Decibel Deathmatch (or how I learned to love logarithms)

I have noticed that one of the most confusing topics in ham radio is the decibel.  I believe a lot of the confusion relates to the complex look of the formula:

 That “log” really freaks people out, especially if you've never taken a math class that included logarithms in the curriculum.  Logarithms are a way of multiplying or dividing large numbers by adding smaller ones.  Another area of confusion is in the descriptions of the inverse operation, that is, taking a decibel number and working it backwards to get to the number that was multiplied or divided by.

Decibel calculations are not intuitive.  You have to practice and pay attention to what the calculations mean.  The mechanics of the formula are fairly straightforward and today’s scientific calculators do all the heavy lifting for you.  You literally just have to push a button to get the answers.  Unfortunately, if you  don't understand what’s going on you won’t perform the steps in the correct order.

First you should take a look at your calculator and notice that the key labeled “log” has a second function above it.  That second function is the inverse operation of “log” and is labeled as “10^X.”  You pronounce that “ten to the X” and all that means is you are raising the number 10 to the power of the number in the calculator’s display.  If the number in the display is 2, when you press the 10^X key you will get the result of 10² (ten squared, or 10 to the second power) which is 100 (10 times 10 is ten squared).  Logarithms take that relationship and put it into a different form.  In that 10 to the 2nd power equals 100, the base is 10.  There are as many bases for logs as there are numbers, but the one on your calculator, and the one that doesn’t specify a base, is the base 10 logarithm, or log₁₀.  So the log₁₀ of 100 is 2 because 10 to the 2 power is 100.  All you really have to understand is that the 10^X and log key are inverses of each other.

So try it.  Enter 100 into your calculator and press the log button.  The calculator should now show the number 2.  Now press the 2ND button on your calculator (to use the second function of a key) and press log again.  This time because you pressed the 2ND key first you are accessing the 10^X function and should now see 100 on your screen.  See?  We’re back to our starting point.  This is an important point to recognize as we go forward.

Another point of confusion is in which number to put on top in the P_measured/P_reference part of the equation.  If you are looking for a gain you put the bigger number on top and divide by the smaller number.  E.g., if you have a 50 watt radio and your amplifier puts out 100 watts, what is the gain?  Well, in plain numbers your gain is 50 watts.  That’s a doubling of your input power.  If you plug those numbers into the formula as 100/50 you will get 2.  That’s the multiplier.  The log of 2 is the power you raise 10 to in order to get 2 as the answer.  If you accidentally put the numbers the other way, 50/100, then you’d get 0.5 or 1/2.  100 watts is not half of 50 so you know right away that you did something wrong.  So what decibel value represents that doubling of power?  Well, with the original answer of 2 in the display (from dividing 100 by 50) press the log key and you should get a number like 0.3010299 etc.  We’re almost done at this point, all that’s left is to multiply this answer by 10 to get, rounded off, 3.  So a gain of twice our input power is 3dB.  If you had instead used the numbers backwards, so 50/100 resulting in 1/2 (0.5) then when you pressed the log key you would have seen -0.3010299, which when multiplied by 10 would give you minus 3dB!

Eventually most people come to terms with the formula for calculating dB.  The most important thing to remember is that you are dividing 2 power values (or voltages if you are working with voltages) to get the ratio of them.  Gain is what you have when you divide the bigger number by the smaller, and loss (minus dB) is what you get when you divide the smaller by the larger.

Where a lot of people have the most trouble is when given a decibel value and either asked to calculate the multiplication/division factor, or given a dB value and a power and asked to calculate either the starting power or ending power.  For instance, if I tell you that I have an amplifier that provides 7dB of gain no matter how much power is put into it and ask you to tell me how much power out I’d get if I fed it with 50 watts on its input how would you calculate that?  You do it by working the dB formula backwards.  When you calculate the dB value of a pair of power numbers, you first divided the 2 powers, pressed the log key to get the log of that answer, then multiplied by 10 for the final decibel figure.  Here we start with the decibel figure so the first thing we do is divide that dB number by 10.  So we have 7dB divided by 10 equals 0.7 (zero point seven).  The second to last operation was pressing log, but when we divide by 10 to get 0.7 that IS the log of the ratio of the 2 powers!  We have to find out what that ratio is by using the inverse of the log function: 10^X.  So with 0.7 showing on the calculator press the 2nd key and log (to access the 10^X function) and you should see 5.011872…, basically just 5.  5 is the ratio of the input to output power.  If you are given the input power, as we were, you just multiply that by 5 to get the answer.  Here we were given 50 watts in, so 50 times 5 equals 250 watts output!  If you were given the output power and asked to calculate the input power to a 7dB amplifier, you would divide the output power by 5.  Using the same example, we have a 7dB amplifier with 250 watts output.  What’s the input power?  It’s just 250 divided by 5 equals 50!

If you really want to get into logarithms and exponents, check out this page: http://www.mathsisfun.com/algebra/exponents-logarithms.html.  As always I invite discussion and questions.  I really want you to understand this stuff so you can impress all your ham friends with your mastery of decibels.

To the ARRL: How to alienate faithful members.

One of the things I try to do is to support organizations that further my interests. For instance, I love to hike and appreciate the beauty of nature and so I belong to several hiking organizations that maintain trails and advocate for conservation of the natural environs.

I also like ham radio and as such am a member of the ARRL (the American Radio Relay League), which is the premier advocate for supporting amateur radio activities.  They also advocate for legislation that helps further the hobby.  When I renew, I usually do so as soon as I get my notice that my membership is going to expire soon, and I normally renew for more than 1 year at a time.

Good member, right?  Well you know the old saying, "the squeaky wheel gets the grease?"  I was hanging out one day with a fellow ham and I noticed that he had a really nice collection of ARRL publications.  Since I have many of those same books myself I know they are worth a good bit of change.  I remarked to him that he must spend as much as I do on books, but he said not really.  It turns out that if you don't renew your ARRL membership when it comes do they will send you an incentive in the form of a book.  So my friend (lots of them it turns out) doesn't renew until they offer the free book.  He does this every year and so HIS membership is apparently worth a lot more than mine!

This makes me feel like a chump.  Why should I renew for multiple years, on time or ahead of schedule, for the full membership fee, when I can just wait a few weeks and get a free book.  Most of these books average in the $20 to $30 range, the median being around $25.  With a one-year membership currently going for $39, they are effectively paying only $14 a year for their membership.

I know the ARRL wants to keep member roles up, but they should offer something to those of us who renew right away too.  At least that's my opinion on the matter.  What do you think?

Kevin, AB2ZI

How to NOT shit in the woods!

Ok, so what does shitting in the woods have to do with ham radio?  Well, first a little background...

One day back in the early 90's I was wandering through a bookstore (remember those?) and happened to glance an unusual title on one of the shelves:  "How to Shit in the Woods, An Environmentally Sound Approach to a Lost Art" by Kathleen Meyer.  "Hmm," I said to myself, "this sounds hilarious, plus it's written by a woman, therefore I must have this book," and so I bought it.

The book is mostly written for the woman hiker who finds herself among nature when the call of duty comes (see how I did that?) calling.  You see it's well understood that for men the world is our toilet, though tips on proper environmentally friendly solid waste disposal, and the consequent paper (or leaf) work resulting from said waste disposal, are welcome to us too.

But I digress... Allow me to get more to the point.  As you can probably tell from this blog's title and subject matter (for the most part) I am an amateur radio operator.  I also have a real love for hiking and the views from atop a nice high mountain summit.  I have recently begun to combine these 2 hobbies by taking part in SOTA operations.  SOTA stands for "Summits On The Air" and involves hiking to the top of a mountain and operating at least 4 other stations for it to count as an official SOTA activation.  The activator gets points for this and so do any hams who contacts him/her.

One of the things I don't like about hiking (besides rain) is having nature call when I'm trying to enjoy nature.  Peeing is one thing.  That's no big deal for guys and we pretty much do it anywhere we like (though there are places we pee that we won't admit to among mixed company).  I'm talking about shitting.  Pooping, dropping a load, taking a dump, crapping, number 2 (not the pencil) or whatever psychologically damaging term your parents made you use as a small child.

I hate it because not all poop is created equal.  It's a rare bowel movement that allows you to take your time finding the perfect spot, one with no snakes, mosquitoes, ticks, angry beavers or large groups of other hikers with women and children among them.  Usually it's a sudden case of diarrhea coming on from that 7-11 sushi you had the night before followed by an old burrito you found in the back of your freezer from the 1972 super bowl back when the Miami Dolphins had an undefeated season and won super bowl VII against the Washington Redskins 17-0, ah, good times.  Anyway, back to the woods and our problem...  So you get one of "those" attacks that demand you find a suitable spot NOW otherwise you're going to have some splainin to do Lucy when you get back home and your wife sees the mess in your shorts!

So you find a spot, drop trou and get into position, find relief and then realize you don't have any toilet paper with you, and neither does anyone you're with (or at least they won't give it up just in case they should find themselves in your position).  Now you need to make due with leaves, grass, moss, poison ivy, hey, whatever's at hand.  Do this a couple of times and I guarantee you'll start putting waste management to the top of your hiking preparation checklist.

Now, all of that said, here's the point of this post:  I don't like to shit in the woods and so I have a system to keep from having to do so!

First, watch what you eat the night before.  The old (or new) bean burritos, sushi, pizza and ice cream, or anything else that you know has a history of giving you the trots.  They call it the "runs" for a reason.

Second, make sure you wake up early enough so you have at least an hour at home before you need to leave.  Get up, make some strong coffee and have your breakfast.  The hour is to give your bowels time to react to the coffee (if you're like me and most people) and let you evacuate in the comfort of your own bathroom where there's plenty of toilet paper and soap and water for the clean-up.

Third involves the secret magic pill:  Immodium A-D.  I buy the generic brand at Costco.  Right after you have your coffee you will want to take 2 of these, then another right after your first poop.  Even if you don't have diarrhea and never get diarrhea or can't spell diarrhea, you want to do this.  I find it keeps me from having to worry about any trail maintenance well into the next day.

There's nothing like NOT having to worry about where you're going to have to shit.  Be it the woods, that questionable looking toilet at the rest area or a spackle bucket on the side of the road.  Home is best and that lets you enjoy your activities.

If you'd like more information about SOTA, check out the website at: http://www.sota.org.uk/

If you want to check out Kathleen Meyer's book, you can get it on Amazon.com.

73 for now and good hiking!
Kevin AB2ZI

So many resources for ham radio, so little time...

I wish half the resources for learning about ham radio were around when I was a kid trying to get a license or for anything else I wanted to research back in the bad old days before the internet.  With all the websites and search engines available today there's absolutely no reason for anyone not to be able to learn about just about any topic they choose.

When I was trying to get licensed back in the 70's, my resources were a book full of old tests put out by a company called Ameco and their LP Morse Code record (all at 5 wpm).  I didn't have any good theory books breaking it down for beginners.  There was no YouTube with videos to help me.  There was the ARRL Handbook with lots of schematics of tube transmitters and receivers and plenty of ads for Vibroplex "bugs" but nothing like what we have today.

The hardest thing about learning today is with all the resources available you can get sidetracked into different topics fairly easily.  You start researching resistors and end up taking an algebra class to tweak your understanding of ohm's law.

The biggest obstacle to understanding I see these days is that people are lazy!  Too many want to be spoon fed everything they need to know.  They don't put in the effort to find things out on their own, and when I say "on their own" I mean most often not bothering to do any internet searches.

1. Want to learn something?  Your first stop should be Google.  Google is a website and these days it's also a verb.  You hear it all the time.  "I Google'd that" or "Why don't you Google it?" etc.  Go to Google's search page and type in various words to find websites that can help you learn what it is you want to learn about.
   
2. Bookmark your sites and organize them by topic.  Researching low pass filters?  Google "low pass filter", visit some of the sites and copy their locations into a bookmark folder or subfolder.  Here's just part of the listing I got from that search:
   
   
   
   
   Go to any of the sites and do some reading or play with some of the calculators they bookmark the most useful ones for later.  Speaking of useful sites:
   
3. Wikipedia.  Wikipedia is awesome!  Sure, some of the content is not absolutely accurate, but most of the scientific articles (at least those not dealing with evolution) are accurate, plus you should always look at the "references" and "external links" list at the end of the articles to find sources that are referenced.
   
4. The ARRL website.  First, I have to say this site is poorly designed.  It's hard to find things on it without spending a LOT of time playing around on it.  After 5 years it's almost just hard to find things.  That said there are a lot of really good resources on the site -- if you can find them.  The QST archives alone are worth a visit and search through.  Here you'll find information on question pools (also available elsewhere), test sites, license classes, FCC rules notices, and lots more.
   
5. YouTube.  This one should probably be listed 2nd, but they're all great resources.  YouTube has videos on more than just surprised cats and talking dogs.  You can find just about anything on YouTube.  The electronic videos range in quality and content so you may need to browse through a few on any given subject.  Some of the best (and worse) are the old military training videos.  The graphics are really cheeseball compared to "Transformers 3D" but they get the ideas across.  If you're a real egghead you can even find engineering level videos and stuff from classrooms like MIT lectures.

So, asking people for the answers is OK, most hams love to share their knowledge with others, just be aware that there are a ton of resources out there for you to use and if you do you'll soon find yourself bogged down with people coming to YOU for answers all the time.

73 and good learning.  Kevin AB2ZI

Working Amateur Satellites: My Adventure, Part 3

Day 3:

Success!  There was a nice high SO-50 pass today at 13:59 local time.  8 minutes over the horizon with an elevation of 78 degrees at mid-pass.  Picked up the bird in the middle of the pass and heard Pete, W2JV on the air.  Threw my call and he came back to me for my first Satellite QSO.  Before the pass was over I was able to make another contact with WB2SIH who was operating up at Lake George, NY in grid FN33.

OK, now I'm bored... :-)

73, Kevin AB2ZI

Working Amateur Satellites: My Adventure, Part 2

Day 2 continued...

Decided to work on that VX-7R programming cable.  Got my soldering iron and magnifying headset out and laid out the cable.  Here's what it looked like:

I cleaned off the old solder from the center conductor that the red wire had broken off of from the twisting and put just a touch of flux on the exposed red wire and carefully soldered it back on:

Next I tried to figure out where they had soldered on the ground lead, but there was no obvious spot which means it was poorly soldered in the first place.  I picked a clean spot, added a drop of flux, then heated up the body and attached the ground to it:

Before doing anything else I let it cool off then attached it to the VX-7 and first read the radio.  The software downloaded the programming without a hitch so it was time for the big test -- writing to the VX-7!  I opened up the file I had gotten by downloading the radio the day before, put the VX-7 into receiving clone mode and hit the "OK" button on the software.  It worked like a champ!  The VX-7 updated perfectly.  Now I just had to add the shrink wrap and I'd be all done.

I made it back outside for the next low pass of the afternoon, this one in front of my house (still a ton of trees).  I got a lot more audio from stations working the "bird" but wasn't able to make a QSO.  At least I've got things set up for success, now all I need to do is work on my technique.

More to come as I keep trying for my first satellite "Q."  There's a really high pass tomorrow afternoon around 2 p.m. that I'm hoping will do the trick.  Until then...

73, Kevin AB2ZI

Working Amateur Satellites: My Adventure, Part 1

Day 1:

So, after Pete, W2JV's great presentation at the ARRL Centennial last weekend, I decided to finally put together the Arrow 2m/440 Satellite Antenna that had been sitting next to my operating position for about a year now and take a crack at some satellite QSO'ing.

I checked the SO-50 schedule (this was Tuesday, July 22nd) and saw there were a couple of 80 degree plus passes in a couple of hours.  I figured putting the antenna together (very fast) and programming SO-50's uplink and downlink frequencies with several plus and minus shifts to account for doppler into my Yaesu VX-7R wouldn't take too long and I'd probably have time to relax before the passes.

Well, the antenna went together extremely quickly, but I encountered some unexpected problems with the HT.  Having bought the radio back in 2008--before all the USB to radio cables were available--I had been using a Belkin USB to serial adapter with the Yaesu pigtail that screws into the mic jack for programming.  I'd never had any trouble before and so wasn't expecting any now.   The software read the radio just fine, but when I went to write (clone) to the HT I got an error.  Not only did it give me an error, it also erased the radio and all my settings.

I proceeded to try all manner of fixes for the problem.  Removing and reinstalling the cable on the HT (about 30 times), trying different ports and a couple of other computers, all to no avail.  By now I'd missed the passes and had to get ready for the evening's class, so I sat down and patiently programmed 9 memories with cross-band frequencies (aka "odd split"), PL tones (TX only) and turned off the squelch (set to zero as so often stressed by Pete and others who operate satellites -- you have to hear the squelch 'quiet' when the HT starts receiving the satellite).

I saw there were a pair of 30 degree passes, short ones, on the sked for tomorrow (July 23rd) so I'd give them a try before messing with the radio programming any more.  In the mean time I'd check out my programming cable(s) for problems.  I also went on Amazon.com and ordered a straight USB to Yaesu programming cable with a supposedly guaranteed FTDI chipset that wouldn't give me any problems like most of the pirated Chinese cables.

Day 2:

My programming pigtail never fully locked into the HT.  Upon further examination I noticed the plug on the HT end was able to be rotated independently of the cable.  That's not good!  I had to cut off the plastic covering the plug and found one solder connection (a ground I believe) broken off and one of the other wires also fell off during the exploratory surgery.  OK, have to get out the soldering iron and fix that later.

Today's first pass was a low one, 30 degrees, and also brief.  It was an 8 minute window staring at 174 degrees, rising to 30 degrees at azimuth 113, then falling off at about 54 degrees.

I had my digital recorder hanging from the HT on its strap and the radio on with the volume turned up.  A couple of minutes into the pass I figured the doppler wasn't going to be as much of an issue with such an oblique pass and went through the frequencies until I had some audio coming through.  It was very weak (I'm covered in trees here and trying to work the satellite through them) and I could barely make out any of what was being said, but it was exciting and I knew I was at least on the right track.  My next opportunity today, for another low pass is at 3:13 PM.  This one will be 9 minutes and get up to 32 degrees (whoo hoo).  In the meantime I'm going to see if I can repair this cable and get the programmer working... I'm living dangerously because if I try to program the radio and wipe it again I'm probably not going to want to reprogram it by hand until I get over the disappointment.

...to be continued.

Kevin AB2ZI