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Naturally, such ideal energy conversion cannot take place; however we can see that there is a correspondence between the four electrical quadrants of Figure 1133 and the mechanical power output of the motor: namely, if the voltage and current are both positive or both negative, the electrical power will be positive, and so will the mechanical power This corresponds to the forward (i, v both positive) and reverse (i, v both negative) motoring operation Forward motoring corresponds to quadrant I, and reverse motoring to quadrant III in Figure 1133 If the voltage and current are of opposite polarity (quadrants II and IV), electrical energy is owing back to the electric drive; in mechanical terms this corresponds to a braking condition Operation in the fourth quadrant can lead to regenerative braking, so called because power is regenerated by making current ow back to the source This mode could be useful, for example, to recharge a battery supply, because the braking energy can be regenerated by returning it to the electric supply A simple circuit that can accomplish the task of providing a variable DC supply from a xed DC source is the step-down chopper (buck converter), shown in Figure 1135 The circuit consists of a chopper switch, denoted by the symbol S, and a free-wheeling diode, such as the one described in Section 115 The switch can be any of the power switches described in this chapter, for example, a power BJT or MOSFET, or a thyristor; see, for example, the BJT switch of Figure 114 The circuit to the right of the diode is a model of a DC motor, including the inductance and resistance of the armature windings, and the effect of the back emf Ea When the switch is turned on (say, at t = 0), the supply VS is connected to the load and vo = VS The load current, io , is determined by the motor parameters When the switch is turned off, the load current continues to ow through the freewheeling diode, but the output voltage is now vo = 0 At time T , the switch is turned on again, and the cycle repeats Figure 1136 depicts the vo and io waveforms The average value of the output voltage, vo , is given by the expression vo = t1 VS = VS T (1117)
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Figure 1135 Step-down chopper (buck converter)
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vo VS < io > < vo > 0 0 t1
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Figure 1136 Step-down chopper waveforms
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where is the duty cycle of the chopper The step-down chopper has a useful range 0 vo VS (1118)
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It is also possible to increase the range of a DC-DC converter to above the supply voltage by making use of the energy-storage properties of an inductor; the resulting circuit is shown in Figure 1137 When the chopper switch, S, is on, the supply current ows through the inductor and the closed switch, storing energy in the inductor; the output voltage, vo , is zero, since the switch is a short
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Tm m
Figure 1137 Step-up chopper (boost converter)
11
Power Electronics
vo (t)
<vo> VS
circuit When the switch is open, the supply current will ow through the load via the diode; but the inductor voltage is negative during the transient following the opening of the switch and therefore adds to the source voltage: the energy stored in the inductor while the switch was closed is now released and transferred to the load This stored energy makes it possible for the output voltage to be higher than the supply voltage for a nite period of time To maintain a constant average load current, the current increase between 0 and t1 must equal the current decrease from t1 to T Therefore,
Figure 1138 Step-up chopper output voltage waveform (ideal)
t1 0
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