Electronics Basics #17 | BJT Voltage-Divider Bias: Exact Thevenin Analysis Step by Step

Instructor: Dr. Süleyman Burak ÇELİK

The emitter resistor tamed the drift — but beta is still in the formula, and a leash that depends on the dog is only half a leash. Today we build the bias circuit real designs actually use: the voltage-divider bias. And we make a bold promise at the start: at the end of the lesson we swap the transistor for one with FOUR times the beta, and watch the collector current move by about one percent. Given: 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 — exactly. What you'll learn along the way: - The tempting shortcut almost everyone takes: slapping the divider formula on a LOADED divider — and why the exact method respects the base current - The Thevenin equivalent, taught slowly: the base cannot see behind the wall of two resistors, so we replace the wall with one battery and one resistor that behave identically - Experiment 1 (kill the source): R_Th = R1 parallel R2 = 3.545 kilo-ohms — watch the two resistors visually merge into one - Experiment 2 (open the terminal): the divider current 0.5128 mA gives V_Th = 2 V — and the whole wall collapses on screen - The reflected resistance returns: (beta plus one) times R_E = 211.5 kilo-ohms dwarfs everything else in the loop - A quietly beautiful check: the divider promised 2 V, and the loaded base sits at 1.98 V — the ladder sagged by only 21 millivolts (the river-versus-straw intuition, 85 to 1) - The beta duel: a live side-by-side experiment — fixed-bias current doubles when beta doubles, while the voltage-divider circuit barely notices Results: R_Th = 3.545 kilo-ohms, V_Th = 2 V, I_B = 6.045 microamps, I_C = 0.846 mA, I_E = 0.852 mA, V_CE = 12.26 V (active region, beta-proof Q-point). Chapters: 0:00 Intro 0:03 The leash worked — but beta is still in the formula (today's promise) 1:00 The circuit + the trap: the divider is loaded 2:25 Thevenin experiment 1 — kill the source: R_Th = 3.545 kilo-ohms 3:53 Thevenin experiment 2 — open the terminal: V_Th = 2 V 5:20 Walk 1 — the input loop: I_B = 6.045 microamps 7:08 Both currents, one line each: I_C = 0.846 mA 8:07 Walk 2 — the output loop: V_CE = 12.26 V + the 21 mV sag 10:15 The experiment: swap the transistor, watch both circuits (beta 70 to 280) 12:19 The whole point + next lesson: we earn the right to be lazy Next lesson: the approximate method — three lines, within two percent of everything we computed today. Reference: Boylestad, Electronic Devices and Circuit Theory