Electronics Basics #18 | BJT Voltage-Divider Bias: The Approximate (Stiff-Divider) Method

Instructor: Dr. Süleyman Burak ÇELİK

Last lesson we solved the voltage-divider bias circuit the exact way, with Thévenin — and we ended on a striking number: half a milliamp poured down the divider while the base sipped only six microamps. 85 to 1. A sip that small does not move a river. Today we cash that in: if the base current is truly negligible, drop it, and the whole Thévenin detour collapses into three short lines — with beta crossed out entirely. Same circuit as last time: V_CC = 22 V, R1 = 39 kilo-ohms, R2 = 3.9 kilo-ohms, R_C = 10 kilo-ohms, R_E = 1.5 kilo-ohms, beta = 140. Find: I_C and V_CE — the quick way. What you'll learn along the way: - The stiff-divider criterion: when is the base current safe to ignore? The rule of thumb is beta times R_E at least ten times R2 (here 210k versus 39k — it passes comfortably) - Why a stiff divider lets you read the base voltage straight from the plain voltage-divider rule: V_B = 2.0 V, no Thévenin equivalent, no base loop, no reflected resistance - The headline of the whole method: beta never appears. The base voltage is set by two resistors, the current by that voltage and the emitter resistor — so the operating point does not depend on beta at all - Why the source crossed beta out: swap in a transistor with beta 50 or beta 300 and the circuit lands on the very same point - The exact-versus-approximate duel: every quantity agrees to within about two percent (V_B, I_C, V_CE side by side) — the engineer's bargain when the divider is stiff Results: V_B = 2.0 V, V_E = 1.3 V, I_C = I_E = 0.867 mA, V_CE = 12.03 V. Compared with the exact method from last lesson (I_C = 0.846 mA, V_CE = 12.26 V), every number matches to within roughly two percent. Chapters: 0:00 Intro 0:03 Recap: the exact method and the 85-to-1 sip 0:46 First, the stiff-divider criterion: β·R_E at least 10·R₂ 1:56 Step 1 — the base voltage in one line: V_B = 2.0 V 2:53 Step 2 — the current, and why β never shows up: I_C = 0.867 mA 4:08 Step 3 — the output loop: V_CE = 12.03 V 5:09 Exact vs approximate: every pair within about 2% 6:16 The whole point + what comes next Next lesson: a different kind of transistor — the field-effect transistor — where a voltage, not a current, is in command. Reference: Boylestad, Electronic Devices and Circuit Theory