Fundamentals of Class D Amplifiers
`maximintegrated.com/en/design/technical-documents/app-notes/3/3977.html
`
`APPLICATION NOTE 3977
`
`Abstract: A Class D amplifier's high efficiency makes it ideal for portable and compact high-
`power applications. Traditional Class D amplifiers require an external lowpass filter to
`extract the audio signal from the pulse-width-modulated (PWM) output waveform. Many
`modern Class D amplifiers, however, utilize advanced modulation techniques that, in various
`applications, both eliminate the need for external filtering and reduce electromagnetic
`interference (EMI). Eliminating external filters not only reduces board-space requirements,
`but can also significantly reduce the cost of many portable/compact systems.
`
`Introduction
`Most audio system design engineers are well aware of the
`power-efficiency advantages of Class D amplifiers over linear
`audio-amplifier classes such as Class A, B, and AB. In linear
`amplifiers such as Class AB, significant amounts of power are
`lost due to biasing elements and the linear operation of the output
`transistors. Because the transistors of a Class D amplifier are
`simply used as switches to steer current through the load,
`minimal power is lost due to the output stage. Any power losses
`associated with a Class D amplifier are primarily attributed to
`output transistor on-resistances, switching losses, and quiescent
`current overhead. Most power lost in an amplifier is dissipated as
`heat. Because heatsink requirements can be greatly reduced or
`eliminated in Class D amplifiers, they are ideal for compact high-
`power applications.
`
`In the past, the power-efficiency advantage of classical PWM-
`based Class D amplifiers has been overshadowed by external
`filter component cost, EMI/EMC compliance, and poor THD+N
`performance when compared to linear amplifiers. However, most
`current-generation Class D amplifiers utilize advanced
`modulation and feedback techniques to mitigate these issues.
`
`The Basics of Class D Amplifiers
`While there are a variety of modulator topologies used in modern
`Class D amplifiers, the most basic topology utilizes pulse-width
`modulation (PWM) with a triangle-wave (or sawtooth) oscillator.
`Figure 1 shows a simplified block diagram of a PWM-based, half-
`
`1/13
`
`IPR2022-00716
`Apple EX1009 Page 1
`
`

`

`bridge Class D amplifier. It consists of a pulse-width modulator,
`two output MOSFETs, and an external lowpass filter (L and C )
`F
`F
`to recover the amplified audio signal. As shown in the figure, the
`p-channel and n-channel MOSFETs operate as current-steering
`switches by alternately connecting the output node to V and
`DD
`ground. Because the output transistors switch the output to either
`V or ground, the resulting output of a Class D amplifier is a
`DD
`high-frequency square wave. The switching frequency (f
`) for
`SW
`most Class D amplifiers is typically between 250kHz to 1.5MHz.
`The output square wave is pulse-width modulated by the input
`audio signal. PWM is accomplished by comparing the input audio
`signal to an internally generated triangle-wave (or sawtooth)
`oscillator. This type of modulation is also often referred to as
`"natural sampling" where the triangle-wave oscillator acts as the
`sampling clock. The resulting duty cycle of the square wave is
`proportional to the level of the input signal. When no input signal
`is present, the duty cycle of the output waveform is equal to 50%.
`Figure 2 illustrates the resulting PWM output waveform due to
`the varying input-signal level.
`
`
`Figure 1. This simplified functional block diagram illustrates a
`basic half-bridge Class D amplifier.
`
` Read this
`Next
`
` High-
`Efficiency
`Class D
`Audio
`Amplifiers
`Extend
`Battery Life
`in Portable
`Applications
`
` Review
`Featured
`Products
`
` MAX98358
`
` MAX98308
`
` Visit the
`Product Page
`
` Class D
`Amplifiers
`
`2/13
`
`IPR2022-00716
`Apple EX1009 Page 2
`
`

`

`
`Figure 2. The output-signal pulse widths vary proportionally with
`the input-signal magnitude.
`
`In order to extract the amplified audio signal from this PWM
`waveform, the output of the Class D amplifier is fed to a lowpass
`filter. The LC lowpass filter shown in Figure 1 acts as a passive
`integrator (assuming the cutoff frequency of the filter is at least an
`order of magnitude lower than the switching frequency of the
`output stage) whose output is equal to the average value of the
`square wave. Additionally, the lowpass filter prevents high-
`frequency switching energy from being dissipated in the resistive
`load. Assume that the filtered output voltage (V
`) and current
`O_AVG
`(I
`) remain constant during a single switching period. This
`AVG
`assumption is fairly accurate because f
` is much greater than
`SW
`the highest input audio frequency. Therefore, the relationship
`between the duty cycle and resulting filtered output voltage can
`be derived using a simple time-domain analysis of the inductor
`voltage and current.
`
`The instantaneous current flowing through the inductor is:
`
`where V (t) is the
`L
`instantaneous voltage
`across the inductor using
`the sign convention shown
`in Figure 1.
`
`) flowing into the load is
`Because the average current (I
`AVG
`assumed constant over one switching period, the inductor current
`at the beginning of the switching period (T ) must be equal to
`SW
`the inductor current at the end of the switching period, as shown
`in Figure 3.
`
`In mathematical terms, this means that:
`
`3/13
`
`IPR2022-00716
`Apple EX1009 Page 3
`
`

`

`
`Figure 3. Filter inductor
`current and voltage
`waveforms are shown for a
`basic half-bridge Class
`D amplifier.
`
`Equation 2 shows that
`the integral of the
`inductor voltage over
`one switching period
`must be equal to 0.
`Using equation 2 and
`examining the V (t)
`L
`waveform shown in
`Figure 3, it is clear that
`the absolute values of
`the areas (A and
`ON
`A
`) must be equal to
`OFF
`each other in order for
`equation 2 to be true.
`With this information,
`we can now derive an
`expression for the
`filtered output voltage
`in terms of the duty
`ratio of the switching
`waveform:
`
`Substituting equations
`4 and 5 into equation 3
`gives the new equation:
`
`Finally, solving for V
`O
`gives:
`
`where D is the duty ratio of
`the output-switching
`waveform.
`
`Using Feedback to Improve Performance
`Many Class D amplifiers utilize negative feedback from the PWM
`output back to the input of the device. A closed-loop approach
`not only improves the linearity of the device, but also allows the
`device to have power-supply rejection. This contrasts with an
`open-loop amplifier, which inherently has minimal (if any) supply
`rejection. Because the output waveform is sensed and fed back
`to the input of the amplifier in a closed-loop topology, deviations
`
`4/13
`
`IPR2022-00716
`Apple EX1009 Page 4
`
`

`

`in the supply rail are detected at the output and corrected by the
`control loop. The advantages of a closed-loop design come at the
`price of possible stability issues, as is the case with all systems
`utilizing feedback. Therefore, the control loop must be carefully
`designed and compensated to ensure stability under all operating
`conditions.
`
`Typical Class D amplifiers operate with a noise-shaping type of
`feedback loop, which greatly reduces in-band noise due to the
`nonlinearities of the pulse-width modulator, output stage, and
`supply-voltage deviations. This topology is similar to the noise
`shaping used in sigma-delta modulators. To illustrate this noise-
`shaping function, Figure 4 shows a simplified block diagram of a
`1st-order noise shaper. The feedback network typically consists
`of a resistive-divider network but, for simplicity, the example
`shown in Figure 4 uses a feedback ratio of 1. Also, the transfer
`function for the integrator has been simplified to equal 1/s
`because the gain of an ideal integrator is inversely proportional to
`frequency. It is also assumed that the PWM block has a unity-
`gain and zero-phase-shift contribution to the control loop. Using
`basic control-block analysis, the following expression can be
`derived for the output:
`
`
`Figure 4. A control loop with 1st-order noise shaping for a Class
`D amplifier pushes most noise out of band.
`
`Equation 8 shows that the noise term, E (s), is multiplied by a
`n
`highpass filter function (noise-transfer function) while the input
`term, V (s), is multiplied by a lowpass filter function (signal-
`IN
`transfer function). The noise-transfer function's highpass filter
`response shapes the noise of the Class D amplifier. If the cutoff
`
`5/13
`
`IPR2022-00716
`Apple EX1009 Page 5
`
`

`

`frequency of the output filter is selected properly, most of the
`noise is pushed out of band (Figure 4). While the preceding
`example dealt with a 1st-order noise shaper, many modern Class
`D amplifiers utilize multi-order noise-shaping topologies to further
`optimize linearity and power-supply rejection.
`
`Class-D Topologies—Half Bridge vs. Full Bridge
`Many Class D amplifiers are also implemented using a full-bridge
`output stage. A full bridge uses two half-bridge stages to drive the
`load differentially. This type of load connection is often referred to
`as a bridge-tied load (BTL). As shown in Figure 5, the full-bridge
`configuration operates by alternating the conduction path through
`the load. This allows bidirectional current to flow through the load
`without the need of a negative supply or a DC-blocking capacitor.
`
`
`Figure 5. A traditional full-bridge Class D output stage uses two
`half-bridge stages to drive the load differentially.
`
`6/13
`
`IPR2022-00716
`Apple EX1009 Page 6
`
`

`

`Figure 6 illustrates the output waveforms of traditional BTL,
`PWM-based, Class D amplifiers. In Figure 6, the output
`waveforms are complements of each other, which produce a
`differential PWM signal across the load. As with the half-bridge
`topology, an external LC filter is needed at the output to extract
`the low-frequency audio signals and prevent high-frequency
`energy from being dissipated in the load.
`
`
`Figure 6. Traditional full-bridge Class D output waveforms
`complement each other, thus creating a differential PWM signal
`across the load.
`
`A full-bridge Class D amplifier shares the same advantages of a
`Class AB BTL amplifier, but adds high power efficiency. The first
`advantage of BTL amplifiers is that they do not require DC-
`blocking capacitors on the outputs when operating from a single
`supply. The same is not true for a half-bridge amplifier as its
`output swings between V and ground and idles at 50% duty
`DD
`cycle. This means that its output has a DC offset equal to V /2.
`DD
`With a full-bridge amplifier, this offset appears on each side of the
`load, which means that zero DC current flows at the output. The
`second advantage they share is that they can achieve twice the
`output signal swing when compared to a half-bridge amplifier with
`the same supply voltage because the load is driven differentially.
`This results in a theoretical 4x increase in maximum output power
`over a half-bridge amplifier operating from the same supply.
`
`A full-bridge Class D amplifier, however, requires twice as many
`MOSFET switches as a half-bridge topology. Some consider this
`to be a disadvantage, because more switches typically mean
`more conduction and switching losses. However, this generally is
`only true with high-output power amplifiers (> 10W) due to the
`higher output currents and supply voltages involved. For this
`reason, half-bridge amplifiers are typically used for high-power
`applications for their slight efficiency advantage. Most high-power
`full-bridge amplifiers exhibit power efficiencies in the range of
`
`7/13
`
`IPR2022-00716
`Apple EX1009 Page 7
`
`

`

`80% to 88% with 8Ω loads. However, half-bridge amplifiers like
`the MAX9742 achieve power efficiencies greater than 90% while
`delivering more than 14W per channel into 8Ω.
`
`Eliminating the Output Filter—Filterless Modulation
`One of the major drawbacks of traditional Class D amplifiers has
`been the need for an external LC filter. This need not only
`increases a solution's cost and board space requirements, but
`also introduces the possibility of additional distortion due to filter
`component nonlinearities. Fortunately, many modern Class D
`amplifiers utilize advanced "filterless" modulation schemes to
`eliminate, or at least minimize, external filter requirements.
`Figure 7 shows a simplified functional diagram of the MAX9700
`filterless modulator topology. Unlike the traditional PWM BTL
`amplifier, each half bridge has its own dedicated comparator,
`which allows each output to be controlled independently. The
`modulator is driven with a differential audio signal and a high-
`frequency sawtooth waveform. When both comparator outputs
`are low, each output of the Class D amplifier is high. At the same
`time, the output of the NOR gate goes high, but is delayed by the
`RC circuit formed by R and C . Once the delayed output of
`ON
`ON
`the NOR gate exceeds a specified threshold, switches SW1 and
`SW2 close. This causes OUT+ and OUT- to go low and remain
`as such until the next sampling period begins. This scheme
`causes both outputs to be on for a minimum amount of time
`(t
`), which is set by the values of R and C . As shown
`ON(MIN)
`ON
`ON
`in Figure 8, with zero input, the outputs are in phase with pulse
`widths equal to t
`. As the audio input signals increase or
`ON(MIN)
`decrease, one comparator trips before the other. This behavior,
`along with the minimum on-time circuitry, causes one output to
`vary its pulse width while the other output pulse width remains at
`t
` (Figure 8). This means that the average value of each
`ON(MIN)
`output contains a half-wave rectified version of the output audio
`signal. Taking the difference of the average values of the outputs
`yields the complete output audio waveform.
`
`8/13
`
`IPR2022-00716
`Apple EX1009 Page 8
`
`

`

`
`Figure 7. This simplified functional diagram shows the
`MAX9700's filterless Class D modulator topography.
`
`
`Figure 8. The input and output waveforms are shown for the
`MAX9700's filterless modulator topography.
`
`Because the MAX9700's outputs idle with in-phase signals, there
`is no differential voltage applied across the load, thereby
`minimizing quiescent power consumption without the need for an
`external filter. Rather than depend on an external LC filter to
`extract the audio signal from the output, Maxim's filterless Class
`D amplifiers rely on the inherent inductance of the speaker load
`
`9/13
`
`IPR2022-00716
`Apple EX1009 Page 9
`
`

`

`and the human ear to recover the audio signal. The speaker
`resistance (R ) and inductance (L ) form a 1st-order lowpass
`E
`E
`filter which has a cutoff frequency equal to:
`
`With most speakers, this
`1st-order rolloff is enough to
`recover the audio signal and
`prevent excessive amounts
`of high-frequency switching
`energy from being dissipated in the speaker resistance. Even if
`residual switching energy results in speaker movement, these
`frequencies are inaudible to the human ear and will not adversely
`affect the listening experience. When using filterless Class D
`amplifiers, the speaker load should remain inductive at the
`amplifier's switching frequency to achieve maximum output-
`power capabilities.
`
`Minimizing EMI with Spread-Spectrum Modulation
`One disadvantage of filterless operation is the possibility of
`radiated EMI from the speaker cables. Because the Class D
`amplifier output waveforms are high-frequency square waves
`with fast-moving transition edges, the output spectrum contains a
`large amount of spectral energy at the switching frequency and
`integer multiples of the switching frequency. Without an external
`output filter located within close proximity of the device, this high-
`frequency energy can be radiated by the speaker cables.
`Maxim's filterless Class D amplifiers help mitigate possible EMI
`problems through a modulation scheme known as spread-
`spectrum modulation.
`
`Spread-spectrum modulation is accomplished by dithering or
`randomizing the switching frequency of the Class D amplifier. The
`switching frequency is typically varied up to ±10% of the nominal
`switching frequency. While the period of the switching waveform
`is varied randomly cycle-to-cycle, the duty cycle is not affected,
`thereby preserving the audio content of the switching waveform.
`Figures 9a and 9b show the wideband output spectrum of the
`MAX9700 to illustrate the effects of spread-spectrum modulation.
`Rather than having the spectral energy concentrated at the
`switching frequency and its harmonics, spread-spectrum
`modulation effectively spreads out the spectral energy of the
`output signal. In other words, the total amount of energy present
`in the output spectrum remains the same, but the total energy is
`redistributed over a wider bandwidth. This reduces the high-
`frequency energy peaks at the outputs, therefore minimizing the
`chances of EMI being radiated from the speaker cables. While it
`is possible that some spectral noise may redistribute into the
`audio band with spread-spectrum modulation, this noise is
`suppressed by the noise-shaping function of the feedback loop.
`
`10/13
`
`IPR2022-00716
`Apple EX1009 Page 10
`
`

`

`
`Figure 9a. The wideband output spectrum is shown for the
`MAX9700 using
`a fixed switching
`frequency.
`
`
`Figure 9b.
`Spread-spectrum
`modulation
`redistributes the
`spectral energy
`of the MAX9700
`over a wider
`bandwidth.
`
`Many of Maxim's
`filterless Class D
`amplifiers also
`allow the
`switching
`frequency to be
`synchronized to
`an external clock
`signal. This
`allows the user to
`manually set the
`switching
`frequency of the
`amplifier to a
`less-sensitive
`frequency range.
`
`While spread-
`spectrum
`modulation
`significantly
`improves EMI
`performance of
`filterless Class D
`amplifiers, there is typically a practical limit on the length of the
`speaker cables that can be used before the device begins to fail
`FCC or CE radiated-emissions regulations. If a device fails
`radiated-emissions tests due to long speaker cables, an external
`output filter may be needed to provide additional attenuation of
`the high-frequency components of the output waveform. In many
`applications with moderate speaker cable lengths, ferrite
`bead/capacitor filters on the outputs will suffice. EMI performance
`is also very layout sensitive, so proper PCB-layout guidelines
`should be strictly followed to guarantee compliance with
`applicable FCC and CE regulations.
`
`11/13
`
`IPR2022-00716
`Apple EX1009 Page 11
`
`

`

`Conclusion
`Recent advancements in Class D modulation techniques have
`allowed Class D amplifiers to flourish in applications where linear
`amplifiers once dominated. Modern Class D amplifiers include all
`of the advantages of Class AB amplifiers (i.e., good linearity and
`minimal board-space requirements) with the added bonus of high
`power efficiency. Currently, there are a wide variety of Class D
`amplifiers available, thus making them suitable for numerous
`applications. These applications range from low-power portable
`applications (e.g., cell phones, notebooks) in which battery life,
`board-space requirements, and EMI compliance are of utmost
`importance, to high-power applications (e.g., automotive sound
`systems or flat-panel displays) where minimizing heatsinking
`requirements and heat generation is vital. Having a fundamental
`understanding of Class D amplifiers and their recent
`technological advances will aid designers in selecting the correct
`amplifier for their application and allow them to successfully
`weigh the advantages and disadvantages of specific features.
`
`
`
`Related Parts
`
`MAX9742 Single-/Dual-Supply, Stereo 16W, Class D Amplifier with Differential
`Inputs
`
`MAX9741 12W+12W, Low-EMI, Spread-Spectrum, Stereo, Class D Amplifier
`
`MAX9714 6W, Filterless, Spread-Spectrum Mono/Stereo Class D Amplifiers
`
`MAX9713 6W, Filterless, Spread-Spectrum Mono/Stereo Class D Amplifiers
`
`MAX9709 25W/50W, Filterless, Spread-Spectrum, Stereo/Mono, Class D
`Amplifier
`
`MAX9708 20W/40W, Filterless, Spread-Spectrum, Mono/Stereo, Class D
`Amplifier
`
`MAX9704 10W Stereo/15W Mono, Filterless, Spread-Spectrum, Class D
`Amplifiers
`
`MAX9703 10W Stereo/15W Mono, Filterless, Spread-Spectrum, Class D
`Amplifiers
`
`MAX9744 20W Stereo Class D Speaker Amplifier with Volume Control
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`Free
`Sample
`
`12/13
`
`IPR2022-00716
`Apple EX1009 Page 12
`
`

`

`Related Parts
`
`MAX9715 2.8W, Low-EMI, Stereo, Filterless Class D Audio Amplifier
`
`MAX9701 1.3W, Filterless, Stereo Class D Audio Power Amplifier
`
`MAX9700 1.2W, Low-EMI, Filterless, Class D Audio Amplifier
`
`Free
`Sample
`
`Free
`Sample
`
`MAX9789 Windows Vista-Compliant, Stereo Class AB Speaker Amplifiers and
`DirectDrive Headphone Amplifiers
`
`MAX9776 2 x 1.5W, Stereo Class D Audio Subsystem with DirectDrive
`Headphone Amplifier
`
`Free
`Sample
`
`MAX9775 2 x 1.5W, Stereo Class D Audio Subsystem with DirectDrive
`Headphone Amplifier
`
`Next Steps
`
`EE-Mail
`
`Subscribe to EE-Mail and receive automatic notice of new documents in your
`areas of interest.
`
`Download Download, PDF Format
`
`© 31 Jan, 2007, Maxim Integrated Products, Inc.
`
`The content on this webpage is protected by copyright laws of the United States and of
`foreign countries. For requests to copy this content, contact us.
`
`APP 3977: 31 Jan, 2007
`
`APPLICATION NOTE 3977, AN3977, AN 3977, APP3977, Appnote3977, Appnote 3977
`
`
`
`
`13/13
`
`IPR2022-00716
`Apple EX1009 Page 13
`
`