What is the EMF equation of a DC generator?

E = k × Φ × ω, where Φ is the flux per pole, ω the angular speed and k a constant of the winding. The generated voltage is proportional to the speed and to the flux.

What does the commutator do in a DC generator?

It acts as a mechanical rectifier. Every coil produces alternating voltage, but the commutator and brushes reconnect the coils at the right moment so that the terminals deliver direct voltage.

Why does the terminal voltage fall when you load a DC generator?

Because of the voltage drop in the armature resistance and brushes, and because armature reaction weakens the flux. In a shunt generator, the falling voltage also reduces the field current, which makes the drop larger.

What is residual magnetism and why does a self-excited generator need it?

It is the weak flux left in the pole iron. It induces the first few volts that start the field current to flow and build the flux up. Without it, a shunt or series generator cannot start unless the field is flashed from a battery.

Which DC generator has the flattest voltage characteristic?

A compound generator with the right amount of series turns. The series winding adds flux as the load increases and cancels the voltage drop, so the voltage is almost the same from no load to full load.

How a DC generator works: EMF, commutator and excitation

A DC generator turns shaft power into direct-current electricity. A prime mover spins an armature in a magnetic field, Faraday's law induces an EMF E = k × Φ × ω in its conductors, and the commutator turns the alternating voltage in the coils into a one-way voltage at the terminals. The terminal voltage is lower than E under load, by the armature resistance drop, the brush drop and armature reaction.

Updated November 8, 2026

Faraday's law and the generated EMF

A conductor that cuts magnetic flux has a voltage induced in it, in proportion to the rate of cut flux. A DC generator packs many conductors on a rotating armature and moves them through the field of its poles. For the whole winding this gives

E = k × Φ × ω

where Φ is the flux per pole, ω the angular speed of the armature in rad/s and k a constant fixed by the winding (number of conductors, parallel paths and poles). The voltage is proportional to speed and to flux, and these are the two knobs that control a DC generator: double the speed with the same field and the EMF doubles, or hold the speed and strengthen the field.

Flux does not rise forever with field current. The iron saturates, so the plot of no-load EMF against field current, the magnetisation or open-circuit characteristic, bends over. A generator is normally run near the knee of this curve.

What the commutator does

The voltage induced in a single coil is alternating: each coil sees a north pole, then a south pole, and the induced voltage reverses sign every half turn. The commutator is a segmented copper ring on the shaft, and the brushes are stationary contacts that rub on it. Each time a coil passes through the neutral zone, where its EMF is zero, the commutator switches that coil to the other brush. Seen from the terminals, every conductor under a north pole always feeds the same brush and every one under a south pole feeds the other.

The result is a mechanical rectifier: the armature carries alternating EMFs, and the terminals deliver a unidirectional voltage. With many coils and segments the ripple is small. The price is wear at the brushes, sparking and maintenance, which is why most power generation moved to alternators with diode rectifiers, while DC machines remain in teaching, small portable generators and specialised drives.

Excitation: separate, shunt, series and compound

The field winding sets the flux, so how it is fed defines the behaviour of the generator.

Separately excited: the field comes from an independent supply, so the flux does not depend on the output. This is the simplest and most predictable machine.
Shunt: the field winding is connected in parallel with the armature and fed by the generator itself. It is a high-resistance winding that carries only a few per cent of the rated current.
Series: the field winding is in series with the load and carries the full load current, so the flux and the voltage rise with the load.
Compound: a shunt winding plus a series winding that aids it. The series turns add flux as the load grows and compensate the voltage drop, so the voltage stays almost flat from no load to full load. With extra series turns the machine is over-compounded and the voltage rises with load.

The characteristic of interest is the external characteristic, terminal voltage against load current. It is nearly flat for compound, falling for separate and shunt, and rising for series machines.

Terminal voltage under load

The EMF is not the voltage you get at the terminals. By the generator convention

V = E − I_a × R_a − V_brush

where I_a is the armature current, R_a the armature resistance and V_brush the brush contact drop, a couple of volts. On top of that, armature reaction matters: the armature current produces its own magnetic field, which distorts and slightly weakens the main flux, so E itself falls as the load grows.

Voltage regulation measures the net change:

regulation = (V_no-load − V_full-load) / V_full-load

In a shunt generator there is a second effect. As the terminal voltage falls, the field current, and with it the flux, falls too, so the voltage drops further. Past a certain load the output voltage and current both collapse, which is why a shunt generator cannot be short-circuited usefully.

Worked example: a 10 kW, 230 V, 43.5 A, 1500 rpm separately excited generator with R_a = 0.25 Ω and a 2 V brush drop. At full load E = 230 + 43.5 × 0.25 + 2 = 242.9 V The corresponding k × Φ is 242.9 / (2π × 1500 / 60) = 1.55 V·s/rad. Run it at 1200 rpm with the same field and E is 242.9 × 1200/1500 = 194.3 V.

Self-excitation and residual magnetism

A shunt or series generator has no external supply, so how does it start? The answer is residual magnetism, a small amount of flux left in the iron of the poles from earlier operation. When the armature turns, this flux induces a few volts. In a shunt generator that small voltage drives a small current through the field winding. If the field current strengthens the flux, the EMF rises, driving more field current, and so on, until the voltage settles where the magnetisation curve crosses the straight line V = R_f × I_f of the field circuit resistance.

The build-up can fail for four reasons:

The field resistance is above the critical value, which is the slope of the magnetisation curve at the origin. The line is steeper than the curve and they meet near zero.
The speed is below the critical speed, which lowers the whole curve.
The field winding is connected the wrong way round, so its current cancels the residual flux instead of reinforcing it.
There is no residual magnetism at all. The usual remedy is to flash the field briefly from a battery.

A series generator needs a load resistance below a critical value to build up, so with an open circuit it stays near the residual voltage.

How the simulator models the generator

Curvo Studio's DC generator simulator is a steady-state teaching model with a hard prime mover (the speed does not drop under load) and a bank of lamps as the load. The flux follows a saturating magnetisation curve with an adjustable residual level. The rated field current is about 4% of the rated current, the brush drop is fixed at 2 V, and armature reaction removes 10% of the flux at rated armature current. The compound machine is cumulative long-shunt, with the series winding carrying 30% of the rated field MMF. Commutation, interpoles and compensating windings are not modelled.

For the default machine (10 kW, 230 V, 43.5 A, 1500 rpm, R_a = 0.25 Ω, shunt, 80% lamp load, 3% residual flux) the simulator gives a terminal voltage of 239.9 V at 36.3 A, an EMF of 251.5 V, a no-load voltage of 287.5 V and a regulation of 19.8%. The critical speed is about 822 rpm and the build-up takes about 2.2 s.

Try it in the DC generator simulator

Set Field connection to Separate and move Lamp load between 0% (open circuit) and 100%. The Terminal voltage falls from about 270 V to 230 V, a regulation of 17.3%. Repeat with Shunt (a drop from 287.5 V to 230 V) and Compound (about 229.8 V at no load, 230 V at full load, almost zero regulation).
With Shunt, lower the Prime-mover speed. The EMF follows the speed down, and below the critical speed of about 822 rpm the Self-excitation readout changes from Built up to Partial or Failed.
Raise the Field rheostat to 300%. The field resistance passes the critical value, Self-excitation shows Failed and the Terminal voltage collapses to about 12 V at the default 80% lamp load (about 15 V at no load).
Set the Shunt field polarity to Reversed. The field opposes the residual flux and the generator does not start.
Compare Series at an open circuit and at 100% load, and look at the Load characteristics chart and the Start-up chart (voltage build-up and load connection).

The Generated EMF, Terminal voltage, Voltage regulation, Shaft input power and Total losses readouts update with each change.

Try it in the simulator

Open the DC generator simulator

Frequently asked questions

What is the EMF equation of a DC generator?: E = k × Φ × ω, where Φ is the flux per pole, ω the angular speed and k a constant of the winding. The generated voltage is proportional to the speed and to the flux.
What does the commutator do in a DC generator?: It acts as a mechanical rectifier. Every coil produces alternating voltage, but the commutator and brushes reconnect the coils at the right moment so that the terminals deliver direct voltage.
Why does the terminal voltage fall when you load a DC generator?: Because of the voltage drop in the armature resistance and brushes, and because armature reaction weakens the flux. In a shunt generator, the falling voltage also reduces the field current, which makes the drop larger.
What is residual magnetism and why does a self-excited generator need it?: It is the weak flux left in the pole iron. It induces the first few volts that start the field current to flow and build the flux up. Without it, a shunt or series generator cannot start unless the field is flashed from a battery.
Which DC generator has the flattest voltage characteristic?: A compound generator with the right amount of series turns. The series winding adds flux as the load increases and cancels the voltage drop, so the voltage is almost the same from no load to full load.