Designing Control Loops for Linear and Switching Power Supplies: A Tutorial Guide Christophe Basso October 2012 Last update March 3 rd 2014

Transcription

1 Deigning Control Loo for Linear and Switching Power Sulie: A Tutorial Guide Chritohe Bao October Lat udate March 3 rd 4 Correction of tyo, mitake and error found by reader or by the author himelf. Secial thank go to Mr Toma Gubek from Cech Reublic who really crutinied the text line by line and caught a lot of tyo and error! Page 9: Pleae note that the rie time i meaured from to 9 ercent of the outut waveform, y(t), in the cae of the damed reone. For an under-damed reone, like what we will tudy in Chater 3, the rie time i meaured from to ercent. Contributed by Krihnakumar Goalakrihnan, May 3 Page 34: equation (.34) i revered:.5 Q.64 5 Page 37: in (.4) it denominator ha indeed the dimenion of a time contant. Page 56: th line from the to: before tranmitting it to the load (not ource) Page 6: Figure.5: lower ide: the label i not v out (t) but mut be i out (t) Page 6: Figure.6: uer ide: the µ label mut be 3 µ. Page 65: Figure.7, cation: if the ero of the numerator would lie Page 65: in Figure.7, the total hae lag reache 8 and not -8 Page 68: ome of the exreion could include bracket to avoid confuion: C R4 R3 R R Z R R R R (.36) in 4 3 C (.38) C R4 R3 R R Contributed by Raymond Carr, February 4 C Page 69: the final equation hould be labeled (.4) and one of it term ubcrit i wrong C R4 R3 R R Zin R R3 R4 R (.4) C R R3 R4 R Contributed by Raymond Carr, February 4 j jt j Page 73: Equation (.6) hould be e e 4 4 j 4 j Page 8: in Figure 3.5, the middle grah cation hould be 9.3 and not 9.6 jt

2 Page 84: in Figure 3.7, the hae margin ymbol hould be m and not m Page 84: in Figure 3.7, the lower right comment hould be T f 8 L L o Page 98: Equation (3.3) hould be Q R C RC R Page 99: lat bullet, Q >.5, it hould be corrected to: Q >.5 or : Page 5: in (3.5) and (3.5), the Greek letter i igma while it hould be eta: t r co co.6 lim (3.5) (3.5) Page 7: Figure 3.6, cation: ratio when lower than. Page 8: in the text, above Figure 3.33: a ource that add and ubtract Page 8: the fifth reference i miing, it hould be: 5. B. Eriman, R. Redl, Otimiing the Load Tranient Reone of the Buck Converter, APEC 998 roceeding,. 7-76, vol. Page 55: equation dimenion of (4.7) i wrong, it mut be: V Page 57: more friendly to u engineer than equation (4.8), in t it? Page 66: the outut inductor (L ) and the outut caacitor (C out ) in Figure 4.. Page 7: Term in the ln quotient mut be waed, no imact on reult: Q 3.9 ln k ln.5 D d

3 Page 8: in Figure 4.6, C mut be labeled µf not mf Page 8: Equation (4.73) give.4 H, not 4 H. Page 84: In equation (4.77) (4.78) and (4.79), thi i arg H(f c ) and not arg T(f c ) arg H fc 7 boot 36 m (4.77) boot 36 m arg H fc 7 m arg H fc 9 (4.78) boot arg H f (4.79) m c Page 94: Figure 4.39: 58 or - then 9 or -7 at the bottom Page 96: in the text, above (4.7): Suoe we need a hae boot of, then Page : in Figure 4.44, in thi articular cae, the label 46 H i obviouly milaced and hould occur before the 48-H label, at. Page 3: in equation (4.4), it mut be arg H(f c ) and not arg T(f c ) boot arg H f m c Page : in Figure 4.57, v out (t) i the firt curve on to, the quare below i i out (t) Page 5: in (4.59), we have 5 krad/: 5 krad, 4. kh G f f G Page 6: a mall hould be in equation (4.9) and (4.9): D... and Z... Page 6: (4.9) ero featuring the inductance mut be revered: Page 5: in (4.6) the - ign mut recede the arenthei: 4Q Q Q Q Q Z out out L... r L Page 5: in Figure 4.98, the ymbol next to the unit mut be and not a croed box! Page 5: in Table 4E., in exreion for PI, PI, PID and PID, to maintain a dimenionle exreion, the term G i actually, the - croover ole divided o

4 by the t ero. For clarity, G can go and all exreion are divided by factor now dimenionle. in the numerator, you have o. If you o G where the mid-band gain G i Action Mode Baic Element Tranfer Function Imlementation Bode Plot G Tye Proortional P G k k Log f Integral I V G k in - i V Log out f Derivative Proortional Integral Proortional Integral + t - order lag Proortional Integral Derivative Proortional Integral Derivative + nd order lag D PI - PI G G - G V o out Log f PID G k d G G G G PID G G G o + - o G - + o Log f Log f G o Log f G G Log f a 3a Page 55: below equation (5.7): According to (5.5), to amlify the inut ignal by Page 66: Figure 5., cation ; thi i the tye b argument. Page 74: omething went wrong here: G GG Page 96: in Figure 5.34, cation: Here, the current loo chain i not rereented. Page 3: but alo in the mid-band gain definition. Page 3: Suoe we need to create an attenuation of at H.

5 Page 33: Figure 5.4 i wrong. The right icture hould be thi one: G H G f -9. arg G f -8-7 arg G H 7-36 k k f Figure 5.4: Thee ac reult how the correct attenuation value at H. H Page 36: the text below equation (5.94) mut be relaced u to than in firt. Exreion and definition now differ from what we originally derived for the claical tye comenator. In (5.3), auming C i much maller than C, then the gain G i defined by (5.). In the above exreion, however, auming than R i much maller than R, the gain G in (5.89) imlifie to C C. If we equate both exreion (we want a imilar mid-band gain with both configuration) and extract C, we have C CR R. A R i maller than R, then C will be much larger than C. Therefore, a the entire current defined by (5.85) will cro C at tart-u, we can exect a longer charging time than with the traditional tye configuration. Page 37: the text after and 6.5 H mut be udated a below: For the firt cae, Figure 5-5, C equal 38 nf and C i 6 nf. A exected, for a imilar ole/ero arrangement, the econd configuration (Figure 5-43) lead to a C value of 54 nf. f f Page 3: in equation (5.9), R uer i R : C3 R f f

6 f f 3.5k 769 Page 33: in equation (5.34), R uer i R : C3 nf R f f 6.8k 3.5k 769 f f Page 37: in equation (5.46), R uer i R : C3 R f f Page 3: in equation (5.59), R ulldown i R ullu Page 33: the hae mut be booted by 5. Page 344: in the text below equation (5.36): imilar to that of the tye 3 definition in (4.3) that Mr. Venable uroely quared: k venable boot tan 45 4 (5.363) Page 345: Figure 5.7: boot k tan 45 Page 35: The entence i a bit mileading I believe. I meant that the eak amlitude decreae by.5 diviion. Perha it i imler like that: increae it until the modulation occuie 7 diviion eak to eak. Thi oint correond to a 3- dro from the reference oint at H: Page 358: equation (6.6) need to be cleaned u: R lower V Vout R lower R Page 377: ye, the ratio between the 5-ut and the.5-v reference i, not.5! Therefore (6.9) i boot5 V tan Thi would not allow a hae boot larger than =9.5. Page 385: In figure 7., the bandga Page 386: After equation (7.): Thi i the value dilayed in Figure 7- over the ref node. Page 387: the aragrah below 7.. need a light correction:

7 working a a differential amlifier. However, the key oint i the tranconductance ath from the V ref node to Q 6 collector (alo to Q 9 collector) that i much higher than the tranconductance affecting the ame V ref node to Q collector. We can how that the firt tranconductance involving Q 6 (or Q 9 ) i an exonential function while that involving Q i a linear function. So when the loo leave equilibrium and force an increae of V ref, Q 6 (Q 9 ) conduct more current than Q and the cathode-anode voltage goe down via Q and Q. Not for incluion: The below figure how how thee current diverge when the.5-v reference level i left. Equilibrium i reached at V ref equal.5 V, both tranitor ink the exact ame current and the TL43 cathode-anode voltage doe not change. If V ref increae, current in Q 6 increae at a ignificantly larger ace than that of Q, uetting equilibrium: V KA goe down. Book ection highlighted by Toma Gubek, January 4 Figure udate kindly contributed by Petr Kadanka, January 4 Page 388: Figure 7.4: of coure, the µ had to tranform into m Ye, you hould read 3 µv and 6 µa. Page 394: In (7.6) the term V f hould be relace by. Page 44: the entence below (7.95) hould be: A the total caacitance i 68.3 nf Page 433: Figure 7.35: of coure, the µ had to tranform into m Ye, you hould read µf and. µf for the ca. Page 437: the firt arameter hould be I Zbia. Page 443: Q (if decreae) Page 445: Figure 7.47: the ign ha gone in the right ide of R LED. Page 446: Figure 7.49: the ign ha gone in the right ide of R LED.

8 Page 455: middle of the age: account for hi reence for it reence Page 455: in (8.),.7 hould be.8 Page 495: ome of the ign have gone during the rint: Figure 9.8, a minu ign i miing cloe the econd arrow vertically ointing to the circle. Page 499: the ign ha gone during the rint: Figure 9., a minu ign i miing in the triangle, it i G() of coure. Page 5: a quetion mark i in the middle of the entence and ha nothing to do here. at oint B in relation? to cae, i delayed by 9. Page 54: equation 9.6: the numerator i not Z out of coure, but Z in : T in Verr Z G H V Z Z c out in Contributed by Thoralf Roahl, February 3 Page 54: equation 9.43, the denominator R 3 hould obviouly be the reult of 9.4 (.35 k). RulluCTR max 3.3k.4 G 3.4 or.7 R.35k 3,max In the text, reult found in (9.43) :.7 minimum gain. Contributed by Toma Gubek, February 4 Page 55: in the text, nd aragrah, there i a reference to a ource B that i not labeled in Figure 9.9. It i actually the ource right to the inut ource V 6, (V(err)-.6)/3 Contributed by Toma Gubek, February 4 Page 59: in figure 9.4, thi i µ and not m. Contributed by John Pearon, February 3 Page 53: in the uer ection, reference [7] i wrong and it hould be [4] Contributed by John Pearon, February 3 Page 54: ome ubcrit have diaeared when going to rint. In figure 9.47/9.48/9.49 and 9.5, the π in r π i gone, a well a in I b (). Figure 9.5 i ok though. Page 54: oo, I goofed the equation by relacing r π by h : Cbr Contributed by Toma Gubek, February 4 Page 543: the entence above (9.5), and olving for the bae current, we have: Contributed by Toma Gubek, February 4

9 Page 543: in the entence (9.6), thi i R FB not RFB. Contributed by Toma Gubek, February 4 Page 55: to match equation below, in the uer comonent lit 73. Contributed by Toma Gubek, February 4 Page 555: in (9.49), it i Contributed by Toma Gubek, February 4 Page 556: in (9.55) and (9.56), it i C Q R (9.55) L R C Q R R L P (9.55) Contributed by Toma Gubek, February 4 R I, W R R rm Page 56: in Figure 9.69/9.7, C i µf not mf