deal swich characerisics. onsider he swiching circui shown in Fig. P. wih a resisive load. Assume he swich is ideal and operaing a a duy raio of 4%. (a) Skech he waveforms for i sw and v sw. (b) Deermine he average oupu volage. (c) Deermine he average oupu power delivered o he load (d) Deermine he average oupu power supplied by he source. (e) Deermine he efficiency of he circui. i sw v sw v o 5Ω ON.4 OFF ON Fig. P. a) i SW on off.4 v SW off on Where, on A 5 off A on off
.4 b) o, ave 4.4, o o 8W c) P i v d () d o ave d) P D, ave (8) 8W Po, ave 8 e) η % % % P 8 D, ave. onsider he wo-swich circui given in Fig. P.. Assume ideal S and S wih he shown swiching sequence. Use a load of 5Ω. Skech i sw, v sw, i sw and v sw. Deermine (a) he average oupu volage, (b) average power delivered o he load, and (c) he efficiency. Soluion: i v o S
i SW A.5.9.4 v SW i SW A v SW a).4.4 o, ave 8 b).4.9 Po, ave iovod d d.5.8 6W P D, ave.4.4 6W Po, ave c) η P % % D, ave
.3 he circui shown in Fig. P.3 is known as a curren-driven full bridge inverer. Assume S, S, S 3 and S 4 are ideal wih heir swiching waveforms as shown. Skech he waveforms for i o, v o, v sw, i sw, v sw4 and i sw4, and derive he expression for he average oupu volage. SW - i SW S - vo i o S 3 S,S :.5 ON OFF isw 4 S 3,S 4 : SW 4 - S 4 S θ θ θ δ v ( o, avg θ ) δ θ δ
S, S.5 S, S 3 4 ω θ θ ω i SW ω v SW 4 ω v SW ω i SW 4 ω i o ω v o ω
Non-ideal Swiching haracerisics.4 Use Fig. E. and by assuming ha he swiching waveform has he following parameers, on A, off 5, off ua, on, s -4 s, d 9ns, fall ns, rise ns. Deermine he equaion for he insananeous power and find P ave. υ sw off on ι sw off on d d fall s ( d rise ) s d s s Fig. E. Waveforms for Exercise. Soluion onon d off on fall onoff Pins ( ) on off rise - on d off ( ) ( - ) - ( ) s ( ) s fall rise [ ( )] P ave off on d rise s P avg. 3W d d fall d d d fall d fall s - s d s - d s ( ) d rise s rise - d
.5 epea Problem. by assuming he swich has a.ω on-sae resisance and forward drop during conducion. Soluion: (a) i SW 8.85A.4 v SW i SW 8.85A v SW (b).4 98 o, ave 78. 4 P.4 o, ave iovod d 477. 84 (c) 8.85 98 P diss (.4 8.85 ) 3. 6W W
Po, ave (d) 477.84 η % % 99.99% P P 477.84 3.6 o, ave diss.6 epea Problem P.3 by assuming each swich has a.ω on sae resisance and a forward volage drop during conducion. Soluion: S, S4 (a) / S, S 3 θ vo D i o D D D D M M M 3 M 4 oave, v () d o ( ) d.5 δ.5 δ δ
.8 onsider he ransisor swiching circui and is swiching waveforms in Fig. P.8 (a) and (b), respecively. (a) Skech he waveforms for i D and v D. (b) alculae he average power dissipaed in he ransisor. Use f s khz, d 5ns, r ns, s ns and f 5ns. 5 in A o v D i D D i i v E _ Fig. P.8(a) i i o d r s- f s in v E d r d f s Fig. P.8(b)
Soluion: b) P s s i v d c ce ( ) d d s s r f s icvced icvced icvced icvced s d d r s ( s f ) in ro in fo s oin 5 ( r f ) (5ns 5ns) 3W s ( µ s). onsider he half-bridge inverer circuis wih he unidirecional MOSFE swiching a resisive load given in Fig. P.. Use Ω (a) Deermine he average power delivered o he load when S and S are assumed ideal. (b) epea par (a) for DS (on).ω for each MOSFE. (c) Find he efficiency of he circui in par (b). S : ON OFF ON 6 6 Load S v o io Ω S S : OFF.5 ON OFF 6 6A v o, i o -6-6A.5 Fig. P.
Soluion: a).5 6 6 Pave o. o. d 6 d 6 d.5 5.5 6 3.6 W if b) For Ω, Po,ave 36kW, η %.5 6 6 Poave, o. o. d d.. P diss 6.. c) 6 P oave,. η % % % Poave, Pdiss 6 (.) (.). 4 Ω, and r. Ω, P 34.6 W, P 69 W, and η 98% ON o, ave diss. alculae β forced in Fig. P. (a) and (b) for kω, and kω. Assume E.75 and E,sa.4. v E,sa v E i D o ma A D 5 v E,sa _ ve o 5 (a) (b) Fig. P. Soluion:
When on and D off, c ma i o o () from and we ge i i i E Esa E Zsa.75.4.4.75.65.65 ma β Force.65. ().3 onsider he Darlingon ransisor pair given in Fig. P.3. Assume ransisor Q is driven ino sauraion wih E,sa.3 and β,forced.4. alculae β,forced and E,sa. Use E E.7, and 5. KΩ k Q Q v E _ - E Fig. P.3 Soluion:
.5 ma.44 ma 3.6 4.5 ma.44.4.4 ma 3.6.4 5 5 ma 4.5 ma 4.5.7.3,forced,,, forced Z Z Z sa Z sa Z β β