The weird relationship between range and output power

By | October 29, 2022

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00:00:00 – Bardwell can't do basic math
00:00:59 – RC hobbyists can benefit from basic RF principles
00:01:57 – Think in ratios, not absolute amounts
00:04:53 – The formula for decibels
00:05:38 – Conversion from dB to ratio
00:06:13 – The inverse square law
00:07:45 – 4x the power = +6 dB = 2x the range
00:08:50 – You can add dB together
00:10:02 – 3 dB = 2x the power = 1.4x the range
00:10:34 – Practical Application 1
00:11:09 – Practical Applicaton 2
00:11:36 – Effect of inverse square on vTX power
00:13:32 – Have I earned your support today?
00:14:38 – Receive sensitivity is the other side of the coin
00:16:00 – Find your receiver sensitivity spec
00:17:32 – Practical Application 3
00:18:26 – Bardwell can't do math?
00:19:17 – What about antenna polarization


I've never been accused of being great At math but I do know basic addition and Subtraction and that's why it was really Confusing to people when I said in my Review of the jumper t18 that 500 Milliwatts is closer to 300 milliwatts Than 100 milliwatts Seems pretty dumb right 500 minus 300 is 200 300 minus 100 is 200 aren't they the Exact same distance from each other the The topic that we're going to explore in This video because when you're thinking About the way that output power relates To the range that you get from your Device the difference isn't as simple as Addition and subtraction and this Matters because when you're thinking About your video transmitter if you Increase your video transmitter power From 100 milliwatts to 200 milliwatts How much more range are you going to get I'm Joshua Bardwell and you're going to Learn something today I'm gonna be Honest with you this video is a little Bit math heavy now I'm going to try and Make it as simple and understandable as I can because the topic is actually Really important to everybody in the RC Fpv hobby we are using radio Transmitters your video transmitter your Controller we are using radio links and Yet most of us lack the basic Understanding of how output power Relates to the range of a radio link so

When we hear that there's a 2500 Milliwatt video transmitter it seems Like a big number but we don't have a Perspective on how that actually relates To the range of say a 1 000 milliwatt Video transmitter or what have you if You've got Express lrs or Crossfire and You turn your output power up from 250 Milliwatts to 1 watt how much more range Are you really going to get it turns out That there's actually an answer to that Question and that answer is what we're Going to be seeing speaking in this Video and the first concept we have to Introduce when we talk about RF signals And range is that we're going to be Thinking about them in terms of ratios So for example if uh if I you were to Ask me how heavy is your quadcopter one Answer to that question might be 500 Grams or 700 grams but another way to Approach that question would be for me To say how heavy is your quadcopter well Mine is 75 of that weight You can express Concepts as absolute amounts but you can Also Express them as the relative Strength or the relative amount between Two things and that is usually how People think about radio signals the Exact reason why not that important for This video we're going to try and keep It high level so we're going to think About RF signal to propagation in terms

Of multiply and divide in other words Going from X output power to Y output Power will give me double the range Going from A to B output power will give Me one quarter the range and the this Matters because the absolute amount of Range you're going to get it will vary Depending on environmental conditions How much range will you get out of a one Watt video transmitter I don't know are You flying in open air are there trees Are there buildings but if we go from One output power to another output power The proportion of range that we're going To get in the same environment that is Something that we can actually calculate And predict and the unit that is used to Express these ratios is the decibel now You probably heard about decibels in the Context of sound decibels is how loud Sound is and that is in fact where Decibels came from but they're actually Used to express relative power levels of Many different things including RF Signals and the thing about decimals That you need to know is that they do Not express the absolute amount of Anything so here is the absolute amount Of gas in your gas tank 14 gallons Amount of fruit you bought at the store One pound of fruit how long is this Meeting gonna be I got to be somewhere It's going to be 60 Minutes long how far Is it from City a to City b 300 miles

How much money is in your bank account 20 how many goals did they score in the Game six goals how heavy is your quad 650 grams these are all absolute Measurements that Express an absolute Amount of liquid mass time distance Etc decibels Express the ratio of two Amounts rather than an absolute amount Of anything so we could say Jill has Twice as much money as Jack it's one Quarter the distance from here to City a As it is from here to City B your quad Weighs 85 percent as much as mine they Scored 35 percent more goals than the Second place team or this meeting will Be five times longer than the last one Decibels always express a ratio between Two things I'm going to show you the Mathematical formulas for calculating Ratios and for converting between a Decibel and a ratio don't freak out We're not going to actually dive into These too much but I just want to show Them to you so that you know that this Is we're not just making this up so to Go from a ratio to a decibel you use This formula and to go from a deep Decibel to a ratio you use this formula But I prefer to just forget the formula And use a table and I'm going to put an Imager link to this table uh in the Video description and if you want to Pull this table down and print it out And look at it you can you could also go

Into a spreadsheet if you like to do That kind of thing and you could put These formulas into a spreadsheet and You can generate this table yourself That's how I did it so we can use this Table to convert between a decibel Difference and a ratio for example a 0 DB difference means that the two things Are the same a 3db difference means that One of the things is twice as much as The other a 10 DB difference means that Two things are one of the things is 10 Times as much as each other and so on And so on negative decibel amounts would Mean one-half 1 4 1 10. so a minus 2 DB Would mean that one thing was 1 over 1.58 of the other it's not that Intuitive to have a decimal in a Fraction but the concept is basically The same now how does this relate to the Range of an RF signal because that's What we're trying to get to at the end Of the day the range of an RF signal is Related to the power that it's output at Via something called the inverse Square Law and the gist of the inverse Square Law is that if we transmit a certain Amount of energy we can think of that Energy coming out of the antenna and Let's just imagine that it was a sphere So think of it like a spherical bubble That is slowly expanding with real Antennas the shape of the propagation is Not spherical it's stronger in some

Areas and weaker in others but think of It as a sphere and as we transmit that Energy there is a shell of that sphere And a certain amount of of RF energy is Spread out across that shell and as the Distance from the antenna gets larger The SP the shell of the sphere gets Larger and the energy that is spread out Across that shell is spread thinner and Thinner that means that the further you Are from an antenna the weaker the Signal Right obviously we know that and that's The fundamental reason why that happens So in this diagram we can see that at a Certain distance there is a certain Amount of area that the energy is spread Over and as that distance increases the Area that the energy is spread over gets Larger and larger And this is defined by the inverse Square law in summary the way the Inverse Square law works is that 4 times The power equals 2 times the range 9 Times the power equals three times the Range 16 times the power equals four Times the range and 25 times the power Equals five times the range and you can See that there is a non-linear Relationship here it's not as simple as Twice the power equals twice the range And that otherwise this would be a very Very short video because we're using Squares the numbers get unwieldy really

Fast right 25 16 9. the next number After 25 would be 636 and then it just Gets unwieldy really fast the inverse Square law is much easier to use when You work with decibels instead of ratios So 4 times the power is the same as plus 6 DB is the same as 2 times the range And I want you to remember that that's a Number that there's very few things in This video that I'm going to say oh you Should memorize this but that's one of Them Four times the power 6 DB two times the range because you can Add the decibels together to get the Total change in range so for example if We had an 18 DB difference in output Power 18 DB is the same as 6 plus 6 plus 6 DB 6 plus 6 plus 6 is 18. we convert That to a multiplier and say 2 times 2 Times 2 to other range and then that's 8 Times the range 18 DB is eight times the Range so we can start to work this with Powers of 6 6 12 18 and so on notice in This formula that the decibels add up But the ratios multiply so here is a Table where we convert the decibel Difference To the range difference between two Things and now we're starting to get to The point of this video the range Difference column shows the increase in Range when adding that many DB or when Multiplying Power by that ratio so if we

Add 6 DB That is 3.98 I said four times the array Of 4 times the power 60b is actually 3.98 we're rounding a little bit for the Sake of Simplicity and that gives you Just about 2.0 times just about double The range if we have a different Difference of 2 DB that would give us 1.26 times the range and so on and so on Another number that I like to memorize To give me just a little bit more Flexibility in doing head math because I Don't have this table with me all the Time is that 3 DB difference is 1.4 Times the range 3 DB difference is 1.4 Times the range 6 DB is 2 times the Range you could of course memorize this Whole table if you prefer to and then You have a lot of resolution at your Fingertips but these two together can Actually by using this adding and Multiplying trick can actually give you A quick reference for the difference in Range between two things without having To refer to a table so let's do some Examples of practical application let's Work some of these how much will your Range increase if you turn your video Transmitter up from 25 milliwatts to 100 Milliwatts for first we find the ratio 100 milliwatts equals 4 times 225 Milliwatts we don't need a table for That that's just basic math next we find The line on the chart that most closely

Matches the ratio four times ratio Equals 6 DB so we'll look down the ratio Here and we'll find 3.98 and that's Pretty close to 4 that's 6 DB that's Double the range going from 25 millibots To 100 milliwatts will double your range Let's do another example how much will Your range increase if you turn your Expressolarus module up from 100 Milliwatts to 1 watt first we find the Ratio one watt equals 10 times 100 Milliwatts right that's just basic math So we're going to go down the chart and We're going to find 10x on the chart and Then we can see that that is a Difference of 10 DB and a range Difference of 3.16 it's about 10 10 10 DB is about triple the range the inverse Square law has an interesting Implication uh on the effect of output Power as it relates to range Um because you need four times the Output power to get two times the range And so the amount of power that's needed To extend your range quickly becomes Impractical let's say that you got two Kilometers of distance off of one watt Of VTX power now do you think that two Two kilometers is excessive or not Enough doesn't matter it's just an Example but let's say that you got two Kilometers of distance off a one watt of Etx power to get four kilometers you'd Need four watts to get eight kilometers

You'd need 16 watts to get 16 kilometers You'd need 64 Watts the amount of power Needed to extend your range quickly Becomes unwieldy and this is one reason Why when you're trying to get more range Out of your system increasing output Power only works up to a point it's why You don't often see video transmitters For fpv that are more than about one or Two Watts going from 25 milliwatts to 100 milliwatts will double your range And is pretty easy it doesn't require Any addition Regional output power or Cooling or anything like that in your Video transmitter going from 500 Milliwatts to 2 Watts also doubles your Range and is a lot harder at least when We're talking about the constraints of An fpv drone then going from two watts To 8 watts also doubles your range and Is very very difficult on an fpv drone Due to size heat and output power Requirements so you might say well if We've got a two watt video transmitter Why don't we go to a three watt video Transmitter or a 4 watt video Transmitter and it turns out that we're In this place of diminishing returns Where to increase our range we would Need to double our output power and that Is a lot more power when you're going From two watts to four Watts than when You're going from 500 milliwatts to 1 Watt or 25 milliwatts to 50 milliwatts

Now the next topic we're going to talk About is receiver sensitivity because There's two sides of any RF link one is The transmit power which we have been Talking about and the other is the Receiver sensitivity on the receiving End before we do that though can I take A second to remind you that I have a Patreon patreon is a website where you Can subscribe to me for as little as two Dollars a month or more if you feel like I've earned it the amount you subscribe At is totally up to you and you can Unsubscribe or stop anytime you feel Like you want to patrons get access to My Discord server where they can chat With other people in the fpv community And they get access to podcast downloads Of all of my live streams if you like to Listen to them on your car instead of Watching them on YouTube but mostly what Patrons get is the feeling of giving Back and if today's the day that you Want to have that feeling if you're like This is great content I'm really I'm Really liking this Slideshow about math Hey if that's you then there's a link Down in the video description where you Can subscribe to my patreon if today's Not the day then uh keep watching the Content I'll keep making it maybe that Day will come so receive sensitivity it Refers to the weakest signal that the

Receiver can successfully lock onto and Modern RF receivers can lock on to Extremely weak signals numbers for Receiver sensitivity are basically never Expressed as milliwatt because it would Look like this 0.0001 milliwatts oh and here's another Receiver that is 10 times more sensitive While or less sensitive it can receive Down to 0.0001 milliwatts oh see the difference No It's ridiculous so receiver sensitivity Is basically always expressed in numbers Uh in units of dbm decibel milliwatts And I said earlier that dbm that Decibels only express a ratio they don't Express an absolute amount well it turns Out that a decibel can be used to Express an absolute amount if you just Fix the thing that it's compared to and What a dbm is doing is it saying that 0 Dbm equals one milliwatt and everything Else is pegged to the one milliwatt uh Comparison so negative dbm numbers refer To values less than one milliwatt Positive dbm numbers refer to values Greater than one milliwatt and it's just A ratio relative to one milliwatt so uh We might see receiver sensitivity Expressed as a number like negative 95 Dbm in order to use this information You're going to need to find your Receiver's receiver sensitivity

Specification for example here's a table From the espresso RS website which shows The receiver sensitivity or the they Call it desensitivity limit for various Packet rates different packet rates Would have longer or shorter ranges and There's something a little bit Counterintuitive about receive Sensitivity the larger the negative Number the more sensitive the receiver Is because it the larger the number the Weaker the signal because it's a Negative number So a receiver with a negative 117 dbm Sensitivity will have more range than a Receiver with negative 105 dbm Sensitivity it is a higher sensitivity Threshold so it needs a stronger signal So it has less range you could also just Think about it as the bigger numbers Give you more range Right to negatives sort of cancel out One negative 117 dbm is a higher Absolute value than negative 105 and has More range by the way this is the Express lrs table which the express Alerts devs kindly put on their website Immersion RC ghost puts these numbers in Their user manual as well for Crossfire I think that some of the numbers are in The crossfire manual but not all and I'm Not sure if trace the numbers are Published for Tracer they are out there Someone knows them but I'm not sure

Whether all of them have been published Oh and for free Sky Spectrum Etc no idea So let's do a practical application of Receive sensitivity what is the range Difference between Express lrs at 100 Hertz versus Express lrs at 500 Hertz The exact same things we did earlier With transmit power related to ratios And so forth still apply 100 Hertz is -117 dbm sensitivity 500 Hertz is -105 That's a difference of 12 DB 10 117 Minus 105 is 12 DB remember that this Very can convenient that that's 12 Equals 6 plus 6. I didn't do that on Purpose but it's nice that it worked out That way because we're going to be able To do this math really easily 6 DB Difference is 2 times the range I told You to memorize that earlier right 12 DB Equals 6 DB plus 60 B that means it's Two times the range times two times the Range equals 4 times the range in other Words 100 Hertz Express lrs has four Times the range of 500 Hertz Express lrs All else being equal that's how we work These numbers so let's go back to these Comments where I said that 500 Milliwatts is closer to 300 milliwatts Then 100 milliwatts is closer to 300 Milliwatts and now we are prepared to Understand that that claim because 300 Milliwatts is 4.7 DB greater than 100 Milliwatts and 500 milliwatts is 2.2 DB Greater than 300 milliwatts because

We're working off of ratios 300 is more than twice as much as 100. But 500 is less than twice as much of 300 because everything is a ratio here We can see that the range you will get Off of 500 milliwatts is closer to the Range you will get off of 300 milliwatts Than 100 is to 300 and that is what I Meant when I was sort of talking off the Cuff in that review video so now you Know about the effect of range on Transmit power and receiver sensitivity What about antenna polarization that's Another topic that a lot of people don't Fully understand DJI goggles have left Hand polarization analog typically uses Right hand does it even matter I've got A video about left versus right versus Circular polarization and which is Better and I'll put a card on screen if You want to check that out happy flying