# Chopper Fed DC Motor Drives

If the source of supply is d.c. (for example in a battery vehicle or a rapid transit system) a chopper-type converter is usually employed. We know that with the help of chopper circuit, the average output voltage can be varied by periodically switching the battery voltage on and off for varying intervals.

The principal difference between the thyristor-controlled rectifier and the chopper is that in the former the motor current always flows through the supply, whereas in the latter, the motor current only flows from the supply terminals for part of each cycle.

A single-switch chopper using a transistor, MOSFET or IGBT can only supply positive voltage and current to a d.c. motor, and is therefore restricted to quadrant 1 motoring operation. When regenerative and/or rapid speed reversal is called for, more complex circuitry is required, involving two or more power switches, and consequently leading to increased cost.

Many different circuits are used and it is not possible to go into detail here, though it should be mentioned that the chopper circuit discussed previously only provides an output voltage in the range 0 < E, where E is the battery voltage, so this type of chopper is only suitable if the motor voltage is less than the battery voltage.

Where the motor voltage is greater than the battery voltage, a ‘step-up’ chopper using an additional inductance as an intermediate energy store is used.

## Performance of Chopper Fed D.C. Motor Drives

We saw earlier that the d.c. motor performed almost as well when fed from a phase-controlled rectifier as it does when supplied with pure d.c. The chopper-fed motor is, if anything, rather better than the phase-controlled, because the armature current ripple can be less if a high chopping frequency is used. Typical waveforms of armature voltage and current are shown in Figure 1(c): these are drawn with the assumption that the switch is ideal.

A chopping frequency of around 100 Hz, as shown in Figure 1, is typical of medium and large chopper drives, while small drives often use a much higher chopping frequency, and thus have lower ripple current. As usual, we have assumed that the speed remains constant despite the slightly pulsating torque, and that the armature current is continuous.

The shape of the armature voltage waveform reminds us that when the transistor is switched on, the battery voltage V is applied directly to the armature, and during this period the path of the armature current is indicated by the dotted line in Figure 1(a).

For the remainder of the cycle the transistor is turned ‘off’ and the current freewheels through the diode, as shown by the dotted line in Figure 1(b). When the current is freewheeling through the diode, the armature voltage is clamped at (almost) zero.

The speed of the motor is determined by the average armature voltage, (V_{dc}), which in turn depends on the proportion of the total cycle time (T) for which the transistor is ‘on’.

If the on and off times are defined as T_{on} = kT and T_{off} = (1 – k)T, where 0 < k < 1, then the average voltage is simply given by V_{dc} = kV from which we see that speed control is effected via the on time ratio, k.

Turning now to the current waveforms shown in Figure 1(c), the upper waveform corresponds to full load, i.e. the average current (I_{dc}) produces the full rated torque of the motor.

If now the load torque on the motor shaft is reduced to half rated torque, and assuming that the resistance is negligible, the steady-state speed will remain the same but the new mean steady-state current will be halved, as shown by the lower dotted curve. We note however that although, as expected, the mean current is determined by the load, the ripple current is unchanged, and this is explained below.

If we ignore resistance, the equation governing the current during the ‘on’ period is

Since V is greater than E, the gradient of the current (di/dt) is positive, as can be seen in Figure 1(c). During this ‘on’ period the battery is supplying power to the motor.

Some of the energy is converted to mechanical output power, but some is also stored in the magnetic field associated with the inductance. The latter is given by ½ Li^{2}, and so as the current (i) rises, more energy is stored.

During the ‘off’ period, the equation governing the current is

We note that during the ‘off’ time the gradient of the current is negative (as shown in Figure 1(c)) and it is determined by the motional e.m.f. E. During this period, the motor is producing mechanical output power which is supplied from the energy stored in the inductance; not surprisingly the current falls as the energy previously stored in the ‘on’ period is now given up.

We note that the rise and fall of the current (i.e. the current ripple) is inversely proportional to the inductance, but is independent of the mean d.c. current, i.e. the ripple does not depend on the load.

To study the input/output power relationship, we note that the battery current only flows during the ‘on’ period, and its average value is therefore kI_{dc}. Since the battery voltage is constant, the power supplied is simply given by V(kI_{dc}) = kVI_{dc}.

Looking at the motor side, the average voltage is given by V_{dc} = kV, and the average current (assumed constant) is I_{dc}, so the power input to the motor is again kVI_{dc}, i.e. there is no loss of power in the ideal chopper.

Given that k is less than one, we see that the input (battery) voltage is higher than the output (motor) voltage, but conversely the input current is less than the output current, and in this respect we see that the chopper behaves in much the same way for d.c. as a conventional transformer does for a.c.

## Torque Speed Characteristics and Control Arrangements

Under open-loop conditions (i.e. where the mark–space ratio of the chopper is fixed at a particular value) the behaviour of the chopper-fed motor is similar to the converter-fed motor.

When the armature current is continuous the speed falls only slightly with load, because the mean armature voltage remains constant. But when the armature current is discontinuous (which is most likely at high speeds and light load) the speed falls off rapidly when the load increases, because the mean armature voltage falls as the load increases.

Discontinuous current can be avoided by adding an inductor in series with the armature, or by raising the chopping frequency, but when closed-loop speed control is employed, the undesirable effects of discontinuous current are masked by the control loop.

The control philosophy and arrangements for a chopper-fed motor are the same as for the converter-fed motor, with the obvious exception that the mark–space ratio of the chopper is used to vary the output voltage, rather than the firing angle.