How To Heatsink

[pacificblue]

After reading posts that talked about chipamps running hot being answered with: "It's probably oscillating" I have wondered many times how could that be? Can an amplifier, which is obviously working and sounding well be oscillating so strongly that it heats up significantly?

After a few threads about heatsinking during the last days, I found there may be a different reason for hot chipamps than oscillation. And while I myself have counseled other members to use the Overture Design Guide to determine their heatsinks, I am herewith warning everybody to simply take the numbers from that tool without further thought. There are two reasons for that.

• - The heatsinks derived from the Overture Design Guide or from the tables in the datasheet are absolute maximum ratings. An adequate heatsink must be significantly bigger, i. e. have a lower thermal resistance than that.
  - If you buy a heatsink, a thermal resistance is given. Yet this number may not be significant for the task at hand, because a heatsinks thermal resistance decreases with increasing temperature. The trouble with heatsinks is, there is no norm on how to measure or specify their thermal resistance. So, as long as you do not know at which temperature the thermal resistance was measured, that figure is useless.

So let me try to shed some light on heatsinking and the correct heatsink choice.

It is probably not necessary to explain, why a heatsink is needed, so I shall start with how much power a heatsink has to dissipate.
This is the power dissipation formula

Pd = Vrailtot²/(2*PI²*Rl]

followed by an example to make things more clear. If you have 24 V rails and an 8 Ohm speaker your heatsink has to dissipate

Pd = 48²/(2*PI²*8) = 14,6 W


Now there are two temperatures that are important. The IC junction temperature and the heatsink temperature. No, they are not the same.

The LM3886T with 24 V rails, 8 Ohm load and a 2 K/W heatsink may serve as example. Its thermal resistance is 1 K/W. Thermal grease and washers can be assumed as 0,2 K/W.

The heatsink's DeltaT would be

2 K/W * 14,6 W = 29,2 K

The heatsink temperature would be

Tamb + 29,2 K, e. g. 49,2 °C, if the ambient temperature is 20 °C.

The limit should be 60 °C, if you use the heatsink outside of the case. This heatsink would be fine up to an ambient temperature of 30,8 °C. Just okay for a not too hot summer day.


The IC's Delta T would be

(1 K/W + 0,2 K/W + 2 K/W) * 14,6 W = 46,72 K

The IC temperature would be

Tamb + 46,72 K, e. g. 69,72 °C, if the ambient temperature is 20 °C.

The limit is 150 °C before the SPiKe protection system starts to react. It is wise to reduce that temperature by a safety margin of 25 °C. On that conditions this heatsink would still be fine up to 78,28 °C.


Take into account that the temperature inside of a case will be higher than outside of it. So mounting the heatsink inside will allow you to use a higher heatsink temperature at the cost of having to calculate with a higher ambient temperature.

Now compare that to the recommendation from the Overture Design Guide: 6,92 K/W.

Heatsink's DeltaT 6,92 K/W * 14,6 W = 101,032 K -> 121,032 °C for 20 °C ambient temperature. Far too hot to touch.
IC's DeltaT (1 K/W + 0,2 K/W + 6,92 K/W) * 14,6 W = 118,552 K -> 138,552 K for 20 °C ambient temperature. Above 31,448 °C the SPiKe protection system will start to bother you. And there is reason to believe that it will reduce power even before that. Transients may heat the IC up to above average for short moments, tripping SPiKe to reduce power.

Now you may wonder, why I repeatedly used the term "temperature would be" before the above calculations. The reason is that a heatsink with 2 K/W at 14,6 W Pd may not exist. The following diagram from Alutronic's catalog 2008 belongs to a heatsink that is sold by an electronic dealer as 1,8 K/W with a cross section of 100 x 40 mm and 50 mm length.



You will not find the thermal resistance for 14,6 W, because the table only goes from 20 to 60 W. At 40 K it is specified with 1,81 K/W. Let us pretend the characteristic were a straight line. That is not exactly correct, but sufficiently exact for out purpose. Just to get the idea.

Thermal resistance at 20 W is 2,07 K/W.
Thermal resistance at 40 W is 1,64 K/W.
So the change in thermal resistance per W is (2,07-1,64)/(60-20) = 0,01075.
20 W - 14,6 W = 5,4 W.
So the thermal resistance of this heatsink at 14,6 W is approximately 2,07 + 5,4 * 0,01075 = ~2,13 K/W.


While you must have expected a heatsink 10 % better than needed, you actually got one that is 6,5 % worse. So instead of decreasing the calculated temperatures about 3 K as expected, they would actually be increased about 2 K. And the bigger the heatsink, the more it will deviate from the published specs, because bigger heatsinks will be measured and specified with higher Pd.

Conclusion.

• - Don't rely on the Overture Design Guide or the datasheet diagrams alone.
  - Try to find out the heatsink's thermal resistance for the actual Pd you need.
  - Don't save on heatsinks, even if you don't always run the amplifier on worst case conditions. Some day you will.

[AndrewT]

Hi,
I agree with the conclusions.
Use a heatsink about twice what National specify.

[CJ900RR]

Excellent thread. Much appreciated!

This one should be a sticky

[westers151]

Just one question, but what is PI and how did you calculate it? I've seen you refer to that variable in the other thread, but I can't find an explanation as to what it stands for, nor how to determine it.

Thanks, and excellent education.

[AndrewT]

circumference of a circle is diameter times Pi (Greek symbol)
C=3.14159*D
Pi is usually on a calculator.
Pi is sometimes in a spreadsheet as pi()

[HK26147]

I found there may be a different reason for hot chipamps than oscillation.

I very humbly submit additional reasons: The nature of the load, and the operating environment.
Confining this to audio amps - They usually are loaded with reactive circuits, not resistive loads. Reactive circuits introduce current phase shift and varying current demands with frequency. It is no secret that some amps do not operate well with some speaker loads. Owners of speakers that present a "capacitive" can have serious amp issues.

* The discussion of work of Matti Otala and the subject of EPDR ( on another forum ) between myself and an amp designer caused a large debate, which I don't want to cause here. But I feel it definitely is related to the subject at hand: Amp stability and heatsink requirements.

See:

http://stereophile.com/reference/707heavy/index.html
http://stereophile.com/reference/707heavy/index1.html
http://stereophile.com/reference/707heavy/index2.html

http://sound.westhost.com/patd.htm
http://sound.westhost.com/soa.htm

[westers151]

Oh dear - how stupid do I feel. Thanks for that.

[AndrewT]

Hi,
that Stereophile report is an eye opener.
I thought that using maximum current <=Vpk/RLoad/0.35 was a reasonable maximum that covered severe speaker loads.
There's evidence that the 0.35 could be as bad as 0.2 to 0.25 for severe reactance speakers and much worse for electrostatic speakers.

[pacificblue]

Originally posted by AndrewT
I thought that using maximum current <=Vpk/RLoad/0.35 was a reasonable maximum that covered severe speaker loads.
There's evidence that the 0.35 could be as bad as 0.2 to 0.25 for severe reactance speakers and much worse for electrostatic speakers.

Yes, I remember that our profs told us 25 years ago, 0,35 was a reasonable average number for inductive motors, but we should be aware that there could be far worse.

[HK26147]

AndrewT
Over the course of years Jon Atkinson presented his measurements of speaker systems that included impedance/phase graphs. He usually provides a synopsis of it. There is a striking relationship between reactive loads that present extreme - phase values @ low values of impedance and how severe a load it is deemed to present to an amp.
Low impedance and extreme neg shift, you need lots of current. Current equals heat. A 10 degree ( C) rise in component temp results in reduction of life by 50%.

Perhaps the biggest point of contention to some, is not If EPDR is an issue, but the degree to which it should be considered an issue.
Having owned the same amps for years and running many different loads on them you notice that the amp may run hotter on some loads, which I attribute in large part to the widely varying reactive loads, even though they maintain the same nominal impedance.
I contended that if I want to torture an amp I could place a large woofer in a tuned cab and tune it to produce a large neg phase with a low impedance at close to line frequency, and feed it a signal rich in content @ that frequency 50/60Hz. Also some amps should not be used with piezos, or at least very carefully
Some argue that this doesn't represent "reality". But since all complex waves can be assembled by individual sine waves, It then becomes a matter of how much of the wave is at those "danger frequencies".
The same large woofer in a closed box presents a very easy load with it's soft phase curve that has much less shift, and less drift from zero degrees, closer to a stable resistive load.
Ported and tuned properly the neg phase shift doesn't occur at an impedance minima.
The super long straight horns 30' + can have very little phase shift.

Syd