Electronics Tutorial - 1/3 Driving multiple BJT transistors in parallel

[@WalidIssa]

Thanks for this one .. I like long videos. The title should say for BJT. I hope the next one is for MOSFETs, or why MOSFETs fail

[@FesZElectronics]

Thanks for the suggestion! I will try to do that in the near future!

[@murad19882003]

Mosfets mainly die because of 3 main reasons according to my experience; first is temperature dissipation, second is over driving the gate and third is spikes on the drain or gate. It could be also high reflections from the load to the transistor drain depending on your application.

[@p_mouse8676]

@@murad19882003 Correct. They are also so much sensitive for over voltage in general. Most BJTs are a lot more forgiving.

[@Stelios.Posantzis]

Very nice circuit explanation.

[@philippeversailles2170]

Hi really impressive. We heard very often about what not to do ! But we have here a fantastic illustration and solutions !! . On top of that your videos are improving. Thanks a lot.

[@piconano]

Very juicy video. Chuck full of bits and bites of solid reasoning and clever design tips. I wonder why no one uses PTC power resistors for RE! It should prevent thermal runaways in MOSFETS. Logically, it should work, but I've never seen one!

[@Epaniale]

FesZ has been upload a new video. I'm now busy performing another things. So... go in, like the video, and return to watch it later! XD

[@david_6063]

Hello Fesz! Really interesting subject. Very well done. A few comments and questions. To start at the very beginning we could look at a single BJT wired up as your BJTs were wired up: base and collector to the V+ supply, with a current limiting resistor in the base, and the emitter at ground. Once we apply power the transistor will start to heat. Given the thermal time constant associated with the heating of the junction, the thermal resistance between junction and ambient and the applied voltage, it is in the nature of a BJT that it will either stabilize at some elevated temp or it will blow up. The possible blow up is as you said, due to a positive feedback loop. The nature of this loop is that as heat is added to the junction, the kinetic energy of the valence band electrons is increased to the point where they can pop up into the conduction band. Since the depletion region is relatively low in carriers, these thermally generated carriers make a difference and the forward current increases. More current produces more heat, more heat produces more current, and so on. This is called "thermal runaway." The increased current as a function of temperature is expressed by the Ebers-Moll equation, which you indicated. The most effective remedy is negative feedback using what you properly described as emitter ballasting. Here, as soon as the junction begins to heat, the increased current presses against the resistor, raising the emitter voltage, which decreases the VBE. Since the current is exponentially dependent on this voltage, this is a powerful lever. Note that the improved matching when you went from an RE of 3 Ohms to an RE of 5 Ohms was only about 3% (currents went from 108 and 101 to 102 and 98, a delta decrease from 7 to 4 on averages of 104.5 and 100), at the cost of a 66% increase in dissipated power. Knowing the best amount of voltage drop across RE is best determined from historical experience (rule of thumb), as you have pointed out. In an IC, the NPN power transistors are well matched, and in that case the current difference between transistors comes from voltage drops along the common ground (which put the emitters at different voltages). The remedy is the same, an emitter ballasting resistor. Finally, since this problem exists in all BJTs, we also see it small-signal amplifiers. There, the ballasting resistor is called "emitter degeneration" and it stabilizes the collector bias (DC) current over changes in the ambient temp. Here the delta Ic is (the temp change x 2mV/degree)/RE. RE also sets the small-signal gain, unless you don't want it for that, in which case it can be bypassed. My first question would be: since this problem is inherent in the BJT, are there any circuits that you know of that don't use an emitter resistor? I can think of only two, a temperature sensor and a logarithmic amplifier, but you know applications much better than I do, and I would be curious to know what other circuits BJTs show up in without needing a emitter resistor. Also, related to applications, do you still see that BJTs are being used in power? Because of thermal runaway and secondary breakdown (which is a different failure mechanism associated with turn-ON and turn_OFF), in "Fundamentals of Power Electronics 2nd Ed, Erickson and Maksimovic say that "At voltage levels below 500V, the BJT has been almost entirely replaced by the MOSFET in power applications" (page 86). This was written in 2004, and these guys are college professors, so what is your opinion? Do you still see BJTs in power applications? Lastly I would love to understand the circuit that you came up with for reducing the drop across the ballasting resistor, but I was massively confused. The LTSpice schematic showed the anode of Schottky D3 at ground and its cathode at the emitter of Q47. Looks reverse biased, no? Also there is a ground symbol connected to the positive terminal of V23? Anyway, looking at the white board (excellent diagram) that you show above the built circuit in your lab, the drop across the ballasting resistor is now (the voltage on the emitter of the power transistor VE, minus the negative supply plus the 3.3V Zener). OK, fine but what value is the negative supply and how did you choose it? More importantly what is diode D2 doing? You said you "added the current sink and diode to supply the emitters of the (low power) transistors". It looks to me from the circuit on the whiteboard that positive current from the emitter of the low power transistor would be reverse current in Schottky D2. On the other hand, the drop across the ballasting resistor is the VBE of the small power transistor minus the reverse voltage across the Schottky, which sounds like what we want. Is the Schottky reverse biased on purpose? I'm just ignorant of this kind of thing. Would love to have it fully explained. I had to stop here, because there's too much I don't follow. Anyway, beautiful work and presentation as always, thank-you so much!!

[@FesZElectronics]

Hello David! You are right, bipolar transistors are rarely used in power electronics. Any SMPS I worked on either had external or internal Mos-Fet's. The only common usecase for BJT i've seen is with things like digital signal switches - here the RE is not used, but its not needed anyway. I haven't really worked with, but in high power (1000W+) applications you have the IGBT which is somewhat of a hybrid between the BJT and MOSFEt, which is still in common use. On the other hand, with audio or other linear signal amplifiers, the BJT offers more linearity than MOS-Fets; as long as the amplifier is not working in Class D then the BJT seems to be preferred. Regarding the other point, lets start with the schematic on 14:28 - V23 has the positive terminal to GND so that its negative terminal is a negative voltage in reference to GND - the emitters of Q48/Q49 are at -5V in reference to GND. The point of the current mirror (Q48/49) is to set a current going from GND to -5V trough D3. This sets the cathode of D3 to ~(-0.3)V in reference to GND. With the whiteboard ( at 16:30 ), I did forget to add the "GND" but its the Cathode of D1. The negative supply is now 3.3V in reference to GND thanks to the D1 (the value was chosen mostly by what diode I had available - I only needed a voltage sufficient to keep D2 polarized and to keep the current mirror operating correctly). D2 again is directly biased, so its cathode is at ~(-0.3V), so below GND - the schematic could have been maybe drawn a bit better... In both cases, the signal driving the active ballast transistor is the RE voltage drop plus the D2 voltage drop. Let me know if this makes sense. Fesz

[@david_6063]

@@FesZElectronics Hello Fesz! Thank you so much for your detailed explanation! I do understand everything now. I learned some cool stuff and am very happy. Let me say this though. In introducing the LTSpice schematic with the Schottky diode offset, you said not one word about introducing a negative supply. Remember we are seeing this for the first time. Furthermore, the ground symbol used to define that negative supply had a wire running over it, somewhat obscuring the ground symbol itself. I know LTSpice lets you do this, but, in my humble opinion, it is not a good practice. I think the rail-to-rail environment (the supplies) are the essential framework of a circuit and should be noted. It is all obvious to me now. Here is how I see the offset working. With the addition of D3 and the current sink Q49, we may start at the collector of Q49 where the voltage is about 0.3V below ground. Moving up, through the emitter of Q46, we then reach the base of Q46, which is the voltage across the ballasting resistor and this is (-0.3 + 0.6) = 0.3, and you have reduced the voltage across the ballasting resistor by the drop across D3, just as you said. This is a beautiful way to create a desired offset. The voltage on one end of the ballasting resistor is pulled down by the drop across the Schottky, while its other end is grounded. Very, very cool. I am looking forward to learning more. Finally, you mentioned that: "with audio or other linear signal amplifiers, the BJT offers more linearity than MOS-Fets; as long as the amplifier is not working in Class D." Do you have any videos that talk about audio and linearity? Like how do we measure linearity, what does it look like in a circuit, how would an output be more linear with a BJT than with a FET, etc. Just anything to learn about linearity in an application. Any videos on that? Thanks again for your amazing work!!

[@FesZElectronics]

Hello David, I did not cover linearity in any video yet. Don't get me wrong, you can make a perfectly good amplifier both with BJT and M-FET. The BJT is cheaper, and from a linearity point of view, the driving the FET is like driving a capacitor - the gate-source capacitance can be in the order of nF so you need completely different current to drive it at 20Hz and at 20KHz. Also for FET's you have the transition between linear and saturation regions at quite large drain-source voltages - so the change in behavior needs to be taken into account. J-Fets on the other hand are far more linear. To be honest I did not study this problem in to much detail so I may be missing some points. P.S. I will try to keep my schematics more easy to understand, and go into more explanation details. Thanks for pointing this out.

[@david_6063]

@@FesZElectronics Hello FesZ, It is always great to read your comments! Yes, JFETs are interesting. When I worked with power op-amps (hybrid circuits) the differential pair was typically built with JFETs. Flicker noise in MOSFETs is associated with the thin -oxide (carriers get trapped there and released, if I recall correctly). JFETs have no thin-oxide, so no flicker noise (if I am wrong let me know). Your work is a tremendous help and asset to me. Thank you so much for what you do!

[@FesZElectronics]

Indeed, JFET's are known for being low noise - they are often used as high impedance input stages - in IC's as you mentioned, but even in things like oscilloscopes, the very first component the signal sees, is usually a JFET. From what I read only BJT can be built with lower noise than JFet but you need some current to drive them, so a Jfet input stage in an op-amp has a much lower input bias current. I guess the only problem with JFets is that they usually come in low power versions. On the other hand, for a final stage in an amplifier, it does not matter if the MosFet is noisy, since its contribution to system noise is minimal.

[@kamleshchavan7451]

Great video, some for me was easy to understand, and some part was a bouncer. Sir any video explaining working of RF transmitter receiver module circuits diagram

[@electroquests]

Thank you for the video! I learnt a lot. They never taught this at grad school

[@shamalperera4875]

Very good tutorial sir....

[@StephenCooteNZ]

Thank you ! Best wishes from New Zealand. ZL3ABX.

[@abhishekKumar-ry9en]

Sir You looks like professional, really 👍

[@EliteHEAD]

excellente

[@joejane9977]

thank you was explained with precision

[@egbertgroot2737]

Can you do a vlog about MOSFET totempole constructions without using a MOSFET driver IC?

[@grahamhall2662]

Excellent video, Perhaps one could match the small emitter resistor transistors from a batch of many to pick them with the same hfe gain rating? Learned a lot thank you.

[@soothcoder]

Nice! I think they call that method of limiting current a 'current foldback' on some old circuits. I've seen this in old oscilloscpe schematics for example. The current mirror with the transistors nearly looks like a diff pair attached to the emitters. Last circuit looked half-way to an op-amp!

[@hugoribeiro8281]

Hi Fesz, what a cool video! thanks. I've dealting with this issue in audio amplifiers and isn't easy to calculate with precision the emitter resistors to avoid positive feedback and with reduced dissipated power... normally I do a fast test with a heat air flow and adjust the resistor for a pessimistic scenario. It typically gives a value minor then 0.22R... However, to have some margin I always finishing by using the typical value of 0.22R 😄. Best Regards, Hugo

[@FesZElectronics]

Hello Hugo! I'm happy you enjoyed the video! What sort of currents did you have running trough each transistor when you used the 0.22r in the emitter?

[@hugoribeiro8281]

Honestely Fesz this was for a project that was never been finished... but I remember that I have done some trials for 3A to 5A of peak current in each device and after some calculations the resistor adopted was 0.22R. I don't remember the exact values but the question was something like this: ok 0.07R is enough but 0.22R gives a better current distribution and the dissipation is acceptable 2.5W... so let's use 0.22R 😄. In fact, this resistor has some impact in THD. This is a very interesting theme and there are few information about it. I've done a couple videos, in Portuguese, talking about these resistors and respective design criteria. Maybe you can talk a little bit about this in the next videos. My approach at the time was: assume a maximum delta vbe deviation between the 2 devices, ok 350mV... (one hot and the other cold) and calculate the resistor that gives this voltage drop with the maximum expected current, 3A or 5A. My final project only uses one device, STD03, so i don't have this issue 😉 but even in this case it uses 0.22R 😄. A big hug 😊👍

[@herbalhealing39]

Nice demonstration 👍

[@FPiorski]

If we're just trying to get the power transistors (DC) current balanced with as low of a voltage on the current sense resistora, like with the circuit @ 16:24, I think at this point it's better to just bite the bullet and use an LM358 to provide the feedback. I do appreciate the discrete component circuit, but with the cheapest LM358 costing just over 2 cents at lcsc, it is such a cheap and jellybean component that it may be worth it in this application and I'm pretty sure it could work with just 100mV on the sense resistor. Anyway, I do see that the video had a clear progression and considering the next circuit described it all makes sense, just thought I'd put my two cents (heh) in.

[@FesZElectronics]

Well, I was testing in DC because that is easiest to show, but the same methods can be applied even if the circuits have a certain frequency signal going trough. I guess the biggest problem with the op-amp method is that you need to take care of the bandwidth of the circuit, and also the op-amp needs to be close to the power transistor, otherwise you could get oscillations and other fun stuff. Thanks for the input!

[@mahdavimail]

Your setup looks like each transistor has it's own seperate load! I always thought we have only one big load which is connected to 2+ collectors your setup looks to me like a common collector than parallel! But a lot of good information in video , thanks a lot

[@Tortuga2321]

BCP56 is sot223 smd package. I assembled a lot on the machine :)

[@qazimtahir]

Very detailed video. Thanks 👍 I need your help to build a variable Power supply but high amperage, may be UpTo 50 amps. Can you make a circuit and video like this?

[@DiegoColl44]

Great..!! I was waiting for this video..!! Thanks..!!

[@KiwiMechEng]

Nicely explained, thank you!

[@AKorzenny]

Very good!

[@IntuitiveInfo]

Great video! I have a quick question. How to change the Vth of a MOSFET in LTspice? For example, if I am trying to simulate the parallel MOSFETs and taking a model from a vendor, let's say CREE, and importing it in the LTspice. Since the real devices have variation in Vth and R(ds)on that leads to the imbalance. How to vary Vth and R(ds)on in LTspice to study that imbalance? Thanks in anticipation! Keep up the good work!

[@FesZElectronics]

Hello Tahir! The threshold voltage is the VTO parameter in the mosfet model - you can play around with it; but the Rdson I think is calculated from other parameters, so I do not know of a direct way to modify it.

[@IntuitiveInfo]

@@FesZElectronics VTO can be changed for the Si MOSFET model. Unfortunately, the SiC MOSFET model by CREE has no VTO parameter in the model file. I'd be glad to hear if you got any clue for changing these parameters in the case of SiC models. Thanks for the answer and keep up the good work. I look forward to the next video!

[@rezareza-j9x]

Thanks a lot

[@q12x]

Foarte tare ! Excellent explained and presented !

[@shamalperera4875]

Sir bjt output stage amplifier cuircuit to convert mosfet ,,??

[@kabandajamilu9036]

So nice

[@xrphobby1341]

Hi trying to use transistors to drive LEDS using arduino and Max7219. My project works with small 7-segment LEDs using the supply of Arduino. However when I use 13V external supply for a bigger display, the LEDs are ON all the time. I'm using NPN to drive the DIGITS and PNP to drive the SEGMENTS. What could possibly be the problem why my project doesn't work anymore when higher voltage is used, the negatives of Arduino and external supply are joined together. Many thanks for your help.

[@bogdansofalca6946]

Great video as allways! One thing to note: mosfets, as opposed to bjts do not need matching for this type of application and can be directly connected in parallel as the rds_on has a positive temperature coefficient, providing in by itself the needed negative feedback -> adding source degeneration as suggested at min 9 may be a bit of a overkill. Spor in ceea ce faci omule, esti cel mai tare eevloger din cate stiu!

[@axk1]

If you drive the MOSFETs in the linear region that's true, but then in the saturation region the temperature coefficient is negative and the same problem arises.

[@bogdansofalca6946]

Not correct what you say, in fact Rds_on exibits PTC behaviour in saturation (MOSFET fully on). Nexperia application note AN11599 chapter 2 treats exactly this subject.

[@axk1]

@@bogdansofalca6946 Confusingly what is called saturation for bjts is linear region for MOSFETs, so you're reffering to the linear region. electronics.stackexchange.com/a/18904

[@david_6063]

@@axk1 I did not know that. What you say is very interesting. In the linear region the flow through the channel is resistive and the resistance goes up with increasing temperature because the mobility goes down. The mobility goes down because at higher temperatures the crystal atoms are vibrating more widely, which restricts the electron flow. In saturation on the other hand, the electron flow at the drain is either pinched (long channel device) or velocity saturated (short channel device). Why would, say pinch-off, change the temperature behavior? I mean, do you have any explanation for why the resistance doesn't increase with temperature in saturation? I don't. Would appreciate your thoughts on this. Thank-you!

[@FesZElectronics]

@Bogdan Sofalca @LeshaKu @David_60 - thank you for all these comments! I will be doing a second part regarding MosFets and try to address the issues that you all mentioned.

[@Sophie-oq5nd]

Very clear explanation ! With this i could eliminate output voltage instability in my high PSU for my Ham radio. thank you. Question: what simulating software are you using? Maybe a link to its website? Thanks :-)

[@FesZElectronics]

I'm happy you found this useful! I use LTspice in all my videos ( www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html )

[@janpolanton5574]

Hello! nice video. Could you show us how to modelise Ge transistors like AC or OC series with datasheets?

[@guilldea]

I've got a class H audio amplifier with tons of MOSFET in parallel, the amplifier is a couple of decades old and some of them get super hot (even on idle) while others are at room temperature, I got a feeling it's got to do with this?

[@FesZElectronics]

I guess if the problem was current sharing, the heating up should have occurred from the very beginning when the amplifier was built. Since its so old, I think it might be some other issue.

[@planker]

Excellent.

[@amratsingh5206]

Is it true that with single supply and schottky diode with current sink, you get less voltage on the current sense resistor but increase in overall voltage drop leaving slightly less voltage for the load? Due to the added zener diode?

[@Davidsmith218]

How would this work on MOSFETs

[@CrisDFF30917]

Hello, please help me to understand something, lets suppose you need to provide 3 A to a load, and you are using NPN type transistor on common-emitter mode, so lets say we use 3 TIP31C transistors and we place them in parallel, but as you said we need the emitter resistor, but that resistor must be able to handle 1 A of current, so are they a special type of resistor?

[@FesZElectronics]

Usually its not the current that is a problem but rather the power dissipation and power rating - for example if its a 1R resistor (P=R*I^2) you need a resistor rated for more than 1W; if its 0.01R, it just needs to handle 10mW; the choice of resistor will be done based on the exact power that will get dissipated

[@Davidsmith218]

I'm using irfp260n MOSFETs and using a checker to get the gate voltage as close as possible so could I place a 3 to 5 ohm resistor on the gates and that should match them even closer even though they are closely matched already

[@FesZElectronics]

I'm not sure if just connecting the transistors in parallel is a good idea at high frequency - because of the distance in-between you will get phase variations in the signals that reach the gate and are then interconnected after the drain. I think some sort of trace length equalization will also be needed.

[@custodiogomesbarcellos4972]

Cool video!!

[@EhsanAlnazi]

Great video!!

[@lucemferr1]

Nicely explained! :-) Thank You

[@grzesiek1x]

Thank you!! It really helped with my project! I have used many controllers but recently I was looking for something cheap and simple that I could use to controll powerfull devices! And it really works! I just need to balance all the transistors better ( I have a 20 mA difference sometimes for 600 mA in total but it is ok in my project, the problem is I don't have a few values power-resistors - only 1 ohm - 5WATT and of course normal resistors are not good here, just need to order more usufull different values and it will work perfectly! ). I was really surprised how well I can controll my DC motor with my 4 transistors (PN2222) as well as with more expensive motor drivers like L298N etc. :D

[@FesZElectronics]

I'm happy this video helped, but I do have to ask, why bother using multiple transistors in parallel at such low currents, would it not be easier to use a slightly higher current transistor? Also, if your maximum motor current is 600mA, its just on the maximum limit of the transistor, so even a single PN2222 should be enough. Or maybe I misunderstood.. One more more thing that might be helpful, there is a lower current alternative to the L298 - the L293. It should also be cheaper than the 298.

[@grzesiek1x]

@@FesZElectronics what I do it is only for learning ;) I know that there are multiple options and high current mosfets ,circuits etc. but it was just to find out how in the cheap and easy way i could the same result :)

[@grzesiek1x]

@@FesZElectronics I use all of them but this time it was just to find out what I can do :)

[@grzesiek1x]

@@FesZElectronics Also I learn electronics as in extra/additional thing to my programming/coding (so the perpuse is to learn and understand electronics and what happens for example in the computers or machines etc. - this is why I go a little bit differently than other people). I have noticed also that people use "already made" things but at the same time they don't learn this way because there is somebody else made it! With some stuff of course I buy "ready to use" things when fabricte or make for my own is too hard or more time consuming (like drone frame for example or sensors which I just can't fabricate at home haha LOL ) :D

[@grzesiek1x]

another thing ... my PN2222 should handle 0.8 A but maybe I have some faulty transistors because even at 0.6 A they become realllllly hot and they easy burn themselvs above 0.6 A...

[@manojpokhriyal1183]

Sir can you please explain how to find the reverse recovery characteristics for diode using Ltspice...

[@david_6063]

Make a series circuit with a voltage supply, a resistor and a diode. Apply a large enough voltage with the supply, say 5V, to put the diode in forward bias. The other 4.4V is across the resistor. Then apply a fast step change to the supply, say a 1 ns fall time to -10V to put the diode in reverse bias. The total time taken for the -10V to be placed across the reverse biased diode is the reverse recovery time. It consists or two parts: a delay and then an RC charging part. The delay is the time taken for the minority carriers associated with forward bias to be removed. These carriers can be removed in two ways, through recombination and through the reverse current. The rate of recombination is expressed in the Spice model with the TT term (transit time). The smaller this number, the faster the rate of recombination and the faster the diode can switch from ON to OFF. Once the minority carriers are removed, the forward bias on the diode will go down to zero. After that, the RC charging of the depletion region takes place as the depletion region expands until the full reverse bias voltage is placed across the diode. In the RC charge time to establish the reverse bias, the C is from the diode's depletion region capacitance and the R is the resistor in the circuit.

[@alexlo7708]

Seems very complicated in the last section circuit. Kudo to those who's designed such a messy one.

[@ahmatrizki5154]

So its how audio amplifier works

[@robr8554]

Awesome 😊

[@bilalasim3427]

What is the name of this simulator?

[@FesZElectronics]

Its LTspice - this is what I use in all my videos.

[@bilalasim3427]

@@FesZElectronics thanks

[@tomboxyz5564]

Using current mirrors made of discrete components is a bad idea, especially if you don't use massively oversized transistors, you run into that same problem you tried to mitigate here, they heat up and runaway, I've made that mistake when designing a 4-20mA output for a controller, at the full 24V supply it ended up not going below 40mA at the 0mA setting, and the transistors were basically right against each other, connected by copper planes, to keep them at the same temperature

[@david_6063]

Yes, keeping them at the same temperature provides negative feedback from the mirror transistor to the load transistor. I had a colleague who was building a discrete high power PNP current mirror and he forgot to put them on the same thermal substrate. The load transistor blew up. What happens is that the load PNP will start to experience thermal run away, partly because with a ground connected load its VDS is large and partly because that is just what BJTs do. However, with a common thermal substrate the heat in the load PNP is communicated to the mirror PNP. As the mirror PNP feels this heat, its VBE will go down because with a fixed current (defined somewhere else), it can conduct that current with a smaller VBE. The mirror PNP and load PNP share the same VBE, so as the common VBE decreases, the current in the load PNP is brought back down and thermal run away is avoided. Emitter resistors should probably also be used. Your comment about this problem pertaining to discrete components is correct as PNPs in an IC are on the same substrate and so negative feedback based on a thermal link is automatically provided.

[@ikbendusan]

given that you're making all these pcbs, do you have an acid bath ready to go at all times or something? lol

[@FesZElectronics]

I normally use iron chloride (FeCl3). I feel like its the fastest way when I need a simple board done fast. I know that in the past nitric acid (HNO3) was also used to make boards, but that is quite hard to get, and dangerous; but you can also etch boards with sodium persulfate (Na2S2O8) - this last one should be the safest method.

[@creatorchris712]

You almost look like Alexander the great

[@plabandebbarma155]

এত হেডার হেডার করলে ভিডিও কোন সময় দেখাইবা চান্দু

[@HeathLedgersChemist]

Please stop saying 'exact same' - it's incorrect & inane.

[@saint_and_holy_unicorn]

I liked a lot the explanation!!✌️✌️ thanks