by an electronically controlled switching device made of thyristors, transistors, or, formerly, mercury arc rectifiers. Series-parallel Series-parallel control was the standard method of controlling railway traction motors before the advent of power electronics. An electric locomotive or train would typically have four motors which could be grouped in three different ways: All four in series (each motor receives one quarter of the line voltage), lowest speed Two parallel groups of two in series (each motor receives half the line voltage) All four in parallel (each motor receives the full line voltage), highest speed This provided three running speeds with minimal resistance losses. For starting and acceleration, additional control was provided by resistances. This system has been superseded by electronic control systems. Field weakening The speed of a DC motor can be increased by field weakening. Reducing the field strength is done by inserting resistance in series with a shunt field, or inserting resistances around a series-connected field winding, to reduce current in the field winding. When the field is weakened, the back-emf reduces, so a larger current flows through the armature winding and this increases the speed. Field weakening is not used on its own but in combination with other methods, such as series-parallel control. Chopper In a circuit known as a chopper, the average voltage applied to the motor is varied by switching the supply voltage very rapidly. As the "on" to "off" ratio is varied to alter the average applied voltage, the speed of the motor varies. The percentage "on" time multiplied by the supply voltage gives the average voltage applied to the motor. Therefore, with a 100 V supply and a 25% "on" time, the average voltage at the motor will be 25 V. During the "off" time, the armature's inductance causes the current to continue through a diode called a "flyback diode", in parallel with the motor. At this point in the cycle, the supply current will be zero, and therefore the average motor current will always be higher than the supply current unless the percentage "on" time is 100%. At 100% "on" time, the supply and motor current are equal. The rapid switching wastes less energy than series resistors. This method is also called pulse-width modulation (PWM) and is often controlled by a microprocessor. An output filter is sometimes installed to smooth the average voltage applied to the motor and reduce motor noise. Since the