by F. Equations describing the average waveforins of CCM PWM converters can be adapted to apply tt) full-wave ZCS quasi-resonant converters, simply by replacing the duty cycle d vifith the normalized switching frequency F. The conversion ratios of full-wave quasi-resonant converters exhibit negligible dependence on the load current.

The variation of the switch conversion ratio ji with f and is plotted in Fig. 20.19. For a typical voltage regulator application, the range of switching frequency variations is much smaller in the full-wave mode than in the half-wave mtxie, tjecause judoes not depend on the load ctirrent. Viiriations in the load current do ntit induce the controller to significantly change the .switching frequency.

20.3 RES(1NANT SWITCH TOPOLOtJIES

So far, we have considered the zero-current-switching quasi-resonant switch cell, illustrated in Fig. 20.20. The ideal SPST switch is realized using a voltage-bidirecrional or current-bidirectional two-quadrant switch, to obtain half-wave or full-wave ZCS quasi-resonant switch networks, respectively.

The resonant elements and can be moved to several different positions in the converter, without altering the basic switch properties. Forexample, Fig. 20.21 illustrates connection ofthe resonant tank capacitor between the cathode of ditxle Dj, and the converter output or input tenninais. Although this may change the dc component of the tank capacitor voltage, the ac components of the tank capacitor voltage waveform are unchanged. Also, the terminal voltage waveform is unchanged. Tbe voltages vit) and v(/) contain negligible high-frequency ac components, and hence the converter input and output terminal potentials can be ctmsidered to be at high-frequency ac ground.

A test to determine the topology of a resonant switch network is to replace ail low-frequency filter inductors with open circuits, and to replace ail dc sources and low-frequency tiller capacitors with short circuits [13]. The elements of the resonant switch cell remain. In the case t)f the zero-current-switching quasi-resonant switch, the network of Fig. 20.22 is always obtained.

It can be seen from Fig. 20.22 that diode Dj switches on and off at the zero crossings of the tank capacittw voltage VjWi while the switch elements and D, switch at the zero crossings of the tank inductor current i(;). Zero voltage switching of diode highly advantageous, tjecause it essentially eliminates the switching loss caused by the recovered charge and output capacitance of diode fij. Zero current switching tif Qf and Dj can be used tt) advantage when Qj is realized by an SCR or IGBT. However, in high-frequency converters employing MOSFETs, zero ctirrent switching of Й; and D( is generally a poor cht)ice. Significant switching loss due to the output capacitances of fij and O, may be observed. In addition, in the full-wave case, the recovered charge of diode D[ leads to significant ringing

[ Switch network \ ZCS quasi-respnam switch cell

Fig. 20.W Basle ZCS qiiasi-resonani switch cell.

782 Softswitching

V2(0 C

ZCS guasi-tesonatu switch

\ ZCS quasi-resonant switch \

Fig. 20.21 Connection of the tank capacitor of the ZCS quasi-re.itiant cell to other points at ac ground: (a) con-necdon to the dc output, (h) connection to ihe dc inpui. la each case, the ae components of the wuveforms are unchanged.

Fig, 20.22 Eliinination of convener low-frcqucncy elements causes the ZCS quasi-resonant switch cell to reduce to ihis network.

and switching los.s at the end of subinterval 2 [3].

The ZCS quasi-resonant switch exhibits increased conduction loss, relative to an equivalent PWM switch, because the peak transistor current is increased. The peak transistor current is given by Eq. (20.17); since /. £ 1, the peak current is /pjt S 2/2. In addition, the full-wave ZCS switch exhibits poor efficiency at light load, owing to the conduction loss caused by circulating tank currents. The half-wave ZCS switch exhibits additional conduction lo.ss due to the added forward voltage drop of diode . The peak transistor voltage is V which is identical to the PWM case.

20.3.1 The Zero-Voltage-Switching Quasi-Resonant Switch

The resonant switch networlt illustrated in Fig. 20.23 is the dual ofthe network of Fig. 20.22. This network is known as the zero-voltage-switehing quasi-resonant switch [4]. Since the tank capacitor appears in parallel with the SPST switch, the elements d and D used to realize the SPST switch turn on and off at zero voltage. The tank inductor is effectively in series with diode Dji hence dit)de switches at zero current. Converters containing ZVS quasi-resonant switches can be realized in a number of ways. The only requirement is that, when the low-frequency fiiter inductors, filter capacitors, and sources are replaced by t)pen- or short-circuits as described above, then the high-frequency switch network of Fig, 20.23 should remain.

For exaraple, a zero-voltage-switching quasi-resonant buck converter is illustrated in Fig. 20.24(a). Typical tank capacitor voltage and tank inductor current waveforms are given in Fig. 20.24(b). A current-bidirectional realization of the two-quadrant SPST switch is shown; this causes the ZVS quasi-resonant switch to operate in the half-wave mode. Use of a voltage-bidirectional two-quadrant SPST switch allows full-wave operation.

By analysis similar to that of Section 20.2. itcan be shown that the switch conversion ratio fioi the half-wave ZVS quasi-resonant switch is

Fig. 20.23 Eliminaiion of converter low-frequency elementi reduces the ZVS qua.si-re.sonant .switch cell to this neiwork.

(20,61)

The function PU) is again given by Eq. (20.46), and thequantity is defined in Eq. (20.44). For the full-wave ZVS quasi-resonant switch, one obtains

(20.62)

where f(7j) is given by Eq. (20.58). The condition for zero voltage switching is

(20.63)

Thus, the zero voltage switching property is lost at light load. The peak transistor voltage is given by

peak IranJifstor voliage V , = {1 + /,) (20,64)

This equation predicts that load current variations can lead to large voltage stress on transistor Qj. For exaraple, if it is desired to obtain zero voltage switching over a 5:1 range ofload current variations, then should varj between 1 and 5. According to Eq. (20.64), the peak transistor voltage then varies between two braes and six times the applied voltage Vj.The raaximum transistor current is equal to the apphed current /j. Although the maximum transistor current in the ZVS quasi-resonant switch is identical to that