Yannick Deplaedt

Transformation of the Japanese Board Game Market Shifting from amateurship to professionalization

Keywords: Japan, board game, doujin, amateur

The Japanese world of tabletop games is undergoing transformations that outside observers find difficult to interpret, and it is essential to intervene today, looking at it through the lens of economic development, to help decipher what this potentially large market envisions for tomorrow. The major changes currently underway in the Japanese board game industry are mainly oriented around the professionalization of publishing and authorship. After more than 10 years of experiencing success through the sourcing of Western publishers, via Japanese organizations helping them, small publishing companies and amateur designers are starting to develop ambitions that recall the changes that the European markets experienced.

Introduction

The board game market in Japan is mainly seen through a fantastical lens of Orientalism, rather than that of an understanding of its real development and distinctive cultural features.

With a large population and a public with very volatile tastes, where surprising fashions are made and unmade at the speed of light, the national board game industry seems to be struggling within Japan. Western publishers, as well as Asian countries with an increasing interest in this industry (Taiwan or South Korea to name a few), followed by local publishers, are trying to widen the audience for board games, without any real success. What are the current developments happening within Japan? Surprisingly, although there is an impressive commercial potential, an economic downturn and diminishing prospects have become the reality.

The objective of this article will be to show what changes have taken place in recent years, by what means these have been implemented, how amateur designers began to realize that making a living from their passion was an achievable goal, and how the entire market is about to move from a primarily amateur system to a more established market that tends towards globalization.

TRANSFORMATION OF THE JAPANESE BOARD GAME MARKET SHIFTING FROM AMATEURSHIP TO PROFESSIONALIZATION. 2 Foreword I have been living in Japan for the last 17 years and been interested in the Japanese board game industry -professional as well as amateur -for more than 10 years now. For the last 7 years, I have helped foreign publishers visit the Game Markets in Tokyo and Osaka by doing translation work. Since the Japanese game world is still an unknown territory for many people involved in the board game industry around the world, and one could say this is mostly the case with the playing of board games in most Asian countries, I have been trying to focus on this market to shed some light on it.

Up to today, I have been involved with Japanese board game reviews (Ludovox 1 , Tric Trac 2 ...), as well as some articles (for Plato magazine 3 ) and podcast recordings (Proxi-Jeux 4 ) about the Game Markets held in Tokyo and Osaka and the Japanese board game industry overall. Creating video reviews in English about hard-to-find board games or explaining what kind of game trends are popular here or how local publishers and designers work -all this has deeply helped me understand how this very particular industry has been growing and changing over the years.

Obviously, with several hundreds of amateur games published every year, with print runs ranging from 10 to 500 copies, it is very difficult to keep up with the entirety of the Japanese creations.

Helping western publishers navigating through the difficult language barriers of the Game Markets has also given me some precious insight on how most Japanese designers consider the design of board games as a « business » as well as a « hobby ». Among the difficulties imposed by the language, we mainly notice the very limited access to information concerning the releases and the pre-order system set up by many groups of designers as well as the direct communication with the designers.

In the recent few years, I have also decided to get more involved, and started being part of the doujin 5 scene, the amateur designers' scene, along with my daughter Lana. Being able to see the numerous hurdles along the way to go from the idea of a game to its completion as a productdevelopment, finding a theme, an illustrator, a factory, how to get a booth at the Game Market, how to promote and sell, how to decide of a price -all these steps that lead to the designers being able to bring a game to its audience. It made me realize even more how different the industry was in Japan compared to European countries or the US, to cite two strongly active areas of the board game world. The biggest difference between these markets is the process that leads a designer to a published game. It is rare today that a designer has to personally take care of the artwork for his or her game, or the communication with the factory that will manufacture it.

From amateurship…

I will first go through what we think used to be -even if this situation is still well alive as of today -the Japanese board game industry with a very amateurish way of designing, publishing and promoting local board games.

There is definitely a confusion for most foreign publishers when they first discover the local way of doing things. More often than not, foreign publishers will visit the Japanese board game events and not fully grasp why they can't get access to games, or why the designers don't seem particularly interested in having their games published abroad.

There are many reasons that explain this reality and I will explain a few, before showing how the market has shifted recently in quite an abrupt way.

One thing that amazes most people when they first set foot in a Game Market is how blurry the frontier is between publishers and designers. Designers, naturally assimilated as publishers of their own games, are generally amateurs, self-financed, giving way to only the fulfillment of their passion, driven by objectives where sales figures, percentage of copyright and publishing contracts are aspirational and little-known concepts. Since most games are self-published, with designers going from the very first step of creating a game that works (well not every time but still...) to the final product by themselves and using their own money to do so, the market seems very amateurish at first sight. And it is, but that is probably what makes it so interesting for foreign publishers and visitors. It is still common to see designers or groups of designers not understanding the approach of a foreign publisher. The notion of an extraterritorial "publication" of a game is part of a fairy-tale-like imagination for a Japanese designer. There is also the fear of being scammed, a mindset shared by many designers. The people in charge of sourcing Japanese games are often obliged to go through already-known designers who can act as a bridge to communicate with the young designers contacted. There is a benevolence of the regulars, the designers who have already had games published outside Japan, that helps reassure the newcomers.

As I have already said, most games are printed in very small numbers, often between 50 and 100 copies, sometimes less than 10. Often, games are only available in very small quantities at a fair. The number of copies produced, for the most inexperienced designers, rarely exceeds 10 to 50. It also happens regularly that these games disappear in the first minutes after the opening of the show. Reservations or pre-orders are sometimes set up a few days or weeks before the fairs, TRANSFORMATION OF THE JAPANESE BOARD GAME MARKET SHIFTING FROM AMATEURSHIP TO PROFESSIONALIZATION. 4 but for games with such limited quantities, this is a virtually impossible mission for foreign publishers, either because of language concerns or simply because of the time difference (some pre-orders are only open for a few hours). Many games are therefore like chimeras that exist on the market only for a few minutes before disappearing forever. The poetic beauty of such an approach is opposed to that of the publishers, who sometimes regret not being able to add new products to their product range -games that could nevertheless appeal to a wider audience.

Sometimes some famous local designers will be able, financially, to make more copies, but that phenomenon started only in the last few years. A lot of games that might theoretically become popular -since it's hard to get a chance to play a game before first buying it here -are difficult to find, or sold out in the first 10 to 30 minutes of the show. Which makes sourcing very difficult for publishers who have not yet been in contact with the designers.

Distribution is also something that is done by the designers themselves. Most of the time, designers will just send a few copies of their games, if they have any left after the show, to shops here and there in the country. Stores used to be mostly about selling imports, and most of the shops translate game rules in-house, creating a situation where every shop has a different translation... The market also used to be very self-centered, with Japanese designers making games for players in Japan without even thinking there was a real business side to the board game industry.

It's a passion overall, as are most doujin activities and hobbies. The word doujin is on point, since everything they do revolves around having fun and showing their own creations to a group of people that have the same hobby and background than they do.

It is also a very costly passion. Production used to be made in Japan, and the costs are very high (as an example, our 2022 game released at the Tokyo Game Market in April,ケッコーデス! Kekko desu! is made of 63 bridge size cards, a two B5 size color rulebook and a small box. We produced a hundred copies. Each copy costs 1500 yens to produce, roughly 11.5 US dollars), compared to China or Taiwan. Making just a few copies creates an even more expensive process. Some designers manage to cut costs by making the illustrations on their own, putting components in boxes by themselves as well as spending the night in karaoke places to lower the costs of their trip to Tokyo or Osaka...

The Game Markets: where everything began

The incredible growth of the Game Market is a good starting point to realize how much the situation has changed over the years. When the event was created, the people behind the event had Essen Spiel (a very important event in the international board gaming world) in mind. Of course, it was a very ambitious project, but you will see that, for the last two years, the ambition has somewhat turned into reality.

TRANSFORMATION OF THE JAPANESE BOARD GAME MARKET SHIFTING FROM AMATEURSHIP TO PROFESSIONALIZATION. 6 instead of self-published designers. It is important to note that there is yet very little documentation on the Japanese board game market. There are regularly articles written by specialized journalists, but generally, the publications concern games that have already found a publisher outside of Japan. To say it simply, these articles are mostly reviews of games that were originally released in Japan as amateur board games. Some texts are written by Japanese game designers, explaining their background and the reasons that led them to create games, but the research is still in its infancy. The use of board games in the foreign language classroom, for teaching French or English in particular, is often mentioned; but the market itself, the creation that drives it, and the economic models that sustain it are still in the shadow of academic research. Therefore, at least for the time being, I need to resort to analyses and surveys that were also born of the amateur scene.

The first image 8 below explains the different steps for a doujin designer to go from the initial idea for a game to entering the facility of the Game Market where the designer will be able to sell directly to his or her audience. It is a very simple but efficient guide for new designers, and the illustration has been shared a lot among designers.

The title of the illustration is "How to make a board game as a beginner : the road to the Game Market" From 1 to 7 : finding a game idea, test play, creating the art design, planning the production, preparing the games 8 Illustration created by なべしゃっちょカンナジャパン社長, a game designer who wanted to share his own experience creating his first game for the Tokyo Game Market.

YANNICK DEPLAEDT

7

(a lot of designers add components to the boxes by themselves to save a few hundred US dollars), having some change handy, and entering the venue right before the fair start to create a unique space to sell the game.

As a follow-up to this illustration, I have found some questions asked directly to small designers on Twitter -the most useful source for finding information about games, designers and micro publishers. The questions asked were:

1. How many copies of your game did you produce: less than 100, between 100 and 200, between 200 and 300, or more than 300? 39% of the game designers answered: less than a hundred copies. For the most popular titles, it basically means that the game will be sold out in less than an hour after the beginning of the fair.

2. The costs involved in making your games: about 1000 US dollars, between 1000 and 3000, between 3000 and 5000, or more than 5000 US dollars? The expensive cost can be explained by the fact that games are mostly made in Japan. For some of the bigger amateurs, the production is now done in Taiwan or China, to lower the cost. Unfortunately, for most small designers, it is very hard to have their games produced in these countries due to the minimum TRANSFORMATION OF THE JAPANESE BOARD GAME MARKET SHIFTING FROM AMATEURSHIP TO PROFESSIONALIZATION. 8 number of copies that need to be printed.

These amounts are very close to the numbers my daughter and I personally know, since all three of our games, produced in Japan with just 200 copies, cost us between 3000 and 4000 US dollars to produce. With such high costs to produce just a few copies of a game, most designers and small designers have to accept that they will lose money, unless they can sell all their game copies during the fair and hope for a reprint (reprinting a game is usually less expensive).

Overall, the board game industry is very minimal in terms of money involved. Compared to what the Cosplay scene is worth (406 billion yen), the numbers might look ridiculously low. It is said that the Japanese board game industry overall is worth between 400 and 500 million yen.

Compared to the video game or smart phones game industry, it is even more impressive how big the difference is.

…to professionalization

The Japanese world of tabletop games is undergoing transformations that outside observers find difficult to interpret, and it is essential to help decipher how this potentially large market is transforming. The big changes currently happening in the Japanese board game industry are mainly oriented around the professionalization of some of the board game industry's main actors.

After more than 10 years of experiencing success with the publishing of many games through western publishers, thanks to some Japanese organizations helping designers in Essen 9 or Gencon 10 (notably Japon Brand 11 , but also sourcing specialists), small publishing companies are starting to develop bigger ambitions for the near future. There is also a new audience that has started showing an interest in light fare or party games, a very different audience from the one that used to be seen walking along the Game Market's alleys.

For the past few years, the development of Board Game Cafés that also act as publishers in Japan has been impressive. It has become an essential spot to spend an afternoon or an evening with friends or for couples, and an efficient marketing device for designers and small publishers 11 Japon Brand is a non-profit organization, a collective of Japanese small (it is important to note that the term indie is also used when defining amateur board game designers in Japan) designers of board and card games. Besides handling the collective annual trip to SPIEL, Japon Brand also acts as an intermediary agent when foreign publishers want to license Japanese games without running into the language barrier. The Japon Brand booth at SPIEL every year is famous for being crowded at the opening day, as the games brought are very limited in quantity. As Japon Brand isn't a publisher per se, every year's line-up will differ, as the participating indie designers (independent producers) vary from year to year. Most of the games that Japon Brand represents are indie games in small print runs that are usually only available at the Game Market fairs in Tokyo and Osaka every year, and are thus generally hard to get, unless the games are licensed by a foreign publisher.

12 A documentary about the Board Game Cafés in Japan can be seen on the Youtube channel Archipel ((in Japanese with English subtitles): https://youtu.be/QvaIPViU-dc 13 はぁって言うゲーム, published by the book publisher Gentosha. The game was originally published by the Board Game Cafés chain Jelly Jelly Café. The principle of the game is very simple: players are given a number from 1 to 10 that corresponds to a specific feeling or emotion and must, through a different intonation and pronunciation of the same repeated words, make a player guess which number corresponds to the sound they voiced.

14 たった今考えたプロポーズの言葉を君に捧ぐよ, from the publisher CulaGula. The game consists of using the cards the players have been given to propose to a person around the table. The cards propose expressions that make up a sentence. The originality of the proposals makes the game very interesting. The theme is generally considered problematic by foreign publishers, because of the discomfort that such a playful activity could generate.

groups of people. The release of a game by an amateur designer/group of designers, if it creates enough buzz, can sometimes give access to professionalization -as was the case with the designer of the game of marriage proposals (TATTA IMA...).

What used to be a well-done mix of amateurs/doujin and professionals has turned into two different areas. It is physically obvious when we compare the previous events' map to the latest one, from November 2020. These changes have occurred in the last two years, when the show became a 2-day event with the old ambition of looking like Essen Spiel becoming somewhat of a reality.

When looking at the map for the Tokyo Game Market, it can be noticed that small designers are in the same alleys as the bigger ones. A and B booths are professionals or big booths while katakana 15 labeled booths are for amateurs. Now, instead of having well-known publishers and doujin sharing the same space, there is a clear spatial division that also clearly involves a division of audiences. Families and youngsters are mostly in the hall where professionals and big booths are, while the usual audience keeps spending most of the time at the venue in the doujin area.

15 Katakana (片仮名、カタカナ) is a Japanese syllabary, one component of the Japanese writing system along with hiragana and kanji. In contrast to the hiragana syllabary, which is used for Japanese words not covered by kanji and for grammatical inflections, the katakana syllabary is used for transcription of foreign-language words into Japanese and the writing of loan words; for emphasis; to represent onomatopoeia; for technical and scientific terms; and for names of plants, animals, minerals and often Japanese companies.

One of the most recent Tokyo Game Market maps shows two halls. Hall A is for big booths and Hall B for small designers. The small designers mostly had the impression that the audience was staying in Hall A where famous games were sold, making it very difficult for them to sell their amateur production.

Through Japon Brand's activities at the Game Markets as well as in Essen and the visit of many foreign publishers, as well as the people from Board Game Geek 16 , the biggest database about board games online, the Japanese board game world has been under the spotlight for a few years now, and consequently, many Japanese board games are being released around the world.

Many foreign games are now translated into Japanese, with a new audience in mind, an audience that won't go through the hurdles of translating the games by themselves, or play a game in a foreign language. Some big platforms, such as Kickstarter 17 , have started to aggressively try to incite a lot of designers to launch crowdfunding campaigns... The impact of Kickstarter is still to be proven here; but the partnership between a famous publisher, such as Kodansha 18 and Kickstarter leads one to think that, in the next few years, what seems to be the biggest source of revenue for the US company, board games, might influence the Japanese market 16 BoardGameGeek (BGG) is an online forum for board-game playing hobbyists and provides a game database that holds reviews, images and videos for over 125,600 different tabletop games, including European-style board games, war games, and card games. 17 Kickstarter is an American public benefit corporation based in Brooklyn, New York, that maintains a global crowdfunding platform focused on creativity. The company's stated mission is to "help bring creative projects to life". As of July 2021, Kickstarter has received nearly 6 billion US dollars in pledges from 20 million backers to fund 205,000 projects, such as films, music, stage shows, comics, journalistic works, video games, technological products, publishing, foodrelated projects, and board games.

18 Kodansha Ltd. (株式会社講談社) is a Japanese privately held publishing company headquartered in Bunkyō, Tokyo.

Kodansha is the largest Japanese publishing company, and it produces the manga magazines Nakayoshi, Afternoon, Evening, Weekly Shōnen Magazine and Bessatsu Shōnen Magazine, as well as the more literary magazines Gunzō, Shūkan Gendai, and the Japanese dictionary Nihongo Daijiten. Kodansha has been pushing Kickstarter in Japan, especially in the board game world.

TRANSFORMATION OF THE JAPANESE BOARD GAME MARKET SHIFTING FROM AMATEURSHIP TO PROFESSIONALIZATION. 12 and the way designers publish their games.

More and more publishers with international ambitions also started showing up at Game Markets. Most people who are into board games know about the Japanese publisher Oink Games19 , known for its remarkable art and unique design identity, but there are many newcomers, such as the people at Itten20 , designers of TOKYO HIGHWAY21 , Arclight Games22 , Hobby Japan23 and Sugorokuya24 , a shop/publisher that has a real impact on families playing board games.

A recent example of how Sugorokuya has been able to change in an important manner the introduction of board games in the Japanese households is a game called NANJA MONJA25 , originally a Russian game, that was seen in many popular YouTube videos in 2020 and 2021, creating an incredible enthusiasm toward it. The sales were impressive for the Japanese market, with 20,000 copies sold every month; but during the lockdowns due to the Covid-1926 , those numbers rose to 200,000 copies a month.

The Board Game Café phenomenon is also something that has changed the way Japanese youngsters see board games. With new places popping up here and there every few weeks, university students and young adults see these places as a new way of spending time for little money. The same phenomenon has occurred in South Korea a few years before Japan, and it has had a real impact on sales and the popularity of board games.

In May 2021, the number of Board Game Cafés in Japan has highly increased (up to 453 places), and more have been announced. Among them, 393 have a public list of games available. Board Game Cafés have become a new spot for young couples and groups of students. The prices are easily affordable, and students often spend the whole afternoon or evening for a fee of less than 5 US dollars. Some consequences of this new situation can already be clearly seen. The number of party games has greatly increased with the Board Game Café phenomenon: easy rules, fast gameplay, high player count. Most Board Game Cafés have a few copies of the most popular games to sell, but according to some Board Game Café owners I asked, it doesn't happen often that visitors ask whether they can purchase the games. The hourly price of a Board Game Café here being very cheap, it is much better to just come and play with some friends, especially since bringing people home to play board games is not an easy hurdle to jump over in Japan27 .

A new generation of doujin focusing on easy-to-make/-sell games with simple rules act in accordance with the Board Game Café audience. I have seen a new Doujin scene coming to the Game Markets recently. There has always been a very big fluctuation of designers, with most of them making a game or two and then disappearing forever (I have chosen this strong expression on purpose), but the number of new party game designers has really increased a lot.

There are in fact two different audiences: deeply involved players that buy many games from Japan or Japanese localizations of foreign games and newcomers that don't really think about spending money on games... Some publishers are trying to create bridges between these two audiences but that is easier said than done.

What used to be just a few games being sourced and published abroad in the early 2000s has become a plethora of new games from Japan. If you add games available through Kickstarter as well, the number of Japanese designs that hit shelves in stores around the world is now quite impressive. Japanese game designers and/or publishers now have a name that resonates with board game players deeply involved in the hobby. This result is not only due to Japon Brand's activity but also to many other people trying to bring Japanese games to other countries: agents, independent publishers, big or small, passionate players who introduce Japanese games they love to foreign companies... The number of sources to this wave of Japanese games pouring into markets all over the world is important.

The famous game designer Bruno Faidutti 28 also coined a word to define a new « type » of games: The Japanese minimalism 29 . He has seen this new phenomenon in board-game playing arise when he visited Japan and the Essen Spiel fair. Of course, every label has a lot of exceptions, and the creative Japanese board game scene also brings more complex games full of components, but the constraints of costs are still a very big part of the creation here, which explains why making small games with just a few components is the way to go for most designers.

Conclusion

The Japanese board game industry has been a unique and isolated market for a long time, but the situation is changing quickly. With Japanese games now being translated into many languages around the world, what used to be a market for connoisseurs only is now becoming a goldmine for foreign publishers. There are always a lot of newcomers introducing their first designs at the Tokyo Game Market every year, and this always renewed designer's scene is one of the reasons why it is so important to visit the fairs.

Foreign publishers still face the same difficulties, of course, with the language barrier and cultural differences, but it has become an unmissable event for many of them. The creative freedom that comes with amateurism and the absence of economic pressure or the need to make a profit allows for the creation of new and refreshing playful concepts in a globalized market that is more and more interested in discovering this new territory.

In a recent publication in the game magazine Spiel Doch! 30 , Sybille Whitehill 31 interviewed Japanese designers, publishers, reviewers as well as illustrators. She explains in her article the Japanese context and the reasons that allowed the development of this amateur scene. This article 28 Bruno Faidutti is a prolific French game designer, historian, and sociologist who frequently collaborates with other game designers, including Alan R. Moon, Bruno Cathala, and Michael Schacht, although he has also done many designs on his own, including what is perhaps his most famous game, CITADELS. 29 Article published in 2013: https://faidutti.com/blog/blog/2013/12/27/minimalisme-japonais-japanese-minimalism/ 30 Spiel Doch! is a German magazine focusing on board games. 31 Sybille Whitehill wrote an article for the Spiel Doch! magazine about the Japanese board game scene, Game-Playing in Japan. The article was published in September 2021. As a side note, Sybille was also a great help to this article. is one of the first to really take a close look at the market in its entirety and through its most important players.

The big Japanese game companies are not left behind and have understood that there is a growing audience. They have therefore launched themselves, such as Kodansha via Kickstarter, in the conquest of this new territory in the entertainment market. Among the big companies that started lurking into the board game industry, Daiso is the most famous one. Daiso is a 1-dollar store that has many stores in Japan and a few other countries. The idea behind Daiso's project of creating and publishing games just under a dollar each is to bring this hobby to most Japanese homes. People not living in Japan are often surprised at how much a board game costs here. A 20-30-euro/-dollar game will most of the time double in price in its Japanese version. The people at Daiso thought that this was a hobby too pricey to be part of a stable business that could reach a wide audience. There is a very interesting interview of the person in charge at Daiso available in Japanese online32 . What I found most interesting was that someone who never experienced playing board games saw the potential with the clientele of the store. It shows that board games are still an undiscovered territory for many people out there. Daiso is one of the most popular 1dollar stores in Japan, and they have 5500 stores in Japan and abroad. This project has just started, and it is still too soon to analyze it efficiently, but it will probably be a fascinating phenomenon to look at closer in the next few years. I wonder how publishers overseas will receive this new ambition coming from Japan. If it is a success, the current price range of board games might be in danger since the mindset of customers will change drastically.

As of now, with games that have different levels of quality, in terms of gameplay, it is a great way of bringing games to many new households, even if there is a big downside to it, since this new business plan might break the fragile doujin scene's economy.

It will be interesting to see how the Japanese board game industry will continue to develop, become more professional, and offer new things. More and more designers are making a name for themselves abroad, giving young designers the desire to follow the same path. However, there are still many obstacles, even if they tend to diminish little by little, for curious publishers coming from abroad in order to source unique games.

The game industry in numbers (in billions of yen)

  Compared to the video game industry, the analog game industry is way behind. It can also be noted that board games are, strangely enough, added to the 3-D puzzle category. Out of the 115 billion yen indicated here, the board game industry only represents 400 to 500 million.

	Video games	4369 billion
	Smartphone games	5468 billion
	Arcade games centers	4550 billion
	The toy industry in numbers (in billions of
	yens)
	Educational games/toys	1690 billion
	Hobby: toys for adults (miniatures, plastic	1383 billion
	models of famous series like Gundam…)
	Trading card games	1130 billion
	Board games, 3D puzzles…	165 billion
	Jigsaw Puzzles	115 billion

  as well12 . This new audience discovering board games has been quickly noticed by the network of Board Game Cafés, and the Board Game Cafés propose short games with easy rules that create a cheerful atmosphere around the table. This attraction for light games, generally integrated under the genre of party games, has, in turn, inspired many young designers. The Tokyo Game Market catalog, which until recently offered mainly games for experienced players, is now filled with word games, communication games, and ice-breaking experiences that allow the discovery

of others through a third-party element. Some of the best-selling games are based on riddles, or phrase-based propositions that are meant to make people laugh or create a fun atmosphere. The most relevant examples are: HAA TO IU GAME 13 and TATTA IMA KANGAETA PROPOSE NO KOTOBA WO KIMI NI SASAGU YO 14 , two games based on communication from original angles. Icebreaker games have become an essential part of the Board Game Cafés' game inventory. The games are short, fun and can be played by larger 9 Internationale Spieltage SPIEL, often called the Essen Game Fair after the city where it is held, is an annual four-day board game trade fair in October that is also open to the public. It is considered as one of the most important fairs for the board game industry worldwide. 10 Gen Con is the largest tabletop game convention in North America by both attendance and number of events. It features traditional pen-and-paper, board, and card games, including role-playing games, miniature war games, live action roleplaying games, collectible card games, and strategy games.

The 500-yen games challenge has been initiated by a group of designers in 2013 (Seiji Kanai, Hisashi Hayashi, Masato Uesugi, Susumu Kawasaki and many more). The idea was to create designs for a very cheap price but with a highly replayability value.

Micro publishers are often small groups of designers who publish their own games in very small quantities. They mostly operate as amateurs and don't have an official financial structure like established publishers do.

Oink Games is one of the most famous Japanese board game publishers. They have an office in Germany in addition to the headquarters located in Tokyo. Their unique graphic design approach has made them very popular among board gamers abroad. Two of their famous titles are DEEP SEA ADVENTURE and DUNGEON OF MANDOM.

Itten is a small game publisher who has become popular thanks to their most successful game, TOKYO HIGHWAY.

In TOKYO HIGHWAY, published in 2016, players compete to place all of their cars on the road -but to do that, they will first have to build the roadways. Over the course of the game, players construct columns of varying heights by using the 66 squat cylinders in the box, then connect those columns with sticks that serve as roadways, with the columns not necessarily being the same height when connected. If a stretch of highway is placed well, you can place one or more cars on it to score.

Arclight Games is a board game publisher founded in 1998.

Hobby Japan is a Japanese publishing company founded in 1969 known for publishing and releasing books, magazines, light novels, board games, and collectibles.

Sugorokuya is a board game shop located in Tokyo. The store is known for publishing games for the whole family. They have been involved in localizing games for the past few years, with a focus on Haba (Habermaaß GmbH is a German toy manufacturing company based in Bavaria) and family-centered games.

Toddles-Bobbles, the English title of the game, is a fun and dynamic game that develops imagination and attention. The players take turns to draw a card from the pack and reveal it. There is a picture of a Toddle-Bobble on the card. If this Toddle-Bobble appears for the first time, the player who revealed the card gives him a name. Everyone needs to remember this name. The player who remembers the name correctly and is the first to shout it out next time when the Toddle-Bobble comes up in the game, will claim all the revealed cards to his winning pile.

Tabletop games on a roll as families in Japan stay home in pandemic, by Alex K.T. Martin for the Japan Times: www.japantimes.co.jp/news/2020/08/13/business/tabletop-games-japan-coronavirus/

The average size of a Japanese house, as seen by people from other countries, is extremely small. On top of that, it is said that in the Japanese tradition, it is extremely difficult to overcome the anxiety of being judged when guests visit one's house. Nevertheless, it is common to invite children's friends over for their birthday party.

The interview (in Japanese) can be seen on the You Tube channel 深夜のジレンマラジオ (Shinya no Dilemma Radio): https://youtu.be/KJFrlcb6uVU

Attendance over the years (blue) / number of booths (red)

The first Tokyo Game Market in 2000 had just a few hundred visitors (some sources indicate 300 to 400) and a very limited number of booths (between 20 and 30) ... Less than 20 years later, the event is now a big machine with thousands of visitors (10,000 to 15,000 before Covid-19 hit Japan and imposed very strict measures to access the event in November 2020). The same goes with the number of booths, which is now close to 700. That number might actually be bigger since booths are distributed on a random basis, meaning that some designers or doujin circles tried to get a booth and did not get picked... When the Game Market had become a popular event, 2014 was a big turning point in terms of the designers, and foreign publishers also started to visit, mostly Taiwanese, Korean, French and US based publishers. The Game Markets are the most important events in the Japanese game scene in number of visitors but also as a creative bubble. Challenges -for instance, the 500-yen games 6 -gave the world some very good games, such as Seiji Kanai's LOVE LETTER, a cornerstone of the Japanese board game scene.

Here are some of the sources that allowed me to find numbers to back my analysis of the Japanese board game industry. Since it is a very amateurish scene, it is also very hard to find concrete numbers. Most sources are from designers or micro publishers 7 , as I like to call them,


Ammar Chafi

Member, IEEE Nadir Idir

Member, IEEE Arnaud Videt

Member, IEEE Hassan Maher

Design method of PCB inductors for high-frequency GaN converters

Keywords: PCB inductor, flexible magnetic sheets, optimization of volume, thermal issues, GaN converters

The new power GaN transistors allow to increase the operating frequency of converters to megahertz range, thanks to their low switching time that is of a few nanoseconds or less. This permits to reduce the values and the volume of the passive components, and enhance the power density of power converters. However, inductors needed for energy storage still take a large volume in converters compared with the others components, because of their weak energy density. Further, highfrequency operation require low-losses magnetic materials. In this paper, a design method of PCB inductors is proposed. A flexible ferrite sheet is used to enhance the inductance value and ease the realization of custom-shape devices. The design method of the inductor is based on the optimization of the inductor volume taking into account thermal issues of the magnetic sheets. Also a simulation method is proposed to calculate the equivalent stray capacitance of the inductors. The proposed method provides a losses-volume trade-off that helps designers to optimize the inductor for their application.

I. INTRODUCTION

P OWER electronics has undergone a strong progression in past decades, thanks to the development of new technologies of passive and active components needed for high frequency power converters. This allows to enhance the power density and the efficiency of power systems and reduce their cost [START_REF] Anderson | All-silicon 99.35seven-level hybrid neutral point clamped/flying capacitor inverter[END_REF], [START_REF] Schrittwieser | 99three-phase matrix-type dab buck-boost pfc rectifier[END_REF]. The increase of the switching frequency of Gallium Nitride (GaN) transistors reduces the values and the volume of the passive components, mainly inductors which take a large volume in converters. This increase in the switching frequency is mainly linked to the reduction of the switching time of the active components. Compared with other components based on Silicon (Si) and Silicon Carbide (SiC), transistors based on GaN offer a lower switching time, thanks to the high electron mobility of Gallium Nitride material, which increases the current density of GaN transistors, and reduces therefore their channel length and parasitic capacitances [START_REF] Millan | A survey of wide bandgap power semiconductor devices[END_REF], [START_REF] Ji | High-frequency high power density 3-d integrated gallium-nitride-based point of load module design[END_REF]. However, very fast switching is limited notably by parasitic inductances in the switching mesh, and is associated to possible electromagnetic compatibility (EMC) issues [START_REF] Nie | Evaluation of conducted EMI in GaN and Si based isolated converters[END_REF], [START_REF] Han | Trade-off between switching loss and common mode EMI generation of GaN devicesanalysis and solution[END_REF]. Thus, power density improvement also relies on the development of magnetic and dielectric materials A. Chafi is with University of Lille 1 and University of Sherbrooke 2 (email: ammar.chafi.etu@univ-lille.fr) N. Idir and A. Videt are with 1 Univ. Lille, Arts et Metiers Institute of Technology, Centrale Lille, Yncrea Hauts-de-France, ULR 2697 -L2EP, F-59000 Lille, France (email: nadir.idir@univ-lille.fr ; arnaud.videt@univ-lille.fr) H. Maher is with 2 Laboratoire Nanotechnologies Nanosystèmes, CNRS UMI-3463, Institut Interdisciplinaire d'Innovation Technologique, Université de Sherbrooke, Sherbrooke, QC J1K OA5, Canada (e-mail: hassan.maher@usherbrooke.ca) that enhances the energy density and the efficiency of inductors and capacitors [START_REF] Su | Design and evaluation of a highfrequency LTCC inductor substrate for a three-dimensional integrated dc/dc converter[END_REF], [START_REF] Goualard | Integrated dc-dc based-gan converter with screen printed capacitors allowing double side cooling[END_REF].

Inductors are required in converters for energy storage and filtering [START_REF] Zaidi | Optimization method of CM inductor volume taking into account the magnetic core saturation issues[END_REF], [START_REF] Cuellar | Characterization and modeling of hysteresis for magnetic materials used in EMI filters of power converters[END_REF]. They suffer from a weak energy density compared to capacitors. They are often the largest components in converters ; thus, designers must pay attention to their volume when selecting their inductance value and core shape. PCB inductors are simple to realize, low cost and allow to have planar shapes of small thickness. Several issues appear for the design of these inductors for high-frequency converters like: the choice of the appropriate magnetic material, the resonance frequency, AC copper and magnetic losses that increase with frequency, temperature rise, etc.

Magnetic material allows to improve the energy density of inductors. The Manganese-zinc (ZnMn) and Nickel-zinc (NiZn) ferrites are the most common magnetic materials used for medium and high frequency applications, thanks to their low losses and high relaxation frequency [START_REF] Rylko | Magnetic material selection for high power high frequency inductors in dcdc converters[END_REF].

The capacitive effects due to parasitic capacitance between windings reduce the operating range of inductors in high frequency. The calculation of the stray capacitances of inductors is based on analytical formulas by using some approximations [START_REF] Kovacic | Analytical wideband model of a common-mode choke[END_REF], [START_REF] Massarini | Self-capacitance of inductors[END_REF], and simulations based on finite element method [START_REF] Liu | FEM modelling of three-phase common mode choke for performance evaluation[END_REF], [START_REF] Yu | A study on stray capacitance modeling of inductors by using the finite element method[END_REF].

Losses produced by inductors represent an important part of converters losses. AC copper losses and magnetic losses become more important in high frequency. Dowell and Ferreira formulas are often used to estimate the AC resistance of inductors needed for AC copper losses calculation in low frequency [START_REF] Dowell | Effects of eddy currents in transformer windings[END_REF], [START_REF] Ferreira | Appropriate modelling of conductive losses in the design of magnetic components[END_REF]. In high frequency, the AC resistance calculation is based on simulation tools, because of the difficulty to predict the magnetic flux lines [START_REF] Pereira | Comparison between numerical and analytical methods of ac resistance evaluation for medium-frequency transformers: Validation on a prototype and thermal impact analysis[END_REF]. Magnetic losses due to hysteresis and eddy current are often calculated with Steinmetz formulas [START_REF] Steinmetz | On the law of hysteresis[END_REF], [START_REF] Liu | A method for inductor core loss estimation in power factor correction applications[END_REF]. Thermal issues of magnetic materials used for inductors are not often considered in literature [START_REF] Bakri | Planar transformer equivalent thermal resistance variation with ambient temperature and power losses[END_REF], [START_REF] Delhommais | Thermal model of litz wire toroidal inductor based on experimental measurements[END_REF].

In this paper, a two-layer PCB inductor is considered for high frequency DC-DC converter [START_REF] Dou | PCB embedded inductor for high-frequency ZVS SEPIC converter[END_REF]. The aim of this work is to propose a simple design method based on 2D finite-element method (FEM) that notably links together electromagnetic (EM) and thermal aspects, including geometric optimization as well. Various modeling methods exist, especially for toroidal and planar cores [START_REF] Li | Modeling of planar inductors with non-uniform flux distribution and non-linear permeability for high-density integration[END_REF]- [START_REF] Ropoteanu | A comparative simulation analysis of toroid and planar magnetic cores near MHz region[END_REF] but seldom for PCB-integrated inductors [START_REF] Tang | A low-profile power converter using printed-circuit board (PCB) power transformer with ferrite polymer composite[END_REF], [START_REF] Pascal | Study of a topology of low-loss magnetic component for PCB-embedding[END_REF]. While 3D FEM is usually used for non-PCB inductor design, 2D FEM is preferred in this work so as to optimize a PCB-integrated device. Since the considered geometry can be considered near-axisymmetric, 3D FEM can be avoided to save computing time. First, the structure of the PCB inductor and the chosen magnetic sheets will be presented. Second, the algorithm based on the optimization of the inductor volume is executed for many inductance values. The optimal inductance value needed for the converter is chosen from a Losses-Volume curve. The last section is dedicated to the experimental validation of the chosen PCB inductor. The inductor will be realized, characterized and tested with the GaN-based synchronous boost converter in order to evaluate its electrical and thermal characteristics. Simulation results will be compared with experimental data to validate the proposed method.

II. DESIGN METHOD OF THE PCB INDUCTOR

The PCB inductor is designed for a GaN-based synchronous boost converter with these specifications; switching frequency f = 1 MHz, power of P = 100 W, input voltage V i = 48 V and output voltage V o = 100 V. The inductor structure, the inductance value and the design method must be defined to realize the PCB inductor for converter.

A. Structure of the PCB inductor

The considered geometry of the PCB inductor is shown in Fig. 1a. The windings of spiral form are realized on the two copper layers. This structure is chosen because of the simplicity of its realization compared to toroidal PCB inductor. The advantage of the magnetic sheet is that it can be cut into various shapes of different custom dimensions for PCB inductors, so that the optimal size obtained by the design method presented in this paper can be easily realized. This is not allowed with magnetic cores that have a standardized dimensions and shapes in manufacturer catalogs. Due to the small thickness of magnetic sheets, such inductors are thin and avoid additional height taken on the PCB faces compared with toroidal cores for instance. Fig. 2 shows the complex permeability of three magnetic sheets of different manufacturers; 38M6 from Fair Rite, MHLL from Lairdtech and IFL10M from TDK. Other characteristics like saturation curve B(H) are not provided by manufacturers. The ideal case for the choice of the appropriate magnetic material is to have high initial permeability to increase the energy density of the inductor without magnetic losses that are represented by the secondary permeability µ r (f ). The 38M6 is characterized by high initial permeability of µ ri = 230 up to 5 MHz, and its losses start to increase from 2 MHz. The IFL10M initial permeability is smaller and the magnetic losses are less important compared to 38M6. The MHLL has the advantage that magnetic losses are negligible before 20 MHz. Even though permeability curves are obtained with small-signal excitation, it is assumed that the material power losses can be neglected in the inductor design due to MHLL µ (f ) remaining very small for the first ten significant switching harmonics of a 1-MHz-operated converter. The high relaxation frequency of this material is suitable for inductors designed for megahertz switching power converters. Therefore, the MHLL magnetic sheets is chosen for the realization of the PCB inductor. It should be noted that the primary application of commercially available magnetic sheets is for EM shielding rather that power electronics inductors and their operating temperature range is limited below 100 • C; however manufacturers may eventually increase this limit and provide materials more adapted to HF power electronics applications.

B. Choice of the inductance value

As given in equation 1, the inductor current ripple ∆I L of the converter shown in Fig. 3 is inversely proportional to the inductance value L for a given duty cycle D, input voltage V i , and switching frequency f .

∆I L = D × V i L × f (1)
Fig. 4 shows the evolution of the current ripple ∆I L as a function of the inductance value needed for the GaN converter. The inductor current is going negative for inductance values smaller than L = 6 µH. Inductors with small inductance values take less volume, but their AC copper losses increase with current ripple. This may cause thermal issues for magnetic sheets of the PCB inductor. So, in this study, the research for the inductance value needed for the converter is done in the interval when the inductor current is positive to reduce AC copper losses and so the temperature rise of the magnetic sheets. It is well known that the volume and DC copper losses are more important for inductors with large inductance value. Also, they suffer from a small resonance frequency that reduces its operating range in high frequency.

C. Calculation tool used for the PCB inductor design

The PCB inductor is designed for 1 MHz converter. The inductance value must be calculated at this frequency. Even though analytical calculations can be done with simple coils [START_REF] Mohan | Simple accurate expressions for planar spiral inductances[END_REF], they can hardly be applied with the magnetic sheet including large air gaps: the prediction of the magnetic flux path becomes complex especially in high frequency where skin and proximity effects change the current distribution and the magnetic flux path. In this case, FEM simulations are usually needed for magnetic devices analysis [START_REF] Reatti | Comparison of various methods for calculating the ac resistance of inductors[END_REF]. Then, FEMM simulation tool based on finite element method will be used in this work with some hypotheses to design the PCB inductor:

• The spiral form of winding are replaced by circular form in the 2D axisymmetric simulation as shown in Fig. 1b. Spiral form requires 3D simulation tools that are time consuming.

• Small signal design: saturation is not taken into account.

• Magnetic losses are neglected because the imaginary part of the complex permeability µ r of MHLL is negligible before 20 MHz. The magnetic simulation example in Fig. 5 shows how the magnetic sheet captures magnetic field lines and plays an important role on magnetic field around the copper turns, which requires FEM models for accurate analysis. Note that the 2D axisymmetric model is also simplified to a quarter section by considering plane symmetry properties in the twolayer arrangement shown in Fig. 1b.

III. DETERMINATION OF THE GEOMETRICAL PARAMETERS OF THE INDUCTOR

For each inductance value, there is 8 parameters to determine as shown in Fig. 6: the number of turns N , the inner radius r i , the spacing between tracks s, the width of tracks l, the external distance d e , the thickness of the magnetic sheets h m , of copper h, and of Epoxy h pcb . PCB with high thickness of copper allows to reduce the inductor DC losses. Then, a double copper layers PCB is chosen with h = 105 µm of copper thickness and h pcb = 1.6 mm for Epoxy. It is the PCB with highest copper thickness found on the market. In order to increase the energy density of the PCB inductor, the spacing between tracks s is fixed to the minimal distance s = 0.25 mm defined by our engraving copper process. An algorithm based on the optimization of the inductor volume is used to determine the other five parameters taking into account thermal issues of the magnetic sheets. Also, a simulation method is proposed to calculate the equivalent stray capacitance of the PCB inductor allowing to determine its resonance frequency. The PCB inductor should keep inductive behavior at the switching frequency of the converter.

A. Optimization algorithm of the inductor volume

The algorithm allowing the determination of the geometrical parameters of the PCB inductor is shown in Fig. 7. It is based on the optimization of the inductor volume using Matlab and FEMM softwares. The spacing between tracks s, the thickness of PCB h pcb and of copper h shown in Fig. 6 are defined as input parameters of this algorithm. The other parameters N , r i , d e , and h m are defined as output parameters. The algorithm is executed for different inductance values from L = 6 µH to 70 µH, in order to choose the best inductor to meet with the GaN-converter specifications. For each inductance value, the main algorithm is executed for a width of tracks l that varies between l 0 = 0.5 mm and l max = 2 mm with a step of ∆l = 0.5 mm. Discrete numbers like the number of turns N are not computed by the used optimization tool based on Gradient method. Then, an iteration loop is used to

N = N 0 Optimization V opt (L(l, N )) N = N + 1 V opt (L(l)) = min(V opt (L(l, N ))) N opt (L(l)), r iopt (L(l)), d eopt (L(l)), h mopt (L(l)) T max (L(l)) < 100 o C inductor volume h, h pcb , s FEMM-M C p (L(l)) =? r io , d eo , h mo of L = L 0 l = l max exist! l = l 0 L = L next FEMM-E L = L f inal l = l + ∆l L(l) Losses Volume Losses-Volume curve Choice of the best inductor l, N, r i , d e , h m Optimal FEMM-T Input parameters
Initial points the of Fig. 7: Flow chart of the inductor volume optimization algorithm solve this issue. The algorithm calculates the optimal volume V opt (L(l, N )) for each number of turns, and it exits from the loop when the computed number of turns gives an inductance value greater than that defined in the constraint. The optimal inductor volume V opt (L(l)) is the smallest volume in the vector volume V opt (L(l, N = N 0 : N max )). Note that r io , d eo , h mo in Fig. 7 designate the initial guess required by the optimization procedure for the r i , d e , h m parameters defined in Fig. 6. Likewise, N 0 and l 0 are user-defined initial parameter values that will be subsequently iterated by the proposed algorithm. Different inductances values are tested from L 0 to L f inal where this range can determined based on the converter specifications [START_REF] Li | Selection of the current ripple ratio of converters and optimal design of output inductor[END_REF] to avoid testing unrelevant inductance values.

Calls from MATLAB to FEMM are initiated at different places in the flowchart depending on the kind of requested FEM analysis: FEMM-M is a short name for magnetic simulations performed both in DC and in AC for the first ten relevant switching harmonics; FEMM-E is a short name for electrostatic simulations that are performed to compute the inductor equivalent capacitance; and FEMM-T relates to thermal simulations detailed in section III-C. Then each FEMM simulation result is sent back to MATLAB in which the optimization itself is implemented

The maximal temperature of the magnetic sheets will be checked later. If it is lower than the maximum temperature allowed of 100 • C, the equivalent stray capacitance of the inductor will calculated in order to verify that its resonance frequency is superior than the switching frequency of the converter. Next, the optimized inductor design L(l) for the current track width l will be appended to a Losses-Volume data set for further plotting of the results. Then the algorithm will be executed for the next width of tracks increased by ∆l up to the maximal user-defined value l max , where the algorithm will move to the next inductance value L next . The optimization tool stops calculation when the computing inductance is equal to a maximal user-defined value L f inal = 70 µH. User-defined boundaries are just a means of avoiding nonrealistic parameter values so as to provide only relevant information for designers. Thus, the best inductor for the operating of the converter will be eventually chosen from the obtained Losses-Volume curve that will be discussed in section III-D.

B. Calculation of the equivalent stay capacitance

The PCB inductor is designed for 1 MHz converter. Therefore, its resonance frequency must be higher than this switching frequency. For this reason, it is necessary to calculate the equivalent stray capacitance of the inductor. Because of the complexity of analytical calculations, the determination of the equivalent stray capacitance of the inductor is made by electrostatic simulation on FEMM software using the concentric Circular spiral geometry

V1 V2 V3 V4 V5 V6 V7 V8 N=1 N=2 N=3 Concentric circles geometry V 1 V 2 V 3 V 6 V 5 V 4 N=4 N=5 N=6 N=1 N=2 N=3 N=4 N=5 N=6
Fig. 8: Approximation used to calculate the stray capacitance

u r u z u θ Axis of symmetry V 1 ∆V V 2 V 3 V 4 V 5 V 6
Fig. 9: Electrostatic simulation of the PCB inductor circles geometry as shown in Fig. 8. Voltages of turns are not varying with u θ axis as shown in Fig. 9, because of the limitation of the axisymmetric simulation. These voltages are calculated from the root mean square of voltages of turns for the spiral form as given in equation 2 because the variation of the electrostatic energy is proportional to the square voltage. Voltages of spiral turns V i are calculated from the voltage drops caused by the turns.

V i = (V 2 i + V 2 i+1 )/2) (2)
After setting the V i turns potentials, an electrostatic FEM simulation (FEMM-E call in Fig. 7) is performed to build the electric field map and determine the overall stored electrostatic energy. This energy is linked to the equivalent stray capacitance and the difference of potentials between the first and the last inductor turns, which allows to determine this capacitance value.

C. Calculation of the temperature rise

The maximal operating temperature of the used magnetic sheets is limited to 100 • C. This constraint must be taken into account in the design of the inductor. 3D simulation tools are needed for the thermal simulation of the PCB inductor integrated to the converter. Also, losses of the other components of the converter must be evaluated. For this work, the maximal temperature of the magnetic sheets is calculated by FEMM 2D-axisymmetric simulation neglecting the thermal interaction between the inductor and the other devices of the converter (FEMM-T call in Fig. 7). The half-cross section of the inductor for thermal simulation is shown in Fig. 10. The vertical disposition of the inductor is chosen to facilitate the temperature measurement in the two sides of the inductor and to enhance its cooling.

The coefficient for the natural convection by air is fixed to h c = 16 W/(m 2 K). This value is determined from measurements made on an other PCB inductor. The thermal simulation

Optimization of

∆T co = |T coopt -T coF EM M | P copper (T amb ) T amb T cuopt FEMM-T T co P copper (T cu )
Fig. 11: Algorithm for the calculation of inductor temperature with FEMM software does not take into account the variation of copper losses with temperature rise due to resistivity change. Then, to avoid this constraint, the algorithm shown in Fig. 11 is used to calculate the maximal temperature of the magnetic sheets. It evaluates the copper temperature difference between that calculated by FEMM software T co F EM M and that previously obtained by the proposed algorithm T coopt until convergence to the same value. More specifically, assuming an initial resistivity at 25 • C, copper losses are first calculated and temperatures are determined for each winding turn. Next, the copper resistivity is updated for each turn according to these newly found temperatures, resulting in a updated losses distribution among the turns. Therefore the process is repeated with another evaluation of temperatures based on the new power losses. Iteratively, copper tracks resistivities are updated again and the process is repeated until a fixed point is obtained where temperature stabilizes between two iterations. At this point, the power losses and actual temperature of each turn is obtained, which improves accuracy of the thermal analysis.

It should be noted that, due to the harmonic content of triangular-shaped inductor current quickly decreasing with frequency, speed-up of FEM computation is obtained by considering only the DC component and the first ten harmonics for losses estimation. Notably, the fundamental switching harmonic at 1 MHz is responsible for most AC losses. Even though the AC RMS value is small compared with the DC component, its contribution to losses must not be neglected because of larger AC resistance as will be presented in section IV-A.

D. Simulation results

When the proposed algorithm from Fig. 7 is executed, the optimal geometry is determined for each inductance value L including the best number of turns N to minimize its volume. Thermal verification is performed in the process to avoid exceeding the specified maximum temperature. Various inductance values are mapped in this way, each one obtained with optimal turns number, which allows proper selection of inductor design based on a losses-volume trade-off curve as presented in Fig. 12. Thus, the algorithm output leaves the final choice for the designer to emphasise efficiency or power density, while each point in Fig. 12 is volume-optimized for a given inductance value. Inductors that not respect the constraint of temperature are not presented in this curve. The objective is to provide a trade-off comparison between losses and volume of inductors, so that designers can select the appropriate inductor realization for their application. It should be noted that in this work, magnetic sheet thickness was constrained by the manufacturer. While a standard 1.6mm PCB thickness has been considered, the method could be applied to smaller values as well; however copper thickness should not be reduced as the losses penalty would be significant. As previously mentioned, the spacing between tracks is kept minimal to reduce total copper length and thereby losses.

In Fig. 12, the minimum of losses P = 1.45 W corresponds to the 20 µH inductor for a width of tracks l = 2 mm and a volume V = 5 cm 3 . The 30 µH inductor with a width of tracks l = 1 mm has the minimum volume of V = 2.8 cm 3 with P = 2.55 W of losses. The 1.1 W of difference between the two inductors losses represents 1.1 % of the power of the converter. The 30 µH inductor volume is more smaller compared with the volume of the 20 µH inductor by a factor close to the half. Therefore, because inductors are the largest components in converters and the difference in losses between the two inductors represents 1.1 % of the power converter, the 30 µH inductor is chosen and will be used in the converter in the following section.

IV. EXPERIMENTAL VALIDATION

The realized inductor without and with magnetic sheets is shown in Fig. 13. Its external diameter is about 40 mm with a width of tracks l = 1.5 mm and number of turns N = 14. Obviously, the occupied area may be larger than standard offthe-shelf components, as a counterpart of avoiding additional height on the PCB faces. Still, the custom-shape magnetic material allows optimized realization according to the algorithm outputs, and applications with different parameters such as switching frequency might result in even better trade-offs using the same proposed method. This inductor will be characterized and tested with the GaN converter in order to evaluate its electrical and thermal performances. In these tests the converter and inductor are placed in free air without additional air flow, so as to comply with the natural convection conditions considered in section III-C. Forced air flow would require different heat exchange parameters in the simulation setup.

A. Small signal characterization

The measurement of the inductor impedance with impedance analyser (Agilent 4294A, 40Hz-110MHz) is shown in Fig. 14. The first resonance frequency of the realized inductor of 7 MHz is suitable for 1 MHz switching frequency of the GaN converter. Table I shows the comparison between simulation and measurement results for the first resonance frequency. The inductance value is extracted from the inductor measured impedance at 1 MHz. The equivalent stray capacitance linked to the inductor is determined using the RLC model shown in Fig. 15, where R 0 is the DC resistance and the three parallel R, L, C sections resonate around the respective maxima of

L1 = 32µH C1 = 16pF R 0 = 0.42Ω R 1 = 18kΩ R 2 = 2kΩ R 3 = 0.8kΩ L2 = 1.2µH L3 = 0.2µH C2 = 19pF C3 = 18pF

B. Saturation of the inductor

The DC current flowing through the inductor may cause its saturation and reduces its inductance value. To verify this phenomenon, the test bench setup shown in Fig. 17 is used. The characterization method is based on S-parameters named "Multiprobes measurement method" [START_REF] Tarateeraseth | Accurate extraction of noise source impedance of an SMPS under operating conditions[END_REF], [START_REF] Li | Multiprobe measurement method for voltage-dependent capacitances of power semiconductor devices in high voltage[END_REF]. The inductor impedance Z L is determined using equation 3. Where Z setup and K are respectively the impedance of the test bench setup and the coefficient of coupling between the setup wire and the current probes. A vector network analyzer (VNA: Agilent E5071C, 9kHz-4.5GHz) is used to measure the S-parameters S 11 and S 21 through two current probes CIP (Current Injection Probe: FCC F-120-3, 10kHz-100MHz) and CRP (Current Reception Probe: FCC F35, 1kHz-100MHz). A DC current source is used for the polarization of the inductor.

Z L = K • S 11 + 1 S 21 -Z setup (3)

C. Inductor tested with the GaN converter

The realized inductor is tested with a GaN Systems converter board where inductor current is monitored by means of a 100-MHz-bandwidth Hall effect current probe (Keysight N2783A) as shown in Fig. 19. The experimental validation of the inductor was made for this operating point; V i = 48 V, I i = 2.1 A, V o = 96 V, and f = 1 MHz. The measured inductor current ripple is about ∆I L = 0.9 A as shown in Fig. 20. It is higher than the theoretically value of 0.83 A, probably because of the saturation of the inductor and the ideal model of converter used to calculate the current ripple (drop voltages are considered nulls for inductor and transistors, also the switching times). Fig. 21 shows the thermal photo 22, where the x-axis can be interpreted as the radial distance along a symmetry axis crossing the inductor center in the PCB plane. This profile is extracted from simulated and measured temperature data matrix and shows that the difference in temperature rise between the two profiles is 13% at maximum in the center of the inductor. The origins of this difference can be justified by the error on the DC resistance of the inductor and the saturation of the magnetic sheets which is not taken into account in the design of the inductor. Also, the coefficient for the natural convection by air is defined constant on the two sides of the inductor for the thermal simulation. This coefficient varies with temperature rise which is not uniform on the inductor sides. Also, the coefficient for natural convection by air varies with inductor dimensions and temperature rise.

V. CONCLUSION

In this paper, a design method for PCB inductor is proposed. A high frequency ferrite sheet is used as magnetic material for the inductor in order to enhance its energy density. The inductor is destined to 1 MHz GaN DC/DC converter. Circular spiral shape is chosen for the realization of inductor tracks allowing The thermal constraint of the magnetic sheets is taken into account in the algorithm. Also, a simulation method is proposed to calculate the equivalent stray capacitance in order to evaluate its resonance frequency that must be higher than the switching frequency of the converter. The inductance value needed for the converter is chosen from a Losses-Volume curve of inductors that respect the constraint of maximum temperature. The chosen inductor was realized and characterized in small signal. The error between simulation and experimental results is due mainly to the realization of the inductor. The inductor is thereafter tested with the GaN converter in order to evaluate its electrical and thermal performances. The difference between the simulated and the measured temperature profiles is produced mainly by error on the DC resistance of the inductor and the definition of the coefficient for natural convection by air. Thus, the proposed method allows optimal design of high-frequency custom-shape PCB integrated inductors by means of flexible magnetic sheets, with the advantage of 2D FEM that takes into account both electromagnetic and thermal aspects with satisfactory speed and accuracy due to solving axisymmetric equivalent problem.

On the other hand, even though FEMM-MATLAB communication benefits from existing programmation interfaces (API), frequent data exchange between the two softwares might penalize the total speed of the optimization procedure. Also, the realized inductor has small thickness and larger area compared with standard components, which depends on switching frequency and inductor construction. Thus, perspectives of this work include the reduction of inductor volume using other structures such as multilayer PCB windings and the design of inductors taking into account saturation issues of the magnetic sheets for multi-megahertz power converters. Compared with more conventional inductors designs, the full covering of PCB inductor windings by magnetic sheets may provide additional shielding effect, that could also be a subject of future research focusing on radiated performance.

VI. ACKNOWLEDGMENT

This work has been achieved within the framework of CE2I project (Convertisseur d' Énergie Intégré Intelligent). CE2I is co-financed by European Union with the financial support of European Regional Development Fund (ERDF), French state and the French Region of Hauts-de-France

Fig. 1 :

 1 Fig. 1: PCB inductor structure a) circular spiral form (3D) b) concentric circles (2D)

Fig. 2 :Fig. 3 :

 23 Fig. 2: Complex permeability of magnetic sheets

Fig. 4 :

 4 Fig. 4: Inductor current ripple as function of inductance value

Fig. 5 :Fig. 6 :

 56 Fig. 5: Flux density plot using FEMM software

- 2 .k - 1 Fig. 10 :

 2110 Fig. 10: Thermal simulation the PCB inductor

Fig. 12 :

 12 Fig. 12: PCB inductors losses as function of volume

Fig. 13 :Fig. 14 :

 1314 Fig. 13: Realization of the PCB inductor

Fig. 15 :

 15 Fig. 15: Modeling of the PCB inductor

Fig. 18 Fig. 17

 1817 Fig. 18 shows the variation of the inductance value as a function of the DC current. It decreases from 32 µH without

Fig. 18 :

 18 Fig. 17: a) Test bench setup b) Equivalent model circuit

Fig. 19 :Fig. 20 :

 1920 Fig. 19: Experimental setup used to test the PCB inductor with the GaN converter

Fig. 21 :Fig. 22 :

 2122 Fig. 21: Measured temperature in the inductor

TABLE I :

 I

	Experimental	32.5	16	0.41
	Simulation	31.3	13.79	0.34
	Error	4%	14%	17%

Comparison between simulation and measurement results for the first resonance frequency

L [µH] C p [pF] R dc [mΩ]

This is author's version of this paper. Final published version is available at: https://doi.org/10.1109/TPEL.2020.3000438