1. INTRODUCTION

Adaptive Input FilterCompensation for SwitchingRegulators

S.S. KELKARBell Laboratories

F.C. LEEVirginia Polytechnic Institute and State University

An input filter is frequently employed between a switching

regulator and its power source. However, its presence often results

in degradation of dynamic performances and stability. The

detrimental interaction is between an input filter and a switching

regulator and is a function of the input filter parameters and also of

the supply voltage. An earlier paper presented an analysis and

design procedure aimed at developing a feed-forward loop to cancel

this undesirable interaction. The feed-forward design is extended

here to encompass a scheme that automatically accounts for changes

in the supply voltage; the result is an adaptive compensation that

tracks the input voltage variations. Experimental results are

presented that confirm the adaptive nature of the design.

Manuscript received June 30, 1980; revised September 8, 1983.

Authors' present addresses: S.S. Kelkar, Electronic Power SystemsLaboratory, Bell Laboratories, Whippany, NJ 07987; F.C. Lee,Department of Electrical Engineering, Virginia Polytechnic Institute andState University, Blacksburg, VA 24061.

0018-9251/84/0100-0057 $1.00 © 1984 IEEE

An input filter is often required between a switchingregulator and its power source. The filter serves toprevent the regulator switching current from beingreflected back into the source and also to isolate sourcevoltage disturbances from being propagated to theswitching regulator payload downstream. The presence ofan input filter, however, often results in regulatorperformance degradations [1-51. Excessive peaking of theoutput impedance at the resonant frequency of the inputfilter interacts with the regulator control loop and canresult in a sharp reduction in loop gain. This sharpreduction of loop gain invariably results in degradation oftransient response, audiosusceptibility, output impedance,and even possible instability. The extent of loop gainreduction depends on the converter load, the input filterpeaking, and also the supply voltage to the regulator.

A novel input filter compensation scheme using afeed-forward loop to completely cancel the effect ofpeaking of the output impedance of the input filter waspresented in an earlier paper [5]. The input filtercompensation scheme was implemented on a buckregulator operating at a fixed supply voltage.Measurements of the open-loop gain and phase of thebuck converter employing a single-stage and a two-stageinput filter confirmed the design [5]. It was also verifiedthat the proposed feed-forward compensation is adaptiveto various filter configurations and is independent of inputfilter parameter values. As a result, a much strongerconclusion was reached that the proposed feed-forwardloop effectively isolates the switching converter from itssource [5], thus eliminating any possible interactionbetween the source with an unknown dynamic impedanceand the regulator control loop or loops.

This paper extends the design and proposes a feed-forward compensation scheme that automatically changesthe gain in accordance with supply voltage variation, thusresulting in an adaptive feed-forward compensation thattracks supply voltage variation. Experimental results arepresented that show excellent correlation with theory.Measurements of the closed-loop frequency responsessuch as audio susceptibility and output impedancecharacteristics are shown to have remarkableimprovement when the proposed feed-forward loop isemployed.

11. INPUT FILTER INTERACTION WITHREGULATOR CONTROL LOOP

The peaking of the output impedance of an input filtercauses sharp fluctuation in open-loop gain and phase [1-5]. The interaction between the output impedance and theregulator control loop can be illustrated using the openloop transfer function. Fig. 1 shows a multiloopcontrolled buck regulator with a two-stage input filter [7,8]. The parameters of the converter are

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-20, NO. 1 JANUARY 198457

F12 - FDI FP1= [VO (RL - D2Z) (1 + SCRC)]

0 ts)

FiAC

F-77~~~~~~~~~~~

PULSE MODULATOR ERROR PROCESSOR

Fig. 2. Small signal block diagram of Fig. 1.

/(D [D2Z (1 + sCRL) + a1])

D = duty cycle = VO V,, V, = supply voltage

a, = s2LCRL + sCRL [(RI + Rc +LICRL] + RL.

Duty cycle-to-inductor-current transfer function

F22 - FD2 FP2

= LVO RL (RL - D2Z) (1 + SCRL)]

/(DRL [D2Z (1 + SCRL) + a,]).

(6)

(7)

(8)

(9)

The power stage transfer functions F12 and F22include the parameter Z which is the output impedance ofthe input filter. For the two-stage input filter of Fig. 1 theoutput impedance is

Z(s) = (Z1 + RL2 + SL2)

/l1 + SC2 (Z1 + RL2) + S2L2C2]where

Input Filter:RL1 = 0.2 flCl = 200 ,uFC2 = 20 pLF.Power Stage:L = 230 p1HC = 300 ,uF

PO = 20 W.

Feedback Loops:R, = 33.3 kflR4 = 40.7 kQl

L, = 325 1H1RL2 = 0.02 fl

RA = 0.2 flL2 = 116 ,uH

RI = 0.2 f RC = 0.067 fRL = 200 Ql(load) VO = 20 V

R2 = 16.7 kf R3 = 47 kfR5 = 2 kQ N = 0.65

ER = 6.7 V C1 = 5600 pF C2 = 0.01 ,uF.Pulse Modulator (constant V1TO, duty cycle control):M = V,TOn = 0.88 X 10-3 V s. M is constant for theconstant volt-second control used.

The small signal block diagram of the multiple-loopregulator illustrated in Fig. 2 can be expressed as [7-91:

GT(S) = FdC FM FD1 FPI + Fac FM FD2 FP2 (

where

Fdc = (1/sC'1) [g/(R3 + R) + 1/Zc]

Rx = R1//R2; g = RxIRI; Zc = Rs + 1/sC'2 (

FM = 2 R4 C,/(N M) = pulse modulator gain

Fac = (1IsClR4)) (sNL).

FdC, FM, F3, and Fac are the feedback loop transferfunctions, while F12 and F22 are the power stage transferfunctions:

Duty cycle-to-output transfer function

Z1 = (RLI + SL1) // (1/SC1)

Z2 = RL2 + SL2 + (1/SC2). (10)

It is to be noted that (6) and (9) are completelygeneral in the sense that they can be used for any inputfilter configuration provided the correct expression forZ(s) is used. The effect of the input filter on the open-

loop gain GT(s) is thus characterized by a simpleparameter Z(s), the output impedance of the input filter.The forward transfer function H(s) of the input filter [61affects only the closed-loop transfer function of theregulator; thus the input filter need only be represented byits forward transfer function H(s) and its outputimpedance Z(s) in order to completely characterize itseffect on regulator dynamic performance [1-51.

For the two-stage input filter of Fig. 1 at the tworesonant frequencies provided by L,, Cl and L2, C2 theoutput impedance Z(s) and the forward transfer functionH(s) [6] will peak, and from (6) and (9) it is obvious thatat the two frequencies there will be a corresponding lossof gain in F12, F22, and therefore also in the open-loopgain GT(s). The loss in gain will be accompanied by a

corresponding disturbance in phase margin. It isinteresting to notice that the peaking of the outputimpedance Z(s) and of H(s) affects only the power stagetransfer functions and not the feedback loop transferfunctions. Thus the conclusion to be drawn is that theinput filter will affect the regulator dynamic performanceregardless of the type of control used, whether singleloop or multiloop, voltage feedback superconductingmagnet (SCM) type, or current injected control [1-4].The disturbances in open-loop gain and phase at theresonant frequencies of the input filter will also adverselyaffect the closed-loop transfer function

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-20, NO. 1 JANUARY 1984

d (a)

s8

v.

Fig. 1. Two-loop controlled switching buck regulator.

(audiosusceptibility), transient response, and the outputimpedance [1-5].

Ill. EFFECT OF SUPPLY VOLTAGE VARIATION ONINPUT FILTER INTERACTION

The extent of reduction in open-loop gain GT(s) at theresonant frequencies depends on the extent of peaking ofthe output impedance Z(s), as is evident from (6) and (9).In these two equations peaking of Z(s) leads to areduction in the numerator term (RL - D2Z) and anincrease in the denominator. However, the extent ofreduction depends also on the load RL and the duty cycleD. Supply voltage variation will change the value of theduty cycle D as is evident from (7). For the same inputfilter configuration therefore it is evident that the effect ofpeaking of Z(s) will depend also on the supply voltage;for a low value of supply voltage the duty cycle D ishigher and close to unity and therefore the extent ofopen-loop gain GT(s) reduction would be greater at theresonant frequencies.

The extent of open-loop gain reduction and itsdependence on supply voltage were studied using acomputer program. The program was written to calculatethe open-loop gain and phase margin for the converter ofFig. 1 with and without an input filter, at various valuesof supply voltage.

The open-loop transfer function GT(S) with input filteris given in (1)-(12), for the case without input filter (1)-(9) apply except that Z(s) = 0. Figs. 3 and 4 show thecomputed and measured values of open-loop gain andphase margin with and without a two-stage input filter forsupply voltages V, = 25 V and 40 V. The followingobservations are made:

1) The two-stage input filter resonates at twofrequencies, 880 Hz and 3 kHz approximately, and at

8

(a)

8

FREQ ( HZ )

(b)

Fig. 3. (a) Open-loop gain at V, = 25 V; calculated values andmeasured values (A) without feed forward. (b) Open-loop phase marginat V, = 25 V; calculated values and measured values (A) without feed

forward.

KELKAR & LEE: ADAPTIVE INPUT FILTER COMPENSATION 59

FREQ(HZ)

(a)

-! l 1. _,.,I-

I .E+3FREQI HZ)

(b)

Fig. 4. (a) Open-loop gain at V, = 40 V; calculated values andmeasured values (zA) without feed forward. (b) Open-loop phase marginat V, = 40 V; calculated values and measured values (A) without feed

forward.

each frequency the peaking of the output impedancecauses sharp fluctuations in open-loop gain and phasemargin, as both the measurement and computer valuesshow.

2) The peaking of the output impedance at the firststage resonant frequency is more pronounced and has agreater effect on the regulator than at the resonantfrequency of the second stage. It should be noted that avery small damping resistor RA is used in thedemonstration.

3) The measurements made on the circuit agree fairlyclosely with the computed values using the model, thusindicating the validity of the model.

4) The effect of input filter peaking varies withsupply voltage, as pointed out earlier. At a supply voltageof 25 V the duty cycle D is approximately 0.8 and the

effect of peaking is greater than at 40 V when D has anapproximate value of 0.5. Thus for the same input filterconfiguration the extent of open-loop gain reductiondepends on the supply voltage.

The reduction in open-loop gain and phase margincause degradation of transient response andaudiosusceptibility and other control-loop relatedperformance specifications [1-5], and can also result inloss of stability. Thus it is important to control the effectof peaking of the output impedance of an input filter inorder to avoid serious degradation of regulator dynamicperformance.

IV. ADAPTIVE INPUT FILTER COMPENSATION

Earlier work [5] presented a detailed analysis anddesign procedure that results in a feed-forwardcompensation scheme capable of canceling completely thepeaking effect of the input filter. The scheme wasimplemented using a buck regulator operating at a fixedsupply voltage.

The proposed feed-forward loop senses the small acsignal across the input filter capacitor, and the analysisand design procedure [5] results in the following gain ofthe feed-forward loop.

C2(s) = -D2/VOFM.Using the proposed feed-forward loop the open-looptransfer function is modified thus

(11)

(12)GT'(s) = FdCFm F12 + F3FacFM F22

where

F12' = VORL (1 + sCRc)/(D al )

F22' = VO (1 + sCRL)/(D al ).

(13)

(14)

The open-loop gain GT' (s) and the power stagetransfer functions F5'2 and F'2 are now independent of theinput filter output impedance Z(s) and are now only afunction of feed-back loop parameters and the powerstage parameters, unlike GT(S) of (1) which is affected byZ(s).

As shown in Fig. 5 the implementation of the feed-forward is easy [5] if the supply voltage V, is keptconstant since then D, VO, and FM will all be constants.The input filter capacitor voltage contains dc and this is

Cf

TOPULSEMODULATOR

Fig. 5. Nonadaptive feed-forward circuit.

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-20, NO. 1 JANUARY 1984

1 kll

60

Vc" 'C 27 FInputFilter 0 |CapacitorVoltage dQn h n

ToPulseModulotor

Output 1l kO

Fig. 6. Adaptive feed-forward implementation for variable voltagesupply.

first blocked out using a capacitor in series; the gainbeing implemented using a simple resistor dividernetwork. Extensive experimental results [5] confirmed thedesign.

For the case where the supply voltage varies theextent of the effect of peaking of Z(s) is dependent onsupply voltage, as described earlier, and thus the amountof compensation required to cancel the effect of peakingshould also be supply voltage dependent. From (7) it canbe seen that the duty cycle depends on the supply voltageand thus this provides an effective way of realizing asupply voltage-dependent compensation scheme.Substituting (4) and (7) into (11), it leads tothe followingfeed-forward loop gain

C2(s) = VO M/ (V12 (2R4 C,) N) (15)which is supply voltage dependent.

A circuit that implements the above feed forward andadjusts the gain automatically as V, changes has beendeveloped and is shown in Fig. 6 [6].

The input voltage V, in Fig. 6 is allowed to varybetween 25 V and 40 V. It is fed to a voltage divider andthen squared. The input filter capacitor voltage consists ofa large dc component and this is blocked out using a 27gF capacitor in series with the feed-forward path. Thesmall signal variation and the small magnitude componentat switching frequency are then divided by the squaredinput voltage. A pair of resistances provides the final gainand the result is then added to the feedback signal at theoutput of the integrator. The switching frequencycomponent in the input filter capacitor voltage is verysmall compared to the corresponding component in thefeedback signal and thus its effect on the duty cycleimplementation is negligible. The gain of the feedforward is thus a function of supply voltage V, and ismade adaptive to changes in V,. The feed forward is thuscapable of tracking any variations in supply voltage.

V. EXPERIMENTAL RESULTS

The effects of the feed forward loop on regulationstability, audiosusceptibility, output impedance, and

transient responses are examined experimentally in thissection.

A. Effects of Feed Forward on Open-LoopCharacteristics

A buck regulator with SCM control [7, 8] is used inconjunction with a two-stage input filter. The keyparameters of the regulator are identified in this paper.The feed-forward circuit used is shown in Fig. 6.

Measurements of the open-loop gain and phasemargin are made at supply voltages of 25 V and 40 Vusing the same adaptive feed forward of Fig. 6. Theresults are presented in Figs. 7 and 8, which are plots ofthe calculated values of gain and phase margin with andwithout the input filter and also of the measured gain andphase margin with feed forward.

It can be seen that the expressions for the open-loopgain and phase without input filters are identical to thosewith feed forward, as examination of (1), (6), (9), (12),(13), and (14) show. Setting Z = 0 in (1), (6), and (9)gives the open-loop gain and phase without input filterand these are the same expressions as (12), (13), and(14). The following observations are made.

1) The addition of feed forward effectively eliminatesthe disturbances in the open-loop gain and phase marginat all values of supply voltage.

2) The analytical prediction that the open-loop gainand phase margin with feed forward are identical to thosewithout input filter is confirmed as the plots show.

Thus the open-loop gain and phase are made immuneto the peaking effect of the input filter output impedance.The circuit implementation is relatively straightforwardand is free from the use of any frequency-dependentelement.

B. Effects of Feed Forward on AudiosusceptibilityThe closed-loop input-to-output transfer function

(audiosusceptibility) of a switching regulator is animportant characteristic. It refers to the regulator's abilityin attenuating small signal sinusoidal disturbances

KELKAR & LEE: ADAPTIVE INPUT FILTER COMPENSATION 6-1

FREQ ( HZ)(a) FREO( HZ)

(a)

(b)

Fig. 7. (a) Open-loop gain at V, = 25 V; calculated values andmeasured values (A) with feed forward. (b) Open-loop phase margin at

V, = 25 V; calculated values and measured values (A) with feedforward.

propagating from the regulator input to its output. Thegain of function should be as small as possible; thus theregulator will effectively attenuate the audio noise at theinput so as not to affect operation of the regulatorpayloads. Unfortunately, as pointed out in the literature[1-4], the peaking of the output impedance of the inputfilter and the peaking of the forward transfer function ofthe input filter increase the audiosusceptibilitysignificantly, unless a heavier filter is employed.Measurements of the audiosusceptibility were made byinjecting a small signal sinusoidal disturbance at the inputV, to the buck regulator; the corresponding frequencycomponent at the output VO divided by V, gives theaudiosusceptibility at that frequency.

Figs. 9(A) and (B) show the measured values of theaudiosusceptibility with and without feed forward at twovalues of supply voltage, V, = 25 V and 40 V, using the

FREO( HZ)

(b)

Fig. 8. (a) Open-loop gain at V, = 40 V; calculated values andmeasured values (A) with feed forward. (b) Open-loop phase margin atV, = 40 V; calculated values and measured values (A) with feed

forward.

same feed-forward circuit. It can be clearly seen that theaudiosusceptibility is degraded at the two resonantfrequencies where the output impedance Z(s) and thetransfer function H(s) of the input filter peak, with thefirst stage resonating around 600 Hz and the second stagearound 3 kHz. It is also evident from the figures that theaudiosusceptibility is dependent on duty cycle D or thesupply voltage. At higher values of supply voltage whenthe duty cycle is low, the audiosusceptibility is lower.The addition of feed forward substantially improves theoverall audiosusceptibility, as is evident uponexamination of Fig. 9. The peaking effect ofaudiosusceptibility with the feed-forward loop is morepronounced at the two resonant frequencies of the two-stage input filter; this is explained by noting that theaudiosusceptibility is affected both by the peaking of Z(s)

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-20, NO. 1 JANUARY 198462

(a)FREG( HZ)

(a)

1 .E+3FRED( HZ)

FREQ ( HZ)

(b)Fig. 10. (a) H(s) of two-stage input filter, R3 = 0.075 Ql. (b) Z of

two-stage input filter, R3 = 0.075 Ql.

(b)

Fig. 9. (a) Audiosusceptibility with and without feed forward at V,25 V. (b) Audiosusceptibility with and without feed forward at V, =

40 V.

characteristics. The audiosusceptibility with feed forwardis affected by the peaking of H(s) since the effect ofpeaking cannot be eliminated via any control means.

and by the peaking of the forward transfer function H(s)of the input filter. The peaking of H(s) cannot becontrolled in any fashion by the addition of a feed-forward loop since the control loop is not affected byH(s); thus the feed-forward loop is effective only incanceling Z(s), while the peaking effect of H(s) ismanifested in the audiosusceptibility. The peaking effectof H(s) can only be controlled by proper design of theinput filter.

Figs. 10(a) and (b) show the transfer functions H(s)and Z(s) of the two-stage input filter used and thepeaking of H(s) at the two resonant frequencies is clearlyseen.

It can therefore be concluded that the addition of feedforward significantly improves the audiosusceptibility

C. Effects of Feed Forward on Closed-Loop OutputImpedance

The closed-loop output of a switching regulatorshould be as low as possible so that the regulator behavesas much as an ideal voltage source as possible. However,as pointed out in the literature [8], the peaking of theoutput impedance of the input filter increases the closed-loop output impedance of the regulator.

Figs. 1 1(a) and (b) show the measured values ofoutput impedance with and without feed forward at fourvalues of supply voltage V,, using the same feed-forwardcircuit in all cases and RA = 0.075 fl (ESR of C1).

It can be clearly seen that the output impedance isincreased at the two resonant frequencies of the two-stage

KELKAR & LEE: ADAPTIVE INPUT FILTER COMPENSATION 63

A single-stage input filter was used with the followingparameters:

RLI = 0.2 fl; L, = 325 p.1H; Cl = 220 p1F.

Fig. 12 illustrates the output voltage waveforms when theinput voltage is abruptly switched from V, = 30 V to 40V.

FREQ( HZ)

(a)

(a)

Fig. 11. (a) Output impedance with and without feed forward (x) at V,25 V. (b) Output impedance with and without feed forward (x) at V,

40 V.

input filter. This is a consequence of the disturbance inthe loop gain produced at those frequencies by thepeaking of the input filter output impedance Z(s). Sincethe effect of Z(s) on the loop gain depends on the dutycycle D, the effect on the output impedance would alsobe duty-cycle dependent. This is confirmedexperimentally from Fig. 11 where it can be seen that atlower values of supply voltage the disturbances in theoutput impedance are greater.

The addition of feed forward almost totally eliminatesundesirable perturbances in the output impedancecharacteristics.

D. Effects of Feedforward on the TransientResponse

The effect of the feedforward loop on transientresponse is studied for a step change in supply voltageand also for a step change in load.

Fig. 12. (a) Output ripple voltage without feed forward.

It can be clearly seen that the transient response isimproved with the addition of feedforward. The amountof overshoot is less with feedforward. The magnitude ofthe oscillations in the output voltage caused by theinteraction between the input filter and the regulatorcontrol loop are also lessened with the addition of feed-forward. This can be credited to the boost of the regulatorloop gain provided by the feed-forward circuit.

Comparison of the waveforms of input filter capacitorvoltage, output filter inductor current, and the controlvoltage do not reveal much difference between the twocases (with and without feed forward).

For step change in load, the buck regulator of Fig. 1was used with the parameters as specified earlier with thefollowing changes: V, = 25 V, and R3 = 3.69 kQ. Theload was switched repetitively between RL = 10 nI and20 Ql using a transistor switch. Figs. 13(a) and (b) showthe output voltage ripple without and with feed forward,as the load is switched. The output voltage ripple withoutfeed forward, Fig. 13(a), shows distinct oscillationscaused by the interaction between the input filter and theregulator control loop. The oscillation frequency

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-20, NO. I JANUARY 1984

8

FREQ( HZ)

(b)

64

(b)Fig. 13. (b) Output ripple voltage with feed forward. Vertical: 0.1 V/

div. Horizontal = I ms/div.

coincides with the input filter resonant frequency. Theseoscillations are eliminated with the addition of the feed-forward loop, as is evident in Fig. 13(B).

Other large signal transients such start-up were alsoexamined [10]; input filter feed-forward loop is shown tohave no effect on start-up behavior. In addition, a circuitwas made unstable due to inadequate filter design andwas shown to be stabilized in the presence of an inputfilter feed-forward loop [12]. For detailed experimentalresults, please refer to [10-12].

Vl. CONCLUSIONS

The peaking of the output impedance of an input filterinevitably interacts with the regulator control loop andresults in degradation of regulator performance and loopstability. The extent of the interaction depends not onlyon the peaking of the output impedance but also on thesupply voltage. In an earlier paper [5], it was shown thata feedforward loop could be implemented employing asimple gain circuit that eliminates the detrimental effectsof input filter peaking. The gain of the feedforwardcircuit is dependent on supply voltage and the type ofduty cycle control used and is independent of input filterparameters and also of input filter configuration. The

proposed design was implemented and tested using abuck regulator with constant input voltage and a constantvolt-second duty cycle control.

In this paper the feed forward compensation isextended to a scheme that automatically adjusts the gainin accordance with changes in supply voltage. The designthus results in an adaptive feed-forward compensationscheme that tracks the supply voltage variations. Theadaptive feed-forward design is verified through a set ofmeasurements of the open loop gain and phase marginover a wide range of supply voltage variations.

It is important to note that this adaptive feed-forwardcircuit retains all the features of the earlier nonadaptivecircuit [51 and has no adverse effect on switchingconverter operation. The important features of theproposed feed-forward compensation can be summarizedas follows.

1) The feed-forward compensation circuit design isindependent of the input filter configuration and also ofinput filter parameter values. The input filter inductorcurrent informatin is not needed; the only input to thefeed-forward circuit being the input filter capacitorvoltage.

2) From earlier work [5] and from the resultspresented in the present paper, it is logical to concludethat the proposed feed-forward circuit can provideeffective compensation for an unknown sourceimpedance. The adaptive feed-forward circuit caneffectively isolate the switching regulator from its source,thus preventing interaction between the switchingconverter and equipment upstream.

3) The pulse modulator transfer function FM is anintegral part of the adaptive feed-forward circuit design.For a single-loop controlled regulator only, a gainadjustment is necessary for different types of duty cyclecontrol. However, for multiloop controlled regulators, anadaptive feed-forward design could be considerablydifferent for different types of duty cycle control, becausethe duty cycle modulator gain is a function of theparticular multiloop implementationn.

4) The measurements show that the use of feedforward can lead to significant improvement in stability,audiosusceptibility, output impedance, and transientresponse.

From the work presented in this paper and earlierresults [5, 6, 11, 12], it is evident that the feed-forwardloop acts as a buffer between the source (includes theinput filter) and the switching regulator. It can eliminateinteraction between the regulator and the arbitrary sourcewith an unknown dynamic impedance. This importantproperty of the feed-forward compensation scheme greatlyfacilitates design of a stable large-scale power systemwhere regulators are placed in series/parallel in order toprocess power for various payloads.

KELKAR & LEE: ADAPTIVE INPUT FILTER COMPENSATION 65

REFERENCES

[I] Yu, Y., and Biess, J.J. (1971)Some design aspects concerning input filters for dc-dcconverters.In 1971 IEEE Power Conditioning Specialists ConferenceRecord, pp. 66-76.

[2] Middlebrook, R.D. (1976)Input filter considerations in design and application ofswitching regulators.Presented at the IEEE Industry Applications Society AnnualMeeting, Chicago, Ill., Oct. 11-14, 1976.

[3] Middlebrook, R.D. (1970)Design techniques for preventing input filter oscillations inswitched-mode regulators.In Proceedings of the 5th National Solid State PowerConversion Conference, 1970.

[4] Lee, F.C., and Yu, Y. (1979)Input-filter design for switching regulators.IEEE Transactions on Aerospace and Electronic Systems,Sept. 1979, AES-15, 627-634.

[5] Kelkar, S.S., and Lee, F.C. (1983)A novel feedforward compensation canceling input filter-regulator interaction.IEEE Transactions on Aerospace and Electronic Systems,Mar. 1983, 19, 258-268.

[6] Kelkar, S.S., and Lee, F.C. (1982)Adaptive feedforward input filter compensation for switchingregulators.Proceedings Power Con 9, 1982.

[71 Lee, F.C., and Yu, Y. (1980)An adaptive-control switching buck regulator-Implementation, analysis, and design.IEEE Transactions on Aerospace and Electronic Systems,Jan. 1980, AES- 16, 84-99.

[8] Lee, F.C. (1980)User's Design Handbook for a Standardized Control Module(SCM) for DC to DC Converters, Vol. 11.Virginia Polytechnic Institute and State University,Blacksburg, Va., Apr. 1980.

[9] Lee, F.C., Carter, R.A., and Fang, Z.D. (1983)Investigation of stability and dynamic performances of acurrent-injected regulator.IEEE Transactions on Aerospace and Electronic Systems,Mar. 1983, 19, 274-287.

[10] Kelkar, S.S. (1982)Input filter compensation for switching regulators.Ph.D. dissertation, Virginia Polytechnic Institute and StateUniversity, Blacksburg, Va., Oct. 1982.

[11 Kelkar, S.S., and Lee, F.C. (1983)The effects of an adaptive feedforward compensation schemeon converter dynamic characteristics.Proceedings Power Con 10, 1983.

[12] Kelkar, S.S., and Lee, F.C. (1983)Stability analysis of a buck regulator employing input filtercompensation.In Record of the IEEE Power Electronics SpecialistsConference, 1983.

S.S. Kelkar received the B.Tech. (Hons.) degree in electrical engineering in 1974fromn the Indian Institute of Technology, Kharagpur, India, the M.Tech. degree fromthe Indian Institute of Technology, Bombay, India, in 1976, and the Ph.D. degree inelectrical engineering from Virginia Polytechnic Institute and State University,Blacksburg, Va., in 1982.

From 1976 to 1977 he was employed as a Senior Research Fellow at the I.I.T.,Bombay, India, where he worked on the development of a printed circuit board motor.In 1977 he joined the Tata Electric Co., Bombay, where he worked on the design andanalysis of electric drives for the operation of off-line isolator switches used insubstations. Since 1982 has been employed as a member of the technical staff at BellTelephone Laboratories, Whippany, N.J., where he is engaged in design, simulation,and analysis of power processing equipment. His research interests include powerelectronics, linear and nonlinear control, computer based simulation, and solid statecontrol of electric motors.

Fred C.Y. Lee received the B.S. degree in electrical engineering in 1968 fromCheng-Kung University, Taiwan, Republic of China, and the M.S. and Ph.D. degreesin 1971 and 1974 respectively, in electrical engineering, from Duke University,Durham, N.C.

From 1974 to 1977, he was employed as a member of the Technical Staff of theControl and Power Processing Department, TRW Systems, where he was engaged indesign, simulation, and analysis for spacecraft power processing equipment. In 1977,he joined the Virginia Polytechnic Institute and State University, Blacksburg, Va., asan Assistant Professor in the Department of Electrical Engineering. He is presently aProfessor with that department. His research interests include power electronics,electric vehicle propulsion, nonlinear modeling and analysis, and design optimizationof power processing components and systems. He has published over 70 articles in theareas of power device and circuit modeling, analysis, and design.

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-20, NO. 1 JANUARY 198466

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