Hi, It's engineering terminology time. We're going to talk about orders of magnitude and you hear me say it all the time. Not just me, but it's a very common term in electronics and other engineering and science, for that matter. Order of magnitude? Exactly.

What does it mean? You hear me use it in terms of oh, I was out by an order of magnitude. Or that was an order of magnitude bigger than I thought. Or it's dropped. Something's dropped by an order of magnitude.

Something like that. What does it mean? It's pretty simple. uh, concept. and it's easy to learn and easy to use.

Incredibly easy in fact, But a lot of people don't really understand it or get it a little bit wrong. So let's take a look at orders of magnitude. And here's a basic table. You're going to be familiar with What is an order of magnitude.

An order of magnitude is just 10 times something. That's it. That's the entire concept. It's incredibly simple.

and here's how it relates to numbers, decades, and the order of magnitude in increasing and decreasing value. So what we've got here in the blue is the order of magnitude. So this is one order of magnitude, two orders of magnitude, six orders of magnitude, and they've got something I've put down minus one order of magnitude. But in engineering, nobody.

it's not very often used Where you say minus three orders of magnitude or something like that. Some people may I personally don't do it. I'll say it's dropped by or it's down by three orders of magnitude. So what does that mean? Well, if you're talking about the number one as your reference point, remember, your reference point doesn't have to be one can be anything.

Your reference point can be 1,000 volts. and if it's an order of magnitude greater than your reference voltage of 1,000 volts, then it's going to be 10,000 volts. One order is just 10 times. So even though I've used one as the reference point doesn't have to be okay.

So it's simple. You know about decades in Um, engineering and scientific notation, and uh, it's basically 10 ^ of 1 is 10, 10 ^ of two is 100, and so on. up to a million and it can go any as far as you like in any direction. So these are common terminology To say something is, you know it's I' I'm an order of magnitude out.

For example, I'll say that commonly in my videos and that could mean if I'm out by an order of magnitude, it means I'm out by 10 times. If I say I'm out by three orders of magnitude. I'm out by a thousand times in either direction because I didn't actually say which direction I was out by. So I'll you might use the common terminology: something: The voltage is dropped by an order of magnitude.

It's dropped from 1 volt to 0.1 volts and that's an order of magnitude. Or it's increased by one volt has increased by an order of magnitude. It's jump jump from 1 volt up to 10 volts. Pretty simple.

So these are common terminologies you'll find in engineering. And just to be clear, when I say that reference point can be anything, it doesn't have to be a power of 10 I Talked in terms of 1,000 volts and 1 volts. but it could easily be say 3.5 Vols or something like that. And if something, if 3.5 volts is increased by an order magude, it's going to be roughly 35 Vols And that's the other thing.

The big thing about orders of magnitude. It's a rough rule of thumb in engineering. It doesn't have to be exact. When you talk in terms of order of magnitude, you're talking about roughly very roughly to be.

Oh, it's a couple of orders of magnitude bigger. or it's an order of magnitude big. or it's an order dropped by an order of magnitude, dropped by roughly 10 times doesn't have to to be exactly 10 times. it might be 11, 12 or something like that, and you can round up either way.

But that's one of the uh, advantages of talking in terms of order of magnitude. It's just a rough rule of thumb that gives you an indication that you're in the ballpark and often a lot of practical Electronics Engineering. You just want to be in the ballpark I Want to choose a onek resistor? That's you know it's going to be correct to the right order. That's another term to the right order.

just means you're roughly within the ballark. And that leads us to one of the big misconceptions and a thing which people get wrong with: order of magnitude. Everyone knows that an order of magnitude is 10 times. That's basic, but some people have the incorrect assumption that two orders of magnitude is 20 times and it's not.

It is 100 times. It goes up by that decade each time 10 to the power of. So don't make the mistake of thinking that, uh, two orders of magnitude is 20. It's not.

It's 100. And there are some people who try and talk in terms of one and a half orders of magnitude. and, uh, probably not technically incorrect, but it's not within the spirit of the order of magnitude, that rough rule of thumb in the ballpark kind of thing. So yeah, I wouldn't make the mistake of going.

You know, trying to make it more precise than what it actually is. So if your one volt has jumped up to 8 volts, don't say it's increased by .8 orders of magnitude. it hasn't. It's one order of magnitude.

Round it up. Now let's take a look at engineering notation that we're familiar with in electronics Powers of three multiples of three. You're familiar with these: kilo Mega Giga Terra mil micro Nano Pico in the negative Direction and it extends beyond that, but that's pretty much probably from Giga down to Pico + 9 -12 orders of magnitude is the range you're typically going to encounter in electronics engineering. If you're working outside of that, you're working on some pretty extreme stuff.

Now let's take let's think about what these orders of magnitude mean: I Mean we can certainly measure down in the Nano volt region and generate things down in Pico amps and stuff like that, and we're able to get generate. You know there's like, well, there's gig ohms and you know we're able to measure and work with these values practically. So what does this entire range mean if you're working from Min -12 Pico if that's your reference. So let's say you've got one Pico Volt for example.

that's your reference. How high is teror up here? It's 24 orders of magnitude greater than your one pea volt reference. So that's what the typical engineering spectrum is going to involve. 24 orders of magnitude doesn't sound very impressive, right? 24? You know it's a pretty low sort of number, but it's two.

It's sorry. it's 10 to the power of 24. And to give you a scale of how massive this range is, that Electronics Engineers work over on a daily basis. So let's use the example of how far Jupiter is from the Sun I'm always saying you can fly to Jupiter on a milliamp, right? So let's actually see how far Jupiter is from the Sun If we take our reference point as 1 mm.

that's 125th of an inch roughly for you. Uh, Yanks Out there now, Jupiter is roughly Um is roughly uh. 1 billion kilomet from the Sun. Roughly, Why? Because we're talking orders of magnitude.

it's actually around about 800. Just over 800. Uh, million kilometers from the Sun at its maximum Um. distance.

But we're talking orders. So we round things so it's a billion kilometers from the Sun. Well, what's that in meters? Well, it's A, billion and millimeters, it's a another thousand. Again, What's that? In orders of magnitude? Count the zeros: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

It's only 15 orders of magnitude. From a millimeter a millimeter to the freaking Jupiter is only 15 orders of magnitude. Engineering works over 24 orders. Wow, How about Proxima centori the nearest star to the sun? Approximately 4.2 light years? Well, what's one lightyear compared to our 1 mm reference? It's 10 the power of 19.

19 orders of magnitude? Not there yet. Turns out we're got to go to the Andromeda galaxy at 2.5 million light years from the sun, which is roughly 10 the power of 25 or 25 orders of magnitude. So if in millimeters, the 1 mm reference. So let's take it as a 10 mm reference.

1 cm. Bingo You've got your 24 orders of magnitude. Incredible. That's how wide this sort of range is that Engineers work over on a daily basis.

Incredible when you think about it. The Andromeda Galaxy, for goodness sake. And here's a practical example of some equipment I've got on my bench here: I've got a Keithly 260 nanov volt source and a 240a high voltage power supply. And with these two instruments here, I can generate a voltage anywhere from Uh .01 Nanov, Volt or 10 PT 10 ^ of - 11 to 1,000 Vols 10 ^ of 3.

And that's 14 in orders of magnitude. Incredible. And one order of magnitude is important in electronics for lots of rules of thumb. Reason, measurement, uh, uncertainties, and things like that.

Let's take an example of a multimeter measuring a resistor divider. Here, we've got two resistors. here. One is a fixed 1 meeg resistor, which we're measuring across with our digital multimeter.

And as you should know, a digital multimeter doesn't have an infinite input impedance. It's going to be roughly 10 megohms or thereabouts. most of them are. anyway.

Now, when you put 10 megaohms across that one Meg resistor, that's going to cause a measurement error. How much? Well, in this particular case, it depends on what value of R1 is. If R1's 100K, you're going to get roughly a 1% error caused by a multimeter. If it's a Uh half, if it's a half rail divider like this with a half volt in the middle, and R1 is one Meg Here you're going to get about a 5% error.

And if it's much bigger and you're measuring a smaller voltage down, Here you're going to get about a 9% error or thereabouts. And roughly you're getting an order of magnitude error. worst case due to that 10 Meg resistor. And in a lot of cases, that's going to get you in the ballpark.

It's good enough If you choose a value uh, for measurement or something like that, you know, like a 1% error for example is not. You know it's not a huge deal in most practical circuit, so that's why you deal with just one order of magnitude. When you're talking about, say, measurement like this, you want your multia to at least be an order of magnitude above what you're trying to measure. Otherwise, you'll disturb it and your error will be too great.

Now, a practical example in electronics where you're going to use this one order of magnitude rule of thumb is in a basic LED circuit like this where you don't have to do any, you don't have to get your calculator out and actually do calculations and things like that. You can just choose a resistor that's going to work without having to do any you know, get into the nitty-gritty of the calculations cuz you're using Ru of thumb back of the envelope calculations. Now let's take the example of we've got a 10vt power supply here and we've got a red LED It's going to drop roughly 1.8 volts or thereabouts over its, uh, you know, over its current range. So 1.8 Vols is roughly an order of magnitude l lower than 10 Vol.

So as is common in electronics, if it's an order magnitude lower or an order magnitude higher, you can safely take it out of the equation. So we're going to not worry about the voltage drop of that lead because it's an order of magnitude out. So we're going to say 10 Vols divided by the resistance gives us the current and we know that an LED is going to. you know, at least turn on anywhere from 1 milliamp up to say 20 milliamps maximum.

Or let's go 10 milliamps like that without blowing the LED Just a bog standard LED So what do we do that? We can calculate the values: One uh, 10 volts uh, divided by Uh 10 milliamps gives us 1K and 10 volts divided by 1 milliamp gives us 10K. So any value within that range is going to be of the right order, so you can safely go to your parts bin and pick out a resistor anywhere within that range and you know you're going to get that led to light up. And that's just a common example of how rough you know, rough rules of thumb and order of magnitude calculations work in electronics. You're going to get this circuit working if you're within the right order.

Another practical example of an order of magnitude is calibration. Let's say I Wanted to calibrate my fluke 87 multimeter here, and it's say, for example, it's 0.1% uh, accurate. and I want to compare it against something else? Well, you want to have something that is an order of magnitude better or 10 times better. So you'd want another meter which is 0.01% instead of 0.1% So comparing against another fluke 87 is no good.

I Need a meter which is an order of magnitude or 10 times better than that to give you a test uncertainty ratio of 10 like a sort of the minimum figure they were Us In the calibration industry might be a test uncertainty ratio of four, but I Ideally that's A, but that's a minimum. Ideally, you would really be shooting for something that's 10 times more accurate than the instrument you're trying to calibrate. So you'll find that order of magnitude 10 times or 1110th come up all the time. In electronics engineering, it basically is just that rough figure where something sort of doesn't matter in a practical sense if it's 10 times bigger, if it's 10 111th, if you know your leakage current is one10 of something else, or if your phase is one tenth of something else, order magnitude out.

It's practically not going to make a huge difference to a working circuit. So you hear the term all the time and it gets thrown around and it's a very good term if you're going. If you're a you know, a graduate or whatever and you're going for a job interview or something like that, there's some real Choice terms you should throw in. order of magnitude is one of them.

Start talking in terms of orders of magnitude. Oh yeah, it's an order of magnitude out a couple of orders. You know you'll sound like you've been in the industry for 20 years and you know what you're talking about. It's like using DBS for everything.

Start using orders and people will think you know what the hell you're on about. So I hope that gave you a bit of an insight into and get a feel for orders of magnitude. Catch you next time and that leads us to one of the biggest misconception misconcep.