In the third part of our series we complement our 1:1 Balun with a 4:1 version. Focus is again excellent common mode attenuation and first class SWR matching. All for high HF output ..
He is one of the very few technical teachers on KZitem, (or in college,) who can explain things so even I can understand them, not just 'learn' them but UNDERSTAND them. Even with his odd accent, pronunciations, word choices, and syntax he STILL communicates for free far better than any professor whose salary I was paying.
@Lukewarm109
8 жыл бұрын
Probably the best series of videos on baluns here on youtube. Excellent work. Cheers 73
@TRXLab
8 жыл бұрын
Hi Luk, thanks for the nice feed-back! 73
@W-733_KWX
4 жыл бұрын
I definitely agree
@jaescalantel2
4 жыл бұрын
I also fully agree, I always found complicated understand the way a balun works, with this series of videos devotes to balun I feel enough confident to get into the interesting part of the electronic
@outalive55
Жыл бұрын
I too agree, thank you for your expert advice and teaching. You have enlighten me and encouraged me to improve my understanding of electronics
@kepkopke
Ай бұрын
Not probably - definetly!
@michaelbarrett8083
6 жыл бұрын
Thank you Peter for a very informative and useful series of videos. I will get to making my 9:1 Balun and 1:1 as soon as the wire arrives. This is probably the best tutorial on the subject. Thanks again
@Millstone_Firewood
8 жыл бұрын
The BEST series of balun videos I have ever seen! Thanks so much for this Peter!!
@TRXLab
8 жыл бұрын
Thank you Mitchell 73
@jimwolsiffer4397
2 жыл бұрын
Awesome series! You should put all your vids on DVDs and offer them for sale. Excellent tutorials and hands on. You have inspired me to get back to the bench and start building again. I have several piles of parts to build projects you have covered. 73, Jim.
@oldbassist60
Жыл бұрын
You answered a question I had about "daisy chaining" 1:1 followed by other ratios of baluns for both matching and CMR. I love the "unfolding" explanation of the phasing. Your numbers stand behind your construction. Well done!!
@acestudioscouk-Ace-G0ACE
4 жыл бұрын
I'm watching this series of videos for the second time because there is so much good stuff to learn, I need to watch it at least twice to take it all in. You have put a lot of work into this and I'm very grateful. I wonder how many people you have saved from radio interference and how many rigs you have saved from too higher SWR! Thank-you.
@tomw3380
Күн бұрын
Thank you for providing such excellent videos. I saw where one individual was critical of you for taking so much time to explain what was on your video. Anyone that thinks it is too long can easily zoom ahead or click it off. Keep providing your knowledge to help us learn the correct way to build balun/chokes using the most efficient toroid material.
@neotoxo54
3 жыл бұрын
Thank you for this education. I just put up a new OFC Dipole using a balun I built per your instructions. It supposed to work from 80 meters to 10 meters BUT I can also tune it to the bottom of 160 meters. My MFJ-929 Intellituner easily tunes on all frequencies. Very happy with the results. 👍🏻👍🏻
@wisecitizenry2844
5 жыл бұрын
Great videos, great instructions! You are helping me better understand the hobby so much, thank you for everything you do.
@AlaskaLinuxUserAKLU
3 жыл бұрын
Most informative video I've ever seen on Baluns! Thank you so much!
@Swoop180
7 жыл бұрын
Thank you, thank you and thank you again. Very nicely done with the thoroughness that really helped me understand exactly how a Balun works.
@TRXLab
7 жыл бұрын
Hi John, glad that it was helpful for you. Thank you 73
@dinosworkshop6870
8 жыл бұрын
Sort of like the icing on the cake. Thanks for another fantastic, well presented tutorial which will be of great value to all here! Absolutely well explained. Terrific work. Top quality. Thanks so much!
@TRXLab
8 жыл бұрын
Thanks for nice feed-back! Glad that you like it 73
@TheRadioShop
8 жыл бұрын
That was a lot of explaining Peter! Very well done my friend. Was a great way to start my day :-)
@TRXLab
8 жыл бұрын
Thank you my friend. Yes a lot of explanation, honestly hope that all are able to build their own balun now. 73
@Factory400
2 жыл бұрын
This is AWESOME! Thanks for the hard work putting this together ❤
@michaelheindl3665
Жыл бұрын
Excellent Video explaining everything about how to make these baluns and why they work to attenuate Common Mode interference and keep your SWR very low across the entire bands.
@photonthief
Жыл бұрын
These videos are exceptional. Thankyou for taking the time to explain these principles so clearly.
@davideisenberger6197
7 жыл бұрын
Thanks again Peter. Your an excellent teacher. Have learned .so much from you! Back in the day, we didn't even know about common mode currents! looking forward to many more of your video projects! 73's de K8KEM David from Ohio USA
@TRXLab
7 жыл бұрын
Hi David, thanks for the nice feed back! I'm glad that you like my videos! All the best to Ohio 73
@kb3svj
6 жыл бұрын
WOW! You really made things clear to me regarding baluns. I must say, I came across this and watched it first but know that you have two oter parts from earlier. I shall surely watch and stash away same. I have been looking high and low for some material that not only show how to build the devices but to also understand how they work. Thank you!
@TRXLab
6 жыл бұрын
Glad that you like it! Thanks for watching 73
@reallybadaim118
4 жыл бұрын
Most impressive construction, demonstration and explanation. This is very impressive. I can't wait to share this. Thanks for your time and sharing it.
@philippe5394
5 жыл бұрын
Hello, this is a very clear explanation on construction, the theory behind, and the testing configuration. I really appreciated the way you have transformed drawings for a better understanding. Thanks a lot.
@TRXLab
5 жыл бұрын
Thanks for feed back! 73
@mikemcelvany9412
7 жыл бұрын
Thanks for such informative demonstrations. I have never seen a better demonstration about baluns.
@TRXLab
7 жыл бұрын
Thank you Mike! 73
@marklowe7431
6 жыл бұрын
Always appreciate people who help others learn. Excellent video. Thank you for all your effort. Great point on the ptfe insulation. makes sense.
@TRXLab
6 жыл бұрын
Glad that you like it Mark! 73
@mikesradiorepair
8 жыл бұрын
Another great video and explanation Peter. Thanks for sharing. Mike
@TRXLab
8 жыл бұрын
Thank you Mike!!
@mikebarton9324
8 жыл бұрын
Another clear explanation of why, as well as how.Thank you for taking the time
@TRXLab
8 жыл бұрын
Thank you Mike! 73
@AntiqueRadioandTV
8 жыл бұрын
Whoa... That's what I call an exemplary explanation of a balun. How you dissected the balun schematicly, (is that a word?), so us "mere mortals" could understand it was fantastic! Talk about performance and flat across the whole HF spectrum. Wow! I think I got 90% of it on the first watch. I think that I'll use up some more bandwidth to watch it a second time after I comment here. Really a great series Peter and I really much appreciate it! 73s Tom
@TRXLab
8 жыл бұрын
Thanks for the kind words Tom! I'm really glad that you liked it! All the best 73's
@leifkristensen7688
7 жыл бұрын
Hello my friend, I, I've been a radio amateur for 37 years I have made many baluns that was not good, after I followed you here on youtube (Now, I understand what it is all about), I made a balun according to your recipe it's the most amazing data I've seen from my mvna. Thanks
@TRXLab
7 жыл бұрын
Hi Leif, thanks for the feed-back. I'm glad that my videos are helpful for you... All the best and 73
@Mr_Meowingtons
7 жыл бұрын
Very well done Peter! i love your videos and ill be making one for my tunner i am working on
@TRXLab
7 жыл бұрын
Hi Matt, thanks for feed-back. Good luck with the project..73
@jimosullivan3454
7 жыл бұрын
Matt K i
@Mr_Meowingtons
7 жыл бұрын
Jim O'Sullivan ????????????
@MrBanzoid
5 жыл бұрын
This wire is available from some sellers on eBay in multiples of one metre. I can't remember the seller but a quick search should find it. This is the best tutorial ever for building baluns. Great explanation and tips about "unfolding" a circuit to make it easier to understand. I built your 1:1 choke and it works brilliantly. I intend to build the 4:1 balun for a delta loop. Thanks and 73 de Malc 2E0EZP.
@TRXLab
5 жыл бұрын
Thanks for feed back, very much appreciated 73
@REKlaus
3 жыл бұрын
Great video series with excellent theory, design and testing. Thank you. 73
@de_w8tam
4 жыл бұрын
Here I am, watching this video, winding another balun. Peter, thank you so much. You are my companion every time I wind one. I think, this might be the 9th one I've wound. We miss you, and hope you can return to KZitem soon! 73 de w8tam
@alistairfyffe
2 жыл бұрын
Excellent - clear and practical. wish I had found this years ago!
@claudioi2ndt313
8 жыл бұрын
waiting for a 9:1 balun... BTW thanks for your videos!!!
@OrbiterElectronics
8 жыл бұрын
A very good series Peter. Thank you Regards John
@TRXLab
8 жыл бұрын
Thank you John! regards my friend
@luisr.3855
6 жыл бұрын
Finally someone fully explains. Thank you for your time sir
@TRXLab
6 жыл бұрын
Thanks for watching 73
@brine1955
2 жыл бұрын
Truly excellent video on balun design and principles! All makes sense now, Sehr Gut!
@karlkaefer2569
3 жыл бұрын
Another real great video, especially when you have read the corresponding web pages of DGOSA (unfortunately SK) before. I´ve gotta go obtaining these special 18 AWG coloured PTFE-wires - not so easy even in Germany itself. Many thanks once again for making all these videos on/for TRX-Bench and best 73!
@jeromewhelan6723
7 жыл бұрын
Thanks for the easily understandable explanation where you derived the single-winding auto-transformer diagram by "drawing-out" the original schematic.
@TRXLab
7 жыл бұрын
Glad that you like it Jerome! Thanks for feed-back 73
@jeffreyrichard9675
6 жыл бұрын
Thank you for making these videos and certainly for doing it in English which made it possible for me to learn from it. Great job! 73
@TRXLab
6 жыл бұрын
Glad that you liked it Jeffery1 73
@josefelixvazquez1935
5 жыл бұрын
again excellent video, waiting for the 2:1 for my full loop antenna. thank you.
@eddiejones8709
7 жыл бұрын
EXCELLENT... Thank you for taking the time to explain this subject. I now have a better understanding of balums.
@TRXLab
7 жыл бұрын
I'm glade that you like it. Thank you Eddie
@gripper021164
8 жыл бұрын
Great video Peter as always. Fantastic explanation on the math theory and the practical and build.....I really enjoyed this..... 73
@TRXLab
8 жыл бұрын
Glad that you like it. Thanks for feed-back 73
@juanluisperezgarcia6333
Жыл бұрын
The best explanation about BALUNs !!👏👏👏👏
@Hungry_Hunter
3 жыл бұрын
Very nicely explained and the maths didnt hurt one little bit. Great stuff.
@randyterrell4704
7 жыл бұрын
All of your balun videos have been outstanding and appreciated. Just a suggestion, since there is now a significant amount of baluns used in high power transistor input and output circuits and their low impedances, you might want to address 1:4 or even 1:9 ratios (12.5:50, 6.25:50) and the considerations of the associated impedances of the windings. Regardless, well done!
@adriaanvandenbrink5025
6 жыл бұрын
Adriaan Ieatned a lot from your video'"s thank you for that
@jurgentraude4365
8 жыл бұрын
Very nicely done Peter! Have not seen such a nice explanation with documentation for a long time! Keep up the good work! 73 VE7FE
@TRXLab
8 жыл бұрын
Thank you Jurgen, Glad that you like it 73
@rickseifert5139
7 жыл бұрын
Peter, super video, I've learnt lots now from all 3 of your video. I can now use this 4:1 and connected to the 1:1 balun in project box to match my new project antenna is cubical quad for 11 m band cb radio frequency for test. Quad shape is diamond pattern. I hope this will balance well and give very good low VSWR across all 11 m. I'm using 27.400 as input freq on driven element.
@TRXLab
7 жыл бұрын
Good luck with the project! 73
@PapasDino
8 жыл бұрын
Thanks Peter, I really liked the way you deconstructed the impedance transformation - transformer and phasing relationships always make my head hurt when winding toroids and binocular cores. I'm going to copy down your diagrams to put them in my bench reference binder (no sense in reinventing the wheel). 73 - Dino KL0S
@TRXLab
8 жыл бұрын
Thanks for the nice feed-back Dino. Yes it is made for bench reference binder and I'm honestly glad the you find it worth to add it to your files.... Have a nice Sunday 73
@jimc5308
4 жыл бұрын
Hello Peter First let me say THANK YOU for showing us how to wind baluns. You explain everything very well. I am grateful for your use of the English language which made it possible for me to learn this art of baluns. I have made several 1:1 and 4:1 baluns while following your videos. I am trying to apply the mathematics using the formula you showed for winding the 4:1 transformer to other ratio transformers. I would like to make a 2:1 to match 100 ohms antenna to 50 ohm coax and a 6:1 to match 300 ohms antenna to 50 ohm coax. I am having difficulty with the formula. N1/N2 = SqRt of R1/R2 For 6:1 I come up with 2 wires at 9 turns left side on core FT240-43 and 2 wires at 13 turns right side of core where N1 = 44 and N2 = 18; SqRT of 300/50 = 2.44 and N1(44)/N2(18) = 2.44 . Also R1= (N1/N2)Squared X 50 so R1 = 298.7? Can you help? Am I correct? However I have not figured out the 2:1 formula yet. Thanks again and best 73 de Jim Hope you are staying safe and healthy!
@johnbellas490
8 жыл бұрын
Peter these videos were certainly VERY GOOD !!! They cleared up 2 questions I have had for a while !!Your graphical schematic was I think the key to my understanding how the transformer action occurs !!!!!This was extremely helpful My Many thanks to you!! You really outdone yourself on this one,and I think a whole lot of people appreciate it !!!! once again MANY THANKS. John A Bellas KC2UVN
@TRXLab
8 жыл бұрын
Hi John, thanks for the kind words! I'm glad that the video was helpful. All the best 73
@hdmalpas
8 жыл бұрын
Wow! I am impressed Peter.
@TRXLab
8 жыл бұрын
Thank you Howard! 73
@petarpetrov6388
7 жыл бұрын
Thank you, Thank you, Thank you! One of a very few videos that is not "do this and do that" but the hole theory WHAT are the processes and the theory behind them.
@TRXLab
7 жыл бұрын
Thanks for your feed-back Petar! 73
@ralph9987
4 жыл бұрын
Danke fur das video. I don’t have access to that wire, so I used enameled 1mm copper wire with the 240-43 core was Very pleased. 0-450mhz under 20db and max swr was 1.2 at that higher freq. spitze!
@k4eqedarklorddesigns480
7 жыл бұрын
Very informative! I'm currently tinkering with some cores now and your videos helped me on wire selection. K4EQE 73
@TRXLab
7 жыл бұрын
Thanks for watching! Glad that you like my video! 73
@LU8HRW
4 жыл бұрын
Thank you for the explanation and the video so clear. I will make a 1: 1 balun but with 1.25MM enameled copper and toroid coated with teflon tape. 73!
@williamna5800
5 жыл бұрын
Very well done, simple and well explained. Great video.
@TRXLab
5 жыл бұрын
Thanks William 73
@watthairston1483
9 ай бұрын
Outstanding video and content! Thanks.
@gpb118
7 жыл бұрын
Hi, Great video, my friends and I have learned a lot but I would really like to test the balun in transmission mode but am struggling to ascertain the resistor setup you use between DUT & DET on the tiny... I look forward to your valued advice. Gary
@mfmoran1
4 жыл бұрын
Wow great info. Thank you for doing this. What are you thoughts on using different mixes for each core. what if you used Mix 43 for the 4:1 and Mix 31 for the 1:1. would that work or would there be issues between the core? Thanks again. Also, if I were to use a larger wire and had to reduce the number of turns, how would i calculate the impact to attenuation? Take care, --Mike
@thuff3207
7 жыл бұрын
Can you tell me if your PTFE AWG 18 silver coated wire is solid or stranded. Thank you
@user-su5sq5ib3i
2 жыл бұрын
You are the man! I love your videos!
@M7XCB
5 жыл бұрын
Very clear explanation you are a good teacher great video
@TRXLab
5 жыл бұрын
Thank you !
@sequri
8 жыл бұрын
Great series; much appreciated; thank you. 👍
@TRXLab
8 жыл бұрын
Thanks fpr stopping by 73
@outlawhead
8 жыл бұрын
Ditto :O) 73
@TRXLab
8 жыл бұрын
+outlawhead 👍👍
@iain777uk
6 жыл бұрын
A superb explanation of baluns.
@TRXLab
6 жыл бұрын
Thank you 73
@rossrogers2979
7 жыл бұрын
This video was great. Thank you for sharing.
@TRXLab
7 жыл бұрын
Thanks for watching Ross 73
@vidasvv
4 жыл бұрын
Great video with excellent explanation ! I wish you would do video on the performance when the cores are heated up a bit. 73 N8AUM
@vk6op648
8 жыл бұрын
@ 33min, like a voltage divider, i suppose thats how it works in a way. Many people are visual learners so the diagrams are key to understanding this. This is where most text books and lecturers fail. You made this very simple. VK6OP
@TRXLab
8 жыл бұрын
Thanks for nice feed-back. Glad that it was helpful for you. All the best 73
@coltronex
6 жыл бұрын
This series is very educational,theory and practice the basis for learning,I wish I could speak German as well as you speak English,superb,regards Colin.
@TRXLab
6 жыл бұрын
Thank you Colin for the kind words...Glad that you like my videos 73
@papafox-jh6rv
Жыл бұрын
In add to the quality content, the Shakespear not being my native language, the wpm is really appreciated for the understanding, thank you very much.
@iblesbosuok
3 жыл бұрын
Excellent video!
@davidgaleski5303
7 жыл бұрын
thank you for the help
@Aleziss
5 жыл бұрын
Can you explain how we could get a 2:1 or 6:1 ? How does the turn count work to acheive a different impedance ratio ?
@georgebrody8243
8 жыл бұрын
peter, thanks for the great videos. tell me what are the resistors and capacitor values in the completed project as i want to build this balun.73
@andya940
5 жыл бұрын
Hi Peter, In video 2 connecting the 1:1 Balun on the input side you connect the centre two orange wires to the centre of the coax. But in video 3 you connect to the two purple wires of the 1:1 Balun to the centre of the SO239 socket. What is the reason for the change? Thanks
@daleeckart6786
7 жыл бұрын
Ok, I bought a FT140-43 toroid and some 22 AWG wire PVC insulated (600 volt) to attempt a lower (100-watt) power winding. However, I can only manage 12 turns around the entire core, let alone 1/2 way. This wire is hook-up wire from Remington Industries, and looks to be about 3/32" (2.38125 mm) in diameter. What style 22 AWG wire is suggested, and who to buy from?
@Betarepair
7 жыл бұрын
I like your taste in Bench top test equipment. I also have a CMT 54. A great piece of all round test equipment.
@TRXLab
7 жыл бұрын
Thanks for feed-back 73
@dennisbauer3315
5 жыл бұрын
Thank you again, I agree with Luke, I learn my math's easier of you TRX Bench, and am able to get a full understand of your teaching, and am able to apply it fully in everyday workings, I am truly grateful.
@TRXLab
5 жыл бұрын
Thank you Dennis! Glad that my videos make sense to you 73
@fenderblues1744
6 жыл бұрын
Peter what effect would this system have on amount of RF from the radio to RF amount leaving the antenna. Have you a way of checking RF the input to RF output of this devise and could you show it in a video on your scope. Thanks.
@jose_simon
8 жыл бұрын
Very useful videos! Thanks!
@TRXLab
8 жыл бұрын
Thanks for watching Ignacio...73
@srickard99
5 жыл бұрын
Hi Peter! After doing more balun research, it appears that the DG0SA balun is a 1:1 choke followed by a single core Guanella 4:1 balun, otherwise known as a hybrid balun. The choke solves the common mode current issue with a single core Guanella balun. Guanella baluns using 2 cores do not appear to have common mode current problem. What are your thoughts on this?
@johnnybigpotato2404
Жыл бұрын
Question: Will adding cores to the stack add any efficiency in this type of balun like a 49:1 does? Or no? Thanks! Great Videos!
@perdidoanonimo
5 жыл бұрын
Peter thank you very much for such great videos! thanks to you I managed to build my first baluns successfully! One question, could you please recommend any book for deeper understanding, possibly with a hands-on/experimental approach ;-) ? Thanks! 73!
@easydogeasydog3225
Жыл бұрын
Peter, what if any changes would I have to make to the Balun, and or the transformer if I am using # 14 7strand wire in an open line configuration with spreader spacers. Planning on making a ZSBKW fed with the homebrew ladder line on an 80 meter 1/2 wave dipole. I have no way to measure the ohms, but from the reading I have been doing I am told that I could expect 600 ohms. There for I thing there maybe changes needed on the transformer to make a better match. appreciate any comment you may have on that set up?
@jeffreyrichard9675
5 жыл бұрын
Maybe this is a silly question... When both coils are completed and soldered together, is it OK to fold them over and mount them stacked in the box to save space or should they stay side by side when mounted to avoid some type of interaction? Thanks.
@JTNicolas
8 жыл бұрын
Esta explicación no puede ser mas clara, Gracias por tu video....
@TRXLab
8 жыл бұрын
Thanks for feed-back 73
@garrykraemer8993
2 жыл бұрын
Outstanding presentations! Now, how long are the dipole wires for a multi band 40M to 10M antenna? Do you use the same AWG18, PETG covered wire? Garry / WD0DUD
@eddy4011
3 жыл бұрын
Thanks for your video only one question. I want to make a balun for 20 meters ,can I use ferrite core ft140-43 is good option for this band even for 7 MHz 40 meters too....? O I have to use ft140-31 Thanks in advance Eddy from 🇺🇸
@Drekkag
5 жыл бұрын
Just one question about the balun setup. You noted that using a tuner and a very short antenna leads to high voltages. Would that be a concern at 100 watts using a 40 metet dipole for all hf including 160 meters? Or is the voltage issue going to be of concern with higher wattages? I really enjoyed all 3 videos and will be using it in my antenna system. Thanks for doing all the hard research and video work. 73, ad0am
@slickman1953
4 жыл бұрын
Great video!!!!
@g0fvt
4 жыл бұрын
Hi Peter, there is another very good configuration for a 4:1 that I have previously used, it too uses 2 seperate toroids. I wonder how it would measure in comparison to yours? My own 1:1 baluns would on FT240-43 cores using a simple pair of teflon wires do not make any attempt to preserve a 50 characteristic impedance but have very wide bandwidth and yield about 35dB of common mode attenuation in a 50 ohm system (measured with a Nanovna). I realise this is one of your older videos but you have covered this subject extremely well. Most of the commercially produced baluns on the market are utter junk.
@morphshag
Жыл бұрын
How critical is it that one side goes over and one side goes under? We built these at my local club and both sides were wound the same direction. We tested it on a 200 Ohm load for SWR and on a Rig Expert and seemed to pass with flying colours? I'm just a noob and put it together the way they told us to.
@shaneeloina8474
Жыл бұрын
Hello, nice work ! You mentioned to have higher power handling to add another 240 size torroid in the first stage (common mode). Is another torroid required in the impedance matching section as well?
@daleaferrrier
7 жыл бұрын
This is a question: So to get a 9:1 balun we could use the same 18 gauge wire except use three strands side by side and wrap it for 8 turns not 12. Then wire it up so that R1 sees 48 turns and R2 sees 16 turns. The math would look like: R1=(48/16)^2 * 50 R1=3^2 * 50 R1=9*50=450 ohms Does that sound correct?
@ericsrussell
3 жыл бұрын
Do you feel this method could be used but alternately wired in a configuration for a 1:4 balun 12.5ohm to 50ohm? Thx, 73
@biringen
2 жыл бұрын
What type of core did you use? FT240-43.. i have a couple of red T200-2 cores laying in my drawer and what would be the practical differance between those two cores at HF 1-30MHz and Power
@norbertstepien9185
3 жыл бұрын
Hi i really enjoy your videos and have constructed the baluns you describe with outstanding success. I was wondering if it's possible to build a 2:1 balun applying the same engineering?
@LU8HRW
4 жыл бұрын
Very well explained and very clear the video. I will put it into practice with FT240-31 one 1: 1 toroids for a bi band dipole (3.7 and 7MHz) and another with the same toroid but 4: 1 for a 7MHz loop delta. Is the cable you use rigid or braid? Thank you for sharing. 73 of LU8HRW
@lonmartinlonm6409
4 жыл бұрын
Do you have any idea what the Z-MAG value is for the 1:1 common mode choke?
@johnpwmcgrath
3 жыл бұрын
Thank you for teaching us about building and testing baluns (ununs). These are amazing videos!!! Please can you recommend the best wire/torroid combination for a similar QRP solution? Thanks again, John VE3JPW
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