Self-Oscillating Modulators for Direct Energy Conversion Audio Power …kazus.ru/nuke/users_files/26112008/2356962.pdf · 2008-11-26 · Self-oscillating modulators for direct energy

Self-oscillating modulators for direct energyconversion audio power amplifiers

Petar Ljusev1, Michael A.E. Andersen1

1Ørsted • DTU Automation, Technical University of Denmark, Kgs. Lyngby, DK-2800, Denmark

Correspondence should be addressed to Petar Ljusev ([email protected])

ABSTRACT

Direct energy conversion audio power amplifier represents total integration of switching-mode power supplyand Class D audio power amplifier into one compact stage, achieving high efficiency, high level of integration,low component count and eventually low cost. This paper presents how self-oscillating modulators can beused with the direct switching-mode audio power amplifier to improve its performance by providing fasthysteretic control with high power supply rejection ratio, open-loop stability and high bandwidth. Itsoperation is thoroughly analyzed and simulated waveforms of a prototype amplifier are presented.

1. INTRODUCTION

The switching-mode power conversion technology hasradically changed the today’s commercial product ap-pearance, making them far smaller than few decades agoand leaving the designers bare hands to experiment withtheir look and feel without being limited by technologybarriers. These benefits are direct result of the improvedefficiency of the power supplies and power amplifiersthat use switching approach instead of the linear one. Asa side effect, the amount of heat-sinking material neededis reduced by at least an order of magnitude, which im-proves the level of integration between the various con-trol and power components, so that the overall boardspace, weight and volume are significantly reduced andpower density is improved. The aforementioned advan-tages are probably most clearly seen in the switching-mode Class D audio power amplifiers, where the new ef-ficient power conversion principle has opened the doorsto some new and challenging application areas, from thesmallest low-end portable devices with extended batterylife to the large high-end audio installations for stage per-formances with tremendously reduced dimensions.

The achievements in the field of switching-mode audiopower amplification in the last few years, described interms of even higher output power levels and improvedaudio performance, are drawing this approach on thetechnology map as one of the most significant break-throughs that is eventually going to replace linear elec-tronics in most of the power processing applications.However, this does not mean that the present Class D au-

dio power amplifiers are the only possible solution thatfits all applications, and much research is done in orderto take the most advantage from the very high conversionefficiency of the switching-mode approach while stillkeeping the complexity and component count to mini-mum. These unique challenges, posed predominantly bythe audio and video product manufacturers wanting topenetrate the low-end market by cutting production costsand introducing cheap products of satisfactory quality,can be answered by further and closer integration ofthe constitutive parts of the audio power amplifier - theswitching-mode power supply and the Class D ampli-fier, which have been till know usually viewed as sepa-rate parts without many touching points. This integrationphilosophy leads to a very compact audio power amplifi-cation solution known as ”SIngle Conversion stage AM-plifier” or SICAM [1], [2], [3], [4], meaning that the newaudio power amplifier is capable of direct energy conver-sion from the AC mains to the loudspeaker output. It istherefore very interesting for the Active pulse modulatedTransducer (AT) [5] intended for use in the new genera-tion of active loudspeaker systems and subwoofer units.

This paper will introduce a new control approach forSICAMs, that utilizes self-oscillating principle to im-prove the performance of present SICAM solutions [2],[6], [7]. The operation principles of the self-oscillatingmodulator for SICAM are thoroughly analyzed, togetherwith the SICAM topology that is considered as the mostsuitable for the purpose. At the end, experimental resultsare shown that prove the feasibility of the approach.

Ljušev and Anderson Self-oscillating Modulators for Direct Energy Conversion Audio Power Amplifiers

AES 27th International Conference, Copenhagen, Denmark, 2005 September 2–4 1

J.nr.: SICAM.01.05.011


ACmains

Inverter Class D

L

C

LPF

Energy flow

A B

-

+

~ ~

Fig. 1: Conventional Class D audio power amplifier

2. AUDIO AMPLIFICATION WITH SICAM

The block diagram of the conventional Class D audiopower amplifier is given in Fig. 1. It can be principallydivided into two parts: switching-mode power supply(SMPS) and Class D audio power amplifier. The simpli-fied front-end SMPS consists of mains rectifier, energybuffering capacitor A, high frequency (HF)-operated in-verter stage, small power transformer, output rectifierand low-pass filter (LPF) with a bulky capacitor B, whichkeeps the voltage of the associated DC-bus to a con-stant value. Heavy filtered DC-bus is used to connectthe SMPS with the Class D audio power amplifier, con-sisting from simple power switches in half- or full-bridgeconfiguration and low-pass output filter. It can be noticedthat this conventional solution incorporates two bulky en-ergy storage capacitors A i B, where the former is usedto overcome the physical constraint of the mains volt-age regular zero-crossings and is therefore compulsory,while the latter is required by the specific topology usedand can be possibly avoided by using some other energyconversion approach. As another drawback, the energydirection is kept unidirectional through the whole SMPS,so that any charge returned back from the Class D ampli-fier accumulates in the B capacitors and causes perturba-tions on the DC-bus voltage that can lead to power supplypumping problems with single-ended Class D amplifiersreproducing low frequency (LF) signals.

The block diagram of the direct energy conversion audiopower amplifier or SICAM is presented in Fig. 2. It is de-veloped from the HF-link power converter topology [8]which is being proposed for use in Uninterruptible PowerSupplies (UPS) and converters for renewables where iso-lation is mandatory. The main feature is the replacementof the SMPS DC-bus with a HF-link, i.e. the isolationtransformer is used as a connection point between thesimplified power supply and the audio power amplifier,now comprising of bidirectional switches which are ca-pable of blocking both voltage polarities and conduct-ing current in both directions. In this way, the whole

Inverter

Energy flow

Audio Amp.

Bidirectionalswitches

A

ACmains -

+

~ ~

Fig. 2: Direct conversion audio power amplifier

power conversion chain is shrunk resulting in higher ef-ficiency, and the bulky LPF with capacitor B in the con-ventional SMPS is removed together with the output rec-tifiers, thus allowing bidirectional output flow throughthe isolation barrier down to the energy storage capac-itor A. Therefore, the power supply pumping problemsare non-existent with the newly proposed SICAM. Thebiggest problem with the presented approach is the loadcurrent commutation between the bidirectional switchesin the amplifier, since the freewheeling path through theMOSFET body diodes in the Class D amplifier disap-pears when using bidirectional switches. Through theyears many different approaches have been proposed tosolve the commutation problem by using special modu-lation techniques [3], dissipative and active clamps [4],[7] or safe-commutation switching strategies [2], [6] andsome of them will be reviewed in the later sections.

In the following sections, the switching stage on the pri-mary side of the main transformer will be referred as in-put stage, primary stage or inverter stage, while the oneon the secondary side will be referred as output stage,secondary stage or bidirectional bridge.

3. SELF-OSCILLATING MODULATORS FORAUDIO AMPLIFIERS

The basic approach of creating Pulse Width Modulated(PWM) output voltage has not changed from the dawnof signal processing era. Essentially, reference voltage isbeing compared against the triangular carrier and theirintersection points define the switching instants. Theperformance of the modulator strongly depends on thecleanliness of the triangular carrier and any distortion ofits shape leads to unpleasant nonlinear effects [9]. Thesources of carrier distortion are often difficult to reveal,since they can be either result of the non-ideal externalcarrier generator or can appear as a side effect of the rip-ple present in the feedback signal from the power stage.


J.nr.: SICAM.01.05.011

The most basic PWM modulators use externally gen-erated triangular and their main advantage is the con-stant switching frequency operation, which makes itvery easy to predict the frequency content of the out-put and filter it accordingly. It also features constantgain, equal to the inverse of the carrier voltage peak Vc,KPWM = 1/Vc, which is independent of the modulationindex or the modulation frequency, up to half the car-rier frequency. Unfortunately, without any power supplyvoltage feedforward implemented, they have low PowerSupply Rejection Ratio (PSRR), which is usually com-pensated by adding additional feedbacks from the am-plifier output and providing high gains within the cor-responding compensators. To decrease the carrier dis-tortion from output voltage ripple residues in the feed-back, the switching frequency is usually chosen an orderof magnitude higher than the power bandwidth and out-put filter cut-off frequency, while the control bandwidthis intentionally limited to reasonable values, thus limit-ing audio performance. Turning to practical implemen-tation, these PWM modulators require expensive highbandwidth operational amplifiers in the external carriergenerator, which makes them less appealing.

PWM modulators, which do not utilize externally gener-ated carrier are the self-oscillating modulators [10], [11],[12]. Since the self-oscillating modulator creates the car-rier and hysteresis window internally using the powerstage, these modulators are usually characterized withvery high PSRR, good cancellation of various errors anddisturbances, open-loop stability and simplicity. Fromcontrol perspective, the modulator itself has the largestpossible bandwidth, which is equal to the switching fre-quency, since that is the oscillation point where the open-loop transfer function has a gain of 1 with phase shiftequal to 180. Disturbances are, however, effectively re-jected in the interval where the open-loop transfer func-tion has substantial gain (ex. 20 dB or more). On theother hand, most of the present self-oscillating modu-lators have variable switching frequency with changingmodulation indexes M, which causes the amplifier to ex-perience very large voltage ripple, low control bandwidthand high distortion close to the maximum modulationindex. This problem is alleviated by limiting the mod-ulation index to a value lower than 1 (ex. Mmax = 0.8)i.e. increasing the power supply voltage with respect tothe maximum load voltage. Despite of the few disadvan-tages, self-oscillating modulators are found in most ofthe commercial Class D audio power amplifiers.

4. SELF-OSCILLATING MODULATORS FORSICAMS

4.1. Application and limitations

The most common modulator for direct conversion au-dio power amplifiers, i.e. SICAMs [2], [3], [4], [6],[7] has up till now been the PWM modulator with ex-ternally generated carrier. Reasons for this are mainlytwofold and arise from the fact that self-oscillating mod-ulators have variable switching frequency that decreaseswith increasing modulation index and the inability to pre-dict and steer switching instants, due to the hysteretic-type control. On one hand, when using self-oscillatingmodulators in SICAMs with PWM modulated trans-former voltages [3], variable switching frequency causesthe transformer design to be suboptimal and its dimen-sions must be chosen to bare the largest magnetic fluxat lowest switching frequency without going into satura-tion. On the other hand, when PWM modulation is usedonly on the secondary side of the transformer in con-junction with some safe-commutation principle [2], therandom switching of self-oscillating modulator makesit very difficult to synchronize the operation of the in-put stage to the output stage. However, this does notmean that self-oscillating modulators are completely use-less in SICAMs, but rather that they are applicable justwith certain SICAM topologies and usually with active[7] or dissipative clamps [4], or conditionally with safe-commutation strategies [2] as means for commutatingthe load current in the output bidirectional bridge.

In the next sections, the use of self-oscillating modula-tors will be analyzed with respect to SICAMs with non-modulated transformer voltages [2], where the input in-verter stage on the primary side of the transformer is op-erated with 50% duty cycle to create rectangular trans-former voltage with maximum width. The operation ofthe input stage is not synchronized to any control signalfrom the secondary side, and therefore the operation ofthe input stage is referred as free-running.

4.2. Operation fundamentals

Self-oscillating modulators can be roughly divided intotwo groups: current mode and voltage mode modulators[12]. There is not bigger difference in their principal op-eration, except that the measured inductor current in theformer group is used directly in the modulator, while inthe latter group the measured bridge voltage must be firstintegrated or processed in some way in the control sec-



J.nr.: SICAM.01.05.011

f1

faZ

. .

HF-link

+_

sgn (v) = +/-1

Amplifier

Hysteresis

MFB

Vref

f-2

fa

LC

Output filter

Fig. 3: GLIM for SICAM

tion [13] or in both control section and power stage [10],[14].

The approach presented in the following few paragraphscan be used to modify particular self-oscillating mod-ulator for SICAM operation in a straightforward man-ner. Without loss of generality, the discussion will dealjust with the Global Loop Integrating Modulator (GLIM)[14], where the integrating transfer function from thebridge voltage to the input of the hysteresis block isobtained by combining the poles of the output filter inthe power stage with the zero in the modulator feedbackblock (MFB) at the output filter cut-off frequency. Thehysteresis block itself is created from the power stagebridge voltage using a resistive divider, as an input to thecomparator.

In all self-oscillating modulators, the polarity of thebridge voltage which is being applied across the outputfilter and loudspeaker is determined solely by the stateof the comparator i.e. the output from the hysteresisblock, since the power supply voltage has constant po-larity. In SICAMs, bridge voltage essentially representsa product of the HF-link voltage and the state of the com-parator. Changing the HF-link polarity causes immediatechange in the bridge voltage and hysteresis window po-larity bound to it, which will surely bring the power stageinto stall due to the ill-posed hysteresis limits. Therefore,any change in the HF-link voltage polarity must be fol-lowed by corresponding change in the direction of inte-gration, which essentially means that the polarity of thefeedforward and feedback signals entering the compara-tor must be reversed. The block diagram of the proposedGLIM self-oscillating SICAM is given in Fig. 3.

Since the operation of the proposed self-oscillating mod-

ulator for SICAMs seems to be determined by the quanti-ties characteristic for the basic self-oscillating modulatorintended for operation with Class D amplifiers, quantitiesassociated with the latter will be called basic quantitiesand will be given asterisk ”*” as superscript. Notice thatmost of these quantities are severely affected and alteredwhen the SICAM HF-link is included in the modulator.

The operation of the self-oscillating modulator forSICAMs depends on the modulation index M of the ref-erence voltage signal at the input of the modulator. LetM∗

lim denote the modulation index limit at which the fre-quency of the basic self-oscillating modulator, equal tothe output stage switching frequency f ∗s2 is two times theswitching frequency of the free-running input stage fs1:

f ∗s2(M∗lim) = 2 · fs1 (1)

4.3. Normal operation with M < M∗lim

Normal operation of the self-oscillating modulator inFig. 3, which occurs for modulation indexes M < M∗

limis shown in Fig. 4. The operation is called normal sinceit resembles very much the operation of a conventionalClass D amplifier with self-oscillating modulator. Withlow modulation indexes M < M∗

lim, the slopes of both theraising portion and the falling portion of the carrier aresteep and the output stage performs several switchingswithin each period of the HF-link voltage vHF . The na-ture of the operation makes it very difficult to determinethe exact switching frequency of the output stage, sinceit depends not only on the feedback quantities but alsoon the instants when HF-link changes its polarity. It canbe, however, assumed that with sufficient level of accu-racy the average switching frequency of the output stagefs2 is equal to the switching frequency of the basic self-oscillating modulator f ∗s2:

fs2(M) = f ∗s2(M) =Vs

41−M2

τintVh + tdVs

∣

∣

∣

∣

M<M∗lim

(2)

where Vs = |vHF | is the absolute value of the HF-linkvoltage, Vh is the hysteresis window width, td is the mod-ulator loop delay and τint is the integrator time constantwhich is equal to the output filter cut-off frequency in theGLIM case. In all practical implementations, the hys-teresis window is formed using the HF-link voltage:

Vh = kh ·Vs (3)



J.nr.: SICAM.01.05.011

HF-linkvoltage

Load voltageCarrier

Hysteresis

Bridge voltage

Secondarygate drive

Fig. 4: Normal operation with M < M∗lim

and MFB in Fig. 3 features attenuation equal to the gainof the SICAM amplifier ka, leading to switching fre-quency of the output stage fs2 which is independent ofthe supply voltage Vs and significantly improving thePSRR:

fs2(M) = f ∗s2(M) =14

1−M2

τintkhka + td

∣

∣

∣

∣

M<M∗lim

(4)

The idling switching frequency with M = 0 is:

fs2,0 =14

1τintkhka + td

(5)

4.4. Locked operation with M ≥ M∗lim

The real difference in the operation between the conven-tional self-oscillating modulator and the one for use withSICAMs is observed with modulation indexes larger thanthe modulation index limit M ≥M∗

lim. As shown in Fig. 5,the bridge voltage of the self-oscillating SICAMs withM ≥ M∗

lim turns into 2-level phase-shifted PWM withconstant frequency two times the HF-link frequency:

fbr = 2 · fs1 (6)

while the output stage switching frequency is exactlyequal to the input stage switching frequency i.e. the HF-link frequency:

fs2(M) = fs1

∣

∣

∣

M≥M∗lim

(7)

HF-linkvoltage

Load voltageCarrier

Hysteresis

Bridge voltage

Secondarygate drive

t+

Tbr

Fig. 5: Locked operation with M ≥ M∗lim

With the duty cycle D defined as ratio between the timeinterval with high voltage on the bridge output t+ and itsperiod Tbr, equal to half the HF-link period:

D =t+Tbr

= 2t+ fs1 (8)

the SICAM output voltage is calculated to be:

vo = DVs − (1−D)Vs = (2D−1)Vs (9)

and the duty cycle dependance on the modulation index:

D =1±M

2(10)

where ”+” sign is used for positive and ”-” sign is usedfor negative reference voltages vre f .

As implied in equations (6) and (7), the frequency ofquantities associated with the secondary stage becomeslocked to the primary side and the HF-link, since theslope of either the raising portion or the falling portionof the carrier has reduced as a result of the large mod-ulation index M ≥ M∗

lim. In this situation, the regularchanges in the HF-link polarity interrupt the slower slopeof one of the carrier portions before it hits the other wallof the hysteresis block, causing a sort of carrier reset.The time interval between the phase-shifted waveforms



J.nr.: SICAM.01.05.011

HF-linkvoltage

Load voltageBridge voltage

CarrierHysteresis

Dt

Dv

21 3 4

Fig. 6: Asymptotic stability of the locked operation

created by the switching of the output stage and the sub-sequent switching of the HF-link is essentially equal tothe time interval with positive bridge voltage t+ and itsdependance on the modulation index is:

t+ = DTbr =1±M4 fs1

(11)

The phase locking property of the self-oscillatingSICAM can be shown to be asymptotically stable. Whendisturbance voltage ∆v is added to the carrier voltage,causing corresponding timing error ∆t at the first switch-ing of the output stage, like shown in Fig. 6, then thefollowing equations for the subsequent errors are valid:

∆t1 = ∆t ∆v1 = ∆v

∆t2 =( 1−M

1+M

)

∆t ∆v2 =( 1−M

1+M

)

∆v

∆t3 =( 1−M

1+M

)2∆t ∆v3 =( 1−M

1+M

)2∆v... ...

∆tn+1 =( 1−M

1+M

)n∆t ∆vn+1 =( 1−M

1+M

)n∆v(12)

Because of the fact that:

1−M1+M

< 1 (13)

the asymptotic stability of the timing interval t+ for thephase-shifted PWM is proven:

∆tn+1 =( 1−M

1+M

)n∆t n→∞−→ 0

∆vn+1 =( 1−M

1+M

)n∆v n→∞−→ 0(14)

With maximum modulation index Mmax=1, the time in-terval t+ of the phase shifted PWM approaches Tbr and0 with positive and negative voltages respectively, whichmeans that at one instant close to the maximum modu-lation the switching of the input and output stage willstart to overlap and the resultant bridge voltage willhave switching frequency equal to the HF-link voltagefbr = fs1 = fs2.

It is interesting to notice that, if the self-oscillating mod-ulator is designed to have basic idling switching fre-quency lower than two times the HF-link frequencyf ∗s2,0 < 2 · fHF , i.e. M∗

lim ≡ 0, then the correspondingself-oscillating SICAM will be in locked operation allthe time. Even more, if the maximum modulation in-dex is limited to value less than one Mmax < 1, then theswitching of both stages is not simultaneous. This meansthat many other SICAM topologies which utilize safe-commutation strategies [2], [6] can be used in conjunc-tion with the proposed self-oscillating modulator becauseof the natural synchronization between the stages duringlocked operation.

4.5. Output stage switching frequency

To summarize, the switching frequency of the outputstage fs2 in the self-oscillating SICAM differs when op-erating in normal or locked mode and can be describedwith the following equation:

fs2 =

14

1−M2

τintkhka + td, M < M∗

lim

fs1 , M ≥ M∗lim

(15)

and represents a discontinuous function, shown in Fig. 7.

5. SICAM WITH ACTIVE CAPACITIVE VOLTAGECLAMP

As mentioned earlier, the load current commutation inthe self-oscillating SICAMs can be most reliably per-formed by using clamps, which clamp the load and out-put filter voltage to the clamp capacitor voltage and pro-vide current path during the dead or blanking time tblbetween the outgoing and incoming switches. The ac-tive clamping technology [7] where the clamped energyis returned to the primary side via an auxiliary smallpower converter is regarded as superior to the dissipa-tive one [4], because of the much higher efficiency, buton expense of few additional components, handling just



J.nr.: SICAM.01.05.011

0 0.2 0.4 0.6 0.8 10

200

400

600

800

1000

1200

Modulation index M

f s2 [k

Hz]

, Qtr[n

C]

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

Pcl

[W]

Mlim

fs2

Pcl

Qtr

Fig. 7: Output stage switching frequency, transferredcharge and clamp power

C3

D3

D13

D11T11

T12 D12C2 CF

LF

T21 T22

D21 D22

T23 T24

D23 D24

. ..

TR

vHF

+

vHF

+

.

.

.

T3

TR aux

Active capacitive voltage clamp

-

+

~ ~

ACmains

-

+

~ ~

Fig. 8: SICAM with active capacitive voltage clamp

a small fraction of the output power. The scheme of theSICAM with active capacitive voltage clamp is given inFig. 8.

The voltage of the clamp capacitor is regulated by feed-back to a value slightly higher than the HF-link voltageVcl > Vs, so that the clamp is charged only during theblanking time intervals. The auxiliary converter can bemade in many different topologies, with the flyback con-verter as simplest choice.

The design of the clamp starts with the selection of theclamp capacitor Ccl ≡ C3 in Fig. 8. The primary task ofthe selection process is to limit the voltage ripple ∆Vclduring normal operation or emergency shutdown. By as-

suming that the bulk of the clamp capacitor voltage rip-ple in normal operation is due to its internal equivalentseries resistance (ESR), the following selection rule canbe written for the clamp capacitor ESR:

ESRmax =∆Vcl,max

Io,max(16)

where ∆Vcl,max is the maximum voltage ripple duringnormal operation and Io,max is the peak output current.

During emergency shutdown all the stored energy in theoutput filter inductor is converted into electrostatic en-ergy in the clamp capacitor. By neglecting the presenceof the auxiliary converter due to the unavoidable time de-lay before it catches up with the increased clamp voltage,the clamp capacitor capacitance is limited to:

Ccl,min = L f

( Io,max

∆Vcl,max

)2 (17)

where L f is the output filter inductance and ∆Vcl,maxrefers to the maximum allowed voltage excursion in acase of emergency shutdown.

In the same time, the clamp capacitor must be able tohandle the maximum RMS clamp current during normaloperation:

Icl,rms,max =2π

Io,max√

D =2π

Io,max√

tbl fs2 (18)

The most important quantity for the design of the auxil-iary converter is the maximum transferred charge Qtr,maxfrom the load to the clamp during one period of the auxil-iary converter operation Taux = 1/ faux, assuming that thelatter is able to return that charge to the primary side andregain the balance on the clamp capacitor voltage. Due tothe discontinuity of the output stage switching frequencyfunction in (15), normal and locked operation must bedealt separately:

• normal operation

Qtr,n =fs2,0

faux(1−M2)MIo,maxtbl

dQtr,n

dM

∣

∣

∣

∣

M=Mn

=fs2,0

fauxIo,maxtbl(1−3M2) = 0

Mn =1√3

if Mn < Mlim

Qtr,max,n =2

3√

3

fs2,0

fauxIo,maxtbl

(19)



J.nr.: SICAM.01.05.011

• locked operation

Qtr,l =fs1faux

MIo,maxtbl

dQtr,l

dM

∣

∣

∣

∣

M=Ml

= 0

Ml = Mmax

Qtr,max,l =fs1faux

MmaxIo,maxtbl

(20)

Finally, the maximum transferred charge during oneswitching period of the auxiliary converter is:

Qtr,max = maxQtr,max,n,Qtr,max,l (21)

The charge transferred to the clamp Qtr is depicted inFig. 7.

Power handled by the auxiliary converter Pcl , shown alsoin Fig. 7, is calculated as:

Pcl = VclIcl,av = Vcltbl fs22π

MIo,max (22)

and the clamp power loss is just a fraction of Pcl :

Ploss,cl = η(Pcl) ·Pcl (23)

5.1. Audio distortion

The distortion mechanism in the SICAM with active ca-pacitive voltage clamp is very similar to the one in theconventional Class D amplifiers [15]. The only differ-ence is that during the blanking time periods tbl the loadvoltage is equal to the clamp capacitor voltage Vcl andthe average voltage error ve, shown in Fig. 9 is:

ve =

−2tblVclTs2

, i0 > 0

2tblVclTs2

, i0 < 0(24)

The Fourier coefficients of the voltage error in (24) aregiven by the following equations:

a0 = 0

an = 0

bn = −2tblTs2

Vclsin(n π

2 )

n π2

= 2tblTs2

Vcl(−1)n

(2n−1) π2

(25)

2t V /Tbl cl s2

ve

-2t V /Tbl cl s2

Tm

i<0

i>0

Fig. 9: Average voltage error ve of the SICAM with ac-tive capacitive voltage clamp

and the Total Harmonic Distortion (THD) of the ”condi-tionally” open-loop SICAM power stage with active ca-pacitive voltage clamp is:

T HD =

√

Nmax

∑i=2

b2i

MVs − 4tblVclπTs2

(26)

The notion ”conditionally” means that the THD is calcu-lated for the power stage without any additional correc-tion from feedback loops, although it is obvious that theself-oscillating SICAM cannot operate without the MFB.

The presence of filter ripple current causes the THD ofthe SICAM to decrease as the output current i.e. themodulation index M decreases. This is result of the factthat within one switching period Ts2 the switch currentchanges the polarity, thus effectively cancelling the volt-age error of two subsequent load current commutationsand giving no average voltage error. Therefore, the re-duced THD of the SICAM at low modulation indexescan be taken into account the same way as in the conven-tional Class D amplifier [15]. THD of the SICAM withactive capacitive voltage clamp in ”conditionally” openloop with modulation signal of fm = 1 kHz is shown inFig. 10. THD gradually decreases with higher modu-lation indexes as the result of the falling switching fre-quency and the increased switching period Ts2, while theblanking time tbl stays essentially the same.

6. INTEGRATED MAGNETICS FOR SICAMWITH ACTIVE CLAMP

Although the proposed SICAM with active capacitivevoltage clamp has much higher efficiency due to the re-cycling of the dumped clamp energy, it is by no means



J.nr.: SICAM.01.05.011

0 50 100 1500

2

4

6

8

10

12

14

Output power Po [W]

THD

[%]

Fig. 10: THD of SICAM with active capacitive voltageclamp

Fig. 11: Integrated magnetics

as simple and cost effective as the dissipative clamp so-lutions [4]. One way to reduce the complexity of theactive clamp and reduce component count is to intro-duce special integrated magnetics, which incorporatesthe auxiliary transformer on the same magnetic core withthe main power transformer. The principal approach isshown in Fig. 11, where the main transformer windingN2 creates flux Φ2 in the center leg and outer windings,which is independent of the flux Φ1 = Φ3 flowing en-tirely in the outer legs, caused by the magnetomotiveforces of the serially connected and identical windingsN1 and N3. In this way, the magnetic structure associatedwith the central leg and winding N2 is totally independentfrom the magnetic structure associated with the windingsN1 and N3 on the outer legs.

One particular implementation of the proposed inte-

+ -

~

~

C3

D3

D13

D11

T11

+-

~

~

AC

mains

T12 D

12

C1

C2

CF

LF

T21

T22

D21

D22

T23

T24

D23

D24

Fig. 12: Integrated magnetics for the SICAM with activeclamp

grated magnetics for the SICAM with active capacitivevoltage clamp, where the auxiliary transformer uses theouter legs, is shown in Fig. 12.

7. SIMULATION RESULTS

In order to test the feasibility of the proposed self-oscillating modulators for SICAMs, series of PSpicesimulations were performed. The simulated SICAMprototype with output power of 100W @ 8Ω fea-tures free-running input stage at fs1 = 150 kHz andsingle-ended secondary-side bidirectional bridge withfs2,0 ≈ 450 kHz. It runs a modified GLIM modulator,as shown in Fig. 3.

The simulated waveforms of the output voltage, car-rier voltage, bridge voltage and HF-link voltage of aGLIM self-oscillating SICAM are presented in Fig. 13and the FFT of the output voltage is shown in Fig. 14,with M = 0.75 and 10 kHz reference. Both the nor-mal operation mode with lower modulation indexes andthe locked operation mode with larger modulation in-dexes are clearly visible. Normal operation mode withM = 0.25 < Mlim DC reference and locked operationmode with M = 0.75 > Mlim DC reference featuringphase-shifted PWM bridge voltage are shown in Fig. 15and Fig. 16, which appear the same as in the theoreticalinvestigation.

8. CONCLUSION

This paper presented how common self-oscillating mod-ulators intended for use in Class D amplifiers can be



J.nr.: SICAM.01.05.011

Fig. 13: Output voltage, carrier voltage, bridge voltageand HF-link voltage with M = 0.75 and 10 kHz reference

Fig. 14: FFT of the output voltage with M = 0.75 and10 kHz reference

modified for implementation in direct energy conversionaudio power amplifiers i.e. SICAMs. Although the mod-ification was realized on a GLIM type self-oscillatingmodulator, results are general and widely applicable. Inprinciple, two similar self-oscillating modulators, one forthe positive polarity and one for the negative polarityof the HF-link are operating in parallel and the corre-sponding output is chosen based on the instantaneousHF-link voltage polarity. Two distinct modes of oper-ation, namely the normal variable frequency mode andthe locked constant frequency mode have been identi-fied and thoroughly analyzed. The audio distortion of theself-oscillating SICAM with an active capacitive voltageclamp for easy load current commutation has been foundto have similar form to the conventional Class D ampli-fier. Integrated magnetics has been described, which in-corporates both the main and the auxiliary transformer onthe same magnetic core. Finally, simulated waveformsof a prototype were presented and showed the viability

Fig. 15: Output voltage, carrier voltage, bridge volt-age and HF-link voltage in normal operation mode withM = 0.25 < Mlim DC reference

Fig. 16: Output voltage, carrier voltage, bridge volt-age and HF-link voltage in locked operation mode withM = 0.75 > Mlim DC reference

of the approach.

ACKNOWLEDGMENTThe SICAM project is funded under the grant of the Dan-ish Energy Authority EFP no. 1273/02-0001 and is per-formed in cooperation with Bang & Olufsen ICEpowera/s in Kgs. Lyngby, Denmark.

9. REFERENCES

[1] P. Ljusev and M. Andersen, “Approaches to build-ing single-stage ac/ac conversion switch-mode au-dio power amplifiers,” in Proc. 11th InternationalPower Electronics and Motion Control conferenceEPE-PEMC 2004, (Riga, Latvia), September 2-42004.



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[2] P. Ljusev and M. Andersen, “Switching-modeaudio power amplifiers with direct energy con-version,” in 118th AES Convention, (Barcelona,Spain), May 28-31 2005.

[3] D. Mitchell, “Dc to low frequency inverter withpulse width modulated high frequency link,” U.S.patent 4,339,791, July 1982.

[4] B. E. Attwood, L. E. Hand, and L. C. Santil-lano, “Audio amplifier with phase modulated pulsewidth modulation,” U.S. patent 4,992,751, Febru-ary 1991.

[5] K. Nielsen and L. M. Fenger, “The active pulsemodulated transducer (at) a novel audio power con-version system architecture,” in 115th Conventionof the Audio Engineering Society, AES Proceed-ings, October 10-13 2003. Preprint 5866.

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[7] P. Ljusev and M. Andersen, “Direct-conversionswitching-mode audio power amplifier with activecapacitive voltage clamp,” in 36th IEEE PowerElectronics Specialists Conference PESC 2005,(Recife, Brazil), June 12-16 2005.

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[9] S. Poulsen and M. Andersen, “Self oscillating pwmmodulators a topological comparison,” in Proc.IEEE Power Modulators conference PMC 2004,(San Francisco, USA), 2004.

[10] T. Frederiksen, H. Bengtsson, and K. Nielsen, “Anovel audio power amplifier topology with high ef-ficiency and state-of-the-art performance,” in 109thConvention of the Audio Engineering Society, AESProceedings, September 22-25 2003. Preprint5197.

[11] P. van der Hulst, A. Veltman, and R. Groenenberg,“An asynchronous switching high-end amplifier,”

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[12] S. Poulsen, Towards active transducers. PhD the-sis, Technical University of Denmark, Kgs. Lyn-gby, Denmark, July 2004.

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Self-Oscillating Modulators for Direct Energy Conversion Audio Power …kazus.ru/nuke/users_files/26112008/2356962.pdf · 2008-11-26 · Self-oscillating modulators for direct energy

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