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> APP 3977

Jan 31, 2007

Keywords: Audio, Amplifier, Audio Amplifier,
Stereo, Stereo Class D, Mono, Mono Class D, High Efficiency,
Class D, PWM, Spread Spectrum, EMI, Low EMI, Notebook,
Notebook Audio, Microsoft Vista Audio, Vista Audio, TV, FPTV,
FPD, Cellphone, MP3, PMP
Related
parts

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APPLICATION NOTE 3977

Class D Amplifiers: Fundamentals of Operation and
Recent Developments

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.

Attend
this brief webcast by Maxim on
TechOnline

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-bridge Class D amplifier. It consists of
a pulse-width modulator, two output MOSFETs, and an external
lowpass filter (LF and CF) 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 VDD and ground.
Because the output transistors switch the output to either
VDD or ground, the resulting output of a Class D
amplifier is a high-frequency square wave. The switching
frequency (fSW) for 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.

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
(VO_AVG) and current (IAVG) remain
constant during a single switching period. This assumption is
fairly accurate because fSW is much greater than
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
VL(t) is the instantaneous voltage across the
inductor using the sign convention shown in Figure
1.

Because the average current (IAVG)
flowing into the load is assumed constant over one switching
period, the inductor current at the beginning of the switching
period (TSW) must be equal to the inductor current
at the end of the switching period, as shown in Figure
3.

In mathematical terms, this means
that:

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 VL(t) waveform shown in Figure 3, it
is clear that the absolute values of the areas (AON
and AOFF) must be equal to 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 VO 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 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, En(s), is multiplied by
a highpass filter function (noise-transfer function) while the
input term, VIN(s), is multiplied by a lowpass
filter function (signal-transfer function). The noise-transfer
function's highpass filter response shapes the noise of the
Class D amplifier. If the cutoff 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.

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
VDD and ground and idles at 50% duty cycle. This
means that its output has a DC offset equal to
VDD/2. 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 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 RON and
CON. Once the delayed output of 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
(tON(MIN)), which is set by the values of
RON and CON. As shown in Figure
8, with zero input, the outputs are in phase with pulse
widths equal to tON(MIN). As the audio input
signals increase or 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 tON(MIN)
(Figure 8). This means that the average value of each 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.

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 and the human ear to recover the audio
signal. The speaker resistance
(RE) and inductance (LE) form a
1st-order lowpass 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.

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.

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.

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APP 3977: Jan 31, 2007

AN3977, AN 3977, APP3977,
Appnote3977, Appnote 3977

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