Transistor Amplifier Explorer — ICD, University of Twente

Circuit

BJT common emitterEmitter at ground. Bias set only by R1/R2 — very temperature and β sensitive. BJT common emitter + R_EEmitter resistor gives DC negative feedback: a stable operating point. MOS common sourceSquare-law NMOS, source resistor optional. No gate current at all.

Component values

The stiffness slider scales R₁ and R₂ together, so the Thévenin bias voltage stays put and only the source resistance R_b seen by the base changes. For a bipolar that is not a cosmetic change: R_b/β adds directly to the ohms in the emitter path and therefore stabilises the bias exactly as R_E does.

Device parameters

Display options

Show linearised (small-signal) curve — the tangent at the operating point Neglect saturation / triode region — the ideal exponential (or square law) with no output limit Bypass R_E/R_S with a capacitor (AC-ground the emitter/source) Animate the marker travelling around the curve

large-signal transfer curve small-signal tangent signal waveforms operating point / clipping limits

Operating point & gain

What you are looking at

The output characteristics of the device (output current versus output voltage) for a family of input voltages, together with the load line set by V_DD and R_C/R_D.

The operating point is where the load line crosses the curve belonging to the actual bias input voltage. When a signal is applied, the operating point slides along the load line; the highlighted segment is the swing for the current signal amplitude.

All sliders from the Amplifier tab apply here too — the two views always show the same circuit.

Swing budget

Head-room is the distance from the operating point to clipping. Symmetric head-room gives the largest undistorted output.

curves at stepped input voltages curve at the bias input voltage load line signal excursion

How to use these

Each exercise sets the circuit up for you. Press Set up, switch to the Amplifier (or Load line) tab, look at what happens, form an opinion, and only then reveal the answer.

The model behind the plots

Bipolar transistor

I_C = I_S · (e^V_BE/V_T − 1) · (1 − e^{−V_CE/V_CE,knee}) , I_B = I_C/β , V_T = kT/q

The last factor is a smooth stand-in for the saturation region: it is ≈1 in the active region and forces I_C→0 as V_CE→0, so the transistor can never pull the collector below ground. Tick neglect saturation to drop it and see the unphysical result the plain exponential predicts.

Temperature

I_S(T) = I_S(300K) · (T/300)³ · exp[(T/300 − 1)·E_g/V_T(T)] , E_g = 1.11 eV

This is the standard Gummel-Poon/SPICE law (XTI = 3). It is a very strong dependence: I_S roughly doubles every 5 K, so it changes by about 8× over 10 K and by four decades between 300 K and 350 K. Differentiating I_C = I_S(T)e^V_BE/V_T at constant I_C gives the familiar

dV_BE/dT = (V_BE − E_g − 3V_T)/T ≈ −1.8 mV/K

shown in the read-out. The MOS threshold is given the usual linear drift, V_TH(T) = V_TH(300K) − 2 mV/K · (T−300), which is mild by comparison; mobility drift is not modelled.

g_m = I_C/V_T , r_π = β/g_m , A_v = −g_mR_C (R_E bypassed) , A_v = −g_mR_C/(1+g_mR_E) (not bypassed)

MOS transistor (square law)

saturation: I_D = ½ k (V_GS−V_TH)² triode: I_D = k[(V_GS−V_TH)V_DS − ½V_DS²]

g_m = √(2 k I_D) = 2I_D/(V_GS−V_TH) , A_v = −g_mR_D (R_S bypassed)

Bias solution

The DC operating point is found numerically: the device current is the only unknown, and everything else (V_BE/V_GS, the emitter/source voltage, the output voltage) follows from it. Because the resulting residual is monotonic in the current, a bisection converges to machine precision in ~80 steps — no linearisation, no convergence tricks, valid deep into clipping.

Signals

Coupling capacitors are treated as ideal at the signal frequency, so the input source adds directly to the DC base/gate voltage and the output capacitor removes the DC level. The waveform is then computed point by point with the full non-linear model — which is exactly why you can see the asymmetry and the clipping that a small-signal calculation cannot show. Distortion is measured by integrating the harmonics of the computed output waveform (THD over harmonics 2–9).

Ported from the Java applets CEC.jar / CECFB.jar (ICD group, University of Twente). Same physics, plus MOS, load-line view, distortion measurement and exercises.