RMS value?

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spsnyder

Senior Member
Re: RMS value?

"What is the RMS value of DC signal and why?"

The RMS value of a DC signal is the DC value. For an AC signal you can think of the RMS value as the effective DC voltage. If you look at a standard 120V (RMS) voltage on an O Scope the voltage would peak at 169.7 V (Vrms times sq-rt of 2). In otherwords the voltage would be expressed as 169.7sin(wt). The rms value is 120V. If you attach a resistive heater onto this source it would give the same amount of heat as a 120V DC power supply.

"Can an RMS value and Average value ever be the same"

Yes. All DC voltages have the same RMS and Average values.

FYI, An AC voltage's average value is zero. Obviously the RMS value is much more useful and meaningful for calculations.
 

charlie b

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Staff member
Location
Lockport, IL
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Retired Electrical Engineer
Re: RMS value?

First, you must understand that DC does not have to mean that the value is constant. It only means that current is flowing in one direction only. If you have a signal that varies from moment to moment, but never crosses the zero vallue (i.e., always positive or always negative), then its RMS value could be almost anything. You would have to know the exact shape of the curve.

The RMS value of a constant value DC is the same as the value of the DC. If you have a 12.5 volt DC signal, then its RMS value is 12.5 volts. The reason is that RMS squares the value, takes the average, then takes the square root. If the signal is constant, then this process gives you back your original constant value.

The RMS value and the average value can only be the same if the value is constant.
 

physis

Senior Member
Re: RMS value?

Sooo... the RMS voltage of a 4 volt DC square wave (That's symetrical Charlie :)

I used four cause you can do it in your head.

[ January 27, 2006, 04:45 PM: Message edited by: physis ]
 

rattus

Senior Member
Re: RMS value?

Sam,

If it is a 0 to 4V square wave, the RMS value is 2.8V.

If it is a -2 to 2 square wave, the RMS value is 2V.
 

hardworkingstiff

Senior Member
Location
Wilmington, NC
Re: RMS value?

Originally posted by rattus:
Sam,

If it is a 0 to 4V square wave, the RMS value is 2.8V.

If it is a -2 to 2 square wave, the RMS value is 2V.
rattus, for us dummies (like me), will you explain why? It seems like 0-4V square wave would be 2V and 0-4V sine wave would be 2.8V.
 

apauling

Senior Member
Re: RMS value?

Bas: the easy way to understand the RMS value, is to imagine the top half of a sine wave. it is sort of a hilltop. its height before changing it to rms is almost 170 feet. It has an irregular area and that area is equal to the area of a flat top hill with perpendicuilar sides and a height of 120', or a sine wave with a height of almost 170 volts is equal to a square wave of 120 volts, and that number is arrived at by using the Root Mean Square method. Not very technical but it helped me understand how to see what that voltage meant.

paulse :)
 

rattus

Senior Member
Re: RMS value?

rattus, for us dummies (like me), will you explain why? It seems like 0-4V square wave would be 2V and 0-4V sine wave would be 2.8V.
Stiff,

It's all about power. The power is (4V^2)/R for half the time and zero half the time. For convenience, let R = 1, then,

Pavg = Vrms^2 = 16/2 = 8

Vrms = sqrt(8) = 2.8V

That is, the 0-4V square wave produces the same heating effect as a 2.8Vdc source.

It is a coincidence that a sine wave with peaks at +/- 4V yields an RMS value of 2.8V

PS: RMS (ROOT-MEAN-SQUARE) means the square ROOT of the MEAN value of the SQUARE of the voltage or current. RMS only applies to voltage and current.

[ January 27, 2006, 10:11 PM: Message edited by: rattus ]
 

rattus

Senior Member
Re: RMS value?

Stiff,

The "^" symbol denotes "squared" in certain programming languages. e.g., V^2 means voltage squared. Some languages use a double asterisk, e.g., V**2 = voltage squared. This is necessary because the programming codes cannot express subscripts and superscripts.

PS: Don't be too hard on yourself. There are those who talk the talk as I do. Then there are those who walk the walk as you do, and this is important.
 

RCinFLA

Member
Re: RMS value?

It refers to what the average power would be into a load.

Since power is V^2 x R, the square part is done first. Without getting into calculus, think of a changing waveform as individual little segments that can be approximated as a constant value over a small time segment. This is called piece meal integration and is the way computers do calculus.

Now you have each piece meal voltage segments squared which if divided by load would give the instanteous power of each segment. The average (mean) of these seqments is the overall average power.

To get back to an rms voltage that you can use as a power representing value of the overall waveform you take the square root of this average power to get it to an rms voltage number.

No one said anything about duty cycle on the 0-4 vdc waveform but I will assume it is 50% of the time at 4 vdc and 50% of time at 0 v.

Only need two equal time segments here because of 50% duty cycle.

Power in first segment of 4 vdc = (4)^2 divide by load. = 16/load = Power for this half segment

Power in second segment of 0 v = (0)^2 divide by load. = 0/load = Power for this half seqment.

Total average power assuming both seqments are equal in time (50% duty cycle) = 8/load

RMS voltage is square root of 8 = 2.83 vdc.

If you take normal V^2/load where V = rms voltage
then it checks correct as (2.83)^2/load = 8/load, as we got by averaging individual instanteous power segments.

If 4v/0v at 25% duty cycle then Vrms = 2.00 vrms

Now if you are using a full wave rectified sinewave to charge a battery thing get a bit more complicated to figure what the rms charging current to the battery is. First, no current flows until the rectified voltage exceeds the battery voltage. Only the peaks of the sinewave that exceeds the battery voltage will have current flow. Current is limited by diode drop, resistance of transformer, and resistance of battery.
(this cheapo type charger is not very good and generally people ruin batteries with them)
 

rattus

Senior Member
Re: RMS value?

In other words, the RMS value of a repetitive, rectangular pulse of amplitude Vp, width Tw, and period Tp is,

Vrms = sqrt[(Vp^2)(Tw/Tp)]

Now, for an ideal full wave rectified sine wave, the RMS value is 70.7% of the peak. That is, the RMS value of the voltage is unaffected by the load current.

However, the current may not be sinusoidal, and in this case the RMS value of the current would not be 70.7% of the peak.

[ January 29, 2006, 09:21 PM: Message edited by: rattus ]
 

charlie b

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Staff member
Location
Lockport, IL
Occupation
Retired Electrical Engineer
Re: RMS value?

Originally posted by rattus:RMS only applies to voltage and current.
RMS applies to anything. You can square any function you like, take an average value, then extract the square root. I can plot the Dow Industrial Average versus time over the course of a year, then find the RMS value of that curve. It just wouldn't be useful information.
 

rattus

Senior Member
Re: RMS value?

C. B.,

Yes, you can waste time computing meaningless RMS values, but since they are useless they do not apply to anything--RMS power for example.
 

rick hart

Senior Member
Location
Dallas Texas
Re: RMS value?

Yes, you can waste time computing meaningless RMS values, but since they are useless they do not apply to anything--RMS power for example.
RMS power would give you a way to compare RMS power between different devices- assuming identical source.
 

rattus

Senior Member
Re: RMS value?

Originally posted by rick hart:
RMS power would give you a way to compare RMS power between different devices- assuming identical source.
Rick, how do you define RMS power? My point is that term is undefined. Vrms x Irms x PF yields average power.
 

steve66

Senior Member
Location
Illinois
Occupation
Engineer
Re: RMS value?

Originally posted by rattus:
C. B.,

Yes, you can waste time computing meaningless RMS values, but since they are useless they do not apply to anything--RMS power for example.
Root-mean-square values for statistics are not any more useless or meaningless than terms like "average" or "mean" or "meridian". It is another term used to describe a set of points. See this link for example (and scroll down to Root-mean-square):

statistics definitions

RMS applies to many things besides just voltage and current and statistics. Here are some examples:

Root mean squared pertains to the maxwell distribution speeds at a certain temperature of a certain molecule
In the
lowermost stratosphere root-mean-squared scatter of
the observed differences increases dramatically (above
100 hPa with HALOE and POAM, and above 50 hPa
with SAGE II).
I don't have a clue what that last one means :eek: But pick any topic, and I bet you can find a use for RMS values.

Steve

[ January 31, 2006, 09:36 AM: Message edited by: steve66 ]
 

rattus

Senior Member
Re: RMS value?

Steve,

Granted, there may be applications outside the realm of AC power, but in our little world, RMS values apply to voltage and current--not to power or impedance.
 

hardworkingstiff

Senior Member
Location
Wilmington, NC
Re: RMS value?

Originally posted by charlie b:
I can plot the Dow Industrial Average versus time over the course of a year, then find the RMS value of that curve. It just wouldn't be useful information.
You never know Charlie, it could be the newest buy/sell trigger to trading stocks. :D
 
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