Select a plot above to show its curve.
Inside the model · equations & learning guide
01 / Carrier flow through the base
During forward active operation, the emitter–base junction injects minority carriers into the thin base. Most reach the collector, while a smaller fraction recombines in the base. Forward B–E bias also sends base majority carriers into the emitter: holes in NPN and electrons in PNP. These carriers recombine in the emitter. The base contact supplies both processes.
Base recombination pairs converge and disappear in a brief ring. The upper base-to-emitter stream fades as carriers enter the emitter. Lower β increases the illustrated base-current activity. β sets the combined base-current contribution, and the drawing shows both mechanisms schematically. Charge counts and depletion widths are amplified to make these changes visible. Higher current speeds up the carriers on a capped square-root scale.
02 / Set the drive and device parameters
IB drive sets 0–100 µA and calculates VBE. VBE drive sets 0–0.80 V and calculates IB. Both modes use VCE from 0 to 5 V with the emitter at 0 V. VA spans 10–300 V and β = βF spans 10–800. NPN and PNP retain their own device settings.
For cutoff, select voltage drive and set VBE (VEB for PNP) to 0 V. This holds base and emitter at the same potential while collector-junction leakage remains. Current drive at IB = 0 represents an open base; leakage can establish a small forward base bias, especially at higher temperature.
The shaded slider displays the calculated quantity. Switching drive mode retains the operating point within the destination range and uses the closest limit when needed. Clicking a plot sets its horizontal bias; base-voltage plots select VBE drive. Drag or click the Junction header to place the animation above or below the plots.
Equations use s = +1 for NPN and −1 for PNP, uBE = s(VB − VE), uCE = s(VC − VE), uBC = uBE − uCE, and i = sI. PNP controls read VEB, VEC, and −IB. Terminal readouts retain their physical signs, with positive current directed into the device.
03 / Junction currents and Early effect
F and R describe injection at the emitter–base and collector–base junctions. Their exponential voltage dependence shapes the current curves. VT = kT/q and IS follows the selected temperature. βF and βR weight the two base-current contributions.
The Early multiplier M strengthens transport as reverse junction bias widens the depletion region:
P(x) = [x + √(x² + (0.01 V)²)]/2 gives a smooth positive part. Lower VA increases the slope of the forward-active output curves and the illustrated depletion encroachment into the base. In forward active operation, M ≈ 1 + (uCE − uBE)/VA and iC/iB ≈ βFM.
Forward active operation combines forward emitter–base bias with reverse collector–base bias. In saturation, both junctions inject carriers. Current drive solves the displayed base-current equation across these regions. The cutoff label applies when both junctions have zero or reverse bias, or all terminal-current magnitudes fall below 1 nA.
04 / Read the characteristic plots
Large signal: IC/VCE sweeps collector voltage at fixed base drive. Its Show output family checkbox adds curves at IB = 5, 10, 50, and 100 µA, or VBE = 0.55, 0.60, 0.65, and 0.70 V. IC/VBE and IB/VBE sweep base voltage at fixed VCE. The amber line marks zero collector–base bias.
Small signal: gm, ro, fT, and Cdiff show forward-active values. Selecting a plot adds its value to the operating-point row. gm, fT, and Cdiff sweep base voltage; ro sweeps collector voltage at fixed VBE. The gm derivative holds VCE fixed, and the ro derivative holds VBE fixed in either drive mode:
Current plots use linear normalized current or logarithmic magnitude with a 1 fA display floor. ro uses a logarithmic axis. The remaining small-signal plots use linear axes. A dash identifies a small-signal operating point outside the forward-active range.
05 / Diffusion capacitance and transition frequency
Cdiff measures the change in stored minority-carrier charge with base voltage. It rises with gm using the fixed forward transit time τF = 1 ns. fT estimates the frequency where short-circuit current gain reaches unity. Its capacitance includes Cdiff and the emitter and collector junction terms CJE and CJC. As current rises, the estimate approaches 1/(2πτF) ≈ 159 MHz.
Junction capacitance uses CJ(u) = CJ0/(1 − u/φ)m, with CJE0 = 2 pF, CJC0 = 1 pF, φ = 0.75 V, and m = 0.33. Here u is the corresponding normalized junction voltage. Above u = φ/2, a tangent continuation keeps the capacitance and its slope continuous.
06 / Model assumptions
The curves represent an illustrative silicon device driven by ideal voltage or current sources. Temperature changes VT and IS; β and VA retain their slider settings. Frequency and capacitance values use a forward-active small-signal approximation with fixed transit-time and junction parameters.
The drawing shows carrier paths, recombination, and base-width modulation at a visual scale. Its animation speed communicates current magnitude. Reduced-motion preferences freeze the carriers.