Peak to Peak - RMS made simple - UK Vintage Radio Repair and Restoration Discussion Forum

NorfolkDaveUK · 3rd Oct 2018, 12:50 am

I`m sure that all the good techs on here are well aware that this is not exact but I have just been looking for a simple way to use my scope that has peak to peak measuring to get the RMS figures I need . There is a complicated way of doing it very accurately, and while looking it up and asking for assistance etc people wanted to just give me this complicated equation to go away with . Which , after some time I did figure out how to use , but there is a much simple way to get a close ball park value and its simply to multiply what you need in RMS by 2.83 and that will give you a close enough peak to peak conversion .

So if you want 300 milivolts RMS , the equation would be simply , 0.3 x 2.83 = 0.849 so when your scope reads 0.849v peak to peak , you have a value of 0.3001668286136894V RMS , which is close enough for what we are doing .

333mV needed in RMS = 0.333x2.83 = 0.94239 . That gives you 0.3331851797611952v RMS . So as you can see its a quick and easy way to get you there .

I hope no-one minds me posting this here , it was just something that was driving me crazy and when the penny dropped for me I thought it might be useful to someone esle .

This does depend on the wave you are looking at , this works for a sine wave . I dont know if it works for anything else , I use sine waves pretty much exclusively .

I`m sure this is common knowledge to most here , just posting for the few like me that was confused by the equations.

David

Refugee · 3rd Oct 2018, 1:29 am

Most pocket calculators can do square roots.
All you do is multiply the RMS voltage by the square root of 2 to get the peak voltage and then multiply the result by 2 to get peak to peak voltage.
1.4 or 2.8 is usually good enough for the output of a mains transformer.

NorfolkDaveUK · 3rd Oct 2018, 2:02 am

You may as well be speaking German bud ...lol...to me i mean not trying to be rude . I`m awful with maths .

multiply it by 2.83 , jobs a goodn`..lol

ahh i actually just figured that out ,

press 2 then sqrt button , then x rms then x 2.....ok i get that .....

Diabolical Artificer · 3rd Oct 2018, 6:09 am

"you may as well be speaking German bud" The math's can be a mind bender but the more you use it the less scary it gets. I hardly ever use the P-P value when working stuff out for circuits, just the peak and RMS. I never use a scope to measure voltage, just use a DMM or an old valve voltmeter.

Andy.

Radio Wrangler · 3rd Oct 2018, 7:02 am

Don't forget that all this is only applicable to sinewaves.

For other waveforms the factors can be quite different.

peak-peak to RMS is 2.8-ish for pure sines, 2.0 for square waves, can tend towards 0 for very narrow pulses and tends towards infinity for undistorted noise.

For a digitising scope, a peak to peak measurement is easy, but as a scope can display any old waveform a true RMS measurement would need a much large calculation involving every point on the waveform and would need extra controls to tell it over what part of the picture to do it.

Grandad told me how to understand maths: "You know those sums you do at school, the ones like 'if it takes eleven men a month to dig a trench 3' deep, 2' wide and a mile long, how long does it take for....?' Well, you tell me which is easier - doing the sum or digging the trench?"

Maths is a tool. Maths is a language, Maths is a whole world unto itself, but more importantly, it's a wonderful way of cheating!

David

radiotechnician · 3rd Oct 2018, 7:52 am

Old scopes had a graticule marked p-p and RMS.

A 2 uFd capacitor is connected in series with a 2000 ohm pot
and connected across a 12 volt transformer. Class is told
to adjust until the capacitor equals resistance voltage.

This fairly cements how the square root of two annoys them
when AC and capacitors are involved.

Hooking up a full wave voltage doubler does it for pp.

Radio Wrangler · 3rd Oct 2018, 9:44 am

The p-p and RMS markings on some graticules were only good for sinewaves, of course. But be careful, a lot of graticules have similar-looking markings for use measuring 10% to 90% rise and fall times.

David

NorfolkDaveUK · 3rd Oct 2018, 9:47 am

Thanks guys , to me this is really valuable stuff.

I never really intended to get this involved with this when i started out . I thought oh I`ll get a few gummed up Sonys , put them right and it will keep me occupied but the more I get into it the more enjoyable it is. Eight months ago I wouldn't have known a transistor from a truck, but I've learned so much in short amount of time. I wish I had had the wherewithal to do it when I was in my 20's . Unfortunately life didn't deal me that hand. Hey ho, I'm making up for it now I guess.

NorfolkDaveUK · 3rd Oct 2018, 9:48 am

Quote:

Originally Posted by Radio Wrangler

The p-p and RMS markings on some graticules were only good for sinewaves, of course. But be careful, a lot of graticules have similar-looking markings for use measuring 10% to 90% rise and fall times.

My scope has a peak to peak measure function so I get a number on screen rather than having to count the squares . it measures peak and peak to peak actually .

Skywave · 3rd Oct 2018, 12:22 pm

For sine-waves only: voltage being developed across a resistive load.
Measure the peak-to-peak waveform, volts: call it Vpp.
Measure the load, Ohms, that that waveform appears across: call it R.
Then the RMS value, volts is (Vpp)*(Vpp) / 8R
(That equation is derivable with a bit of basic algebra).

Al.

ms660 · 3rd Oct 2018, 12:32 pm

For peak to peak to RMS just multiply by 0.353

Lawrence.

Ambientnoise · 3rd Oct 2018, 12:36 pm

Al, you have a typo, numerically volts RMS is simply (Vpp*Vpp)/8. Dividing by R gives power in Watts. Of course, the volts are generated across the R.

I find that if using a scope, Vpp/3 is adequate especially given the likely accuracy of a scope and reading from a screen.

Ken

Alistair D · 3rd Oct 2018, 3:48 pm

If your scope has a variable control attached to the Y attenuator you can re-calibrate it to read RMS. Feed say 300mV RMS from a sig gen into the Y input then rotate the variable until the trace fills 3 divisions. Although the display still shows p/p the numerical value will be RMS.

Al

Craig Sawyers · 3rd Oct 2018, 4:24 pm

Quote:

Originally Posted by Skywave

For sine-waves only: voltage being developed across a resistive load.
Measure the peak-to-peak waveform, volts: call it Vpp.
Measure the load, Ohms, that that waveform appears across: call it R.
Then the RMS value, volts is (Vpp)*(Vpp) / 8R
(That equation is derivable with a bit of basic algebra).

Ah. If you measure the rms voltage, whatever the waveform, square it and divide by the resistance, you get *average* power. It is the average power than heats the resistor. RMS power is certainly calculable, but has absolutely no physical meaning.

NorfolkDaveUK · 3rd Oct 2018, 5:21 pm

Quote:

Originally Posted by Alistair D

If your scope has a variable control attached to the Y attenuator you can re-calibrate it to read RMS. Feed say 300mV RMS from a sig gen into the Y input then rotate the variable until the trace fills 3 divisions. Although the display still shows p/p the numerical value will be RMS.

OH thats really handy to know ....

thanks

Skywave · 3rd Oct 2018, 5:59 pm

Quote:

Originally Posted by Ambientnoise

Al, you have a typo, numerically volts RMS is simply (Vpp*Vpp)/8. Dividing by R gives power in Watts. Of course, the volts are generated across the R.

Whoops! Of course, you are correct!

Thank you.
Sincere apologies to anyone who was mislead.
When I wrote that, there was a little voice in the back of my head saying . . . "there's something there which doesn't sound quite right" . . . . but, like a fool, I ignored it

Hopefully, we can put it down to a 'senior moment'.

Al.

TonyDuell · 3rd Oct 2018, 6:04 pm

Isn't (Vpp*Vpp)/8 equal to (RMS Voltage) _squared_ (at least for sine waves)? The version given in other posts is dimensionally wrong for a start (the left hand side has dimensions of voltage^2, the right hand side of voltage).

Some digital storge 'scopes will display the RMS value of the input signal and they seem to do this by calcualting the integral of the squares of the samples, etc, so it will work for any waveform not just sine waves.

Bazz4CQJ · 3rd Oct 2018, 6:06 pm

Quote:

Originally Posted by Ambientnoise

I find that if using a scope, Vpp/3 is adequate especially given the likely accuracy of a scope and reading from a screen.

Yes, and allowing for the possibility (probability?) of a less than perfect impedance match and most hobbyists will make do with Vpp/3.

Of course the other thing is that Google is awash with online calculators for just about any bit of 'radio maths' that you could think of.

B

Ambientnoise · 3rd Oct 2018, 7:26 pm

Quote:

Originally Posted by TonyDuell

Isn't (Vpp*Vpp)/8 equal to (RMS Voltage) _squared_ (at least for sine waves)? The version given in other posts is dimensionally wrong for a start (the left hand side has dimensions of voltage^2, the right hand side of voltage).

Some digital storge 'scopes will display the RMS value of the input signal and they seem to do this by calcualting the integral of the squares of the samples, etc, so it will work for any waveform not just sine waves.

Yes, of course you are correct, the dimensions are wrong so (Vpp*Vpp)/8 does not give Vrms.

Ken

NorfolkDaveUK · 4th Oct 2018, 11:24 am

Come on folks, let's not make this complicated for people.

LOL.

3rd Oct 2018, 12:50 am	#1
NorfolkDaveUK Banned Join Date: May 2018 Location: Norwich, Norfolk, UK. Posts: 605	Peak to Peak - RMS made simple I`m sure that all the good techs on here are well aware that this is not exact but I have just been looking for a simple way to use my scope that has peak to peak measuring to get the RMS figures I need . There is a complicated way of doing it very accurately, and while looking it up and asking for assistance etc people wanted to just give me this complicated equation to go away with . Which , after some time I did figure out how to use , but there is a much simple way to get a close ball park value and its simply to multiply what you need in RMS by 2.83 and that will give you a close enough peak to peak conversion . So if you want 300 milivolts RMS , the equation would be simply , 0.3 x 2.83 = 0.849 so when your scope reads 0.849v peak to peak , you have a value of 0.3001668286136894V RMS , which is close enough for what we are doing . 333mV needed in RMS = 0.333x2.83 = 0.94239 . That gives you 0.3331851797611952v RMS . So as you can see its a quick and easy way to get you there . I hope no-one minds me posting this here , it was just something that was driving me crazy and when the penny dropped for me I thought it might be useful to someone esle . This does depend on the wave you are looking at , this works for a sine wave . I dont know if it works for anything else , I use sine waves pretty much exclusively . I`m sure this is common knowledge to most here , just posting for the few like me that was confused by the equations. David Last edited by NorfolkDaveUK; 3rd Oct 2018 at 12:58 am.

3rd Oct 2018, 1:29 am	#2
Refugee Dekatron Join Date: Apr 2012 Location: Worksop, Nottinghamshire, UK. Posts: 5,554	Re: peak to peak - RMS made simple Most pocket calculators can do square roots. All you do is multiply the RMS voltage by the square root of 2 to get the peak voltage and then multiply the result by 2 to get peak to peak voltage. 1.4 or 2.8 is usually good enough for the output of a mains transformer.

3rd Oct 2018, 2:02 am	#3
NorfolkDaveUK Banned Join Date: May 2018 Location: Norwich, Norfolk, UK. Posts: 605	Re: peak to peak - RMS made simple You may as well be speaking German bud ...lol...to me i mean not trying to be rude . I`m awful with maths . multiply it by 2.83 , jobs a goodn`..lol ahh i actually just figured that out , press 2 then sqrt button , then x rms then x 2.....ok i get that ..... Last edited by NorfolkDaveUK; 3rd Oct 2018 at 2:27 am.

3rd Oct 2018, 6:09 am	#4
Diabolical Artificer Dekatron Join Date: Jul 2009 Location: Sleaford, Lincs. UK. Posts: 7,667	Re: peak to peak - RMS made simple "you may as well be speaking German bud" The math's can be a mind bender but the more you use it the less scary it gets. I hardly ever use the P-P value when working stuff out for circuits, just the peak and RMS. I never use a scope to measure voltage, just use a DMM or an old valve voltmeter. Andy. __________________ Curiosity hasn't killed this cat...so far.

3rd Oct 2018, 7:02 am	#5
Radio Wrangler Moderator Join Date: Mar 2012 Location: Fife, Scotland, UK. Posts: 22,899	Re: peak to peak - RMS made simple Don't forget that all this is only applicable to sinewaves. For other waveforms the factors can be quite different. peak-peak to RMS is 2.8-ish for pure sines, 2.0 for square waves, can tend towards 0 for very narrow pulses and tends towards infinity for undistorted noise. For a digitising scope, a peak to peak measurement is easy, but as a scope can display any old waveform a true RMS measurement would need a much large calculation involving every point on the waveform and would need extra controls to tell it over what part of the picture to do it. Grandad told me how to understand maths: "You know those sums you do at school, the ones like 'if it takes eleven men a month to dig a trench 3' deep, 2' wide and a mile long, how long does it take for....?' Well, you tell me which is easier - doing the sum or digging the trench?" Maths is a tool. Maths is a language, Maths is a whole world unto itself, but more importantly, it's a wonderful way of cheating! David __________________ Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done

3rd Oct 2018, 7:52 am	#6
radiotechnician Pentode Join Date: Jan 2013 Location: Powell River, British Columbia, Canada. Posts: 217	Re: peak to peak - RMS made simple Old scopes had a graticule marked p-p and RMS. A 2 uFd capacitor is connected in series with a 2000 ohm pot and connected across a 12 volt transformer. Class is told to adjust until the capacitor equals resistance voltage. This fairly cements how the square root of two annoys them when AC and capacitors are involved. Hooking up a full wave voltage doubler does it for pp. __________________ Steve Dow VE7ASO

3rd Oct 2018, 9:44 am	#7
Radio Wrangler Moderator Join Date: Mar 2012 Location: Fife, Scotland, UK. Posts: 22,899	Re: peak to peak - RMS made simple The p-p and RMS markings on some graticules were only good for sinewaves, of course. But be careful, a lot of graticules have similar-looking markings for use measuring 10% to 90% rise and fall times. David __________________ Can't afford the volcanic island yet, but the plans for my monorail and the goons' uniforms are done

3rd Oct 2018, 9:47 am	#8
NorfolkDaveUK Banned Join Date: May 2018 Location: Norwich, Norfolk, UK. Posts: 605	Re: peak to peak - RMS made simple Thanks guys , to me this is really valuable stuff. I never really intended to get this involved with this when i started out . I thought oh I`ll get a few gummed up Sonys , put them right and it will keep me occupied but the more I get into it the more enjoyable it is. Eight months ago I wouldn't have known a transistor from a truck, but I've learned so much in short amount of time. I wish I had had the wherewithal to do it when I was in my 20's . Unfortunately life didn't deal me that hand. Hey ho, I'm making up for it now I guess.

3rd Oct 2018, 12:22 pm	#10
Skywave Rest in Peace Join Date: Jun 2006 Location: Chard, South Somerset, UK. Posts: 7,457	Re: Peak to Peak - RMS made simple For sine-waves only: voltage being developed across a resistive load. Measure the peak-to-peak waveform, volts: call it Vpp. Measure the load, Ohms, that that waveform appears across: call it R. Then the RMS value, volts is (Vpp)*(Vpp) / 8R (That equation is derivable with a bit of basic algebra). Al.

3rd Oct 2018, 12:32 pm	#11
ms660 Dekatron Join Date: Apr 2011 Location: Cornwall, UK. Posts: 13,454	Re: Peak to Peak - RMS made simple For peak to peak to RMS just multiply by 0.353 Lawrence.

3rd Oct 2018, 12:36 pm	#12
Ambientnoise Heptode Join Date: Feb 2006 Location: Marlborough, Wiltshire, UK. Posts: 917	Re: Peak to Peak - RMS made simple Al, you have a typo, numerically volts RMS is simply (Vpp*Vpp)/8. Dividing by R gives power in Watts. Of course, the volts are generated across the R. I find that if using a scope, Vpp/3 is adequate especially given the likely accuracy of a scope and reading from a screen. Ken

3rd Oct 2018, 3:48 pm	#13
Alistair D Nonode Join Date: Jan 2010 Location: Edinburgh, UK. Posts: 2,008	Re: Peak to Peak - RMS made simple If your scope has a variable control attached to the Y attenuator you can re-calibrate it to read RMS. Feed say 300mV RMS from a sig gen into the Y input then rotate the variable until the trace fills 3 divisions. Although the display still shows p/p the numerical value will be RMS. Al __________________ I won't tell you how I discovered that.

3rd Oct 2018, 6:04 pm	#17
TonyDuell Dekatron Join Date: Jun 2015 Location: Biggin Hill, London, UK. Posts: 5,215	Re: Peak to Peak - RMS made simple Isn't (Vpp*Vpp)/8 equal to (RMS Voltage) _squared_ (at least for sine waves)? The version given in other posts is dimensionally wrong for a start (the left hand side has dimensions of voltage^2, the right hand side of voltage). Some digital storge 'scopes will display the RMS value of the input signal and they seem to do this by calcualting the integral of the squares of the samples, etc, so it will work for any waveform not just sine waves.

4th Oct 2018, 11:24 am	#20
NorfolkDaveUK Banned Join Date: May 2018 Location: Norwich, Norfolk, UK. Posts: 605	Re: Peak to Peak - RMS made simple Come on folks, let's not make this complicated for people. LOL.