How do civil engineers use grad to measure slopes in construction?

[wirefree]

G’day.

I am here to clear my doubt about the dB scale, in general, and it’s use in calculating received power in a microwave cavity.

Given that I have arrived at received power (P_r in Watts) for a given input power (P_t), I understand that

10*log (P_t/P_r)

yields P_r in dB.

Now, say, the cavity’s a Directonal Coupler, which has an Insertion Loss (I_l) of 0.5 dB. If I substract I_l from P_r (in dB), and obtain a negaive number, that would violate basic principles as it implies P_r > P_t since log₁₀ of a number less than 1 is negative.

Please do correct me.

Best Wishes for the Festive Season,
with kind regards,
wirefree

 

[berkeman]

Given that I have arrived at received power (Pr in Watts) for a given input power (Pt), I understand that

10*log (Pt/Pr)

yields Pr in dB.

That doesn't sound right. 10*log (Pt/Pr) is the ratio of Pt to Pr in dB, If Pt>Pr, it is a positive number, and if Pt<Pr, it is a negative number.

If you want an absolute number, you can use the units of dBm, which is dB above 1mW in a 50 Ohm system. You can express Pt and Pr in dBm, and just subtract to see what your insertion loss is... Does that help?

 

[jim hardy]

Now, say, the cavity’s a Directonal Coupler, which has an Insertion Loss (Il) of 0.5 dB. If I substract Il from Pr (in dB), and obtain a negaive number, that would violate basic principles as it implies Pr > Pt since log10 of a number less than 1 is negative.

Please do correct me.

Is this a real life experiment?

I would be more inclined to question
1. How precise are my "arrived at" numbers for Pt and Pr ?
2. Is that coupler's insertion loss number "0.5db" of the flavor "guaranteed not greater than" , or "guaranteed 0.5±η db " ?
I'd find a way to measure its actual loss.

....... that said. .................

Given that I have arrived at received power (Pr in Watts) for a given input power (Pt), I understand that

10*log (Pt/Pr)

yields Pr in dB.

Power expressed in db is always a ratio and it assumes a reference power.
We usually state what that reference power is The number of db tells how much larger or smaller (compared to that reference) is the power you are describing.
So your expression gives, as Berkeman said, the ratio of transmitted to received powers - not an absolute number for either.

I know nothing of microwaves
I assume there's convenient reference power that's so commonplace people forget to state it.

I do know that in telephony there's a widely used reference power, one milliwatt, that's so commonplace it's on multimeter faces.
When selected to AC volts the bottom scale indicates power referenced to one milliwatt in 600 ohms, about 0.77 volts
In my day we suffixed our db reading with "m", eg db_m to indicate that one milliwatt reference power.

(purple marks mine - jh)

old jim

 

[tech99]

G’day.

I am here to clear my doubt about the dB scale, in general, and it’s use in calculating received power in a microwave cavity.

Given that I have arrived at received power (P_r in Watts) for a given input power (P_t), I understand that

10*log (P_t/P_r)

yields P_r in dB.

Now, say, the cavity’s a Directonal Coupler, which has an Insertion Loss (I_l) of 0.5 dB. If I substract I_l from P_r (in dB), and obtain a negaive number, that would violate basic principles as it implies P_r > P_t since log₁₀ of a number less than 1 is negative.

Please do correct me.

Best Wishes for the Festive Season,
with kind regards,
wirefree

The ratio of Pt and Pr, which you have expressed in dB, is presumably the measured attenuation of the system under test, say L dB. If your system includes, a component, such as a directional coupler, which has 0.5dB attenuation, then the attenuation of the remainder of the system is L-0.5 dB. Yes, the remainder of the system has less attenuation.
On the other hand if you have calculated Pr, then you must have already included the directional coupler in the calculation, so subtracting it will not create negative attenuation.

 

[poor mystic]

Attenuation is measured in dB; so that for example a level of -10dB is the outcome when a signal at a level of 0dB is attenuated by a factor of ten. :)

 

[sophiecentaur]

I assume there's convenient reference power that's so commonplace people forget to state it.

Nah. People are just sloppy and assume they're talking the same terms as the other chap. dBW or dBmW should always be established when talking Power, dB only ever (even with microwaves) refers to a ratio of Powers. (Not Volts! - although that's another common example of sloppiness).
PS I know you know that, Jim.

 

[jim hardy]

(Not Volts! - although that's another common example of sloppiness).

Yep.
$P = \frac{V^2}{R}$

so 1 milliwatt into 600 ohms requires
$V = \sqrt{ {P}X{R}} = \sqrt {{0.001}X{600}} = \sqrt{0.6} = ~0.775 volts$
and 0db on Decibel scale is right underneath that many volts on red 2.5 VAC scale
(note the 2.5VAC scale is ever so slightly nonlinear - that's to handle nonlinearity of the diode rectifiers inside the meter)

3 db doubles power (actually 3.01db)
so $P = Pref X 10^{\frac{dbm}{10}}$ and ${Pref} = 1 milliwatt$

so at 3dbm
10^0.3 = 1.995 , and
to make 1.995 mw in 600 ohms would require $V = \sqrt{ {P}X{R}} = \sqrt {{0.001995}X{600}} = \sqrt{1.197 } = ~1.094 volts$
which indeed is right above the 3db mark

at 6dbm
10^0.6 = 3.981 , and
to make 3.981 mw in 600 ohms would require $V = \sqrt{ {P}X{R}} = \sqrt {{0.003981}X{600}} = \sqrt{2.389 } = ~ 1.545 volts$

at 10 dbm
10^1 = 10 , and
to make 10 mw in 600 ohms would require $V = \sqrt{ {P}X{R}} = \sqrt {{.01}X{600}} = \sqrt{6 } = ~ 2.449 volts$

hmm.
at 6db I see 1.525 volts which would be 5.88 db not 6
either my purple line is just a smidge off, or the scale is.
I'd wager it's my hand drawn purple line.

old jim

 

[sophiecentaur]

@jim hardy I wasn't thinking in terms of Analogue meters because people don't use them very much these days - but there's a different thing:
My problem is that a 240V 1kW electric heater and a 240V 20W lightbulb could be (if the sloppiness were followed through) 0dB different. . . . . and there's the problem with transformers that are sometimes awarded a 'Gain in dB'.

And you can hear the question "Is that dB Volts or dB Power?" Aaargggh.

 

[jim hardy]

That's a "Big Ten-Four" on sloppy...

I taught myself ,
upon encountering any mention of db
to immediately stop and ask "db referred to what ? "

It's a self defense reflex now, against proceeding on a mistaken premise and compounding errors -
"db means a ratio and before i go any further i want to know what's the denominator? "

I flogged this horse for benefit of OP because it seemed to me he wasn't thinking "ratio"
and the analogue meter is my anchor to reality.
After all, at the level of our sensory abilities, Mother Nature is analog

old jim

 

[jim hardy]

My problem is that a 240V 1kW electric heater and a 240V 20W lightbulb could be (if the sloppiness were followed through) 0dB different. . . . . and there's the problem with transformers that are sometimes awarded a 'Gain in dB'.

HiFi gear response is always plotted in db - it looks so much better on the log scale.

 

[wirefree]

Many thanks for all the responses. A special thanks to @jim hardy for the historical/analog, and especially his personal, perspective.

A big thanks to @berkeman & @tech99 for taking the bull by its horns.

Thanks also to @sophiecentaur and @poor mystic for chipping in.

I flogged this horse for benefit of OP because it seemed to me he wasn't thinking "ratio" and the analogue meter is my anchor to reality.

All help appreciated.

Before I proceed, I really must address @jim hardy about the source of this query:

Is this a real life experiment?

How precise are my "arrived at" numbers for Pt and Pr ?

This problem appears in a locally published and prescribed textbook for an undergraduate course in Microwave Engineering.

Next, a note on @tech99’s suggestion:

The ratio of Pt and Pr, which you have expressed in dB, is presumably the measured attenuation of the system under test, say L dB. If your system includes, a component, such as a directional coupler, which has 0.5dB attenuation, then the attenuation of the remainder of the system is L-0.5 dB. Yes, the remainder of the system has less attenuation.

On the other hand if you have calculated Pr, then you must have already included the directional coupler in the calculation, so subtracting it will not create negative attenuation.

I follow your suggestion.

The second paragraph especially interests me. But I maintain my qualms about the subtraction.

Also, you prefer to term the ratio ‘Attenuation’ and not what I refer to it, i.e. ‘P_r’.

Perhaps that’s what’s contentious.

If we were to call it ‘Attenuation’, then I can clearly see now that the attenuation of the Circuit Under Test, with the Directional Coupler removed, would be L-0.5 dB. But, in terms of P_r, I cannot make peace with the given solution — see below the part of the solution to the question after all the mechanics of the DC are complete and all power values have been calculated.

In keen anticipation of your responses,
best regards,
wirefree

 

[tech99]

We only have a snip of the book, but it seems be mixing up decibel and absolute quantities. I am not at all happy about the calculation as shown or the units being used. For instance, power cannot be expressed in dB, only dBW, dBm etc. There must be a reference.
Thank you for your nice comments.

 

[jim hardy]

i lack the vocabulary to decipher this one.

What the heck are "C" and "D" ?
What the heck are "P_f" and "P_b" ?
Where did that 284.6 X10^^-6 come from ? I notice it's 55db down from 90 (P_i ?) and 55 is the sum of "C" and "D". Is that coincidence?

Is "Effective Received Power" P_r' defined someplace?
If -0.445 = $10log\frac{P_r'}{90}$
then 10^^-0.0445 = P_r' /90
and P_r' = 90 X 10^^-.0445 = 90 X .90261 = 81.2 watts ?

 

[DaveE]

I taught myself ,
upon encountering any mention of db
to immediately stop and ask "db referred to what ? "

YES! dB is a ratio, otherwise write the reference in the unit i.e. dBm, dBuV, dBc etc.
Then everyone needs to be on the same page about the 10 or 20 factor. 10 for power, or power related things like dBc. 20 for voltages and currents.
Expressing a ratio of voltages in dB is different formula than expressing a ratio of power in dB and there is often no way of knowing without understanding the context.

 

[davenn]

What the heck are "C" and "D" ?
What the heck are "Pf" and "Pb" ?
Where did that 284.6 X10^-6 come from ? I notice it's 55db down from 90 (Pi ?) and 55 is the sum of "C" and "D". Is that coincidence?

I agree ... really odd
and particularly this part

@wirefree C and D are not even defined in the text you have given us

 

[sophiecentaur]

YES! dB is a ratio, otherwise write the reference in the unit i.e. dBm, dBuV, dBc etc.

It's possible that the person who writes "dBV" knows what they mean by it but a Bell is a ratio of Powers and the Voltage ratio may or may not be the square root of the ratio of the Powers. Inside a circuit, the impedances will very likely be all over the place so dBV is an even more risky thing to use. There is never any actual need to quote dBV so why introduce it?

 

[Averagesupernova]

There is never any actual need to quote dBV so why introduce it?

Do you feel the same way about dBmV and dBuV as well? dBmV is a very established standard in the cable TV industry.

 

[sophiecentaur]

Do you feel the same way about dBmV and dBuV as well? dBmV is a very established standard in the cable TV industry.

Yes I do feel the same. They get away with it because they are, presumably using (or are assuming) the same impedance everywhere and the numbers they happen to be using happen to suit them. It is sloppy usage because it is a non-existent unit. A ratio of Powers is not a ratio of Voltages and neither are the logs₁₀.
So called Standard Practice is often very dodgy and 'in house'. Talk to a plumber about the way pressure actually works and you will get a nonsense answer,. That's despite the fact that the guy can be trusted to fit a central heating system in your house very competently and with no mistakes.
I like a simple life and I resent having to double think such things as dBV before I can decide what they mean.

 

[Averagesupernova]

https://www.maximintegrated.com/en/app-notes/index.mvp/id/808

 

[f95toli]

I agree ... really odd
and particularly this part

@wirefree C and D are not even defined in the text you have given us

It is a directional coupler so it is probably the coupling and the directivity

 

[DaveE]

There is never any actual need to quote dBV so why introduce it?

Perhaps. Then again there's no need for any sort of dB unit. If you could create the engineering units from scratch and educate everyone in their use then there could be no dBV. Kind of what I would like to do with ergs, now there's a stupid unit; unless of course you are that sort of physicist.
However, that's not how the real world works. For better or worse, these units are commonly used. For example the RF emissions standards (CISPR et al) are full of power measurements in dBuV. If you want to talk with those guys it may be easier for you to temporarily adjust than to change all of them. The question in that sort of situation is do you want to argue, or do you want to communicate?
I suspect that these units come from older instrumentation (spectrum analyzers, for example) that actually measured volts and left it to the user to worry about power, impedance, etc.
dBV is also commonly used unit at low frequencies (like control systems) where you really don't worry about power or characteristic impedance like the RF guys do.

 

[sophiecentaur]

https://www.maximintegrated.com/en/app-notes/index.mvp/id/808

The article starts off with the statement that there's not a lot of 75Ω test equipment so the cable TV world needed to get familiar with the conversion. It's an 'isolated community' (a large minority but still a minority).
I would say that the fact that the the article needed to be produced just demonstrates that using dBV is actually confusing and they should never have started that way in the first place. I'm sure one can get used to anything but why should you have to? I realize that the Cable TV industry would have been forced to use 75Ω system to minimise losses on long cables. Life's presumably different in the modern world of twisted pairs and digital signals for wired transmission.

 

[Averagesupernova]

I'm sure one can get used to anything but why should you have to?

Well if the cable TV industry is such a minority as you say, I can't see why itshould bother you. And please tell me why you think anyone unfamiliar to said industry should have anything to say about it? If you were familiar, you would know the reason.
-
dBmV is still a power measurement. 3dB above 0 dBmV is still double the power of 0dBmV. We could have picked a unit called the dBblahblahblah and specified it as 0 being 13.33 nanowatts at 75 ohms and it would be the same signal strength as 0 dBmV and we would be working with the almighty watt as to avoid confusion by mixing in volts and in my opinion it would be crazy. The fact is 0dBm is too much signal for television receivers and instead of always working around -47 dBm, we created a unit that is more suitable.

 

[davenn]

It is a directional coupler so it is probably the coupling and the directivity

maybe... but who knows for sure

just more poor il-defined info

 

[jim hardy]

Kind of what I would like to do with ergs, now there's a stupid unit; unless of course you are that sort of physicist.

What ?
I struggled to change over from dynes and centimeters and ergs and Maxwells to Newtons and meters and Joules and Webers .

Oh well. When in Rome...

 

[sophiecentaur]

Well if the cable TV industry is such a minority as you say, I can't see why itshould bother you. And please tell me why you think anyone unfamiliar to said industry should have anything to say about it? If you were familiar, you would know the reason.
-
dBmV is still a power measurement. 3dB above 0 dBmV is still double the power of 0dBmV. We could have picked a unit called the dBblahblahblah and specified it as 0 being 13.33 nanowatts at 75 ohms and it would be the same signal strength as 0 dBmV and we would be working with the almighty watt as to avoid confusion by mixing in volts and in my opinion it would be crazy. The fact is 0dBm is to much signal for television receivers and instead of always working around -47 dBm, we created a unit that is more suitable.

I did acknowledge that CATV is a Large Minority - clearly not large enough for equipment manufacturers to supply its specific needs, though. 'It" bothers me because I have seen so many mistakes made when Volts and dBs get together - even with experienced Engineers. Why would you think that one would need an intimate knowledge about a particular industry to point out the potential problems of some of its practices?
We will have to disagree about this one. In my book, V stands for Volts and Volts are not Power. I'd be more than happy with your blahblahblah, aamof.
I get what you say about convenient choice of units for a particular application but, if -47dBmW is inconvenient then 23dBnW would be fine for me. But, then, the prefix 'nano' was about as unfamiliar as the words "Capacitor" and "Hz" when they started measuring signal strengths with a rectifier and meter.
I wouldn't be at all bothered if I could be sure that everyone who uses dBV was always aware that the Impedance is highly relevant - hence my remark above about transformers with dBs of 'gain'. How do you avoid that problem?

 

[DaveE]

How do you avoid that problem?

Education. Electronics is complicated. There will always be good engineers who know a lot and bad ones who don't. The good ones know how to adjust to other's communication styles; they know the difference between the fundamental issues and the superficial. The bad ones are going to have a hard time even if you standardize everything. The real trick is to understand the limits of your own knowledge and when to get help. That, and knowing which fights are worth fighting.

 

[Averagesupernova]

I did acknowledge that CATV is a Large Minority - clearly not large enough for equipment manufacturers to supply its specific needs, though.

You are sadly mistaken if you think equipment manufacturers are not catering to the CATV industries needs. Why do you think I have an strong opinion in this area?

'It" bothers me because I have seen so many mistakes made when Volts and dBs get together - even with experienced Engineers. Why would you think that one would need an intimate knowledge about a particular industry to point out the potential problems of some of its practices?
We will have to disagree about this one. In my book, V stands for Volts and Volts are not Power. I'd be more than happy with your blahblahblah, aamof.
I get what you say about convenient choice of units for a particular application but, if -47dBmW is inconvenient then 23dBnW would be fine for me. But, then, the prefix 'nano' was about as unfamiliar as the words "Capacitor" and "Hz" when they started measuring signal strengths with a rectifier and meter.
I wouldn't be at all bothered if I could be sure that everyone who uses dBV was always aware that the Impedance is highly relevant - hence my remark above about transformers with dBs of 'gain'. How do you avoid that problem?

If you want to discuss units causing confusion then where will it end? RMS comes to mind. RMS volts is fine but many people who SHOULD know better talk about RMS watts. As far as people being aware of what the impedance is when using volts with dB, I hope they would know. Not knowing would be like someone trying to measure volts with your DVM set to current. Send them back to the classroom.

 

[sophiecentaur]

You are sadly mistaken if you think equipment manufacturers are not catering to the CATV industries needs. Why do you think I have an strong opinion in this area?

I was only quoting from the link that you.

Not knowing would be like someone trying to measure volts with your DVM set to current. Send them back to the classroom.

There are many workers in Technology who do not revisit the classroom, once they have their qualification certificate. They are very vulnerable to sales talk and practicalities of using equipment.
This is an historical matter, I think. I really appreciate how that dBV terminology could have been launched in the first place, based on measured Volts at the output of a rectifier. Going from that to a Signal Power value would have been another step in the measurement process. I realize that the lower limit for direct measurement of RF Power is nothing like what's needed for measuring most received levels of signals so the equipment will in fact be measuring Volts. Afaik, Power is what's used in the field of microwave comms.

 

[DaveE]

What ?
I struggled to change over from dynes and centimeters and ergs and Maxwells to Newtons and meters and Joules and Webers .

Oh well. When in Rome...

LOL, So sorry to hear of your story of adolescent educational abuse. On the other hand, I was really happy to hear that you recognized the problem and put the effort into your recovery. Sort of proving my point, actually. For everyone that converts from Joules to ergs, there must be 10,000 people that go the other way.
Next on the tirade agenda:
1) The "pound" as a unit of... idk, currency?, force?, whatever else you want to use it for?
2) If x² = -1, then does x = i or does x = j?
3) Who has ever used "grad" to express angles, and why was it put in every calculator ever made?
4) Why can't everyone just switch to Esperanto? There would be so much less confusion in the sciences that way. I know, I should be writing in Esperanto too, but there is a limit to how much effort I will put into these posts.

 

[jim hardy]

Ever run across the Poundal ? Accelerates 1lbm 1 ft/sec²
for me it beats using slugs...

Who has ever used "grad" to express angles, and why was it put in every calculator ever made?

The HP35 calculator instruction book explained where Grads are useful. I used them a few times in early 70's but have forgot why.

Asimov once pointed out our base 360 for angular measurement comes from an archaic (i think)Sumerian number system. They picked 360 because it's evenly divisible by so many numbers

The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, making a total of 24 divisors. 360 is a highly composite number.
360 (number) - Wikipedia

https://en.wikipedia.org/wiki/360_(number)

There was once a movement to change angular measurement to decimal , milliturns . A grad would be 2.5 militurns.
But as you suggest, "Newer" does not equate to "Better".

i DO miss RPN calculators , much preferred them.

But i digress.

old jim

 

[sophiecentaur]

The HP35 calculator instruction book explained where Grads are useful. I used them a few times in early 70's but have forgot why.

Grads are ideal for calculations involving rotations. `There is no need to introduce 360, 60 and 60 into your calculations. But Grads are a bit on the big side even for rough practical work so they are not a very intuitive size. (Same objection as you guys have about kg - too big and g - too small. The oz is pretty much right for most things, I have to admit)
Interestingly, in navigation, it is the practice nowadays to use degrees, minutes and decimals of minutes instead of using degrees, minutes and seconds which was past practice. Your GPS hand held will almost certainly have both options available. I was at sea with a pal and we were busy disagreeing with where we were and I realized he was using mins and secs and I was using decimal mins. The chart, of course was in decimal mins because it was not printed in Victorian times.

 

[wirefree]

Christmas Greetings to All - whichever part of the world you are in. I hope it’s a good end to the year for everyone.

— see below the part of the solution to the question after all the mechanics of the DC are complete and all power values have been calculated.
wirefree

@tech99 @jim hardy @davenn @f95toli @sophiecentaur
Thank you for sticking around.My effort here has been to not expose you to the inner workings of the Directional Coupler. Related to it are concepts such as Coupling (C) and Directivity (D). How they are calculated and what their magnitudes are in this particular question, I hoped, wouldn’t concern you as long as their units were mentioned.The relevant terms remain P_x’s , units of which have been clearly mentioned.Warm regards,

wirefree

 

[jim hardy]

Coupling (C) and Directivity (D). How they are calculated and what their magnitudes are in this particular question, I hoped, wouldn’t concern you as long as their units were mentioned.

Well Thanks for the feedback and kind wishes - they are reciprocal

i only tried to address this query

I am here to clear my doubt about the dB scale, in general, and it’s use in calculating received power

but asked about D and C for fear i had missed something fundamental

i hope you're more confident with db now.

Myself, i was glad to see db is still on the Simpson 260 meter face.
It's the only piece of nostalgia i know that's "still made just like they used to."

old jim

 

[Tom.G]

3) Who has ever used "grad" to express angles, and why was it put in every calculator ever made?

Back when the first pocket scientific calculator became available, a large part of the market was the Civil Engineers.

IIRC, that 'orphan', the grad, is rather handy in infrastructure plumbing such as sewer lines, even when building a home. When laying a sewer line, the construction folks build in a slope so the water will flow down hill rather than just lay in the bottom of the pipe. They refer to the slope as Rise/Run, x feet of rise per 100 feet of run. One foot of rise (or fall) per 100 feet = 1grad.

(irrelevant side story)
As you may have heard, here in California we run into a water shortage on occassion. This of course triggers calls for everyone to use less water, don't water their lawns, flush their toilets less often, etc. Well the sewers, both storm and sanitary, were built ages ago when water was used freely, and they were built with a slope adequate to move the expected solids along with the water flow. Under drought conditions there were problems with the sewers clogging due to the reduced water flow.

Cheers,
Tom