Class D audio amplifier with Ferroxcube gapped toroid output filter

Application Note

The concept of a Class D amplifier hasbeen around for a long time, howeveronly fairly recently have they becomecommonly used in consumer applica-tions. Due to improvements in thespeed, power capacity and efficiency ofmodern semiconductor devices, appli-cations using Class D amplifiers havebecome affordable for the commonperson.The mainly benefit of this kindof amplifier is the efficiency, the theo-retical maximum efficiency of a class Ddesign is 100%, and over 90% isachieve in practice.

Other benefits of these amplifiers arethe reduction in consumption, theirsmaller size and the lower weight.Their advantages are obvious in lowpower battery operated personalaudio players and laptop computer.However they are also progressivelydisplacing more traditional lineardesigns in mainstream applicationssuch as home entertainment systems,automotive sound systems, and pro-fessional installations where high qual-ity audio is important.

Audio Amplifiers

An electronic amplifier is a device forincreasing the current, voltage orpower of a signal. It does this, by tak-ing power from a power supply andcontrolling the output to match the

input signal shape but with largeramplitude. And audio amplifier is spe-cially design for reproducing audio fre-quencies.

Amplifier circuits are classified as A, B,AB and C for analog designs, and classD and E for switching devices. For theanalog classes, each type defines whichproportion of the input signal cycle isused to switch on the amplifying device:

Class A 100%Class AB Between 50% and 100%Class B 50%Class C less than 50%

The letter D used to designate the classD amplifier, is simply the next letterafter the C, and does not stand for dig-ital. Class D and E are sometimes mis-takenly defined as digital because theoutput waveform superficially resem-bles a pulse train of digital symbols.

Class D amplifiers

A class D amplifier is basically aswitching amplifier or pulse widthmodulator (PWM from now on)amplifier. In this kind of amplifier allpower devices are operated in on/offmode, reducing the power losses inthe output devices significantly.

Class D amplifiers can be categorisedinto two topologies; half bridge and full

Class D audio amplifier with Ferroxcube gapped toroid output filter

bridge configuration. Each topologyhas pros and cons. In brief, a half bridgeis potentially simpler, while a full bridgeis better in audio performance.The fullbridge topology requires two half-bridge amplifiers, and thus more com-ponents.

A Class D amplifier works in the sameway as a PWM power supply, exceptthat the reference signal is the audiowave instead of the accurate voltagereference.

Let’s start with an assumption that theinput signal is a standard audio line levelsignal.This audio line level signal is sinu-soidal with a frequency ranging from 20Hz to 20Khz. This signal is comparedwith a high frequency triangle or saw-tooth waveform to create the PWMsignal.The input signal is converted to asequence of pulses whose averagedvalue is directly proportional to theamplitude of the signal at that time.Thefrequency of the pulses is typically tenor more times the highest frequency ofinterest in the input signal.

This PWM signal is then used to drivethe power stage, creating the amplifieddigital signal, and finally a low pass filteris applied to the signal to filter out thePWM carrier frequency and retrievethe sinusoidal audio signal. The result-ing filtered signal is then an amplifiedreplica of the input.

CLASS D Audio PowerAmplifier with GAPPEDFERRITES

One of the most important parts in aclass D, audio power amplifier is theoutput filter.The overall efficiency, reli-ability and audio performance dependson it. A reference circuit has beenmodified in order to substitute aninductor by a gapped ferrite.This com-ponent is designed to behave with thesame performance as the first one.

Output Filter Design

The overall efficiency, reliability andaudio performance depend on thequality and linearity of the output fil-ter.The main goal of the output filter isattenuation of the high frequencyswitching component of the class Damplifier while preserving the signalsin the audio band.

The order of the filter determineshow many poles exist at the same fre-quency, with each order increasing theattenuation above the cut-off frequen-

Figure 1: Block diagram of a Class D audio amplifier

Figure 2: Example of the transfer function of alow pass filter over normalized frequency (f/fc).Several order filters are shown.

cy by –20dB per decade.The switchingfrequency of the amplifier can influ-ence the choice of the filter order, thehigher the fs, the lower the orderrequired to achieve a given attenua-tion within a specified passband. Thiswould seem to dictate the use of thehighest switching frequency possible.The trade-off is that increasing fsincreases the switching losses and theEMI, thus decreasing the efficiency ofthe amplifier.

0 1 100.2 0.3 0.4 0.5 0.6 0.7 0.8 2.0 3.0 4.0 5.0 6.0 7.0 8.0

A second order LC filter is the com-mon approach, as it is lossless and hasa –40dB/decade slope, allowing for areasonable rejection of the carrier ifthe parameters of the filter and theswitching frequency itself are properlydesigned.

The first thing to do is to design thetransfer function for the filter. Usually,a Butterworth or similar frequencyresponse is chosen, with a cut-off fre-quency slightly above the audio band(30-60KHz). Have in mind that one ofthe design parameters is the termina-tion load, that is, the speaker imped-ance. Usually, a typical 4 or 8 ohmresistor is assumed, but that wouldproduce variations in the measuredfrequency response in presence of dif-ferent speakers.That must be compen-

sated for by means of proper feedbacknetwork design. Some manufacturerssimply leave it that way, so theresponse is strongly dependent on theload. Surely a non-desirable situation.

More information about designing theoutput filter as a function of the cut offfrequency and load impedance is pre-sented in annex 2.

The output inductor withstands thewhole output current without satura-tion, as well as keeps the energy forthe off cycle, as in any non-isolatedswitching converter (Class-D halfbridge design is in fact analogous to abuck converter, its reference voltagebeing the audio signal).

The ideal inductor (in terms of linear-ity) is an air-core one, but the size andnumber of turns required for typicalClass-D operation makes it impracti-cal, so a core has to be used in orderto reduce turns count and also pro-vide a confined magnetic field thatreduces radiated EMI. It can be useeither powder cores or ferrite cores.Ferrite cores, must have a “gap” whereenergy is stored.Wire size should alsobe carefully chosen to keep DC andAC losses low (requiring thick wire).

Figure 3: Second order low pass filter structu-re.

Figure 4: Saturation curve: ferrites have lowersaturation, but flat response, while powdercores show high saturation with a continuousslope.

Magnetic core of the output filter

The linearity of the filter versus fre-quency and output power stronglyinfluences the performance of theamplifier and quality of the audio sig-nal.Therefore, care has to be taken inorder to select the optimal magneticcore at a reasonable cost.

Iron powder cores are the cheapestsolution, but the switching frequency(several hundred kilohertz) is too highto make them suitable for this applica-tion.

Powder alloy cores are widely used,mainly because they are very popularas output chokes in DC/DC convert-ers and SMPS.The drawback is that thesaturation curve is not flat, but with aconstant slope drop.To overcome thisproblem the designer has to overspecify the product in the sense thatonly a small region of the saturationcurve is used. Losses at high frequen-cies are also a thread, implying the useof low permeability materials woundwith some 30 to 50 turns.

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Ferrite cores are the third option.They have the lowest losses at highfrequencies, and though the saturationis lower than in powder cores, thecurve is completely flat. This curveallows the designer to optimize thecore volume and gap size to therequired energy to store.The result isvery low distortion with a low turnscount (10 to 25) and, finally, at themost affordable cost.

A practical Class D audio amplifier hasbeen evaluated to measure the influ-ence of the magnetic core on the dis-tortion of the audio signal.The amplifi-er is driven by an InternationalRectifier IR2011S device, delivering upto 500 + 500 watts peak.

The reference design

The reference design is the IRAUDAMP1 from International Rec-tifier. Complete details of the amplifiercan be found at International Rectifierwebsite, in this application we willfocus on the output low pass filterdesign.

The switching frequency is 400 kHz;this frequency will be modulated bythe low frequency audio signal throughthe PWM (Pulse Width Modulator).The MOSFET’s (International RectifierIRFB23N15D) are driven by theIR2011S high speed gate driver.

In the original design, the output filterof each channel is made with an AVXcapacitor (BF074E0474J with 0.47uF)and a Micrometals inductor core(NPT0104, core T106-2). It has aninductance value of 18 µH and it iswound with 37 turns of AWG18 mag-net wire.This filter cut off frequency is50 kHz (see annex 2 for details).

In one of the channels, the originalinductor has been replaced by a FER-ROXCUBE TN26/11-3C20-A113. Ithas also an inductance of 18 uH, but itis only wound with 13 turns of thesame AWG18 wire.

Distortion and noise versus frequencyand power are the key parameters todefine the quality of an audio amplifier.The following curves compare theperformance of the amplifier on eachchannel, taking into account that the

only difference between them is themagnetic material of the inductor andthe winding count.

The measuring equipment used to testthe amplifier performance is AudioPrecision System Two.This equipmentallows easy and fast measurementsunder several conditions. It is widelyused in the audio industry. Each chan-nel has been loaded with a 5 Ohmsresistive load.

This first graph shows the total har-monic distortion and noise powerpercentage versus the output powerof the amplifier. The percentageincreases with the output power dueto longer swing over the saturationcurves (see figure 4). Here we can seethat the performance of the ferrite issimilar and slightly better under highpower conditions.

Figure 5: International Rectifier IRAUDAMP1demo board. Features 500W + 500W peakstereo power, efficiency 93% at 1 kHz and100 watts.Voltage supply ±50 Volts (allowed±25 to ±60). Compact size: 100 x 140 x 38mm.

This second graph shows the sameparameter (total harmonic distortionand noise percentage) over a frequen-

cy sweep over the audio spectrum at afixed output power (in this case 100watts). Again, the same result shows a

Figure 6:Distortion overoutput powerpercentage ver-sus outputpower comparingpowder alloy andferrite coreinductors.Amplifier input10 kHz, load: 5Ohms, voltagesupply ±50 Volts.

Figure 7:Distortion overoutput powerpercentage ver-sus frequencycomparing pow-der alloy andferrite coreinductors.Output power100 watts, load 5Ohms, voltagesupply ±50 Volts

slightly better performance of the fer-rite core over the powder core.

5Ω Loading, ±Vcc = 50V, 100W

Ferrite core design withFerroxcube gapped toroids

Ferroxcube offers a wide range ofstandard gapped toroids fitting in thisapplication. The procedure shownbelow is intended to help the designengineer to choose the optimal (andtherefore the most cost effective)product size and gap. It is important tonote that custom cores and gap sizesare availble upon request.

The procedure starts with 2 basicparameters: the inductance of the out-put filter (see annex to calculate thevalue out of the cut off frequency andload impedance) and the maximumcurrent that will flow through theinductor (derived from the maximumpower of the amplifier).

These parameters will be used to cal-culate the energy stored in the induc-tor:

E = L x I2, where L is the induc-tance in µH, I is the maximum cur-rent in Amperes, and E is energy in µJ

The next parameter to be taken intoaccount is the size of the core in com-bination with the amount of energy tobe stored in the inductor. In most ofthe cases the size of the core is limit-ed by the board layout and mechanicalconstraints, so the designer has to

optimize the core to work in the sat-uration limit.The following graphs helpto choose the right core able to standthe power. For each core size it isplotted the amount of energy capableto be stored and the maximum AL fac-tor of the core. In annex 1 plots forevery standard size can be found.Note that it is possible to make cus-tom sizes and custom AL factors uponrequest.After the selection of the core sizeand AL factor, the next step is to cal-culate the winding. The number ofturns is derived from the next rela-tion:

where L is the inductance in µH andAL is in nH/T2, and N is the number ofturns.

The wire gauge is fixed by the maxi-mum DC resistance allowed for theinductor as well as by the current den-sity that the wire can handle. DCresistance can be estimated with thefollowing formula:

R = (1+OD-ID+2xH)xRLxN,where R is the DC resistance of theinductor in mOhm, OD, ID and H arethe outer, inner diameter and heightof the core in mm, RL is the resist-ance per meter of the selected wiregauge and N is the number of turns.

N = L x 1000AL

Annex 1: I2L curves forFerroxcube gappedtoroids

The following graphs show the energystorage capability of standard Ferroxcubegapped toroids. There are more sizes andAL values available and custom productscan be made upon request.

Product dimensions are described asTN (toroid coated with Nylon) 13(outer diameter) /7.5 (inner diameter)/5 (height).

Annex 2:Filter design basics

The most common and recommend-able output filter is a simple secondorder Butterworth filter.They count aminimum number of components andshow optimal flatness response whilekeeping a sharp cut off frequency.

The transfer function for a secondorder Butterworth filter has to followthis equation:

The cut off frequency for this filter islocated at w0=1 rad/sec, so we shouldscale it by wc=2pfc, being fc thedesired cut off frequency:

The basic construction for such a filteris:

Figure 8: Second order low pass filter.

Calculating the transfer function of thecircuit in the Laplace domain:

Now calculating the L and C values:

These equations show that the induc-tor and capacitor values depend onthe loudspeaker impedance.Thereforeit is recommendable to have a switchto choose between 4 or 8 Ohms.Thismeans that the inductor should have 2windings in series, so the switch willselect the first winding for the lowinductance (and low impedance loud-speaker) or both windings for the highinductance filter.

Depending on the polarity of theamplifier voltage supply (bipolar ±Vccor simple +Vcc) the output filtershould be implemented accordingly, asshown in the following scheme:Figure 10: Double inductor filter for simple

supply.

These equations and figures derive atable with capacitance and inductancevalues for several cut off frequenciesand loudspeaker impedance values.

fc (kHz) R (Ohm) L (µH) L Half (µH) C (µF)20 4 45 23 1.4125 4 36 18 1.1330 4 30 15 0.9450 4 18 9 0.5620 8 90 45 0.7025 8 72 36 0.5630 8 60 30 0.4750 8 36 18 0.28

Figure 9: Simple filter with bipolar supply.

Figure 10: Double inductor filter for simple supply.

Core type AL (nH/T2) µeff

TN13/5-3C20-A40 40 ± 15% 90

TN13/5-3C20-A56 56 ± 15% 125

TN13/5-3C20-A67 67 ± 15% 147

TN13/5-3C20-A72 72 ± 15% 160

TN13/5-3C20-A79 79 ± 15% 173

Core type AL (nH/T2) µeff

TN20/6.4-3C20-A68 68 ± 15% 125

TN20/6.4-3C20-A81 81 ± 15% 147

TN20/6.4-3C20-A87 87 ± 15% 160

TN20/6.4-3C20-A96 96 ± 15% 173

TN20/6.4-3C20-A109 109 ± 15% 200

Core type AL (nH/T2) µeff

TN17/6.4-3C20-A52 52 ± 15% 90

TN17/6.4-3C20-A72 72 ± 15% 125

TN17/6.4-3C20-A88 88 ± 15% 147

TN17/6.4-3C20-A92 92 ± 15% 160

TN17/6.4-3C20-A104 104 ± 15% 173

Core type AL (nH/T2) µeff

TN23/7.5-3C20-A65 65 ± 15% 90

TN23/7.5-3C20-A90 90 ± 15% 125

TN23/7.5-3C20-A106 106 ± 15% 147

TN23/7.5-3C20-A115 115 ± 15% 160

TN23/7.5-3C20-A124 124 ± 15% 173

Core type AL (nH/T2) µeff

TN26/11-3C20-A113 113 ± 15% 90

TN26/11-3C20-A157 157 ± 15% 125

TN26/11-3C20-A185 185 ± 15% 147

TN26/11-3C20-A201 201 ± 15% 160

TN26/11-3C20-A217 217 ± 15% 173

Product range and specifications

The cores are coated with Polyamide11 (PA11), flame retardant in accor-dance with UL94V-2, UL file numberE45228 (M).The inner and outer diam-eters apply to the coated toroid.Contacts are applied on the edge ofthe toroid for isolation voltage test,which is also the critical point for thewinding operation.

Core type

TN13/7.5/5 13 6.6 5.4 2.46 368 30.1 12.2 1.8 1500

TN17/11/6.4 17.5 9.9 6.85 2.24 787 42.0 42 3.7 1500

TN20/10/6.4 20.6 9.2 6.85 1.43 1330 43.6 43.6 6.9 2000

TN23/14/7.5 24 13 8.1 1.69 1845 55.8 55.8 9.0 2000

TN26/15/11 26.8 13.5 11.6 0.982 3700 60.1 60.1 19 2000

Outer diameterD (mm)

Inner diameterd (mm)

Core factor(mm-1)

Effectivevolume(mm3)

Effectivelength(mm)

Effectivearea

(mm2)

Isolationvoltage

(V)

Mass (g)

Height H (mm)

Dimensions (mm) Effective parameters Other

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