(a) *

j I ,(0 I \-

averaged switch model \

+

DCM j

averaged switch model \

big. НЛО Suinmiiry of averaged switch modelitig: (a) general two-swireh network, (b) averaged switch model in CCM, and (c) averaged switch model in DCM.

CCM/DCM \ averaged switch model I

Fig. B.ll A general averaged switch inndel using the equivalent .switch conversion raiio

averaged models suitable for simulation of converters that may operate in either CCM or DCIW.

Figure B. 10 illustrates the general two-switch network, and the corresponding large-signal averaged models in CCIVI and DCIVI. The CCM averaged switch model, which is derived in Section 7.4, is an ideal transformer with tP : (f turns ratio, In DCM, the large-signal averaged switch model is a loss-free resistor, as derived in Section 11.1. Our objective is to construct a combined CCM/DCM averaged switch model that reduces to the tnodel of Fig. B. КЦа) or to the mtxiel of Fig. B. l()(c) depending on the operating mode ofthe converter. Let us define an effective switch conversion ratio ц(г), so that the averaged switch tnodel in both modes has the same form as in CCM, as shown in Fig. B.ll. If the converter operates in CCM, then the switch conversion ratio /(0 is equal to the switch dtity cycle dit),

x = d

If the converter operates in DCM, then the effective switch conversion ratio can be comptited so that the terminal characteristics of the averaged-switch model of Fig. B.ll match the terminal characteristics of the loss-free resistor model of Fig. B. 10(c). Matching the port 1 characteristics gives

which can be solved for the switch conversron ratio ji,

д = !

It can be verified that matching the port 2 characteristics of the models in Figs. B.10(c) and B.ll gives exactly the same restilt for the effective switch conversion ratio in DCM.

The switch conversion ratio ft-iO can be considered a generalization of the duty cycle d{t) of CCM switch networks. Based on this approach, models and results devek)ped for converters in CCM can be used not only for DCM but also for other operating modes or even for other converter configurations by simply replacing the switch duty cycle d(l) with the appropriate switch conversion ratio pit) [21-24]. For example, if M{d) is the conversion ratio in CCM, then Af(;i),with ji given by Eq. (B .7), is the conversion ratio in DCM. The switch conversion ratio in DCM depends on the averaged terminal voltage and cunent, as well iLs the switch duty cycle d thrtMgh the effective resistance If the converter

is completely tinloaded, then the average transistorcurrent (/[(i)),-, is zero, and the DCM switch conversion ratio becomes Ц = 1. As a result, the dc output voltage attains the maximtim possible value V = VjM(I). This is consi.stent with the results of the steady-.state DCM analyses in Chapter 5 and Section 11.1.

To construct a combined CCM/DCM averaged switch model based on the general averaged switch model of Fig. B.l 1, it is necessary to specify which of the two expressions for the switch conversion ratio to use: Eq. (B.5), which is valid in CCM, or Eq. (B.7), which is valid in DCM. At the ССМ/ DCM boundary, these two expressions must give the same result, fi-d. If the load current decreases further, the converter operates in DCM, the average switch current (iit))j. decreases, and the DCM switch conversion ratio in Eq. (B.7) becomes greater than the switch duty cycle d. We conclude that the correct value of the switch conversion ratio, which takes into account operation in CCM or DCM, is the larger of the two values computed using Eq. (B.5) and Eq. (B.7).

Figure B.12 shows an implementation of the combined CCM/DCM model as a PSpice stibeircnit CCM-DCMl. This subcircuit has the same five interface nodes as the stibcircuits CCMl and CCM2 td Section B.l. The controlled sources £, and C,model the port 1 (transistor) and port 2 (diode) averaged characteristics, as shown in Fig. B.ll. The switch conversion ratio p is equal to the voltage v{u) at the subcircuit node u. The controlled voltage source computes the switch conversion ratio as the greater of the two valties obtained from Eqs. (B.5) and (B.7). The controlled current source G , the zero-valtie voltage source V , and the resistor й form an auxiliary circtiit to ensure that the sokition found by the simulator has the transistor and the diode currents with correct polarities, {i(f));;, > 0, (ijit)} > 0- The subcircuit parameters are the inductance L relevant for CCM/DCM operation, and the switching frequency The default values in the subcircuit are arbitrarily set toL 100 \iH atld/j = 100 kHz.

The PSpice sttbcircuit CCM-DCMl of Fig. B.12 can be used for dc, ac, and transient siraula-

CCM-DCM 1

Fig. B.12 ImpIemematioTi of the combined CCM/DCM averaged switch model.

MODEL CCM-DCM1

Application: two-switch PWM ccnvertars, CCM or DCM

UnnitatiOFis: ideal switciies, no transfofmer

Param9ters:

L = equivalent Incluctance for DQbA fs = switchirtg frequency

Nodes:

1: transistor positive (drain for an n-channel MOS)

2: transistor negative (source tor an n-channel MOS)

3: diode cathtxle

4: diode arrade

5: duty cycle ctmtrol input

.subckt CCM-DCM1 1 2 3 4 5

-b params; L=1O0u fslES

Et 1 2 vue={(1 -v(u))v(3.4)A/(u))

Gd 4 3 value=((1-v(u))l(Et)Mu)f

Ga 0 a value={MAX(l(Et),0)}

Vaab

RabOlk

EuuO table (MAX(v(5),

-b V(5) v(5)/{v(5)-v(5)-h2-Lfs-i(Va)/v(3,4)))) (0 0) (1 1) .ends

tions of PWM cotiverters containing a transistor switcti atid a diode switch. This subcircuit is included in the model library .switcli. lib. It can be modified further for use in converters with isolation transformer.

B.2.1 Example: SEPIC Frequency Responses

As an example, Fig. B.13 .shows a SEPIC circuit and the averaged circuit tnodel obtaitted by replacing the switch network with the CCM-DCM 1 subcircuit of Fig. B.12. A part of the circuit netlist is included in Fig. B.13. The connections and the paratneters of the CCM-DCM 1 subcircuit are defined by the hne. In the SEPIC. the inductance parameter L = 83.3 ЦН is equal to the parallel combination of and Lj. The voltage source v. sets the quiescent value of the duty cycle to D = 0.4, and the small-signal ac value io J = !. Ac simulation is performed on a litiearized circuit tnodel, so that amplitudes of iiil stnail-signal ac wavefortns are directly proportional to the amplitude ofthe ac input, regardless ofthe input ac amplitude value. For example, the control-to-output transfer function is Cr = WJ, where v = v(4) in the circuit of Fig. B.13(b). Wecan set the input ac atnplitude to 1, so that the control-to-output transfer function Gcan be measured directly as v(5). This setup isjust for convenience in finding stnall-signal frequency responses by simulation. For measurements of converter transfer futictions in an experitnental circuit (see Section R.5), the actual atnplitude ofthe small-signal ac variation d would be set to a fraction ofthe quiescent duty cycle D. Parameters of the ac simulation are set by the ,ис line in the netlist: the signal frequency is swept from the niininiutn frequency of 5 Hz to the tnaximum frequency of 50 kHz in 201 points per decade.

Figure B.14 shows tnagnitude and phase responses ofthe control-to-output transfer function obtained by ac sitnulations for two different values of the load resistance: Й = 40 Q, for which the converter operates in CCM, and Д = 50 Й, for which the converter operates in DCM. For these two operating