Air Conditioning Load of a Group of People


Quote of the Day

Concentration is my motto. First honesty, then industry, then concentration.

Andrew Carnegie

Figure 1: HVAC Load for 17 People.

Figure 1: HVAC Load for 17 People.

I was reading an article about HVAC (Heating, Ventilation, and Air Conditioning) calculations in the Journal of Light Construction that had a quote I found interesting. It said that

… 17 extra occupants added more than a half ton of cooling load.

Figure 1 shows how to prove this statement assuming that the average person burns 2000 kilocalories a day, which is probably a low number. This problem is all about unit conversion: kilocalories, BTUs, tons of cooling, etc. You might wonder why an electrical engineer would worry about these sorts of things. Unfortunately, I frequently have to specify the cooling capacity required for the electronics that I put into rooms.

Posted in Construction, General Mathematics, General Science | Leave a comment

Accelerometer Power Calculation Example


Quote of the Day

I planned on having one husband and seven children, but it turned out the other way around.

Lana Turner

Figure 1: Monolithic Accelerometer from Bosch. (Source)

Figure 1: Monolithic Accelerometer from Bosch. (Source)

I am working on a product that uses a Bosch BMA253 accelerometer as a motion sensor. This family of products has become a defacto standard for inexpensive motion detection. In this post, I will provide a simple power calculation example along with some empirical data that Bosch provided me. Normally, I would not consider a simple power calculation worth writing about, but the datasheet did not provide a worked example. I also provide an Excel workbook that parameterizes the critical variables.

Here are the critical formulas for low power mode 1. For low power mode 2, the formulas are the same with the 1 subscript changed to 2.

Eq. 1 \displaystyle {{t}_{{active}}}=\left| \begin{array}{l}{{t}_{{ut}}}+{{t}_{{w,up1}}}-0.9\text{ ms, }bw\ge 31.25\text{ Hz}\\4\cdot {{t}_{{ut}}}+{{t}_{{w,up1}}}-0.9\text{ ms, otherwise}\end{array} \right.
Eq. 2 \displaystyle {{I}_{{DDlp1}}}=\frac{{{{t}_{{sleep}}}\cdot {{I}_{{DDsum}}}+{{t}_{{active}}}\cdot {{I}_{{DD}}}}}{{{{t}_{{sleep}}}+{{t}_{{active}}}}}
Eq. 3 \displaystyle {{t}_{{ut}}}=\frac{1}{{2\cdot bw}}
Eq. 4 \displaystyle {{f}_{{Output}}}=\frac{1}{{{{t}_{{active}}}+{{t}_{{sleep}}}}}


  • bw is the bandwidth setting of the digital filter.
  • tut is the updated time for the filter output data.
  • tw,up1 is the data acquisition stabilization time.
  • tsleep is the time during which the BMA253 is put in suspend mode ("sleep").
  • tactive is the time during which the BMA253 is stabilizing and acquiring data.
  • fOutput is the output data rate from the digital filter.
  • IDD is the current draw of the BMA253 when it is performing data acquisition ("active").
  • IDDsum is the current draw of the BMA253 when it is in suspend mode ("sleeping").

Figure 2 illustrates the data acquisition timing.

Figure 2: Data Acquisition Timing.

Figure 2: Data Acquisition Timing.

I can use Equations 1-4 to generate Table 1, which assumes that

  • bw= 1000 Hz
  • tw,up1 = 1.3 ms
  • IDD = 130 μA
  • IDDsum = 2.1 μA
Table 1: Estimated and Measured BMA253 Current Draws.

Table 1: Estimated and Measured BMA253 Current Draws.

What I liked about the data I received from Bosch is that it allows me to determine the accuracy of the current draw formula relative to the measured data.

Posted in Electronics | Leave a comment

State Casualty Rates During the Vietnam War


Quote of the Day

It is foolish and wrong to mourn the men who died. Rather we should thank God such men lived.

— George S. Patton


Figure 1: Ten States with the Highest Military Death Rates During the Vietnam War.

Figure 1: Ten States with the Highest Military Death Rates During the Vietnam War. The population basis was 1975.

My first engineering manager was named Marl Godfrey. He was an excellent manager who also had keen insights into the human condition. These insights made quite an impression on my 22-year old self – I actually kept a notebook of his comments. Some of his most insightful comments were about the US military and the Vietnam War. Marl had grown up in Oklahoma and he had served in Vietnam. He once commented that Oklahoma had very aggressive draft boards, which resulted in Oklahoma having a relatively high death rate during the conflict. I was reminded of this statement when I recently reviewed my quote database. I thought that I should be able to determine how death rates varied by state during the Vietnam War, which is the subject of this post.

Figure 1 shows my results. I determined the rate based on the state populations during 1975, which was the year the war ended. Marl Godfrey was correct – Oklahoma had a very high death rate during the Vietnam War. I should mention that the rate ranking varies depending on the year from which the state population data was taken.

Figure 2 shows a graphic with all the state data plus Washington DC and the territories of Puerto Rico, Guam, and American Samoa. The range of rates is startling – Guam, in particular, paid a heavy price.

Figure 2: US Military Death Rates During Vietnam.

Figure 2: US Military Death Rates By State During Vietnam.

The US Army bore the brunt of the US deaths during the Vietnam War  (Figure 3).

Figure 3: US Military Death Percentages by Service.

Figure 3: US Military Death Percentages by Service.

For those who are interested, my Excel workbook is located here. The raw data came from this website.

Posted in History Through Spreadsheets | Leave a comment

Liberty Ship Production Data


Quote of the Day

Logistics is the ball and chain of armored warfare.

- Heinz Guderian


Figure 1: Photograph of the USS John W. Brown, one of three Liberty Ships serving as museums.

Figure 1: Photograph of the USS John W. Brown, one of two Liberty Ships serving as museums (Source).

One WW2 battle that we hear little about was fought by logisticians. Their battle was between what could be produced versus what could be delivered in time to matter.  This point was driven home to me when I heard a WW2 historian say that the US had the manufacturing capacity to produce 150K tanks, but that level of tank production would consume all the US steel and leave nothing to build the ships needed to carry the tanks to the fight.


Figure 2: Cross-Section of a Liberty Cargo Ship.

Figure 2: Cross-Section of a Liberty Cargo Ship  (Source).

WW2 logisticians needed to balance performance and quality with time to build and deliver. The Liberty Ship was a prime example of this balancing act. It was a key contributor to the timely delivery of war materials to all fronts during WW2. Figure 2 shows the basic layout of a Liberty Ship configured for carrying cargo, which was its most common configuration. These ships could carry just over 10,000 tonnes of cargo. This meant that a Liberty Ship could carry 2,840 jeeps, 440 light tanks or 260 medium tanks, or 230 million rounds of rifle ammunition (Source).

The design of the Liberty Ship was very simple, which allowed it to be built by many shipyards. Its simple design also made it easily configurable for other applications. There were three basic types: Cargo, Tanker, and Collier. However, some of these ended up configured as hospital ships, floating maintenance platforms, boxed aircraft transports (i.e., carried aircraft that were in boxes), and troopships.



I found all the data that I needed in the tables within this pdf document. I extracted the tables using the free tool called tabula. I then used the regular expression processing ability of Notepad++ to tidy up the data for processing. The actual analysis was performed using Excel, Power Query, and pivot tables. My workbook and the associated text files are in this zip files.

Summary Statistics

Table 1 shows the number of Liberty Ships built per year. As you can see, production peaked in 1943. This makes sense when you see that the US was preparing to supply its big push during 1944. Table 2 shows the number of Liberty Ships built per shipyard. There were 16 shipyards that laid keels for 2711 Liberty Ship – one ship, Louis C. Tiffany, was destroyed by fire before it was completed. Table 3 shows how the median number of days to produce a Liberty Ship varied by year. The median number of days required to product a Liberty Ship reached its minimum during the year when production peaked.

Table 1: Liberty Ships Built Per Year. Table 2: Liberty Ships By Shipyard.
Completed (Year)Number Completed
Grand Total2711
Fire During Construction1
ShipyardShips Laid
Total Number of Ships Laid (i.e. Started)2711
Permanente Metals Co Yard489
Bethlehem-Fairfield Shipyards385
California Shipbuilding Corp336
Oregon Shipbuilding Corp322
New England Shipbuilding Corp244
Todd Houston Shipbuilding Corp208
Delta Shipbuilding Co188
North Carolina Shipbuilding Co126
J A Jones Construction Co (Panama City)102
Southeastern Shipbuilding Corp88
J A Jones Construction Co (Brunswick)85
St Johns River Shipbuilding Co82
Alabama Dry Dock Co20
Marinship Corp15
Walsh-Kaiser Co11
Kaiser Co10
Table 3: Median Days to Completion from Laying.
Laid_Down (Year) Median Days to Completion


There was nothing pretty about a Liberty Ship – FDR called it "a dreadful-looking object." It provided sealift when needed to support the major campaigns of 1944 and 1945. It certainly had issues. It was vulnerable to U-boat attack because it was underpowered and slow. Also, a major problem was discovered after three ships split in two while operating in cold water (Figure 3). 30% of the Liberty Ship fleet eventually experienced the cracking problem (Source). A pioneering female metallurgist, Constance Tipper, discovered that the steel used in the Liberty Ships became brittle below a critical temperature. A series of remedies were provided the resolved the issue for later production runs. One contributing factor to the cracking problem was the extensive use of welding in the fabrication of the Liberty Ships. ww2 shipyards had relatively little experience with welding because previous ship designs had been built using rivets – a form of fastening that is much less susceptible to cracking issues, but not applicable to modern mass-production methods. Welding and design practices were eventually developed that made welding a mainstay of the shipbuilding industry.

Figure 3: Picture of the SS Schenectady after a cracking failure.

Figure 3: Picture of the SS Schenectady after a cracking failure (Source).

Because the Liberty Ship's slow speed made it vulnerable to U-boats, the US developed the Victory Ship class that had more powerful engines and higher speed. This made it usable in high-speed convoys, which the lower speed U-boats had more difficulty engaging.

Figure 4 shows my summary of Victory Ship production during WW2. Here is my Victory Ship workbook for those who are interested. There were five wartime Victory Ship variants:

  • VC2-S-AP2: 6,000 SHP steam turbine engine
  • VC2-S-AP3: 8,500 SHP steam turbine engine
  • VC2-M-AP4: single ship, MS Emory Victory, 5,850 SHP diesel engine
  • VC2-S-AP5: Haskell-class attack transport
  • VC2-S-A2: single ship, SS Sea Marlin, built to US Army requirements

This data ignores three Victory Ships made post-war by Alcoa in 1947.

Figure 4: Summary of Victory Ship Data.

Figure 4: Summary of Victory Ship Data.

Posted in Excel, History Through Spreadsheets, Naval History | 1 Comment

Shotgun Bore Diameter Math


Quote of the Day

A successful person finds right places for himself. But a successful leader finds the right place for others.

— John C. Maxwell


Figure 1: Relative Bore Diameters of Shotgun Gauges.

Figure 1: Relative Bore Diameters of Shotgun Gauges. (Source)

I have been doing some metalwork lately that involves using units of "gauge". You will find the term gauge used in the measurement of wire, metal thickness, and pipe bore diameter. This quaint, but confusing, measurement system is slowly falling out of favor (example, sheet metal thickness gauge).

One area where I do not see gauge measurements going away is in the specification of shotgun bore diameters. I was talking to friends recently about their recent hunting adventures, and the subject of shotgun gauges came up. During this conversation, I mentioned that in my youth I hunted using my grandfather's 10 gauge shotgun  – he called it his "goose gun". I was surprised to hear that some folks consider the 10 gauge shotgun obsolete (example). Their arguments were based on old 10 gauge guns only supporting limited chamber pressures compared to newer 12 gauge shotguns.

As we talked, I realized that I did not know how to convert between shotgun gauge and bore diameter. This post examines the derivation of a formula that relates shotgun gauge to bore diameter.


The Wikipedia defines shotgun gauge as

An n-gauge diameter means that a ball of lead (density 11.34 g/cm3 or 0.4097 lb/in3) with that diameter has a mass equal to 1/n part of the mass of the international avoirdupois pound (approx. 454 grams), that is, that n such lead balls could be cast from a pound weight of lead.

This means that a 10 gauge shotgun bore has the same diameter as a 1/10 pound ball of lead. The gauge number and the bore diameter are related by Equation 1.

Eq. 1 \displaystyle {{d}_{G}}\left( {{{n}_{{Gauge}}}} \right)=\frac{{1.67049}}{{n_{{Gauge}}^{{\frac{1}{3}}}}}\cdot \text{in}


  • dG is bore diameter of a shotgun of gauge nGauge
  • nGauge is gauge of the shotgun in question.

Using Mathcad, we can derive Equation 1 as follows.

Figure 2: Derivation of Equation 1.

Figure 2: Derivation of Equation 1.

Example Calculations

We can use Equation 1 to compute some common shotgun bore diameters. I will also compare my computed diameters with the diameters listed on a popular website. I will also compute the equivalent gauge of a 410 caliber shotgun.

Figure 3: Simple Calculation Examples Using Equation 1.

Figure 3: Simple Calculation Examples Using Equation 1.

Hunting Website 410 Caliber in Gauge
Posted in Metrology | 3 Comments

Thanks Team


Quote of the Day

Thoroughly conscious ignorance is the prelude to every real advance in science.

James Clerk Maxwell

Figure 1: A Gift From A Very Fine Engineer. Thanks Becky.

Figure 1: A Gift From A Very Fine Engineer. Thanks, Becky.

I have now started on my next employment adventure. I can only say thanks to the wonderful team of people that I leave behind. They created the products that allowed the Fiber-To-The-Home (FTTTH) market to flourish. Tens of millions of FTTH products are now manufactured every year by companies around the world. These products are amazing in that for very low-cost they can contain such diverse technology: high-speed digital electronics, FPGAs, RF video,  telephony, battery backup, and wireless. The team can be proud of what they have done. You succeeded where many others failed.

Figure 1 shows something that is very special to me. I have stood while working for many years on a beat-up old plastic mat that I referred to as my "anti-cynicism mat." I always told folks that while I was on this mat, there would be no cynicism. I also warned certain people that they should never stand on my mat because their feet burn would through it. On my last day, an engineer presented me with the mat shown in Figure 1. It will occupy a place of honor in my new garage/workshop, and I will cherish it.

Posted in Personal | Leave a comment

Short-Term Solution for Furnace Condensate Freezing Problem


Quote of the Day

Politicians complaining about the press are like sailors complaining about the sea.

— Winston Churchill

Figure 1: My Short-Term Solution to Stop Condensate from Freezing in My Septic System.

Figure 1: My Short-Term Solution to Stop Condensate from Freezing in My Septic System.

Minnesotans have endured a cold winter with relatively little snow, a situation that causes the ground to freeze deeper than expected. In northern Minnesota, we plan for 60 inches of frost depth, but this year the frost has gone much deeper. For those cabins with condensing furnaces, this extra frost depth has resulted in many frozen septic lines. This winter, I have frozen both my cabin and garage septic lines. The problem has been pervasive enough that the local newspapers have covered it (example).

As I have discussed in a previous post, these furnaces generate ~1 gallon of condensate for every 100,000 BTUs of propane burned. On the coldest days, my garage furnace produces 5 gallons of condensate per day, which means that I have a constant trickle of water flowing into my garage septic line. Unfortunately, this flow rate is so small that the water only slowly moves through the pipes. This slow movement of the condensate means that it can freeze, resulting in a clogged septic line.

I first tried a 1-liter condensate pump, which stores 1-liter of condensate before putting it out in a surge. The idea is that 1-liter slug of water will be less likely to freeze than a trickle. Unfortunately, a 1-liter slug of water was not large enough, and it froze in the pipe.

Figure 1 shows the approach that worked. I have the 1-liter condensate pump fill a 110-litter tub. This tub contains a sump pump that puts out a surge of about 40-liters. This surge was sufficient that it did not freeze. Both my garage and my home have the same setup. I should mention that I chose to use a vertical-float switch rather than a tethered-float switch to eliminate the possibility of the tether catching on an obstruction.

Long-term in the garage, I will pound out the concrete floor and put in a sump basket. The sump will be lower than my furnace, which will allow me to use gravity to feed the sump with condensate, eliminating the need for the 1-liter condensate pump. I will put the sump pump in the basket, which will then pump 40-liter surges into my floor drain. Unfortunately, I cannot install a sump pump in my house because its concrete floor contains in-floor heating tubes. For the house, my short-term solution is also my long-term solution.

The following video shows how to install a sump pump in a concrete floor.

Figure 2: Good Video On Installing a Sump Pump in a Concrete Floor.
Posted in Construction | Leave a comment

Number of Space Travelers


Quote of the Day

If you wanna hire great people and have them stay working for you, you have to let them make a lot of decisions and you have to be run by ideas, not hierarchy. The best ideas have to win, otherwise good people don't stay.

— Steve Jobs

Figure 1: Michio_Kaku_(Wikipedia)

Figure 1: Michio Kaku (Wikipedia)

I was watching physicist Michio Kaku on CSPAN last Sunday night talking about his new book The Future of Humanity. I like watching authors speak on CSPAN because they provide an extended interview format for authors. In this interview, the interviewer Brian Lamb mentioned a factoid as part of a question that I thought was worth investigating.

You say in your book that 544 humans who have been in space and that 18 of those have died. What do those numbers mean to you?

Table 1: Space Travelers By Country.
United States333
Soviet Union73
United Kingdom5
South Africa1
Costa Rica1
Saudi Arabia1
South Korea1
East Germany1
Grand Total558

Of course, the number of people who have been in space is changing with every flight into orbit, and this type of fact is guaranteed to be obsolete immediately after publication. I thought I would investigate the number of people who have been in space and how many have died as part of their mission. These numbers were easier to verify than I would have expected.

The Wikipedia has a page that contains a comprehensive list of the people who have been in space. Using Power Query, I downloaded this list, did some routine data clean up, and generated the data summary shown in Table 1. As of this date, 558 people have gone into space. You can see that the US has put the most people into space, which is most likely because the space shuttle could carry more people than the Soyuz spacecraft.

The Wikipedia also has a page with a list of those who have died on space missions, not all of which reached space. As with Table 1, I downloaded the data, cleaned it up, and generated Tables 2 and 3. Table 2 contains the name of those who died going on space missions, and Table 3 shows the number of space fatalities by vehicle. For those who are interested, my Excel workbook and data are here.

As an aside, I watched a TV show years ago that was hosted by Dr. Kaku in which he was the guest of a US Army unit. The US Army drafted Dr. Kaku during the Vietnam War, which ended before he completed his infantry training. During his stay with this unit, he demonstrated some physics while wearing a US Army uniform. You could tell that both Dr. Kaku and the soldiers enjoyed his visit. He seems like a good man.

Table 2: Space Fatalities. Table 3: Space Fatalities By Vehicle.
Vladimir KomarovSoyuz 1
Georgy DobrovolskySoyuz 11
Viktor PatsayevSoyuz 11
Vladislav VolkovSoyuz 11
Christa McAuliffeChallenger
Dick ScobeeChallenger
Ellison OnizukaChallenger
Gregory JarvisChallenger
Judith ResnikChallenger
Michael J. SmithChallenger
Ronald McNairChallenger
David M. BrownColumbia
Ilan RamonColumbia
Laurel ClarkColumbia
Kalpana ChawlaColumbia
Michael P. AndersonColumbia
Rick D. HusbandColumbia
William C. McCoolColumbia
Soyuz 11
Soyuz 113
Shuttle Challenger7
Shuttle Columbia7
Grand Total18
Posted in Space | Leave a comment

Colonoscopy Notes


Quote of the Day

So, in the face of overwhelming odds, I'm left with only one option: I’m going to have to science the shit out of this.

— Mark Watney, The Martian. I love this quote.

Figure 1: Appendix Opening. This is not mine. (Source)

Figure 1: Appendix Opening. This is not a photo of mine. (Source)

I had a colonoscopy yesterday, and it was a great learning experience. I am fortunate that the anesthetic they gave me had little effect, and the doctor was open to answering questions from an inquisitive patient. It probably helped that the doctor was a mechanical engineer that decided to go into medicine – we had lots to talk about. I found it funny when he mentioned that he did not like engineering work on optics – of course, much of my life has been spent designing optics. In the course of this doctors daily work, he uses optics all day long. His gear was from Olympus, some of which is manufactured in Brooklyn Park, Minnesota, which is near my home. Minnesota is known for its medical technology.

Here are the notes I took on the procedure.

  • What is the basic colon inspection procedure

    The doctor told me that they put the probe in all the way to the appendix without really doing any observations. The colon sort of hugs the probe and you cannot see much. Once the probe gets to the appendix, they inflate the colon with CO2 and do their inspection on the way out.

  • How long is the colon?

    Around four feet long – he said the length is correlated with your height. Here is a good image of the colon. You can see the appendix at the beginning of the colon.

    Figure 2: Colon Structure.

    Figure 2: Colon Structure and Endoscope Detail. (Source)

  • Why is carbon dioxide used to inflate the colon?

    While in my upper colon, the doctor told the nurse he wanted to use CO2 to inflate that section. I asked the doctor why CO2 instead of air. He said that CO2 is absorbed by the colon into the bloodstream very quickly and you just breath it out. Air is not so quickly absorbed and, if used, would leave you feeling bloated after the procedure.

  • Has the doctor ever seen an infected appendix?

    He said that he has seen two during his years of practice (I would put the doctor in his late 40s). He said that an infected appendix is no issue as long as it can drain into the colon. An infected appendix will eventually heal as long as it can drain. You get into trouble when an infected appendix cannot drain and it ruptures.

  • I was floored at how much the technology has improved since my last colonoscopy.

    My last colonoscopy was 9 years ago. The screen images back then were low resolution and black and white. These were high-res and in color. The level of detail was amazing. He controlled how the probe moved using a hand control that reminded me of the old hand controls used for remote manipulators.

  • I have seen two types of polyp removal.

    Nine years ago, I had a mushroom-room shaped polyp and it was removed with a lasso-type instrument that both cut and cauterized the polyp. The doctor extracted the polyp, put it into a bag, and sent it for tests (no issue). I had three very small polyps this time. A very small pliers-like instrument was inserted and he just grabbed the polyps, twisted them to remove them, bagged them, and sent them in for tests.

  • Do people ever come in that were not "cleaned out"?

    I was told it happens all the time. They have to go back home and take more laxatives. They colon has to be cleaned out for the doctors to do their work. Personally, I cannot imagine someone following the procedure and not being cleaned out.

Posted in General Science | 3 Comments

Estimating Component Junction Temperature Using Psi-JT


Quote of the Day

Unfortunately, although the electrical and thermal differential equations are analogous, it is erroneous to conclude that there is any practical analogy between electrical and thermal resistance. This is because a material that is considered an insulator in electrical terms is about 20 orders of magnitude less conductive than a material that is considered a conductor, while, in thermal terms, the difference between an 'insulator' and a 'conductor' is only about three orders of magnitude. The entire range of thermal conductivity is then equivalent to the difference in electrical conductivity of high-doped and low-doped silicon.

Clemens J. M. Lasance, Thermal Engineer for Philips. As an electrical engineer, I use lumped parameter models with confidence because I know that my insulators really insulate. The thermal engineer does not have that luxury.


Figure 1: ADN4612 Pin Diagram.

Figure 1: ADN4612 Pin Diagram. (Source)

An engineer stopped by my cube today and asked a question about how to estimate the junction temperature of a part on a circuit card that may have an over-temperature problem. Using the common thermal resistancesJA and θJC), he was obtaining nonsensical results. This problem was a good illustration of the difficulties present in estimating Integrated Circuit (IC) junction temperatures using the commonly supplied thermal resistances.

I will show how I went about estimating the junction temperature of this device and why the methods usually used can provide unrealistic results. My results are estimates, but show that the junction temperature of the ADN4612 is significantly lower than its maximum rating and does not warrant any further analysis. If it were close, I would bring in a mechanical engineer to perform a more detailed thermal analysis.


Problem Statement

With respect to ADN4612's junction temperature in this application, the following characteristics are relevant :

      • power dissipation: PD = 3.5W
      • top of case temperature: TTop = 105°C (measured with thermocouple)
      • via temperature under part: TPCB = 82°C (measured with thermocouple by a via under the part)
    • package: 88-pin Lead Frame Chip Scale Package (LFCSP )
    • junction-to-ambient thermal resistance: θJA = 24°C/W
    • junction-to-case thermal resistance: θJC = 1.7°C/W
    • maximum allowed junction temperature: TMax = 125°C/W

Issues Using Common Thermal Resistances

IC specifications commonly give two thermal resistances, θJA and θJC. These specifications are useful, but frequently misused. The key to their proper use is to understand how they are measured. θJA is measured on a standard PCB as defined by JEDEC JESD51-2. Since every circuit board design is different, θJA is only useful for comparing the relative thermal performance of different packages. It is not useful for predicting component temperatures on a specific PCB and environment that are different from the test configuration.

θJC is measured in a special jig that forces all the heat through some area on the IC's case. For most ICs, the heat is forced through the top of the case. This makes sense if you are going to put a heat sink on the part and your plan is for most of the heat to go out the top. In the case of the ADN4612, it has a copper slug on the bottom of the part. θJC for the ADN4612 is measured by forcing all the heat through the bottom of the part and into the PCB. Again, this situation is not what actually occurs – the part will dissipate heat into the environment through multiple paths (bottom, top, leads).

Ideally, we would thermal models that provided use thermal resistances for all the possible paths for heat to leave a part. These models, called compact thermal models, do exist, but most vendors do not supply all the required parameters (e.g., Figure 2).

Figure 2: Example of a Compact Thermal Model for an IC (also known as Delphi model). (Source)

Figure 2: Example of a Compact Thermal Model for an IC (also known as Delphi model). (Source)

While compact thermal models for every part would be great, most ICs are not going to have temperature issues. An electrical engineer wants a rough estimate of the junction temperature to determine if he needs to bring in a mechanical engineer for a more detailed analysis of a specific part. For this approximate type of work, I prefer to use Psi-JT (ΨJT). This parameter is NOT a thermal resistance and is referred to as a thermal characteristic. It also is defined in JESD51-2. The standard allows for making a simple linear estimate of a part's junction temperature in a typical application using Equation 1.

Eq. 1 \displaystyle {{T}_{J}}={{T}_{{Top}}}+{{\Psi }_{{JT}}}\cdot {{P}_{D}}


  • TJ is the IC junction temperature.
  • TTop is the measured case temperature on the top of the part (the easiest place to get a measurement).
  • PD is the part power dissipation.
  • ΨJT is the thermal characteristic between the junction and the top of the IC case.

Unfortunately, Analog Devices did not provide ΨJT on their datasheet. This is where a bit of digging comes in …


Obtaining ΨJT

Because the datasheet did not contain ΨJT, I started using my usual search engine to do some specification hunting. It turns out that I did find a couple of references to ΨJT for similar packages:

  • an Analog Devices forum discussion on the 24-pin version of this package, which gave a 0.9°C/W for ΨJT.
  • an Analog Devices forum discussion on the 20-pin version of this package, which gives a simulated value of 0.27°C/W for ΨJT. The difference between a simulated value and measured value like this does not shock me at all.

We can also calculate an approximate ΨJT value using the method I outline on this blog post (Figure 3).

Figure: 3: ΨJT Estimate Using Approximation.

Figure: 3: ΨJT Estimate Using Approximation.

For my calculations below, I will assume the worst-case ΨJT  value I found of 0.9 °C/W.

As a cross-check, I can also make an approximation using ΨJV: junction-to-PCB via thermal characteristic, which I obtained from this chart (Figure 4).



Figure 5 shows my calculations to estimate the junction temperature for the ADN4612 using two different parameters: ΨJT and ΨJV.

Figure 5: Two Ways to Estimate Junction Temperature.

Figure 5: Two Ways to Estimate Junction Temperature.


I view my two estimates of junction temperature (108°C and 103°C) as reasonable close for this type of approximate calculation. Both methods show that the part is not operating near its junction temperature limit of 125°C, which is what I needed to know.

I do wish the semiconductor vendors would provide designers with better thermal data and models that would make applying their parts easier. I should not have to search the web and crawl around forum discussions in order to intelligently use a vendor's part.

Posted in Electronics | Leave a comment