Design Example
A few basic calculations can help to estimate a Class-D amplifier thermal load, and thus the die temperature. For example, consider using a two-channel Class-D amplifier with a full-power efficiency of 90% that drives two 4 Ω subwoofers, operating at 60 °C ambient. The supply voltage is 14 Vdc, and the thermal resistance from the packaged die to ambient air (JA) is specified at 5 °C/W. The output peak current limit occurs at I_PEAK = V_PEAK/R_LOAD = 3.5 A. This corresponds to an output peak power of P_PEAK(LOCAL) = (I_PEAK)² R_LOAD = 49 W per channel. Although the subwoofers are modeled as fixed resistors, their system impedance varies with frequency; the 4 Ω value is considered as a nominal value that is present within a narrow frequency band. The rms output power delivered to each speaker for a sinusoidal signal is then P_RMS(LOCAL) = P_PEAK(LOCAL)/2 = 24.5 W per channel. The total peak output power of both channels is then 98 W.

Efficiency for the audio amplifier can then be defined as follows:

Where P_LOAD(rms) is the average power delivered to the load, and P_DISS is the total heat dissipation from the amplifier. The value for P_DISS is then found to be:

The maximum junction temperature T_J(MAX) is a parameter that is not directly related to the amplifier performance. However, junction temperature is significant in defining heatsink size, because a higher T_J(MAX) reduces overall heatsinking requirements. The thermal power dissipation is used to calculate the junction temperature at the die, T_J, as follows:

T_J = T_A + P_DISS × _JA = 85 °C, which is well within the device’s T_J(MAX) rating of 150 °C.

When using a real audio signal, such as music, instead of a pure sinusoidal input signal, it is necessary to consider the dynamic range (the ratio of the peak-power amplitude to the average-power amplitude) of the signal. A standard method of comparing the peak to rms power values of a waveform is to use the crest factor. A typical signal for a music CD has a crest factor ranging from three to 10, and that is expressed in decibels as 10 dB to 20 dB (given that P (dB) = 20 log (V_PEAK/V_REF)), This means the peak power exceeds the true rms power by 10 dB to 20 dB. In contrast, the crest factor for a sine wave is only 3 dB, given that P (dB) = 10 log (P_PEAK/ P_RMS) = 10 log (2).

Therefore, in order for a music signal to pass the loudest portions without distortion, it requires 10 dB to 20 dB of dynamic voltage headroom compared with the average power output. When the Class-D amplifier in this example is operating from a 14 V supply, then 49 W of peak output power is available. Normalizing this peak power (which shall be called P_{PEAK(NORMALIZED 24 W)}) in comparison to the rounded-down value for P_LOCAL(rms) of 24 W, and expressing the ratio in dB is performed as follows:

Subtracting the crest factor restriction to obtain the average distortion-free average output power level yields:

and

Converting these normalized power figures back into rms output power gives:

which yields 490 mW for 20 dB of dynamic voltage headroom, or 4.9 W for 10 dB of dynamic voltage headroom. The specific values of heat dissipation for this design example and maximum junction temperatures are shown in Table 1.

Therefore, the maximum power dissipation for a typical audio CD signal without distortion happens at an average listening level of –6.9 dB. This design example clearly shows that using a sinusoidal signal as a metric for estimating output power levels in an audio amplifier leads to a considerably high power dissipation and junction temperature than a real audio signal. Therefore, it is a good practice to reserve the use of a sine wave for test purposes as a way to evaluate the thermal load that drives the amplifier into thermal shutdown. For a cost-effective design, however, power ratings for the components should be based on power levels produced with a realistic complex audio input signal.

Future Class-D Implementations
Commercially available Class-D chip designs, such as the TDA5414 from Texas Instruments, now comply with Ford Motor Company’s EMC specifications. This will allow the use of these Class-D ICs in stand-alone audio power amplifiers beginning with model year 2009. Given their many advantages, these devices will probably be used for many years to come.

About the Author
Jihad Hammoud is the senior thermal engineer at Ford Motor Co. where he is responsible for development of new thermal management techniques to support electronic systems cooling at the vehicle level. These systems include navigation radios, multimedia components, amplifiers, DVDs and entertainment systems. He has 15 years of experience in electronics cooling, and more than 15 publications on thermal management. He received a Ph.D. from the University of Akron in Ohio in 1996. Prior to that, he earned an M.S. in mechanical engineering from Youngstown State University, and a B.S. in mechanical engineering from the University of Toledo, both also in Ohio. He can be contacted at jhammou3@ford.com.