Collector Feedback Bias

Collector feedback bias connects the base resistor to the collector instead of the supply rail. This single change gives the circuit automatic self-correction, preventing the Q-point from running away when β or temperature changes.

Core Concept

In collector feedback bias (also called self-bias), the base resistor RB is connected between the collector and the base, not between VCC and the base. The voltage at the collector (VCE) drives the base current.

The self-correction works like this. Suppose temperature rises and IC tries to increase. A higher IC causes a larger voltage drop across RC. This means VCE falls. Because VCE is also the voltage at the top of RB, a lower VCE means lower IB. Lower IB reduces IC. This negative feedback pulls IC back toward its original value. The Q-point is stabilized automatically.

The KVL equation for the base loop is more complex than fixed bias because IB flows through both RB and RC. Writing KVL: VCC = IC × RC + IB × RB + VBE. Since IC = β × IB, you substitute and solve for IB. The effective resistance seen by IB is RB + β × RC, which is much larger than fixed bias.

Key Equations

Base current: IB = (VCC - VBE) / (RB + β × RC). Note the β × RC term in the denominator. This is the key difference from fixed bias.

Collector current: IC = β × IB. Collector-emitter voltage: VCE = VCC - IC × RC. Note that in this circuit, VCE is the voltage that feeds back to control IB.

Stability factor: S = (β + 1) / (1 + β × RC / RB). For RC/RB = 1/10, S becomes much smaller than β + 1. A lower S means better temperature stability.

Given:
  VCC = 12V
  RB = 150 kΩ
  RC = 3.3 kΩ
  VBE = 0.7V
  β = 100 (BC547)

Why this formula:
  KVL base loop with RB connected to collector:
  VCC = IC×RC + IB×RB + VBE, and IC = β × IB

Formula:
  IB = (VCC - VBE) / (RB + β × RC)
  IC = β × IB
  VCE = VCC - IC × RC

Substitution:
  IB = (12 - 0.7) / (150000 + 100 × 3300)
     = 11.3 / (150000 + 330000)
     = 11.3 / 480000

Calculation:
  IB = 11.3 / 480000 = 23.54 µA
  IC = 100 × 23.54 × 10^-6 = 2.354 mA
  VCE = 12 - (2.354 × 10^-3 × 3300)
      = 12 - 7.77
      = 4.23V

  Stability factor:
  S = (100 + 1) / (1 + 100 × 3300/150000)
    = 101 / (1 + 2.2)
    = 101 / 3.2
    = 31.6  (much better than fixed bias S = 101)

Final Answer:
  IB = 23.5 µA, IC = 2.35 mA, VCE = 4.23V
  S = 31.6 (compared to S = 101 for fixed bias)

Exam Tip: The IB formula for collector feedback bias has β × RC in the denominator. Students often forget this and use IB = (VCC - VBE) / RB (the fixed bias formula). This is wrong. The correct derivation comes from substituting IC = β × IB into the KVL: VCC - (β×IB)×RC - IB×RB - VBE = 0. Always derive from KVL, not from memory.

Key Properties

• RB connects from collector to base. This provides DC negative feedback, stabilizing the Q-point.
• Stability factor S = (β+1) / (1 + β×RC/RB). With RC = 3.3 kΩ and RB = 150 kΩ, S ≈ 31, far better than S = 101 for fixed bias.
• The feedback mechanism: IC up → VCE down → IB down → IC down. This is a negative feedback loop.
• VCE = VCC - IC × RC. This is the same as fixed bias because the emitter is at ground and there is no emitter resistor.
• A disadvantage: the feedback path also reduces AC gain. RB provides a feedback path for AC signals, reducing amplifier gain compared to fixed bias.
• The input resistance of the stage is approximately RB in parallel with β × re, where re = VT/IC is the small-signal emitter resistance.

Quick Revision

• RB from collector to base. VCE drives IB, providing self-bias.
• IB = (VCC - VBE) / (RB + β × RC). Not the fixed bias formula.
• IC = β × IB. VCE = VCC - IC × RC.
• Stability factor S = (β+1) / (1 + β×RC/RB). Much better than fixed bias.
• Self-correcting: if β increases, IC tries to rise, VCE falls, IB falls, IC is pulled back.
• AC gain is reduced by the feedback. For AC analysis, RB appears in parallel with βre.
• Exam trap: Using IB = (VCC - VBE) / RB (fixed bias formula) for this circuit. The correct formula has (RB + β×RC) in the denominator, not just RB.