乾電池1本から100Vを作る

イチケン / ICHIKEN
23 Feb 202419:38

Summary

TLDRこのビデオでは、1.5Vの乾電池から100Vの電圧を生み出すブーストコンバータの制作過程を紹介しています。有名なコッククロフト・ウォルトン回路の代わりに、シンプルなブーストコンバータを使用し、パワーMOSFET、ダイオード、コンデンサーを活用します。原理説明から実際のPCB製作、そして実験による検証まで、一連の流れが詳しく解説されています。また、乾電池の電圧を5Vに昇圧する村田製作所のモジュールの使用や、複数のブーストコンバータモジュールをカスケード接続して高電圧を得る工夫が紹介されています。最終的には、単一の乾電池で150Vを超える電圧を実現し、その危険性と電圧が負荷によってどのように変動するかについても触れられています。

Takeaways

  • 😀 They will make a 100V dry cell battery using power electronics
  • 👷‍♂️ They will use a boost converter circuit to step up the voltage
  • 🔌 The circuit only needs a single 1.5V AA battery as input
  • ⚡️ The battery voltage is stepped up using an inductor and capacitor
  • 🤔 Driving the MOSFET switch is challenging with only 1.5V input
  • 🙌 Found a Murata module to boost 1.5V to 5V for MOSFET control
  • ⚙️ Connected multiple boost converter modules in series to multiply voltage
  • 🔋 Made a 150V 'dry cell battery' from a single AA battery
  • 📉 Voltage drops under load due to no feedback control
  • 💡Possibility to boost voltage further with more batteries in parallel

Q & A

  • What is the goal of the project in the video?

    -The goal is to create a 100V dry cell battery using only a single 1.5V AA battery.

  • What circuit configuration is used to boost the voltage?

    -A boost converter circuit configuration consisting of an inductor, switch, diode and capacitor is used.

  • How does the boost converter work to increase the voltage?

    -It works by storing energy in the inductor when the switch is closed, and then transferring that energy to the capacitor when the switch is opened, boosting the voltage.

  • Why was the Murata power module used?

    -It was used to boost the 1.5V battery voltage to 5V to provide sufficient voltage to drive the MOSFET switches.

  • How was a 100V output achieved?

    -By connecting multiple boost converter modules together vertically in cascade to achieve a high voltage gain.

  • Why did the output voltage drop under load?

    -Because there was no feedback control, the boost converters moved into discontinuous mode, and the battery voltage sagged under the high load current.

  • What was the maximum output current capability?

    -Only about 1A could be drawn before the output voltage dropped significantly due to battery limitations.

  • What improvements could be made?

    -Add voltage feedback control, parallel more batteries, add more cascade stages, and optimize the circuits for higher load currents.

  • What was learned from this project?

    -That while voltage multiplier circuits can generate high voltages easily, getting them to work properly under load with feedback and control is more difficult.

  • What future applications are possible?

    -With improvements, this circuit technique could generate voltages up to 3kV for specialized applications.

Outlines

00:00

😀 はじめに、ブーストコンバーターの原理説明

ブーストコンバーターはインダクタとスイッチ、ダイオード、コンデンサーから成り、インダクタにエネルギーを蓄え、スイッチのON/OFFによってコンデンサーにエネルギーを移すことで電圧を上げる。基本回路の原理実証のため、試作回路を作成し、入力電圧を上げていくことで出力電圧も上がることを確認した。

05:00

😊 MOSFET駆動用に1.5Vを5Vに昇圧するモジュール

ブーストコンバーターのMOSFETを駆動するのに最低5Vが必要だが、単電池では1.5Vしかない。そこでマウス社のDC-DCコンバーターモジュールを利用し、単三電池の1.5Vを5Vに昇圧してMOSFETの駆動に利用する。

10:02

🤔 1個のブーストコンバーターモジュールだと100Vまで昇圧するのは難しい

1個のブーストコンバーターモジュールで1.5Vを100Vに大きく昇圧しようとすると、インダクターに非常に大きな電流が流れる必要があり、単三電池ではそこまでの大電流は流せない。モジュールを垂直接続してステージを重ねる「カスケード接続」したほうが容易。

15:05

😮 3段階のカスケード接続で1.5Vを150Vに昇圧

3段のブーストコンバーター・モジュールをカスケード接続し、1.5Vを最初に2倍、次に2倍、最後に5倍して150Vに大きく昇圧することに成功した。これを使って単三電池サイズの携帯できる「150V乾電池」を作成した。

Mindmap

Keywords

💡ブーストコンバータ

入力電圧を増幅して出力するDC-DCコンバータの一種。このビデオでは、1.5Vの単3電池から100Vを生成するのに使用されている。

💡垂直接続

複数のブーストコンバータを直列に接続し、各段で電圧を順次増幅していく技術。このビデオでは3段の垂直接続を使用して100Vを生成している。

💡ドライセル電池

液体の電解質を含まない乾電池。このビデオでは1.5Vの単3乾電池を電源として、ブーストコンバータと垂直接続により100Vの乾電池を作成している。

Highlights

Introduction to the concept of creating a 100V dry cell battery using power electronics technology.

Discussion on the challenge of boosting voltage from a single 1.5V dry cell battery and exploring circuit configurations.

Explanation of why the Cockcroft-Walton circuit, often used for DC high voltage creation, is not suitable for this project.

Introduction to using a boost converter as a simple and effective solution for increasing voltage.

Detailed explanation of how a boost converter works, including the roles of its components.

Discussion on the importance of transferring energy from the inductor to the capacitor for boosting voltage.

Practical demonstration of a boost converter increasing the voltage and the challenges faced with MOSFET operation.

Solution for driving MOSFETs with low voltage using a Murata Manufacturing Co. module to boost voltage for the control circuit.

Step-by-step assembly of the boost converter circuit, highlighting the use of components from DigiKey.

Demonstration of the assembled boost converter successfully increasing voltage in a controlled experiment.

Discussion on the limitations of boosting voltage to 100V with a single module due to current and resistance constraints.

Proposal of a cascading approach with multiple modules to achieve higher voltage outputs effectively.

Successful demonstration of cascaded modules boosting voltage significantly, with safety precautions emphasized.

Creation of a 150V dry cell battery casing using 3D printing to house the cascaded boost converter modules.

Final thoughts on the project's success, limitations, and the potential for scaling up the voltage further with additional modules.

Mention of DigiKey's support and the availability of educational content on vector analysis for electronic design.

Transcripts

play00:00

This video is brought to you courtesy of DigiKey

play00:02

Good afternoon.

play00:03

Today we're going to take advantage of power electronics technology.

play00:07

We're going to make a 100V dry cell battery.

play00:10

This is a dry cell power supply that can produce 100V here

play00:13

We use only one 1.5V dry cell battery here.

play00:16

Actually from this one small battery

play00:18

How much voltage can you get out of it?

play00:20

I'm sure many of you are wondering.

play00:22

So that's what we're going to try.

play00:25

First of all, we try to figure out what kind of circuit configuration we want to use.

play00:28

If you search for DC high voltage or something like that, you'll find a lot of stuff.

play00:31

The first one is the Cockcroft-Walton circuit.

play00:34

This is a very famous circuit

play00:36

It is often used to make DC high voltage

play00:39

But if you look closely, you can see that an AC power supply is required.

play00:42

This is a circuit that converts AC voltage to DC voltage

play00:45

But this time, we use DC dry cell batteries.

play00:48

So, with this circuit, it seems to be a little difficult to boost the voltage.

play00:52

Converting AC voltage to AC voltage

play00:54

The circuit that converts AC voltage to DC voltage is

play00:57

There are various

play00:58

Further boosting the DC voltage

play01:00

The circuit that converts a DC voltage to a DC voltage is

play01:02

It looks quite difficult.

play01:03

For example, a flyback converter like this

play01:05

There are some circuits like this

play01:07

It's a little bit difficult to make this transformer part.

play01:11

So this time, number 1 straight forward

play01:14

And I'd like to proceed in a simple way

play01:18

We're going to use a boost converter here.

play01:20

Very simple circuit configuration

play01:23

Boost converter is an inductor switch

play01:25

This time we use a power MOSFET

play01:28

And it can be composed of a diode and a capacitor

play01:30

It's a very simple circuit

play01:33

I'll explain the principle of operation in a moment.

play01:35

For clarity, the MOSFET here is

play01:37

Rewrite it as a switch

play01:39

What's the most important thing about this circuit?

play01:42

The energy that's accumulated in the inductor here.

play01:45

If you accumulate it in the capacitor

play01:47

From inductor to capacitor

play01:48

It's about transferring energy

play01:51

Let's close this switch first.

play01:53

Then here's what happens

play01:55

Current flows through this inductance and battery loop

play01:59

The energy stored in the inductor at this time is

play02:02

1/2 LI².

play02:05

This L is the inductance

play02:06

And I is the current through the inductor

play02:09

And next when the current is flowing in the inductor

play02:12

This switch is opened

play02:15

Then there will be no current flow to this switch, so

play02:18

So current flows through this switch.

play02:20

And that current is

play02:21

It flows into this capacitor here

play02:24

If there is a load

play02:25

Of course it will flow like this with load

play02:28

Let's turn off the load for a moment this time, because it's in the way

play02:31

The energy stored in the inductor

play02:33

It is transferred to the capacitor

play02:34

At this point, the energy in the capacitor is 1/2 CV².

play02:39

C is the capacitance of the capacitor

play02:42

By the way, the voltage of an ultracapacitor is

play02:44

The integral of the current through the capacitor

play02:48

This current charges the capacitor

play02:50

The switch was turned off

play02:52

Turned on again

play02:53

When current flows through the inductor

play02:55

And if you turn this switch off

play02:57

Now we're going to put the current through the capacitor again.

play02:59

Repeat this operation to increase the voltage

play03:03

The current flowing in the inductor boosts the capacitor to

play03:05

Let's estimate how much the capacitor can be charged

play03:08

For example, this circuit

play03:09

1mH inductor and 100µF capacitor.

play03:13

1A flows through this inductor

play03:16

Then the energy stored in the inductor is

play03:18

1/2・LI²

play03:20

Calculation yields 0.5 mJ

play03:24

The energy of this inductor is

play03:25

Assume 100% of the energy is used to charge the capacitor

play03:29

Capacitor energy is 1/2 CV².

play03:32

Actual calculation shows that the voltage of the capacitor is 3.16V

play03:38

As explained earlier

play03:39

By turning the switch here on and off

play03:42

The energy stored in the inductor

play03:43

The energy is transferred to the capacitor

play03:45

By the way, when the voltage is low, it means

play03:48

The voltage of the capacitor can easily go up.

play03:50

When the voltage of an ultracapacitor is high, it means

play03:52

The voltage increase becomes a little more difficult

play03:54

because the energy of the capacitor is

play03:56

because it is proportional to the square of the voltage

play03:59

For example, let's say the initial voltage of a capacitor is 100V

play04:02

If the same energy is stored in a 100V capacitor as before

play04:06

The voltage of the capacitor only rises to 100.05V

play04:11

So the voltage is increased like this

play04:13

By the way, you can watch the following video about boost converters.

play04:16

I made it before.

play04:18

If you watch that video as well

play04:19

You'll learn more about boost converters, and you'll be able to see how to use them.

play04:22

Please take a look.

play04:23

There is a link in the summary section

play04:25

We are going to make a boost converter

play04:27

Whether the boost converter actually works

play04:29

We'll go ahead and verify the principle first.

play04:31

This is Ichiken's original PCB and

play04:34

Combination of inductors, capacitors, power semiconductors, etc.

play04:37

Making a boost converter

play04:42

Electrolytic capacitor

play04:43

Inductors

play04:44

And power semiconductors.

play04:47

This is a diode

play04:49

This is a capacitor in the output section

play04:52

Step-up converter for verification of principle is completed

play04:55

We will run this one.

play04:57

The front side looks like this

play04:58

The reverse side looks like this

play05:00

By the way, here is a breadboard type printed circuit board

play05:02

Sold on Amazon

play05:04

If you would like to use it

play05:05

Please purchase from the link in the summary column.

play05:08

Then we'll do a proof-of-principle test.

play05:10

Here's how it's set up

play05:12

There's a voltmeter.

play05:13

The top is the input voltage

play05:14

The bottom is the output voltage of the boost converter

play05:17

Now let's add the voltage

play05:19

First, we set the input voltage to 5V

play05:23

This time, the voltage is set to be boosted by a factor of 2.

play05:26

Since the output voltage is 9.5V

play05:28

Roughly doubled

play05:30

Let's increase the voltage further

play05:33

Now

play05:35

10V

play05:36

That gives 19.7V

play05:40

Looks about right

play05:41

Here we increase the voltage further

play05:48

It's on fire

play05:50

Thus the boost converter is

play05:52

It was found to be working without any problems

play05:54

There's just one problem

play05:56

What it is is the voltage to run the MOSFETs.

play06:00

This is a MOSFET

play06:01

To run a MOSFET

play06:03

Between this GATE-SOURCE

play06:04

You will need at least about 5V

play06:08

But this time we can use it as a power supply.

play06:10

Only one of these batteries can be used as a power source.

play06:12

The voltage of the battery is 1.5V

play06:15

between gate and source here

play06:16

Not quite the minimum required voltage of 5V

play06:20

So without these power supplies

play06:22

So driving MOSFETs without these power supplies?

play06:24

I'm thinking, "This is going to be difficult.

play06:27

I'm in a bit of a pickle.

play06:28

I was looking for parts on DigiKey.

play06:30

What an amazing part I found!

play06:33

This is a product of Murata Manufacturing Co.

play06:35

This is a module that boosts the voltage of 1.5V of a dry cell battery to about 5V.

play06:39

This time, I will use this for the control circuit of MOSFET.

play06:43

This is the circuit we are going to make.

play06:45

With the Murata power supply module that we just used

play06:47

Boosts the battery's 1.5V voltage to 5V

play06:51

This voltage is used to control the MOSFET

play06:53

This is used for the control circuit part.

play06:56

Now we use the MOSFET as a switch

play06:57

It can now be turned on and off

play06:59

Then you can use a boost converter to turn the voltage of this battery on and off

play07:03

We can now boost the voltage.

play07:05

Now we will actually build the circuit

play07:07

As usual, the printed circuit board is made from scratch.

play07:10

And the components that we use there are

play07:11

purchased from our sponsor DigiKey.

play07:14

This time, I used surface mount components for weak electric circuits.

play07:17

And for the power circuit part

play07:19

We use a lot of through-hole components

play07:22

Assembled as soon as possible

play07:23

There's a printed circuit board, and then we're going to put a stencil on top of it.

play07:26

There is this stencil hole

play07:28

We put solder paste on top of the stencil

play07:33

And then you can use a credit card or something like that.

play07:35

And then you rub it here.

play07:36

Solder paste in the stencil holes.

play07:38

It is an image of pushing it into the stencil

play07:40

It's done.

play07:41

This is the difference between before and after applying solder paste

play07:44

Below is before applying solder paste

play07:46

Above is after applying solder paste

play07:48

The area where solder paste is applied

play07:50

Surface mount components are placed

play07:59

Now that all the components have been placed

play08:00

Next, we will bake them on this reflow plate.

play08:04

We're going to put it on this one.

play08:05

Put the board on top of this

play08:06

Now we will burn it.

play08:09

Now it is heated

play08:11

So the temperature is going up and up and up.

play08:13

I'm going to leave it like this for a while.

play08:19

The solder seems to have melted.

play08:21

Let's take it out.

play08:24

I was able to solder quite nicely

play08:26

First, let's see if it works with just the control circuit.

play08:29

Put a single AA battery in

play08:31

Voltage is 1.5V

play08:33

Now let's look at the control circuit voltage

play08:36

Now there is no battery connected to the control circuit

play08:39

When this jumper is connected

play08:42

Power is supplied to the control circuit and

play08:44

5V voltage is supplied

play08:46

Next, let's look at the voltage between the gate and source of the MOSFET

play08:50

Here we have NE555

play08:52

Pulse wave is emitted from there to drive MOSFETs

play08:55

When you turn on the power

play08:57

Now it looks like this

play08:58

The amplitude of the pulse wave here is 4.5V

play09:01

To drive a MOSFET

play09:02

I found that I needed about 5V

play09:04

4.5V is enough to drive the device.

play09:07

There is no problem with the voltage level.

play09:10

This control part sets the boost ratio of the boost converter

play09:14

There is a trimmer resistor here, but

play09:16

Adjust this part

play09:18

Like this

play09:19

In this state, the pressure increase is not that high

play09:22

Conversely, in this state

play09:24

The boost ratio becomes high

play09:26

That duty ratio.

play09:27

The longer the duration of ON

play09:29

The higher the output voltage of the boost converter

play09:32

Now that we know something is going to work

play09:34

We're going to solder the power circuit components as well.

play09:37

Electrolytic capacitors of 450V/100μF are used

play09:43

Diode, 650V withstand voltage

play09:47

N-channel MOSFET, also 650V

play09:52

Inductor 100μH

play09:56

The circuit is completed as shown here

play09:58

Let's try an actual experiment

play10:01

When you put a battery in

play10:03

First of all, here is the input voltage. Here is the battery voltage.

play10:06

1.5V

play10:07

And right side output voltage

play10:09

It is lower than the input voltage

play10:11

This is because the control circuit is not powered yet

play10:15

It's just the voltage drop across the diode

play10:17

Drop from input voltage

play10:19

Now turn on the control circuit

play10:22

The voltage is boosted

play10:24

It is working properly

play10:25

The variable resistor here can be used to change the boost ratio.

play10:28

Like this

play10:31

Higher or lower voltage

play10:34

Pretty good

play10:35

You can increase the voltage like this

play10:39

I know it works fine and looks good, but...

play10:42

So, if I try to make 100V from here

play10:43

There is only one problem

play10:45

What is that?

play10:46

Just one module here

play10:48

If we try to boost the voltage from 1.5V to 100V

play10:51

A very large current must flow through the inductor

play10:56

And with only one dry cell battery

play10:58

The current cannot be that high.

play11:00

It is possible, but...

play11:02

It's not like the voltage is 1.5 or something.

play11:04

It drops considerably to 0.7V or something like that

play11:08

This is because there is an internal resistance in the battery

play11:11

And also because of the high current

play11:13

Inductor here

play11:14

Worst case scenario, it burns up

play11:16

Other than that, power semiconductors are

play11:18

must withstand high currents

play11:20

So, with one module

play11:22

Boosting voltage from 1.5V to 100V is

play11:25

I guess I better rethink this.

play11:27

I've been trying to think of different ways to boost the pressure.

play11:30

I thought that this is the best way to do it.

play11:33

I came to a conclusion

play11:34

This boost circuit as a single module

play11:36

If we connect the beads like this

play11:39

I think it would be easy to create a high voltage

play11:42

This kind of connection is called a vertical connection

play11:45

Cascade connection.

play11:47

For example, if you had a circuit that doubled the voltage in one module

play11:51

where the voltage is doubled

play11:53

Double here, too

play11:54

And here also doubled

play11:55

Connecting three of them gives a total multiplier of x8

play12:00

So, for example, if you have a 1.5V input

play12:03

This is calculated to be 12V.

play12:07

Besides that, for example, here is 5 times

play12:09

Here is also 5 times

play12:11

And if we multiply the last step by 5

play12:13

That's 5 to the power of 3, so we get 125 times the voltage.

play12:19

Then it is 125 times 1.5V, so

play12:24

That gives 187V

play12:27

So to make a vertical connection

play12:29

We will make several of these modules

play12:32

Three modules are created and connected vertically

play12:35

Boosting the voltage at the first stage

play12:36

Boost the pressure in the second stage as well

play12:38

And the third stage also boosts the pressure

play12:41

We actually turn on the power supply

play12:43

I think we're going to get a pretty high voltage, so

play12:45

I'm going to put on insulated gloves as well.

play12:51

Now we turn on the power.

play12:59

There's a little beeping sound.

play13:01

but it seems to be working fine.

play13:04

I'm going to measure the voltage.

play13:07

Here it comes!

play13:07

156V

play13:09

So the voltage of the dry cell here is 1.5V

play13:13

100 times more than that.

play13:14

The pressure has been boosted.

play13:16

I made this kind of battery type case with a 3D printer

play13:20

There are three modules inside.

play13:22

If you put one AA battery for power supply here

play13:25

Here's the positive pole metal

play13:27

And the negative pole is

play13:28

It is pasted here

play13:30

There is an ON/OFF switch on the back side of the unit

play13:33

Close the lid

play13:36

It's something like this, pretty much like a battery.

play13:40

This is quite interesting.

play13:42

This is a huge 150V dry cell battery.

play13:45

Just like a normal battery

play13:47

If you always put out 150V

play13:49

Very dangerous Dangerous Dangerous Itiken specification

play13:52

So just to be safe

play13:53

I put an ON/OFF switch here

play13:56

But this one is also turned on

play13:58

I don't have any LED indicators or anything on.

play14:00

The switch ON/OFF is the only thing that determines whether the switch is ON or OFF.

play14:03

It is a rather dangerous specification.

play14:06

Let's measure the voltage of this giant dry cell battery again

play14:10

The needle is inserted properly, but

play14:12

Is it 144V?

play14:15

The voltage is firm.

play14:17

Let's do a little experiment

play14:18

Normal dry cell battery, low voltage

play14:21

Even if both ends of this terminal are short-circuited

play14:24

No sparks will be generated.

play14:25

But what happens with these 150-volt dry cells?

play14:29

I'll try an experiment.

play14:30

Here is a mechanical pencil lead

play14:33

I'll try to short-circuit it.

play14:41

It crackles pretty solidly

play14:45

As expected from the high voltage

play14:50

Voltage comes down a little bit

play14:53

This is just one dry cell.

play14:56

It's not as powerful as it should be.

play14:57

I think the voltage drops a lot when you take a load.

play15:00

I think it will drop to about 50V.

play15:05

That's quite a jump, now.

play15:06

Can you hear it crackling a lot?

play15:12

Once it shorts out and discharges

play15:15

Until the voltage rises like this

play15:17

Since it seems to take quite a long time

play15:19

Sparks don't fly easily when discharged continuously

play15:22

If you give it a little time

play15:24

There's a big spark, but

play15:26

If you leave it only for a short time

play15:27

Sparks will be such that they will hardly fly

play15:31

This is because it takes time to charge the voltage booster circuit inside

play15:35

By the way, what happens when you take the load off

play15:37

I'll try it with this resistance

play15:39

If you look at the voltmeter display

play15:40

It is below 50V

play15:42

With no load, 150V was being produced, but

play15:45

When the load is taken like this

play15:46

The voltage drops as soon as it reaches 50V

play15:50

When a load is connected to the step-up circuit

play15:52

The voltage is now lower

play15:55

There are many reasons for this

play15:56

There's about three reasons this time.

play15:59

The first one is

play16:00

is that we don't have voltage feedback.

play16:02

If the circuit converts the voltage in this way

play16:04

Usually there is a voltage divider resistor that monitors the voltage

play16:07

This is how the voltage is input to the control circuit

play16:10

The calculated pulse width is then input to the MOSFET

play16:14

And so the feedback works nicely

play16:16

The output voltage of the load is always constant

play16:19

but this time there is no feedback control

play16:22

This signal is input by fixed input

play16:25

So the voltage of the load goes down.

play16:28

The second one...

play16:29

The current flowing through the inductor here is

play16:31

Very important in a step-up circuit

play16:34

It's called current continuous mode, and

play16:35

There is a mode called current discontinuous mode

play16:38

The boost ratio changes depending on the mode of operation.

play16:41

In this case, the operating mode is not calculated.

play16:44

So the mode changes depending on the load current

play16:46

It means that the voltage will not be increased as expected.

play16:50

And here's reason number three.

play16:51

These dry cell batteries here

play16:53

Actually, the current is always about 1A in the dry cell

play16:57

This current of 1A is

play16:59

This is a very large load for an AA battery.

play17:02

If you put this much current into a battery

play17:04

1.5V will drop to about 1V

play17:09

The voltage at the input drops, which means

play17:11

The output voltage drops as well

play17:14

For this reason, we have changed to this 100V dry cell battery.

play17:18

When I connected a load, the voltage dropped

play17:21

So I'm going to summarize

play17:22

Dry cell here

play17:24

Voltage can be output up to about 150V

play17:27

But if we just take the load

play17:28

I found that the voltage drops accordingly.

play17:32

We are using only one AA battery in this case.

play17:37

If you connect some of these AA batteries in parallel

play17:40

There is a possibility to boost the voltage a little more.

play17:43

We're going to need a more robust battery that we're using for the power supply.

play17:45

And if you increase the number of vertical connections in the module

play17:49

If you go up to about 3kV

play17:51

This circuit configuration seems to work.

play17:53

But what I found out by doing it this time is that

play17:55

The fact that the voltage multiplier circuit itself is somehow working is a good thing.

play17:58

It's easy, but

play17:59

If you try to make it work properly

play18:01

It turns out to be quite difficult.

play18:04

So here's today's sponsor, DigiKey

play18:07

Here you go.

play18:08

I hope you all know that DigiKey has a Japanese YouTube channel.

play18:10

Do you know about DigiKey Japanese YouTube channel?

play18:11

A new series is starting over there.

play18:14

This is a series on vector analysis starting with high school math

play18:18

Physical position, velocity, and acceleration

play18:20

Electrical magnetic and electric fields are often expressed as vectors

play18:25

This series is about what a vector is in the first place

play18:27

Mastering gradients, divergences, and rotations in vector analysis

play18:31

This series is designed to help you use them in your designs.

play18:35

You can see in the video summary section of this series

play18:38

to visualize those vectors and see them clearly.

play18:41

Python programs are also available free of charge

play18:43

Just like the series school lessons here.

play18:46

They want you to remember the formulas as you write them down.

play18:49

Please try this one!

play18:51

Please click on the link in the summary column.

play18:53

And now, last but not least

play18:55

Thank you for watching the video.

play18:58

This is the end of the video.

play19:00

Ichiken channel, please.

play19:01

How about using it for corporate PR?

play19:04

Ichiken advertises products

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Factory tour

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Outreach activities, use for recruitment, etc.

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Please feel free to contact us for more information.

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If you create a video, it will continue to play after that

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The video does the work for you.

play19:20

If you're going to do it, I recommend you do it fast.

play19:22

Email address in the summary section for results and details.

play19:25

Please contact us through our homepage

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We look forward to hearing from you!

play19:30

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play19:32

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