# rms value of a rectangular pulse

#### lucky007tiwari

Joined Nov 21, 2012
6
dear sir
my waveform is rectangular,T on is .25 sec and T 0ff is .75 second so Total Time period is 1 second..there is nothing negative part in it means its a pure positive rectangular pulse having frequency 4 Hz.the value of amplitude is 5 volt............
i am fully confused about the measurement of it....what will happen when i measure it with multimer.......plz help me.................

#### bountyhunter

Joined Sep 7, 2009
2,512
A meter probably can't measure it accurately. Even if it is a true RMS meter, it has limitations on bandwidth and crest factor which will throw the reading off.

#### thatoneguy

Joined Feb 19, 2009
6,359
Mathematically,

RMS of PWM square wave is a√D

Where a is high voltage value, and D is duty cycle.

Meters will measure this in varying ways. A thermal measurement type meter is the most accurate for this type of waveform.

#### lucky007tiwari

Joined Nov 21, 2012
6
sir i have used a multimeter only....at its DC voltage mode........every time when the pulse reaches at its peak the value in multimeter is not repeating...what is the reason behind it....

#### lucky007tiwari

Joined Nov 21, 2012
6
Dear sir acording to my knowledge we calculate RMS value when frequency is very high and the direction goes +ve and -ve continuesly...like an AC current.......but in my case i am talking about a rectangular wave which is always +ve at its ON time and 0 at its off time.........then why i am unable to calculate its exact amplitude value at each time when the pulse is in its on mode....multimeters reading are fluctuating....why is it all happening..

#### Salaja

Joined Jan 27, 2013
23
well, your time varying signal isn't centered around 0v, so it's basically the same as a signal that IS centered around 0v, but with a DC component. maybe this DC component is messing with the multimeter because it wasn't designed to handle DC when measuring RMS. maybe try adding a voltage offset so the average voltage becomes 0v.
NOTE: this is only a guess, i don't know that much about measuring the RMS value of square wave signals.

also, you're measuring a 1Hz signal, is your multimeter rated to a frequency that low?

#### atferrari

Joined Jan 6, 2004
4,122
.
NOTE: this is only a guess, i don't know that much about measuring the RMS value of square wave signals.
Why do you answer then? Guessing could be right or wrong. You do not actually help the OP with that.

Leave that to those that know it better and learn by reading what the say...

#### MrChips

Joined Oct 2, 2009
22,102
What is RMS value?

Exactly that, the Root Mean Square, i.e. the square root of the mean value of the values squared.

To determine the RMS value, you take a series of sampled points, square each value, add the values and take the mean value, then take the square root to give the result.

Does your meter do this? Must likely not.

The only other way is to feed the signal into a resistive heater and measure the power generated in the heater. This is how a hot wire ammeter works.

#### The Electrician

Joined Oct 9, 2007
2,801
Dear sir acording to my knowledge we calculate RMS value when frequency is very high and the direction goes +ve and -ve continuesly...like an AC current.......but in my case i am talking about a rectangular wave which is always +ve at its ON time and 0 at its off time.........then why i am unable to calculate its exact amplitude value at each time when the pulse is in its on mode....multimeters reading are fluctuating....why is it all happening..
The reason why your reading is fluctuating is because your waveform has a period of 1 second. Typical meters are designed to work with 50 Hz or 60 Hz waveforms, and they are designed to take several readings per second.

I set up a function generator to produce your waveform and when I connected my Fluke 189 to measure the True RMS AC+DC, the readings were bouncing all over the place. The Fluke takes about 5 readings per second. What would you expect for a waveform with a period of 1 second? The reading you get is only going to use about 1/5 of a second worth of the waveform. The particular 1/5 of a second that the meter sees will be random, so the reading will not be stable.

In post #3, thatoneguy gave you a formula for the RMS value of your waveform; you can find that formula here:

http://en.wikipedia.org/wiki/Root_mean_square

If you want to actually measure the RMS value, rather than calculate it with a formula, you will probably have to use an oscilloscope that can do waveform math. The attachment shows the result I get with a scope measurement. The formula says the RMS value of your waveform should be 2.5 volts RMS, and that's essentially what the scope says.

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#### bountyhunter

Joined Sep 7, 2009
2,512
The reason why your reading is fluctuating is because your waveform has a period of 1 second. Typical meters are designed to work with 50 Hz or 60 Hz waveforms, and they are designed to take several readings per second.
Exactly. As I said many posts back:

Even if it is a true RMS meter, it has limitations on bandwidth
A 1 Hz signal is too low in frequency to be read accurately

#### The Electrician

Joined Oct 9, 2007
2,801
Exactly. As I said many posts back:
What you said was: "A meter probably can't measure it accurately. Even if it is a true RMS meter, it has limitations on bandwidth and crest factor which will throw the reading off. ", which is not addressing the fact that the meter takes multiple readings during one period of the waveform, the cause of the major fluctuations the OP described. Those fluctuations have nothing to do with limited bandwidth or crest factor. The OP's waveform has a crest factor of 2, well within the allowable crest factor of 3 that a typical DMM can handle.

Limited bandwidth or unfavorable crest factor alone wouldn't lead to major fluctuations in the reading. If those factors were the only source of error exclusive of the undersampling effect, the reading would be stable but wrong.

A 1 Hz signal is too low in frequency to be read accurately
The effect of limited bandwidth on the accuracy of an RMS measurement will depend on just what the bandwidth is (how many harmonics of a non-sinusoidal waveform are taken into account by the bandwidth of the meter). If a particular meter can account for a sufficient number of harmonics to give rated accuracy (.4% for my Fluke 189) at 60 Hz, then with a lower frequency waveform, more harmonics will be taken into account, and accuracy will not suffer because of insufficient bandwidth; the relative bandwidth will actually be more favorable for the lower frquency waveform.

The main difficulty in making a measurement of a 1 Hz waveform with a typical DMM is not the bandwidth of the meter; it's the effect I described where the meter is not sampling the full waveform for a measurement.

Other than because of the undersampling effect, why should it be difficult to accurately measure a 1 Hz waveform? My scope was able to calculate the RMS value of the OP's 1 Hz waveform to better than .1% accuracy.

#### WBahn

Joined Mar 31, 2012
26,304
Unless the meter is AC coupled, how well would you expect the meter to do for a waveform that was, say, 0.01Hz?It wouldn't give you a good average over one cycle, but it would give you good (relatively) instantaneous RMS values that you could note and use to get a good overall average.

#### The Electrician

Joined Oct 9, 2007
2,801
Unless the meter is AC coupled, how well would you expect the meter to do for a waveform that was, say, 0.01Hz?It wouldn't give you a good average over one cycle, but it would give you good (relatively) instantaneous RMS values that you could note and use to get a good overall average.
I can't speak to what an unknown meter might do, but my scope had no trouble with the OP's waveform with the frequency reduced to .01 Hz. See the attachment; note the sweep speed of 20 seconds per division. I had to wait 200 seconds to get the result.

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#### Kermit2

Joined Feb 5, 2010
4,162
RMS value is just a way to state equivalent power vs. DC.

You have a slow SQUARE wave. Root mean square is not needed to get the average power from a square wave.

The average power will be derived from the DC value multiplied by a percentage equal to the ratio of on time/on+off time. Then use Ohms law to figure the power delivered to the load using the average DC value.

SINE waves need the root mean square method. Square waves do not.

#### Potato Pudding

Joined Jun 11, 2010
688
dear sir
my waveform is rectangular,T on is .25 sec and T 0ff is .75 second so Total Time period is 1 second..
That sounds like a 25% duty cycle and for an ideal rectangular or square wave the duty cycle x peak voltage is your rms voltage.

there is nothing negative part in it means its a pure positive rectangular pulse
Also important for the above which assume that your OFF or low range voltage is zero. If you were pulsing from 1 volt low or -5 Volt low that would make the calculation different.

having frequency 4 Hz.
That is incorrect, you must use the total period for calculating frequency and not just your positive pulse width. Your frequency is 1Hz.

the value of amplitude is 5 volt............
Very simply at 25% duty cycle your rms value is 0.25 x 5Volt = 1.25 Volts.

i am fully confused about the measurement of it....what will happen when i measure it with multimer.......plz help me.................
When you measure it with the multimeter most multimeters will lie or get very confused. Low frequency and high frequency response can cost a lot more. Ability to measure anything that isn't a sine wave or dc is also usually extra.

Very good multimeters will tell you a frequency count, peak voltage, RMS voltage and duty cycle. When a good multimeter is telling you all of this, it just means that you really want to use an Oscilloscope to see exactly what is going on.

Every decent electronics course in the world will include a few lab exercises that makes these points and forces you to understand this.

#### bountyhunter

Joined Sep 7, 2009
2,512
What you said was: "A meter probably can't measure it accurately. Even if it is a true RMS meter, it has limitations on bandwidth and crest factor which will throw the reading off. ", which is not addressing the fact that the meter takes multiple readings during one period of the waveform, the cause of the major fluctuations the OP described. Those fluctuations have nothing to do with limited bandwidth or crest factor. The OP's waveform has a crest factor of 2, well within the allowable crest factor of 3 that a typical DMM can handle.

Limited bandwidth or unfavorable crest factor alone wouldn't lead to major fluctuations in the reading. If those factors were the only source of error exclusive of the undersampling effect, the reading would be stable but wrong.

The effect of limited bandwidth on the accuracy of an RMS measurement will depend on just what the bandwidth is (how many harmonics of a non-sinusoidal waveform are taken into account by the bandwidth of the meter). If a particular meter can account for a sufficient number of harmonics to give rated accuracy (.4% for my Fluke 189) at 60 Hz, then with a lower frequency waveform, more harmonics will be taken into account, and accuracy will not suffer because of insufficient bandwidth; the relative bandwidth will actually be more favorable for the lower frquency waveform.

The main difficulty in making a measurement of a 1 Hz waveform with a typical DMM is not the bandwidth of the meter; it's the effect I described where the meter is not sampling the full waveform for a measurement.

Other than because of the undersampling effect, why should it be difficult to accurately measure a 1 Hz waveform? My scope was able to calculate the RMS value of the OP's 1 Hz waveform to better than .1% accuracy.
BANDWIDTH is the range of frequencies that a meter can measure to the specified accuracy limits. Period. It doesn't matter why, it just says that's the limit. If the meter reading is jumping all over the map and reading gibberish, pretty obvious that signal frequency is outside of the usable bandwidth.

#### The Electrician

Joined Oct 9, 2007
2,801
BANDWIDTH is the range of frequencies that a meter can measure to the specified accuracy limits. Period. It doesn't matter why, it just says that's the limit. If the meter reading is jumping all over the map and reading gibberish, pretty obvious that signal frequency is outside of the usable bandwidth.
You're using the word "bandwidth" to mean something other than its commonly understood meaning.

What you're talking about is operational frequency range, a different concept than bandwidth.

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#### The Electrician

Joined Oct 9, 2007
2,801
That sounds like a 25% duty cycle and for an ideal rectangular or square wave the duty cycle x peak voltage is your rms voltage.
This is incorrect.

http://en.wikipedia.org/wiki/Root_mean_square

The RMS value of a waveform such as the OP's is equal to the square root of the duty cycle times the peak voltage.

Very simply at 25% duty cycle your rms value is 0.25 x 5Volt = 1.25 Volts.
The correct value is 2.5 volts. See the image in post #9.

The average power will be derived from the DC value multiplied by a percentage equal to the ratio of on time/on+off time. Then use Ohms law to figure the power delivered to the load using the average DC value.
The highlighted part should be "multiplied by a percentage equal to the square root of the ratio of on time/on+off time."

RMS value is just a way to state equivalent power vs. DC.....SINE waves need the root mean square method. Square waves do not.
If you want the "equivalent power" of any waveform, sine or square or anything else, the RMS value is what must be calculated, or measured.

#### timescope

Joined Dec 14, 2011
298
Very simply at 25% duty cycle your rms value is 0.25 x 5Volt = 1.25 Volts
The formula says the RMS value of your waveform should be 2.5 volts RMS, and that's essentially what the scope says.
So we have two answers to the op's question. Let's vote, toss a coin or derive a new formula to obtain one answer.

Timescope

#### The Electrician

Joined Oct 9, 2007
2,801
So we have two answers to the op's question. Let's vote, toss a coin or derive a new formula to obtain one answer.

Timescope
The available evidence is: