Self-Excitation and the External Characteristic of the DC Generator
Where does the voltage settle, and when does it fail to build?
The small voltage made by residual magnetism drives a field current that strengthens the flux, and that flux raises the voltage further. This feedback stops where the magnetization curve and the field-resistance line (V = Rf·If) meet, and as you raise the field resistance with the slider, the line gets steeper and the intersection drops. The moment the line becomes steeper than the initial slope of the magnetization curve (about 400Ω in this picture), the voltage no longer builds up, and why that happens is the question of this lesson.
The seed is residual magnetism
The pole cores keep residual flux, a trace of having been magnetized once, so when the generator turns, this residual flux induces a small residual voltage in the armature. If the shunt field is connected in parallel with the armature, this voltage drives a small current through the field winding, and that current strengthens the flux and raises the voltage further: positive feedback that lifts itself with no external source. The field connection must strengthen the residual flux, though; connected the other way, it wipes out even the residual flux and the voltage collapses. If the residual magnetism has faded after a long idle period, a brief pulse of external DC through the field magnetizes it again (flashing the field).
Where the feedback stops, the critical resistance
As the voltage rises the field current grows too, but as the core saturates the magnetization curve bends and the voltage can no longer rise in proportion. The field-resistance line V = Rf·If, meanwhile, is a straight line, so the feedback stops where the two lines meet. Raising the field resistance stands the line up and moves the intersection below the knee, and once the line is steeper than the initial slope of the magnetization curve, the only intersection is near the residual point and the voltage does not build up. This limiting slope is the critical field resistance. The magnetization curve stretches up and down in proportion to the speed, so at low speed the voltage may fail to build up even with the same field resistance (the critical speed).
Under load — the external characteristic by excitation
When load current flows, the terminal voltage Vt = E - IaRa falls by the armature resistance drop and by the effect of armature reaction. A separately excited generator, with its own field supply, sags only a little from these two. In a shunt generator, a falling terminal voltage also reduces the field current and drains more flux, so it sags more steeply. In a series generator the load current is the field current, so the voltage first rises and then bends over from saturation and armature reaction; a compound generator adds a series winding to make up for the shunt sag and can be set to stay nearly flat (flat compound) or rise slightly (over-compound) with load.
Back to the first screen
The voltage failed to build up when the field-resistance line was steeper than the initial slope of the magnetization curve and the two met only near the residual point. With residual magnetism as the seed, positive feedback runs, but it stops where the saturation-bent magnetization curve meets the straight field-resistance line. Only when the field resistance is below the critical value does the intersection form high above the knee and the voltage build up. Once established, the voltage falls under load as Vt = E - IaRa: a little for separate excitation, more for shunt, and in their own shapes for series and compound. Both building up a generator's voltage and holding it under load are read on the magnetization curve.
That completes the DC machine. The commutator flips AC into DC (B1), armature reaction shifts the neutral axis (B2), back-EMF sets a motor’s speed and torque (B3), and self-excitation builds a generator’s voltage (B4) — all one machine turning on a single magnetic circuit. The next group C is the induction machine, which makes the rotation itself out of a magnetic field. It begins with how three-phase current weaves a rotating magnetic field.