LanternD's Castle

To begin with

Microstrip is one kind of transmission line in the circuit. We use them to achieve impedance matching or some other application. Here are some simple design examples.

Problems

Design following transmission lines (use simplifying assumptions):

A 50-$\Omega$ microstrip line for a substrate height of 128 $\mu$m and $\varepsilon_r$ of 3 (RT Duroid)

A 50-$\Omega$ microstrip line for a substrate height of 10 $\mu$m and $\varepsilon_r$ of 4.1 (CMOS)

A 50-$\Omega$ microstrip line for a substrate height of 5 $\mu$m and $\varepsilon_r$ of 4.1 (CMOS)

For the CMOS case, assuming the minimum allowable line width and spacing is 2 $\mu$m on the top metal, what is the highest characteristic impedance we can achieve?

What is the lowest characteristic impedance we can achieve? What would be the limiting factor?

Background

I take adaptive control course this semester, and in the homework after the second lecture, we are going to derive the formular for the estimated parameter vector $\theta(t)$ at time $t$.

Some terms we need to demonstrate the problem:

Parametric model (linear): $y(t)=\theta^{*T}\phi(t)$.

$\theta^*$ is the truth value of the parameters in the system, which is what we want to reach or approach. However we only have the knowledge of $y(t)$ and $\theta(t)$. So we are going to estimate $\theta^*$ based on what are known.

$y(t)$ is the output of the system, $1\times1$ scaler, which could be measured and it is known.

$\phi(t)$ is the input or reference of the system, which is also known.

$\theta(t)$ is the estimated system parameter at time $t$, which is what we want.

Cost function $J(\theta(t))$ is what we would like to minimized, so that the error between $\theta\phi$ and $y$ is minimized.

There are two algorithms that can solve this problem. The first one is Gradient (Descent) Algorithm, another one is what we are going to say here, Least-squares algorithm. Basically, the differences between these two algorithms are the cost function they employed and the method to minimize the cost function.

That comes to my mind that I may use my English blog for some academic writting.

It would be better that those complicated mathematics equations and formula can be clearly displayed on the screen. Of cause the first thing came across my mind is MathJax, the one I use in my Chinese blog (not too often though).

The solution I followed is to add the MathJax CDN files in the header part of my HTML code, which could be found in the Theme Edit dashboard. For more info, please visit this StackExchange pages, from which I found the solution.

So here's my try!

$$E=mc^2$$

Isn't that cool?!

Now the next part is inline math expressions. The second parameters estimation algorithm that I learned today on my Adaptive Control course is using the Least-Squre methods, given as defining a cost function like $J(\theta(t))=\frac{1}{2}\int_{0}^{t}|\theta^T(t)\phi(\tau)-y(\tau)|^2d\tau$. Then we take the partial derivative of the formula and set it to 0, then find the corresponding solution $\theta(t)$ as our parameter estimation of the time $t$. In other words, solve the equation $\frac{\partial J(\theta)}{\partial \theta} = 0$.

Yep. It works. Now this marks the start of my academic blog!

Interestingly, I realized that I got two disks in my PC in the lab. One is the default one, installing Windows 10 Education. The other one is an SSD, with Linux Ubuntu installed.

Everytime I start up my computer, the BIOS will choose Windows by default. As time goes by, I gradually forget the existance of the Ubuntu disk. Because I have to interrupt the start process at the BIOS, jump into the "start up device list" and choose SSD to enter Ubuntu.

Today it came to my mind that I hadn't visit Ubuntu world for many months and decided to take a look.

I even forgot the password of the system for a while until I finally made it after several attempts.

That may be interesting. Those things around us, close to us, will be probably forgotten after we neglect them intentional or unintentional for a period of time. Sometimes they will never come into our mind without some "inspiration".

I had finished the QE part A in Jan 2015, which was a "waterloo" for me.

I chose 4 subjects for test, but I failed in one of them and was asked to take 2 remedial courses.

At this moment, I have finished the ECE 320 course and got a 4.0. If I could pass ECE 423, which I think is of no doubt, I could be the formal PhD candidate and continue my road towards my PhD degree.

There is another part of the exam, part B, which is consist of a written report and an oral presentation in front of a review committee.

There are so many things to finish. I'm a little bit overwhelmed. Hopefully I could do well in it. That depends on who would be my review committee.

In Michigan state, one can drive their car on road after passing the writing driving test. But must be in companioin with someone who has already gotten the driver license.

I passed the test and got my driver license in March, 2015 and have been driving car for about 8 months. As a result, some of my friends who would like to learn driving will turn to me for help.

Recently I taught QW how to drive. He bought his first car a couple days ago. The road test includes parking test and road test. First of all, I taught him how to park the car in the certain area, without hiting the sign and mark on the ground. He's kind of having talent in manipulating cars. He made it after I told him the keypoints in backward parking about 3 times.

One hour later, we drove the car on road to practise. At the beginning, the trajactory of the car was like zigzaging. I reminded him to keep the car on the center of the road every now and then. And now he can almost make it to keep the car centered well.

Yesterday he tried highway, which the speed limit is 60 mph. He was in a little nervous thought he controlled the car well. Anyway we came back safely.

This is not the first time I taught someone to drive but it is the first time I taught a tiro. I think his skills improved a lot in a short time.

I moved into a house a couple weeks ago, after which I seldom met people around.

Yesterday I ran 4.2 km around this block. Then I found one of my neighbour was taking photos of his garden. I walked up to him and greeted.

Mr. Smith retired, and takes photography as his hobby. He is trying to capture those wonderful things around and doesn't have perticular subject focus.

He also introduced me some of the houses and neighbours nearby, who are they, what do they do and how many children they have.

Recently I adopted a cat named Hakuna Matata, which means "No problems" in Swahili. There is an animal rescue center nearby called Capital Area Humane Society. They are working hard to help those stray animals to find a forever home.

Upon the day that I adopted my cat, there were 28 cats available for adoption, some of which were sent to pet supermarket for care.

I went to a pet supermarket, PetSmart in Okemos, and got my lovely cat there.

She is pretty, calm and independent, interested in playing with human. She is not afraid of stranger at all.

I think HM is an ideal pet, that I can't expect more.

It has been a long time since I heard of YNP. I was maybe 8 or 10.

Now the dream that paying a visit to YNP came ture. I traveled there for about 8 days last week and took a glimpse of the marvellous scene created by mother nature.

The yellowstone canyon, the mammonth hot spring, and the uncountable geyser and mud vocanos, all this splender landforms are intrigued to millions of visitors like me.

We also went to the Grand Teton National Park, south to the YNP. the lake, the forest and the wonderful Teton Range are truely amazing.

We hiked for about 15 km, climbing up to 1 km, to reach an incredible place, Amphitheater Lake, a place seemed only exist in fairy tale.

I will never forget the moment when I standed on the top of a 3700-meter-elevation mountain top, looked down upon the lake, the meadows, the forest like a bird, like god. How excellent the moment was!

Now I went home, with my 2700+ photos. I hope I could pick out some of them and upload them as soon as possible.

06/20/2015 was the Dragon Boat Festival in China and some other countries. One of the event on that day is making Zongzi, as know as rice pudding.

I haven't eaten it for a really long time. So my roommate and I decided to hold a home party and called up some friends to enjoy making rice pudding.

There were lots of stuff that were required for it. The first one was sticky rice and long leaves. We bought one bag of rice and several dosens of leaves in Oriental Mart. The second is meat and bean. We bought rib, and then cut down some meat from it. We also got red bean, walnut, Chinese chestnut and green bean, as the subsidiary ingredients.

After everything was done, we got started. The first step is folding one leaf into a conical funnel shape. Next is adding some rice into it. And then add meat, bean, and whatever you would like to eat. Finally, add more rice until all the ingredients are covered. Oh, I forgot one thing, after everything is in it, fold the other part of the leaf to cover the top of the rice. And use a one-meter long rope to bind it up.

One zongzi was finished!

A zongzi usually is a little bit smaller than a fist, but you can make it larger.

I thought we have made at least 30 zongzis in total.

It was not yet finished, actually. It should be cooked before consumed. We use a pressure cooker to reduce the time to about 1 hour.

Yummy. It's hard to describe how delicious it tastes unless you try it yourself.

I heard about Kalman Filter about 2 years ago. I was then planning to build my own Tricopter.

But due to the limited time, I hardly set foot on it.

Now is the time to take a glimpse. I downloaded a PDF called An Introduction to the Kalman Filter, by Greg Welch and Gary Bishop.

Now I've had a clear idea about what is it, but knew little about how it works.

The Kalman Filter can be applied to process state estimation in a way that minimizes the mean of the squared error.

I'm going to turn to Page 3 now.

There's one old saying "The more you read the more you can write.

It is definitely true according to my own experience.

But the thing is that, most of what I read are papers, emails, notification and so on. Thus the writing in such article casts no problem to me.

However, the writing in diary does. I seemed have never read any books about fiction, poem, drama etc. in English. I can hardly write a sentence that describe the stuff around me exactly in English. How a mug look like, how I feel after I run 4km, and so on.

I read the prologue of the book The Song of Ice and Fire: A Game of Throne. What I felt was, OMG, there are so many words that I have never seen before? Is it written in English? The writer George Martin uses so many words to describe what someone is dressing, what's the environment, what is the weather like and so on.

That's just overwhelming to me.

Last weekend we went to Indianapolis for vacation.

We hung around the city for 2 days. We tried various exotic food, art museum, downtown and so on.

The Indy500 Final race was on Sunday. The speedway field was crowded. We spent almost 40 min to get our tickets printed and a few ten minutes to approach to get a good viewpoint.

The F1-like cars were impressived. I was stocked by the parameters of the cars. 221 mile/hour, 11484 rpm engine and 200 rounds race for winning. the sound of the engine pierced the air and went through my ears. They swept from my eyes in less than 1 seconds, like a bullet.

After the summer semester begin, the first thing I did was reading the science fiction novel, The three body problem. It's a historical novel writen by Cixin Liu, one of the most famous SF writter.

The first book of the series tell us about how the Earth civilization get the contact with the civilization of three body, a galaxy with three stars. Since this is a quite chaotic and highly unpredictable, the planets surrounding the suns are suffering a horible environment. The aliens on those planets have special ability to suvive from the sudden extremely hot and cold weather.

This is such a terrible living environment, that the only solution to rescure their civilization is to migrate to other planet outside the three body. And occasionally, a signal from the earth boardcast its location...

The later story is trigger by this sending event.

The whole story is based on precise logic and most of the phenomenon can be reasoned by science and technology, sounding like it might happen in the future.

Today I went to Annie's apartment and took photos for her and her 4-months baby son. Annie took the same course as me last semester, where we got to know each other.

Her boy is so cute, with two big eyes stearing the world curiously. I set up the soft light boxes and the white background cloth and started taking photos.

The baby is quiet but active. Sometimes he looked at my lens, but most of the time did't. I gotta change my position and angle to find a better photo composition.

My Diaries here are quite simple. My goal of writing diaries in English is simple, simple as my sentences.

First, I just want to learn more expressions and build my vocabulary. My mother tongue is Chinese, which is a totally different language system from English. Although I have studied English for about 13 years, about Grade 3 in elementary school, I find myself hard to describe things in my life in English. This is the drawback in the English Education in China. I might address this issue some day in the future. So the first step to make a difference is, starting blogging.

Second, it's another way to look at my world. Now I live in the USA, where lots of new things happen in my life. Some of these things are better expressed and explained in English. If translated into Chinese, some of the original meanings lost.

Third, writing the blog in English can improve my typing speed. As far as I'm concerned, I can type Chinese with Pinyin input method in a fast speed, but can't do that in English. This is something called "Muscle Memory". If some of the words are typed frequently, you can type it out without considering which key are to be press. I believe this is a practical skill, especially in writing course project report, papers or something.

The only thing I need to do is - keeping writing without stop.

I run once a week, on every Saturday afternoon, around 5:30 pm.

Yesterday afternoon, I went for a run near my apartment. There is a small park north of the apartment, where the air is fresh due to the high plant coverage rate.

I ran in a relatively slow speed, through a three-meters wide trail, facing the sun over the sky. It was a delightful moment. The deep breath every three steps became the only sound that I could heard.

I ran and arrived at the end of the park, with an outlet prependicular to Lake Lansing Rd. I took a rest and slowed down my heartbeat rate a little bit near the street.

Time to run back home, otherwise my muscle will get sorer. I ran over a 90 degree turn on the trail. After another 60 meters run, a deer with young age was standing by a rail on othe bank of a small river. The horns on its head were not yet fully grown yet.

The deer was vigilant, as I expected. I stopped at 3 meters in front of it, breathing deeply as usual. I walked one step forward, it will walked one step forward too, with its back facing me, turning its head around and staring at me.

I approached my hand, pretended there was some food that could feed it. But it turned out that this didn't work at all.

The neariest distance between me and the deer was about 3 meters, exactly the width of the trail. That happened when I walked straight forward on the right side, while the deer walked from the right to the left.

I continued my run towards home. Looking back, I saw the deer started eating the new-grown sprout on the tree again.