB.

Exam Tip: GATE frequently tests whether students can distinguish between S = dIC/dICBO and other stability definitions. Also remember: for the collector current stability due to VBE variation, a separate coefficient M = dIC/dVBE applies. For ICBO-based stability alone, use the S formula above. The minimum value of S is 1, never 0. If your answer gives S < 1, recheck the formula.

Key Properties

• S = 1 is ideal (IC does not change with ICBO). S = beta+1 is worst case (fixed bias with no emitter resistor).
• ICBO approximately doubles every 10°C rise. For germanium transistors like the OC71, this is especially severe.
• VBE decreases by about 2 mV per °C at constant IC. Over a 100°C range, VBE can drop 200 mV, significantly shifting the Q-point.
• Emitter resistor RE is the primary stability tool. Bypassing RE with a capacitor (CE) improves AC gain but does not affect DC stability.
• Thermal runaway occurs when the power dissipated in the BJT raises junction temperature faster than it can be cooled. A heat sink on a BC547 delays runaway above 500 mW.
• Beta variation between transistors of the same type (e.g., 2N3904 has beta 100-300) contributes to Q-point shift when replacing devices.

Quick Revision

• S = dIC/dICBO: lower is better, minimum is 1.
• Fixed bias: S = beta+1, very poor stability.
• Voltage divider bias with RE: S = 2 to 10 typically.
• ICBO doubles every 10°C; this drives thermal runaway in poorly biased circuits.
• VBE drops ~2 mV/°C, shifting the Q-point even when ICBO is small.
• Bypassing RE with CE preserves AC gain while keeping DC stability unchanged.
• Three stability factors exist: S (for ICBO), M (for VBE), N (for beta). GATE most often tests S.
• Exam trap: Students use S = 1 + beta for voltage divider bias, ignoring the RE term. Always check whether RE is present before picking the formula.