Application Report
SLOA119A – April 2006 – Revised January 2008
Class-D LC Filter Design
Yang Boon Quek
........................................................................................
HPL Audio Power Amplifiers
ABSTRACT
An LC filter is critical in helping you reduce electromagnetic radiation (EMI) of Class-D
amplifiers. In some Class-D amplifiers, you also need the LC filter to ensure high
efficiency outputs. This application report presents the implementations and theories of
LC filter design for Class-D audio amplifiers using the AD (Traditional) and BD (Filter
Free) Class-D modulation designs.
Contents
1
LC Filters Implementation
.........................................................................
2
2
Frequency Response of LC Filters
...............................................................
3
3
Types of Class-D Modulation Techniques
.......................................................
5
4
LC Output Filter for Bridged Amplifiers
..........................................................
7
5
Selecting Filter Components
.....................................................................
10
6
Conclusions
........................................................................................
13
Appendix A
Total Harmonic Distortion Plots for AD and BD Modulation
.......................
14
List of Figures
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A-1
A-2
A-3
A-4
A-5
A-6
A-7
A-8
A-9
A-10
A-11
A-12
BTL LC Filter for AD Modulation
..................................................................
2
BTL LC Filter for BD Modulation
..................................................................
2
LC Filter for Single-Ended Operation
............................................................
3
Effect of Q on Frequency Response
.............................................................
4
AD (Traditional) Modulation
.......................................................................
5
BD (Filter Free) Modulation
.......................................................................
6
LC Filter for AD Modulation
.......................................................................
7
Equivalent Circuit for AD Modulation
.............................................................
7
Recommended Low-Pass Filter for AD Modulation BTL Application
........................
8
LC Filter for BD Modulation BTL Application
....................................................
8
Equivalent Circuit for Differential Mode Analysis
...............................................
9
Equivalent Circuit for Common Mode Analysis
.................................................
9
Impedance and Frequency Responses of Butterworth Filter
................................
10
Impedance and Frequency Responses, Filter With Slight Peaking
........................
11
THD vs Frequency, BD Modulation, R
BTL
= 8
Ω
..............................................
14
THD vs Power, BD Modulation, R
BTL
= 8
Ω
...................................................
14
THD vs Frequency, BD Modulation, R
BTL
= 6
Ω
..............................................
15
THD vs Power, BD Modulation, R
BTL
= 6
Ω
...................................................
15
THD vs Frequency, BD Modulation, R
BTL
= 4
Ω
..............................................
16
THD vs Power, BD Modulation, R
BTL
= 4
Ω
...................................................
16
THD vs Frequency, AD Modulation, R
BTL
= 8
Ω
..............................................
17
THD vs Power, AD Modulation, R
BTL
= 8
Ω
...................................................
17
THD vs Frequency, AD Modulation, R
BTL
= 6
Ω
..............................................
18
THD vs Power, AD Modulation, R
BTL
= 6
Ω
...................................................
18
THD vs Frequency, AD Modulation, R
BTL
= 4
Ω
..............................................
19
THD vs Power, AD Modulation, R
BTL
= 4
Ω
...................................................
19
List of Tables
SLOA119A – April 2006 – Revised January 2008
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LC Filters Implementation
1
2
3
4
5
6
7
Recommended Butterworth LC Filter Component Values
....................................
2
BD Modulation for R
BTL
= 8
Ω
...................................................................
11
BD Modulation for R
BTL
= 6
Ω
...................................................................
11
BD Modulation for R
BTL
= 4
Ω
...................................................................
12
AD Modulation for R
BTL
= 8
Ω
...................................................................
12
AD Modulation for R
BTL
= 6
Ω
...................................................................
12
AD Modulation for R
BTL
= 4
Ω
...................................................................
12
1
LC Filters Implementation
Figure 1
shows the LC filter circuit for AD (Traditional) modulation and
Figure 2
shows the BD (Filter Free)
Class-D modulation The corresponding Butterworth LC filter recommended component values are listed in
(Table
1).
See
Section 3, Types of Class-D Modulation Techniques
for additional analysis.
V
out
+
L
BTL
C
g
C
BTL
L
BTL
C
g
R
BTL
V
out
-
L
BTL
C
g
R
BTL
V
out
+
L
BTL
C
g
V
out
-
Figure 1. BTL LC Filter for AD Modulation
Figure 2. BTL LC Filter for BD Modulation
Table 1. Recommended Butterworth LC Filter Component Values
R
load
(Ω)
8
6
4
8
6
4
f
cutoff
(kHz)
28
31
31
28
31
31
L
BTL
(µH)
33
22
15
33
22
15
C
BTL
(µF)
-
-
-
0.47
0.68
1.0
C
g
(µF)
1
1.2
1.8
0.1
0.1
0.18
Modulation
Mode
BD
BD
BD
AD
AD
AD
1.1
Terminology
AD modulation (traditional)—modulation
scheme with a differential output, where each output is 180
degrees out-of-phase and changes from ground to the supply voltage, V
CC
. Therefore, the differential
pre-filtered output varies between positive and negative V
CC
, where filtered 50 percent duty cycle yields
zero volts across the load. This class-D modulation scheme has the maximum differential voltage at 0 V
output (50-percent duty cycle). The large differential voltage causes high peak output current, which in
turn causes filter loss, thus increasing supply current and lowering efficiency. An LC filter is required with
the traditional modulation scheme so the high switching current is re-circulated in the LC filter instead of
being dissipated in the speaker.
BD modulation (filter-free)—modulation
scheme developed to greatly reduce or eliminate the output
filter. The filter-free modulation scheme minimizes switching current, which allows a speaker to be used as
the storage element in place of an LC filter and still lets the amplifier be very efficient.
2
Class-D LC Filter Design
SLOA119A – April 2006 – Revised January 2008
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Frequency Response of LC Filters
BTL (bridge-tied load)—an
output configuration for power amplifiers, used mainly in audio applications.
The load (for example, a speaker) is connected between two amplifier outputs, bridging the two output
terminals. This can double the voltage swing at the load (compared with SE amplifier operation) if the
outputs are driven in opposite phases.
EMI (electromagnetic radiation)—radiation
that is emitted by electrical circuits carrying rapidly changing
signals, such as the outputs of a class-D audio power amplifier. EMI must be below limits set by regulatory
standards such as CISPR 22 or FCC Part 15 Class B.
SE (single-ended)—
signaling that is the simplest method of transmitting electrical signals over wires.
One wire carries a varying voltage that represents the signal, while the other wire is connected to a
reference voltage, usually ground. The alternative to single-ended output configuration is the bridge-tied
load (BTL) configuration. SE signaling is less expensive to implement; however the signal cannot be
transmitted over long distances or quickly, it has poorer low-frequency response, and a smaller voltage
swing (compared to the BTL amplifier operation).
1.2
Related Documentation
Quek, Yang Boon and Belnap, Kevin. "Flat
panel audio design—where only the screen is flat, not the
audio, EMI Performance and LC Filters"
Audio Design. May, 2006.
Score, Mike. "Filter-free
design helps class-D audio amplifier implementations"
Planet Analog. August,
2004
TPA3007D1 6.5-W Mono Class-D Audio Power Amplifier
Data Sheet, TI literature number
SLOS418,
available on the TI Internet site
www.ti.com.
TPA3106D1 40-W Mono Class-D Audio Power Amplifier
Data Sheet, TI literature number
SLOS516,
available on the TI Internet site
www.ti.com.
TPA3100D2 Audio Power Amplifier EVM with LC Filter
User's Guide, TI literature number
SLOU179,
available on the TI Internet site
www.ti.com.
TPA312xD2 device family employs AD modulation:
TPA3120D2, TPA3122D2,
and
TPA3123D2
2
Frequency Response of LC Filters
An LC output filter attenuates the high-frequency switching frequency of a Class-D amplifier for
single-ended (SE) operation (Figure
3).
L
+
C
+
R
L
V
in
-
V
out
-
Figure 3. LC Filter for Single-Ended Operation
You can derive the transfer function by using a voltage divider equation in which the load impedance is a
parallel combination of R
L
and C.
This transfer function reduces to this equation.
(1)
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Frequency Response of LC Filters
We can equate
Equation 1
to the characteristic equation of a second-order network in a standard form.
(2)
where
w
o
+
1
L
C
is the cutoff frequency in radians.
Q
+
R
L
C and A
+
1
+
w
2
o
L
L C
is a constant.
At the cutoff frequency,
ω
=
ω
o
,
H jw
o
+
w
2
o
*
w
2
)
j
o
w
2
o
Q
+
|
*
j
)
w
2
o
Q|
+
Q
(3)
Q
+
1
Q
u
1
2
and experiences peaking for
2
(Figure
4).
The circuit is critically damped at
20
15
10
Q = 0.707
Underdamped - Peaking
Critically damped - Ideal
Q = 1.4
Q = 0.3
Gain (dB)
5
0
-5
-10
Over damped - High Frequency Loss
-15
-20
-25
-30
3
10
4
5
10
10
f - Frequency (Hz)
Figure 4. Effect of Q on Frequency Response
TI does not recommend using an LC filter that peaks excessively. Tests have shown that high frequency
audio signals generally sound harsh to the human ear. Additionally, high peaking may cause the amplifier
to malfunction, by triggering its over current or short circuit protection circuitry. An overdamped filter can
result in the loss of high frequency audio signals.
TI recommends you use a 2nd-order Butterworth Low-Pass filter, because of its flat pass-band and phase
response. The Butterworth filter can be designed by using
Equation 4
and
Equation 5
to determine LC
values.
1
C
+
w
o
R
L
2
(4)
L
+
R
L
w
o
2
(5)
4
Class-D LC Filter Design
SLOA119A – April 2006 – Revised January 2008
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Types of Class-D Modulation Techniques
Q
+
1
2
.
Note:
The Butterworth filters are critically damped when
3
Types of Class-D Modulation Techniques
The Class-D Modulation Technique section describes how analog signals are converted to PWM signals
to drive the MOSFETs in the H-bridge. Most Class-D amplifiers can be classified as using one of two
modulation techniques, AD (Traditional) or BD (Filter Free) modulation.
3.1
AD (Traditional) Modulation
The traditional switching technique (AD modulation) modulates the duty cycle of a rectangular waveform,
such that its average content corresponds to the input analog signal. The bridge-tied load (BTL) outputs
(Figure
5)
are the inverse of each other. AD modulation has no significant common mode content in its
output. The TPA312xD2 family employs AD modulation. All TAS modulators can be configured for AD
modulation.
Figure 5. AD (Traditional) Modulation
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