BJT Astable Multivibrator & Dual LED Flasher

Upon DC power connection (VCC = 5.0 V nominal), timing capacitors C1 and C2 are initially uncharged. Base pull-up resistors R2 and R3 supply charging current from VCC to the bases of Q1 and Q2. In an ideal mathematical circuit with perfectly identical components and zero noise, both transistors would turn on equally toward a symmetrical equilibrium. In practical physical circuits, microscopic variations in base-emitter threshold voltage (VBE), current gain (hFE), and resistor tolerances, along with power supply rise times and ambient thermal noise, can break symmetry so that one transistor (e.g., Q1) conducts slightly more rapidly than the other. Regenerative feedback immediately accelerates this unbalance: as Q1 conducts, its collector voltage falls, coupling a negative potential through C1 to the base of Q2, which can drive Q2 off and initiate oscillation. This narrative does not guarantee startup for every component selection, supply ramp or temperature.

The following is a pedagogical step model of established oscillation, not a measured waveform: assume fixed conducting-collector voltage, constant illustrative VBE and VCE(sat), negligible base loading, and the stated off-collector voltage. Actual off-collector voltage depends on LED current and capacitor recovery. The general instantaneous coupling relation is VB(after) = VB(before) + VC(after) − VC(before). Immediately before Q1 turns on, Q2 is conducting in saturation with VB2(0-) ≈ VBE(on) ≈ 0.7 V, and Q1 is cut off with its collector resting near (VCC - VF(D1)). When Q1 snaps into saturation, its collector voltage plunges rapidly to VCE(sat) ≈ 0.15 V - 0.2 V. Because the charge on timing capacitor C1 cannot change instantaneously, charge continuity dictates the resulting base voltage of Q2:

In an illustrative simplified step calculation with assumed parameters (the LED datasheet VF at its stated test current is not a measured drop in this circuit) (VCC = 5.0 V, Red LED VF(D1) ≈ 1.9 V, VCE(sat) ≈ 0.2 V, VBE(on) ≈ 0.7 V), the collector voltage step is ΔVC ≈ 2.9 V, which couples across C1 to drive VB2(0+) negative to approximately -2.2 V. This reverse-biases the base-emitter junction of Q2, driving it firmly into cutoff and extinguishing Blue LED D2, while Q1 conducts and illuminates Red LED D1.

While Q2 remains cut off, its collector node is pulled toward VCC through R4 and D2, restoring charge onto the collector plate of C2. Sustained DC base current to keep Q1 saturated is supplied directly from VCC through pull-up resistor R2 (IB1 ≈ (VCC - VBE(on)) / R2). Simultaneously, timing capacitor C1 (whose negative side is connected to Q2's base) discharges its negative potential and recharges toward +VCC through base pull-up resistor R3 (47 kΩ). In this simplified model with a fixed opposite capacitor terminal and negligible transistor input current, the base voltage follows:

Transistor Q2 remains in cutoff throughout the interval until VB2(t) reaches the forward conduction threshold VBE(on) ≈ 0.65 V - 0.70 V. Solving for VB2(T1) = VBE(on) yields the cutoff duration:

When VB2(t) reaches VBE(on), transistor Q2 begins conducting base current. Regenerative cross-coupling rapidly pulls Q2 into saturation. As Q2's collector drops from (VCC - VF(D2)) down to VCE(sat) ≈ 0.2 V, this negative voltage step is coupled through timing capacitor C2 to the base of Q1:

For Blue LED D2 (illustrative VF(D2) ≈ 3.3 V), the collector voltage step ΔVC ≈ (5.0 - 3.3) - 0.2 = 1.5 V drives VB1(0+) down to approximately 0.7 V - 1.5 V = -0.8 V, cutting off Q1 and extinguishing Red LED D1, while Q2 conducts and illuminates Blue LED D2.

Transistor Q1 is held in cutoff while C2 recharges toward +VCC through base resistor R2 (47 kΩ). Sustained base current for Q2 is supplied from VCC through R3. The base voltage VB1(t) rises exponentially until reaching VBE(on), snapping Q1 back on and restarting the cycle.

In standard idealized textbook analysis, diode forward drops and transistor saturation offsets are neglected (VB(0+) ≈ -VCC, VBE(on) ≈ 0). Under these ideal reference assumptions, the half-period equations simplify to:

For symmetrical components (R2 = R3 = 47 kΩ, C1 = C2 = 10µF), this ideal textbook reference yields T ≈ 1.386 · R · C ≈ 0.651 s (f ≈ 1.535 Hz) with 50% duty cycle. In physical circuits, unequal forward LED drops (VF(D1) ≠ VF(D2)), finite collector pull-up recovery via RC, and component tolerances alter the switching thresholds and restore intervals. Accurate prediction of physical waveform timing requires full transient simulation or laboratory oscilloscope measurement.