# Solution to Moore’s Law

Folks,

In a recent post, I discussed Moore’s Law. I challenged readers to solve for “a” and “b” from the equation a*2^(b*(year-1970)) from the graph in Figure 1.

Moore’s Law posits that the number of transistors doubles every two years. If so, “b” should be 0.5. It ends up that “b”, from the solution in Figure 2, is 0.4885, so a double occurs about 1/0.4885 =2.047 years, but this number is really close to two years. The solution follows:

BTW, congrats to Indium Corporation’s Dr. Huaguang Wang as he got a close solution.

Cheers,

Dr. Ron

# Checking Moore’s Law

Folks,

Moore’s Law was developed by Gordon Moore in 1965. It predicted that the number of transistors in integrate circuits would double approximately every two years. Surprisingly, it has held true up to today. Figure 1 shows some of the integrated circuit transistor counts as a function of time. The red line is a good fit.

Figure 1. A plot of transistor count in selected ICs as a function of the year.

A reasonable equation for the red line is Transistor Count = a*2^(b*(year-1970)). What should “b” be if the count doubles every two years? To the first person that can solve for “a” and “b” using the red line and the equation above, we will send a Dartmouth sweatshirt.

Cheers,

Dr. Ron

# Tin: The Foundation Metal of Soldering

Folks,

The vast majority of solders used in electronic assembly have, as their base metal, tin. There are some specialty gold solders, like gold-copper or gold-indium, indium based solders, and a few others that do not contain tin. Although these solders have important applications, the sheer volume of tin-based solders is overwhelming in comparison.

Tin was a metal known to the ancients, and it led them out of the Copper Age into the Bronze Age. Ten to twelve percent tin in copper yields bronze, which is much stronger than copper (see Figure 1) and has the added benefit of melting at about 950°C vs. copper’s 1085°C.

This difference in temperature is significant in that with primitive heating technology, 1085°C is hard to achieve. In addition, since bronze freezes at a lower temperature, it fills molds much better. This property enabled the casting of much more complex shaped objects. See Figure 2. All of these benefits resulted in a dramatically increasing demand for tin. This demand established much more sophisticated trade routes for tin and its most common ore, cassiterite; this enhanced overall trade and accelerated the spread of civilization and learning.

Back to solder. Soldering is a technology that has existed almost as long as the copper age. It is thought to have originated in Mesopotamia as long ago as 4000BC. Soldering was used for joining and making jewelry, cooking tools, and stained glass. Today, in addition to these applications, plumbing, musical instrument repair, and plated metal are common uses. However, electronics assembly is the largest user of tin-based solder by far. See Figure 3.

One of the greatest benefits of solder is its reworkability. This property enables rework of electronics assemblies, plumbing, jewelry, and musical instruments. Without the ability to rework electronics, the industry would struggle to be profitable. Another benefit, of course, is the miracle of soldering I discussed in another post.

So, the next time you stare at your smartphone, tablet, TV, etc., remember tin-based solder and soldering are fundamental to its existence.

Cheers,

Dr. Ron

# SMT Assembly is an Optimization Process

Folks,

SMT assembly is an optimization process. There is no single stencil printing process for all PWB designs. The stencil printing parameters of stencil design, squeegee speed, snap off speed, stencil wipe frequency, and solder paste for assembling all PWBs will not be the same; just as there is no single reflow oven profile for all PWBs. Fortunately, most solder paste specifications give good boundaries for all of these parameters, but typically some trial and error experiments will be needed when assembling a new PWB design that is not similar to past assemblies.

The need for optimization is most obvious when trying to minimize defects. As an example, minimizing graping is often facilitated by using a ramp to peak reflow profile. However, the ramp to peak profile may acerbate voiding. See Figure 1.

Figure 1. The ramp to peak reflow profile may minimize graping, but acerbate voiding.

Thankfully your SMT soldering materials and equipment suppliers deal with these optimization issues on a daily basis. So if you are ever stuck with some challenging SMT assembly process, contact these solder materials and equipment experts first.

Cheers,

Dr. Ron

# The Rule of 72

Four years ago, the big boss, 6′ 6″ tall, 350 pound Mac Savage, said that the goal for the sales of a new product was at least 20% growth rate per year. The team is in a room prepping for a review with Savage (sometimes called Big Mac or, in jest, “The Whopper”) when the person responsible for analyzing the data, Charlie, comments:

“Well in 2016, sales were 100K units and four years later in 2020 they are 200K. So, in four years, sales increased 100%. Therefore, the yearly increase was 100/4 or 25%. So, we beat the goal by 5. So, Big Mac should be happy,” Charlie says.

There is a murmur of agreement among the 10 or so people in the room. And a few comments like, “It’s always good when The Whopper is happy,” were quietly said.

Helen chimed in, “That’s not true; using the ‘Rule of 72,’ the growth rate is 72/4 = 18%. So, we are a bit short.”

Fred, who was always a bit annoyed at smarty-pants Helen chimed in, “I think Charlie is right, 100% growth in four years is 25% per year.”

Helen responded, “With your logic, if the growth rate was 25% after the first year, sales would be at 125%, right?”

Everyone in the room murmured in agreement.

Figure 1. The Team: Helen is to the far left. Charlie is the bald guy with the beard holding a sheet of paper. John is the chap wit his laptop open. Fred has the red shirt on and June is to the right with the long blond hair.

“But would second year sales be 150%?” Helen went on.

There was some mumbling, then John, a young new hire said, “You would add 25% of 125%. My calculator says the total would be 125% plus 31.25% equals 156.25%, not 150%.”

John, then got excited and did some more calculations, “The third year is not 175% with 25% growth per year, but 195.3%, and then the fourth year is 244.14%… much higher than 200%. The growth compounds.”

Everyone groans anticipating the disapproval of “Big Mac.”

Charlie finally asks, “is Helen’s 18% growth rate right?”

John makes a few trial and error calculations and says, “18% seems a little low; it’s more like 18.9%, but it’s not 25% or even 20%. But 18% was a pretty good first estimate.”

“The rule of 72 is an estimate, it gets more accurate around 8 years,” Helen chimed in.

“Jeepers, look at the clock, we only have 45 minutes before Mr. Savage comes to the meeting and wants our report,” June warned.

After a brief chuckle that June was the only one to call the big boss Mr. Savage, instead of Big Mac or The Whopper, the team got to work putting together Power Point slides for Charlie’s presentation. They finished with 5 minutes to spare, enough time to freshen their coffee cups or hit the restroom.

At 11AM sharp, Savage came into the room and Charlie started his presentation. Everyone was nervous about Savage’s response.

Charlie summarized that by using the Rule of 72, the growth rate was short of the 20% per year target, but was more like 72/4 or 18%. He pointed out that a more precise calculation showed that the growth rate was 18.9%.

The entire group expected that Savage was going to blow his top that the 20% target was missed. But, he calmly said, “Well, the 1.1% shortage is unfortunate, but I’m impressed that you didn’t say the growth rate was 25%. I am more impressed that that you knew to use the Rule of 72 and more so that you were able to fine-tune your work to get the more precise. Great work Charlie!”

Everyone in the room rolled their eyes, especially Helen and John. Someone from the group was about to speak up, when Charlie, red faced said, “Sir, I should point out that Helen suggested using the Rule of 72, and John did the more precise calculations.”

“Charlie, you are a good leader, giving credit where it is due. Let’s have this team develop an action plan to improve the growth rate. We should meet in a week to review your plan,” Savage said.

There was a palpable sigh of relief among the team.

Savage, ended with, “Who is this new guy John?”

John was introduced by Charlie as a recent grad of Tech.

“John, I got my MBA from Tech,” Savage said.

“John, I want you to derive The Rule of 72; it will be a good experience for you. See if you can do it without looking anything up,” Savage went on.

John was a bit shaken, but he was able to derive The Rule of 72. See his derivation below.

Cheers,

Dr. Ron

# The Miracle of Soldering

Folks,

Imagine you are Guglielmo Marconi, and you opened the first radio factory in Chelmsford England in 1912. Using Lee De Forest’s 1906 invention, the triode vacuum tube, your early radios needed a way to connect the various electronic components together. Enter soldering. Soldering is the most cost effective and reliable, some might say only, way to connect electronic components together. It has been since the birth of electronics with the radio.

It is interesting to ponder some of the effects that the radio had on civilization and society. Before the radio, most of the United States was disconnected. People in California didn’t know what was happening in New York in anything like real time. There was also no national entertainment. Following early broadcasts in the 1920s, radio was a staple of most American homes by the 1930s. Families would gather around the radio after dinner to listen to the news and comedy, drama, music, etc. This golden age of radio lasted from the 1920s through the 1950s until radio was supplanted by television. See Figure 1.

Figure 1. A young girl listens to the radio in the 1930s. It would be difficult to overstate the impact of radio…all enabled by soldering.

Electronic soldering, in a sense, is a miracle of technology. It enables connecting copper to copper at a temperature of less than 230°C. The connection is reversible, conducts electricity well, and is mechanically strong. This soldering temperature is crucial for electronics, as the printed wiring boards and component packages contain polymer materials that cannot withstand temperatures much higher than 230°C. This low soldering temperature is especially impressive when considering that to bond copper to copper without solder would require temperatures near that of the melting point of copper or 1085°C.

To work its magic, solder forms intermetallics with copper. See Figure 2. The intermetallic closest to the copper is rich in Cu3Sn, and that closest to the solder is rich in Cu6Sn5.

Figure 2. A schematic cross section of a component lead soldered to a PWB pad.

It is important that the soldering bond is reworkable. The electronics industry would have difficulty being profitable without this important feature of soldering as most assembly processes have some yield loss that requires rework.

So, the next time you use your smartphone, PC, or TV, remember it wouldn’t be possible without the miracle of soldering.

Cheers,

Dr. Ron

Figure 1 source: By Franklin D. Roosevelt Library Public Domain Photographs – This media is available in the holdings of the National Archives and Records Administration, cataloged under the National Archives Identifier (NAID) 195876., Public Domain, https://commons.wikimedia.org/w/index.php?curid=2151524

# AI and Autonomous Vehicle Challenges: Common Sense, Flexibility, Dexterity, and Situational Awareness

I have been following advances in artificial intelligence (AI) and autonomous vehicles (AV) for some time now. At first, I was a cautious; then I became a skeptic; and now I am a doubter.

AI can do some amazing things. More than 20 years ago, Deep Blue beat World grandmaster Garry Kasparov. Today, AIs can routinely beat chess grandmasters and other world experts at games like Go.

Although impressive, these accomplishments play to AI’s strengths. Any activity that can be reduced to algorithms are natural for AIs. These AI victories have created a belief by many that AIs will soon take over most jobs and eventually become our masters. Witness such motion picture franchises as The Matrix and The Terminator. Some serious intellects buy into this concern as shown in the book Our Final Invention. This book posits that AIs pose a threat to human existence. The book extrapolates the successes of AIs discussed above and predicts that AIs will eventually be many times more intelligent than humans and will somehow develop something like consciousness. Ultimately, the AIs will seek to eliminate us.

I find these concerns almost comical. AIs connected to robots can do some very impressive things. In electronic assembly, they can hand solder very effectively. Perhaps better than humans, and they don’t get tired. But, they are not flexible. If the hand soldering operation changes to a different design, the AI must be reprogrammed. Whereas a human can quickly change from design to design. Lack of flexibility is a major AI drawback.

AIs also lack common sense. As Stephen Pinker has pointed out, no AI can empty a dishwasher. This is a profoundly common sense operation for humans. Yet this task is not only beyond AIs of today, but likely will be for a long time. Even something as simple as unloading boxes from a truck is a challenge to AIs as pointed out recently in Bloomberg BusinessWeek.[i]

This lack of flexibility and common sense makes it very hard for AIs to compete against humans when multiple tasks are required.

It is also difficult for AI robots to display dexterity. They may be able to pick up a chestnut, but crush a strawberry. This task is simple for an 18-month-old human.

The promise of autonomous vehicles is also greatly exaggerated. For a few years, some self-driving cars have been able to drive 95% of the route from my house in Woodstock, VT, to Boston’s Logan airport. However, they have made little progress in negotiating country roads, detours, and routes with complex signage. In addition, AVs lack situational awareness. As an example, AVs can’t look at a group of people near a street corner and sense if they are planning to cross or not.

So, I don’t see AIs taking all of our jobs or AVs putting truck drivers out of work any time soon. But the good news is that more electronics will be needed as these technologies make their slow advancements. So I see a busy future in the electronics assembly world.

Cheers,

Dr. Ron

Folks,

Mary had worked at a small SMT “mom and pop” shop for 12 years. Business was always good and she moved up to CFO of the 60 person company. Revenue had been over \$12 million for a few years with profits north of \$1 million each year. She marveled how well Fred, the owner,  managed the small firm. As CFO, she was well aware of the strong financial strength of the company.

Mary was stunned when 18 months ago, Fred said he wanted to retire in less than two years, and he wanted her to “buy him out.” Fred was fit and spunky, but 75 years old was now in the rear view mirror.

Mary was more than stunned by the price Fred wanted; it was way, way too low. She even “complained” about this. But, Fred considered her more as a daughter and insisted on the low price. However, one of the concerns they both had was that Fred was really also the chief engineer. They had many loyal workers, as Fred paid 50% over the local rate and provided great benefits, but no one could fill in for Fred in the technical aspects of running the shop.

Fred had been trying to coach Mary for the past 18 months so that she would understand the technical aspects of SMT assembly better. Mary was a fast learner, but with only 6 months left before Fred’s retirement, they both agreed they needed to hire a chief engineer.

So, Fred developed an SMT IQ Test for the candidates. If they could not get at least 80%, they would not be considered. Fred argued that if you were really good enough, you had to know 80% of these questions. Here they are:

1. What does the “A” in SAC305 stand for?
2. The belt speed on a reflow oven is 2 cm/s. The PCB with spacing is 36 cm. What is the maximum time that the placement machines must finish placing the components on the PCB to keep up with the reflow oven?
3. In mils, what is a typical stencil thickness?
4. BTCs are one of the most common components today. A subset of BTCs is the QFN package.
• What does BTC stand for?
• What does QFN stand for?
5. What is the melting temperature of tin-lead eutectic solder?
6. In mm, what is the finest lead spacing for a PQFP?
7. Are solder pastes thixotropic or dilatant?
8. In stencil printing, what is response to pause?
9. For a circular stencil aperture for BGAs or CSPs, what is the minimum area ratio that is acceptable?
10. What are the approximate dimensions of a 0201 passive in mils?

Try the test. Stay tuned for the answers.

Cheers,

Dr. Ron

# Stencil Aperture Design for the Pin in Paste (PIP) Process

Peter writes,

Dear Dr. Ron,

I am trying to implement the Pin-in-Paste (PIP) process. The PWB is 63 mils thick, the component pin diameter is 47 mils, the PWB hole diameter is 87 mils, and the PWB pad diameter is 120 mils. I used the Indium StencilCoach software and the result said that I needed a stencil aperture with a 416 mil diameter for the 5 mil thick stencil I was using.

That stencil aperture diameter is way too big. What gives?

Best,

Peter

Dear Peter,

The issue is that your PWB hole diameter is too large. It is 40 mils greater than the component pin diameter. This situation results in a very large amount of solder required to fill the mostly empty PWB hole. See Figure 1. Since solder paste is about 50% by volume flux, quite a bit of paste is often needed to form a good solder joint.

Chatting with my friends, Jim Hall and Phil Zarrow of ITM and Jim McLenaghan of Creyr Innovation, they all recommend that the PWB hole diameter be in the range of 10 to 12 mils larger than the pin diameter. In your case, this would be a hole diameter of 58 mils (I chose 11 mils greater than the pin diameter) and a PWB pad diameter of say 80 mils. The software calculates that a stencil aperture diameter of 194 mils is required (see Figure 2). It might be better to choose a square aperture of 172 mils on a side as seen in the output below. If this size stencil aperture is still too large, solder preforms can help. I will discuss using them in a future post.

By the way, Jim McLenaghan refined some earlier work that resulted in the formula for the fillet volume used in StencilCoach. Zarrow and Hall just released a book called Troubleshooting Electronic Assembly: Wisdom from the Board Talk Crypt. These three folks are some of the most knowledgeable people in electronics assembly today.

Cheers,

Dr. Ron

# The Area Ratio for Odd-Shaped Stencil Apertures

Joey writes:

Dear Dr. Ron,

I have a stencil aperture with an unusual shape. See Figure 1. How do I calculate the area ratio? The stencil thickness is 5 mils. The dimensions of the aperture are also in mils.

Joey,

The area ratio is simply the area of the stencil aperture opening divided by the area of the sidewalls. For common aperture geometries such as circles, squares, etc. it is easy to derive formulas. See Figure 2.

For an unusual shape like yours, it is easiest to simply calculate and divide the areas. From Figure 1, we get that area of the aperture opening as: 40*24+ the area of the two triangles. A little geometry (can you do it?) shows each triangle to have an area of 89 sq mils. So, the total area is 960 + 2*89 = 1138 sq mils. The perimeter is 40+24+16+16+28+12+16+16 = 168 mils, hence the area of the sidewalls is 168*5 = 840 sq mils. Therefore, the area ratio is 1138/840 = 1.355. Experience has shown that an area ratio of > 0.66 is needed for good solder paste transfer efficiency, so this stencil aperture will do well for transfer efficiency.

Careful thought would suggest that the triangular protrusions alone do not have a good area ratio. Calculations show their area ratios to be 0.37. So, the transfer efficiency in this part of the aperture might not be good. However, the area of the rectangle is so great, more than five times that of the triangles, as to alleviate this concern.

Dr. Ron