Chapter 8. Converter Transfer Functions
Chapter 8. Converter Transfer Functions8.1. Review of Bode .8.Single pole responseSingle zero responseRight half-plane zeroFrequency inversionCombinationsDouble pole response: resonanceThe low-Q approximationApproximate roots of an arbitrary-degree polynomial8.2. Analysis of converter transfer functions8.2.1. Example: transfer functions of the buck-boost converter8.2.2. Transfer functions of some basic CCM converters8.2.3. Physical origins of the right half-plane zero in convertersFundamentals of Power Electronics1Chapter 8: Converter Transfer Functions
Converter Transfer Functions8.3. Graphical construction of converter transferfunctions8.3.1.8.3.2.8.3.3.8.3.4.Series impedances: addition of asymptotesParallel impedances: inverse addition of asymptotesAnother exampleVoltage divider transfer functions: division of asymptotes8.4. Measurement of ac transfer functions andimpedances8.5. Summary of key pointsFundamentals of Power Electronics2Chapter 8: Converter Transfer Functions
The Engineering Design Process1. Specifications and other design goals are defined.2. A circuit is proposed. This is a creative process that draws on thephysical insight and experience of the engineer.3. The circuit is modeled. The converter power stage is modeled asdescribed in Chapter 7. Components and other portions of the systemare modeled as appropriate, often with vendor-supplied data.4. Design-oriented analysis of the circuit is performed. This involvesdevelopment of equations that allow element values to be chosen suchthat specifications and design goals are met. In addition, it may benecessary for the engineer to gain additional understanding andphysical insight into the circuit behavior, so that the design can beimproved by adding elements to the circuit or by changing circuitconnections.5. Model verification. Predictions of the model are compared to alaboratory prototype, under nominal operating conditions. The model isrefined as necessary, so that the model predictions agree withlaboratory measurements.Fundamentals of Power Electronics3Chapter 8: Converter Transfer Functions
Design Process6. Worst-case analysis (or other reliability and production yieldanalysis) of the circuit is performed. This involves quantitativeevaluation of the model performance, to judge whetherspecifications are met under all conditions. Computersimulation is well-suited to this task.7. Iteration. The above steps are repeated to improve the designuntil the worst-case behavior meets specifications, or until thereliability and production yield are acceptably high.This Chapter: steps 4, 5, and 6Fundamentals of Power Electronics4Chapter 8: Converter Transfer Functions
Buck-boost converter modelFrom Chapter 7LLineinputvg(s) –1:Di(s) –Zin(s)Output D' : 1(Vg – V) d(s)I d(s)I d(s)Cv(s) RZout(s)–d(s) Control inputGvg(s) v(s)vg(s)Gvd(s) d(s) 0Fundamentals of Power Electronics5v(s)d (s)v g(s) 0Chapter 8: Converter Transfer Functions
Bode plot of control-to-output transfer functionwith analytical expressions for important features80 dBV Gvd Gvd Gvd 60 dBVGd0 VDD'Q D'R40 dBVf020 dBVD'2π LC0 dBV Gvd–40 dB/decade10 -1/2Q f00 CLVgω 2D'LCω(D') 3RCfz0 2fz /10D' R2πDL(RHP)–20 dBVDVg–20 dB/decade–90 –180 –40 dBV10 1/2Q f010 Hz100 Hz10fz1 kHz10 kHz–270 100 kHz–270 1 MHzfFundamentals of Power Electronics6Chapter 8: Converter Transfer Functions
Design-oriented analysisHow to approach a real (and hence, complicated) systemProblems:Complicated derivationsLong equationsAlgebra mistakesDesign objectives:Obtain physical insight which leads engineer to synthesis of a good designObtain simple equations that can be inverted, so that element values canbe chosen to obtain desired behavior. Equations that cannot be invertedare useless for design!Design-oriented analysis is a structured approach to analysis, which attempts toavoid the above problemsFundamentals of Power Electronics7Chapter 8: Converter Transfer Functions
Some elements of design-oriented analysis,discussed in this chapter Writing transfer functions in normalized form, to directly expose salientfeatures Obtaining simple analytical expressions for asymptotes, cornerfrequencies, and other salient features, allows element values to beselected such that a given desired behavior is obtained Use of inverted poles and zeroes, to refer transfer function gains to themost important asymptote Analytical approximation of roots of high-order polynomials Graphical construction of Bode plots of transfer functions andpolynomials, toavoid algebra mistakesapproximate transfer functionsobtain insight into origins of salient featuresFundamentals of Power Electronics8Chapter 8: Converter Transfer Functions
8.1. Review of Bode plotsTable 8.1. Expressing magnitudes in decibelsDecibelsGdB 20 log 10 GActual magnitudeDecibels of quantities havingunits (impedance example):normalize before taking logZdB 20 log 10ZRbaseMagnitude in dB1/2– 6dB10 dB26 dB5 10/220 dB – 6 dB 14 dB1020dB1000 1033 20dB 60 dB5Ω is equivalent to 14dB with respect to a base impedance of Rbase 1Ω, also known as 14dBΩ.60dBµA is a current 60dB greater than a base current of 1µA, or 1mA.Fundamentals of Power Electronics9Chapter 8: Converter Transfer Functions
Bode plot of fnBode plots are effectively log-log plots, which cause functions whichvary as fn to become linear plots. Given:f nG f060dB2ff0–40dB/decadeMagnitude in dB isGdB 20 log 10ff0n 20n log 1040dBff020dBn–20dB/decade n 0dB Slope is 20n dB/decade Magnitude is 1, or 0dB, atfrequency f f0n 20 dB/decade1–1–20dBn–40dB 2flog scaleFundamentals of Power Electronics10Chapter 8: Converter Transfer Functions
8.1.1. Single pole responseSimple R-C exampleTransfer function is1v2(s)G(s) sC1 Rv1(s)sCR v1(s) –Cv2(s)Express as rational fraction:G(s) –11 sRCThis coincides with the normalizedform1G(s) 1 ωs0withFundamentals of Power Electronics11ω0 1RCChapter 8: Converter Transfer Functions
G(jω) and G(jω) Let s jω:ω1– j ω01G( jω) ω 2ω1 ω1 j ω00Im(G(jω))(jω) G(jω)G( jω) 2Re (G( jω)) Im (G( jω))1ω 21 ω2 GMagnitude is G(jω)Re(G(jω))0Magnitude in dB:G( jω) – 20 log 10dBFundamentals of Power Electronicsω1 ω02dB12Chapter 8: Converter Transfer Functions
Asymptotic behavior: low frequencyFor small frequency,ω ω0 and f f0 :ωω0 1Then G(jω) becomesG( jω) 1 111ω1 ω02 G(jω) dB0dB0dB–20dB–20dB/decade–1ff0–40dBOr, in dB,G( jω)G( jω) 0dBdB–60dB0.1f0f010f0fThis is the low-frequencyasymptote of G(jω) Fundamentals of Power Electronics13Chapter 8: Converter Transfer Functions
Asymptotic behavior: high frequencyFor high frequency,ω ω0 and f f0 :G( jω) ωω0 1ω1 ω022 G(jω) dBω ω00dB20dBThen G(jω) becomesG( jω) 1ω1 ω0–20dB–20dB/decade–1ff0–40dB1ωω02f f0–1–60dBf00.1f010f0fThe high-frequency asymptote of G(jω) varies as f-1.Hence, n -1, and a straight-line asymptote having aslope of -20dB/decade is obtained. The asymptote hasa value of 1 at f f0 .Fundamentals of Power Electronics14Chapter 8: Converter Transfer Functions
Deviation of exact curve near f f0Evaluate exact magnitude:at f f0:G( jω0) G( jω0)dB1ω1 ω00 – 20 log 102 12ω1 ω002 – 3 dBat f 0.5f0 and 2f0 :Similar arguments show that the exact curve lies 1dB belowthe asymptotes.Fundamentals of Power Electronics15Chapter 8: Converter Transfer Functions
Summary: magnitude G(jω) de–30dBfFundamentals of Power Electronics16Chapter 8: Converter Transfer Functions
Phase of G(jω)Im(G(jω))ω1– j ω01G( jω) ω 2ω1 ω1 j ω00 G(jω) G(jω) G(jω)Re(G(jω)) G( jω) tan–1 G( jω) – tan – 1ωω0Im G( jω)Re G( jω)Fundamentals of Power Electronics17Chapter 8: Converter Transfer Functions
Phase of G(jω)0 G( jω) – tan – 10 asymptote G(jω)ωω0-15 -30 -45 -45 G(jω)00 f0-60 -75 –90 asymptote-90 0.01f0ω0.1f0f010f0ω0–45 –90 100f0fFundamentals of Power Electronics18Chapter 8: Converter Transfer Functions
Phase asymptotesLow frequency: 0 High frequency: –90 Low- and high-frequency asymptotes do not intersectHence, need a midfrequency asymptoteTry a midfrequency asymptote having slope identical to actual slope atthe corner frequency f0. One can show that the asymptotes thenintersect at the break frequenciesfa f0 e – π / 2 f0 / 4.81fb f0 e π / 2 4.81 f0Fundamentals of Power Electronics19Chapter 8: Converter Transfer Functions
Phase asymptotesfa f0 / 4.810 G(jω)-15 –π/2fa f0 e f0 / 4.81fb f0 e π / 2 4.81 f0-30 -45 -45 f0-60 -75 -90 0.01f00.1f0f0fb 4.81 f0100f0fFundamentals of Power Electronics20Chapter 8: Converter Transfer Functions
Phase asymptotes: a simpler choicefa f0 / 100 G(jω)-15 -30 fa f0 / 10fb 10 f0-45 -45 f0-60 -75 -90 0.01f00.1f0f0fb 10 f0100f0fFundamentals of Power Electronics21Chapter 8: Converter Transfer Functions
Summary: Bode plot of real pole0dB G(jω) dB3dB1dB0.5f0G(s) 1dBf011 ωs02f0–20dB/decade G(jω)0 f0 / 105.7 -45 /decade-45 f0-90 5.7 10 f0Fundamentals of Power Electronics22Chapter 8: Converter Transfer Functions
8.1.2. Single zero responseNormalized form:G(s) 1 ωs0Magnitude:G( jω) ω1 ω02Use arguments similar to those used for the simple pole, to deriveasymptotes:0dB at low frequency, ω ω0 20dB/decade slope at high frequency, ω ω0Phase: G( jω) tan – 1ωω0—with the exception of a missing minus sign, same as simple poleFundamentals of Power Electronics23Chapter 8: Converter Transfer Functions
Summary: Bode plot, real zeroG(s) 1 ωs0 20dB/decade2f0f01dB0.5f00dB G(jω) dB1dB3dB10 f0 90 5.7 f045 45 /decade G(jω)0 5.7 f0 / 10Fundamentals of Power Electronics24Chapter 8: Converter Transfer Functions
8.1.3. Right half-plane zeroNormalized form:G(s) 1 – ωs0Magnitude:G( jω) ω1 ω02—same as conventional (left half-plane) zero. Hence, magnitudeasymptotes are identical to those of LHP zero.Phase: G( jω) – tan – 1ωω0—same as real pole.The RHP zero exhibits the magnitude asymptotes of the LHP zero,and the phase asymptotes of the poleFundamentals of Power Electronics25Chapter 8: Converter Transfer Functions
Summary: Bode plot, RHP zeroG(s) 1 – ωs0 20dB/decade2f0f01dB0.5f00dB G(jω) dB G(jω)0 1dB3dBf0 / 105.7 -45 /decade-45 f0-90 5.7 10 f0Fundamentals of Power Electronics26Chapter 8: Converter Transfer Functions
8.1.4. Frequency inversionReversal of frequency axis. A useful form when describing mid- orhigh-frequency flat asymptotes. Normalized form, inverted pole:1G(s) ω1 s0An algebraically equivalent form:G(s) sω01 ωs0The inverted-pole format emphasizes the high-frequency gain.Fundamentals of Power Electronics27Chapter 8: Converter Transfer Functions
Asymptotes, inverted poleG(s) 10dB3dBω1 s01dB1dBf02f00.5f0 G(jω) dB 20dB/decade G(jω) 90 f0 / 105.7 -45 /decade 45 f00 5.7 10 f0Fundamentals of Power Electronics28Chapter 8: Converter Transfer Functions
Inverted zeroNormalized form, inverted zero:ωG(s) 1 s0An algebraically equivalent form:1 ωs0G(s) sω0Again, the inverted-zero format emphasizes the high-frequency gain.Fundamentals of Power Electronics29Chapter 8: Converter Transfer Functions
Asymptotes, inverted zeroωG(s) 1 s0–20dB/decade G(jω) dB0.5f0f01dB2f03dB5.7 1dB0dB10 f00 f0–45 45 /decade G(jω)–90 5.7 f0 / 10Fundamentals of Power Electronics30Chapter 8: Converter Transfer Functions
8.1.5. CombinationsSuppose that we have constructed the Bode diagrams of twocomplex-values functions of frequency, G1(ω) and G2(ω). It is desiredto construct the Bode diagram of the product, G3(ω) G1(ω) G2(ω).Express the complex-valued functions in polar form:G1(ω) R1(ω) e jθ 1(ω)G2(ω) R2(ω) e jθ 2(ω)G3(ω) R3(ω) e jθ 3(ω)The product G3(ω) can then be writtenG3(ω) G1(ω) G2(ω) R1(ω) e jθ 1(ω) R2(ω) e jθ 2(ω)G3(ω) R1(ω) R2(ω) e j(θ 1(ω) θ 2(ω))Fundamentals of Power Electronics31Chapter 8: Converter Transfer Functions
CombinationsG3(ω) R1(ω) R2(ω) e j(θ 1(ω) θ 2(ω))The composite phase isθ 3(ω) θ 1(ω) θ 2(ω)The composite magnitude isR3(ω) R1(ω) R2(ω)R3(ω)dB R1(ω)dB R2(ω)dBComposite phase is sum of individual phases.Composite magnitude, when expressed in dB, is sum of individualmagnitudes.Fundamentals of Power Electronics32Chapter 8: Converter Transfer Functions
G0Example 1: G(s) 1 ωs11 ωs2with G0 40 32 dB, f1 ω1/2π 100 Hz, f2 ω2/2π 2 kHz40 dB G 20 dBG0 40 32 dB G G–20 dB/decade0 dB0 dB–20 dBf1100 Hzf22 kHz0 G–40 dBf1/1010 Hz–60 dBf2/10200 Hz–45 /decade–90 –90 /decade10 Hz100 Hz0 –45 10f11 kHz1 Hz–40 dB/decade1 kHz10f220 kHz–135 –45 /decade10 kHz–180 100 kHzfFundamentals of Power Electronics33Chapter 8: Converter Transfer Functions
Example 2Determine the transfer function A(s) corresponding to the followingasymptotes:f2 A f1 A0 dB 20 dB/dec10f1 45 /dec A A dBf2 /10–90 –45 /dec0 0 f1 /10Fundamentals of Power Electronics10f234Chapter 8: Converter Transfer Functions
Example 2, continuedOne solution:A(s) A 01 ωs11 ωs2Analytical expressions for asymptotes:For f f1A0s1 ω A0 1 A011s1 ω2s jωFor f1 f f2A01 ωs s1 ω12Fundamentals of Power Electronics A0sω1s jω1ω A f A0 ω0f11s jω35Chapter 8: Converter Transfer Functions
Example 2, continuedFor f f2A01 ωs 1 ωs 12 A0s jωsω1sω2s jωωf A 0 ω2 A 0 2f11s jωSo the high-frequency asymptote isfA A0 2f1Another way to express A(s): use inverted poles and zeroes, andexpress A(s) directly in terms of A A(s) A Fundamentals of Power Electronicsω1 s1ω1 s236Chapter 8: Converter Transfer Functions
8.1.6 Quadratic pole response: resonanceExampleG(s) Lv2(s)1 v1(s) 1 s L s 2LCRSecond-order denominator, ofthe form v1(s) –CRv2(s)–1G(s) 1 a 1s a 2s 2Two-pole low-pass filter examplewith a1 L/R and a2 LCHow should we construct the Bode diagram?Fundamentals of Power Electronics37Chapter 8: Converter Transfer Functions
Approach 1: factor denominatorG(s) 11 a 1s a 2s 2We might factor the denominator using the quadratic formula, thenconstruct Bode diagram as the combination of two real poles:G(s) 11 – ss11 – ss2a1s1 –1–2a 2withs2 –a11 2a 24a 21– 2a11–4a 2a 21 If 4a2 a12, then the roots s1 and s2 are real. We can construct Bodediagram as the combination of two real poles. If 4a2 a12, then the roots are complex. In Section 8.1.1, theassumption was made that ω0 is real; hence, the results of thatsection cannot be applied and we need to do some additional work.Fundamentals of Power Electronics38Chapter 8: Converter Transfer Functions
Approach 2: Define a standard normalized formfor the quadratic caseG(s) 11 2ζ ωs ωs002orG(s) 11 s ωsQω002 When the coefficients of s are real and positive, then the parameters ζ,ω0, and Q are also real and positive The parameters ζ, ω0, and Q are found by equating the coefficients of s The parameter ω0 is the angular corner frequency, and we can define f0 ω0/2π The parameter ζ is called the damping factor. ζ controls the shape of theexact curve in the vicinity of f f0. The roots are complex when ζ 1. In the alternative form, the parameter Q is called the quality factor. Qalso controls the shape of the exact curve in the vicinity of f f0. Theroots are complex when Q 0.5.Fundamentals of Power Electronics39Chapter 8: Converter Transfer Functions
The Q-factorIn a second-order system, ζ and Q are related according toQ 12ζQ is a measure of the dissipation in the system. A more generaldefinition of Q, for sinusoidal excitation of a passive element or systemis(peak stored energy)Q 2π(energy dissipated per cycle)For a second-order passive system, the two equations above areequivalent. We will see that Q has a simple interpretation in the Bodediagrams of second-order transfer functions.Fundamentals of Power Electronics40Chapter 8: Converter Transfer Functions
Analytical expressions for f0 and QTwo-pole low-pass filterexample: we found thatEquate coefficients of likepowers of s with thestandard formResult:Fundamentals of Power ElectronicsG(s) G(s) v2(s)1 v1(s) 1 s L s 2LCR11 s ωsQω002ω01f0 2π 2π LCQ R CL41Chapter 8: Converter Transfer Functions
Magnitude asymptotes, quadratic formIn the formG(s) 11 s ωsQω00let s jω and find magnitude:G for ω ω0ff01G( jω) ω1– ω02 2ω 12 ω0Q2 G(jω) dBAsymptotes areG 12–20 dB0 dBff0–20 dBfor ω ω0–2–40 dB–40 dB/decade–60 dB0.1f0Fundamentals of Power Electronics42f010f0fChapter 8: Converter Transfer Functions
Deviation of exact curve from magnitude asymptotes1G( jω) ω1– ω02 2ω 12 ω0Q2G( jω0) QAt ω ω0, the exact magnitude isG( jω0) Qor, in dB:The exact curve has magnitudeQ at f f0. The deviation of theexact curve from theasymptotes is Q dBdBdB G Q dB0 dBf0–40 dB/decadeFundamentals of Power Electronics43Chapter 8: Converter Transfer Functions
Two-pole response: exact curves0 Q Q Q 10Q 5Q 2Q 1Q 0.7Q 0.5Q 510dBQ 2Q 1-45 Q 0.7Q 0.20dBQ 0.1 GQ 0.5 G dB-10dB-90 Q 0.2-135 Q 0.1-20dB0.30.50.7123f / f0-180 0.11f / f0Fundamentals of Power Electronics44Chapter 8: Converter Transfer Functions10
8.1.7. The low-Q approximationGiven a second-order denominator polynomial, of the formG(s) 11 a 1s a 2s 2orG(s) 11 s ωsQω002When the roots are real, i.e., when Q 0.5, then we can factor thedenominator, and construct the Bode diagram using the asymptotesfor real poles. We would then use the following normalized form:G(s) 11 ωs11 ωs2This is a particularly desirable approach when Q 0.5, i.e., when thecorner frequencies ω1 and ω2 are well separated.Fundamentals of Power Electronics45Chapter 8: Converter Transfer Functions
An exampleA problem with this procedure is the complexity of the quadraticformula used to find the corner frequencies.R-L-C network example:L G(s) v2(s)1 v1(s) 1 s L s 2LCRv1(s) –CRv2(s)–Use quadratic formula to factor denominator. Corner frequencies are:ω1 , ω2 L/R Fundamentals of Power Electronics2L / R – 4 LC2 LC46Chapter 8: Converter Transfer Functions
Factoring the denominatorω1 , ω2 L/R 2L / R – 4 LC2 LCThis complicated expression yields little insight into how the cornerfrequencies ω1 and ω2 depend on R, L, and C.When the corner frequencies are well separated in value, it can beshown that they are given by the much simpler (approximate)expressionsω1 R ,Lω2 1RCω1 is then independent of C, and ω2 is independent of L.These simpler expressions can be derived via the Low-Q Approximation.Fundamentals of Power Electronics47Chapter 8: Converter Transfer Functions
Derivation of the Low-Q ApproximationGivenG(s) 11 s ωsQω002Use quadratic formula to express corner frequencies ω1 and ω2 interms of Q and ω0 as:ω 1–ω1 0QFundamentals of Power Electronics1 – 4Q 22ω 1 ω2 0Q481 – 4Q 22Chapter 8: Converter Transfer Functions
Corner frequency ω2ω 1 ω2 0Q1 – 4Q 22can be written in the formω2 F(Q)0.75ω0F(Q)Q0.50.25whereF(Q) 1 1 21 – 4Q 2For small Q, F(Q) tends to 1.We then obtainω2 1ω0Qfor Q 12Fundamentals of Power Electronics000.10.20.30.40.5QFor Q 0.3, the approximation F(Q) 1 iswithin 10% of the exact value.49Chapter 8: Converter Transfer Functions
Corner frequency ω11 – 4Q 22ω 1–ω1 0Qcan be written in the formω1 1F(Q)0.75Q ω0F(Q)0.50.25whereF(Q) 1 1 21 – 4Q 2For small Q, F(Q) tends to 1.We then obtainω1 Q ω0for Q 12Fundamentals of Power Electronics000.10.20.30.40.5QFor Q 0.3, the approximation F(Q) 1 iswithin 10% of the exact value.50Chapter 8: Converter Transfer Functions
The Low-Q Approximation G dB0dBQ f0F(Q) Q f0f1 f0–20dB/decadef0F(Q)f2 Qf0 Q–40dB/decadeFundamentals of Power Electronics51Chapter 8: Converter Transfer Functions
R-L-C ExampleFor the previous example:ω01 2π 2π LCQ R CLv (s)1G(s) 2 v1(s) 1 s L s 2LCRf0 Use of the Low-Q Approximation leads toC
Fundamentals of Power Electronics Chapter 8: Converter Transfer Functions3 The Engineering Design Process 1. Specifications and other design goals are defined. 2. A circuit is proposed. This is a creative process that draws on the physical insight and experience of the engineer. 3. The circuit is modeled. The converter power stage is modeled as
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
There are mainly four types dc-dc converters: buck converter, boost converter, buck-boost converter, and flyback converter. The function of buck converter is to step down the input voltage. The function of boost converter, on the other hand, is to step up the input voltage. The function of buck-boost combines the functions of both buck converter
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
data converter architectures is included in Chapter 3 (Data Converter Architectures) along with the individual converter architectural descriptions. Likewise, Chapter 4 (Data Converter Process Technology) includes most of the key events related to data converter process technology. Chapter 5 (Testing Data Converters) touches on some of the key
Keywords: Converter, Boost Converter, Back to Back Converter, Fly-back Converter, Indirect Matrix Converter. I. INTRODUCTION One of the most commonly applied converters in hybrid systems is the AC/DC/AC converter because it has the ability to connect
Fig. 1. Conventional dual-output SC DC-DC converter. 2. Circuit Configuration 2.1 Conventional Converter Figure 1 shows an example of the conventional multi-output SC converter. The converter of figure 1 is based on the serial fix type converter(6) proposed by Suzuki et al. The conventional converter consists of six transistor
The battery is connected to a DC-DC converter (Buck/Boost converter). The DC-DC converter operates as a Buck or Boost converter to charge or discharge the Battery. The DC-DC converter connects to the DC- AC converter via a DC Link system of 3900 micro F capacitors. The DC-AC converter controls the DC voltage (V_dc) on the DC Link.
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
