Confused about how to calculate effective power/voltage/current of a pulse wave

[Mariwan]

Please could any one tell me which one is correct?

I have a pulse as this figure represent power consumption (current required) of an object


the waveform is only positive - no negative part
Now to calculate the effective or the equivalent DC, there are different way to calculate . One is the average and the other is rms.

Using normal multimeter, it calculate the average, while using true rms multimeter it calculate the rms value of the voltage.

Using theoretical method the voltage(rms) = vp * (t1/T)^0.5
the average = vp * t1/T

I used oscilloscope and two different multimeter, each gives a different values .. :shock:

WIKI pedia says that the correct measuremnet is the rms., my teacher says average ..

Note: This kind of waveform could be found in any wireless sender which has a sleep mode. To calculate the power consumes by the device I used a ~7 ohm R in and oscilliscope over the Resistor to capture the wave form.

Which kind of measurement is the correct one, average or rms? why?

Many thanks in advance. :roll:

 

[mtwieg]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

The answer depends on what the load is. If it's just a resistor, then RMS voltage or RMS current is fine. In any other case, you need to simultaneously measure current and voltage, both vs time, and calculate power vs time. Then average power over one period to get average period.

The thing to keep in mind is that the formula:
Prms=Irms*Vrms
Only apply when the load in question is a resistor. If there is any nonlinearity, or reactance in the load, then you can't use it. Also, Prms and Pavg are only equal when the source is a sinusoid (and the load is linear).

 

[Ratch]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Mariwan,

Assuming a resistive load, if the pulse amplitude is constant when it is on, then the RMS voltage is V*√a, where 'a' is is the fractional part of the period when the pulse is on. So if the pulse is on ¼ of a period, then the RMS value of the voltage is V/2. The average voltage would be V/4. Same goes for the current. Always use the RMS value when you want to equate the voltage or current to power. Only at DC is the RMS and AVE the same.

mtweig,

Also, Prms

There is no such thing as Prms, only Vrms or Irms. Pave = Vrms*Irms*cos(θ)

Ratch

 

[albbg]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

If you have a pulse with timing 0 < t < T1 ON and T1 < t < T2 OFF having a voltage constant amplitude A applied to a resistor R, the power consumption during "ON" state will be Pon=A²/R and duriing "OFF" will be Poff=0 the the average power will be:

Pave = [A²/R*T1 + 0*(T2-T1)]/T2 = A²/R*T1/T2

This is the power consumption seen by the generator.

Let's try now with RMS:

V(RMS) = A*√(T1/T2) we haven't "Von" and "Voff", but just "V" because RMS already take into account T1 and T2, then

Pave = [A*√(T1/T2)]²/R = A²/R*T1/T2 the same as before

Then is the same to calculate the power instant by instant and then take the average or calculate the RMS of the voltage and then apply V²/R. However the RMS is applied to the voltage not to the power.

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Still I don't get the point. Yesterday I tried to calculate and measure such a frequency (puls) using multiple multimeter with True RMS and without. Using Oscilliscope avg and rms. Each device gives a reading.
Actually I am trying to measure and calculate power consumed by XBee module while it is with sleep mode- AT mode. I use a 7 ohm resistor in series to the Vcc of the XBee and I capture the waveform using oscilloscope on the 7 ohm resistor. I used the rms to calculate the power consumed but my teacher says it should be average and I shouldn't think about rms since it is only for AC voltage/current.
As we know, none of the pulse waves are only positive part, if we think in Fourier series/transformation, there are always a sin wave with + and - parts. so it should be rms.

this is why I am so confused.

 

[mtwieg]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

mtweig,

There is no such thing as Prms, only Vrms or Irms. Pave = Vrms*Irms*cos(θ)

Of course there is such a thing as Prms. RMS is just a mathematical function which can be applied to anything. Though often people are more interested in Pavg than Prms, and therefore don't refer to Prms.

---------- Post added at 13:40 ---------- Previous post was at 13:35 ----------

Still I don't get the point. Yesterday I tried to calculate and measure such a frequency (puls) using multiple multimeter with True RMS and without. Using Oscilliscope avg and rms. Each device gives a reading.
Actually I am trying to measure and calculate power consumed by XBee module while it is with sleep mode- AT mode. I use a 7 ohm resistor in series to the Vcc of the XBee and I capture the waveform using oscilloscope on the 7 ohm resistor. I used the rms to calculate the power consumed but my teacher says it should be average and I shouldn't think about rms since it is only for AC voltage/current.
As we know, none of the pulse waves are only positive part, if we think in Fourier series/transformation, there are always a sin wave with + and - parts. so it should be rms.

this is why I am so confused.

Well again the answer has to do with the load. You say that you're measuring the power drawn by an Xbee, so I assume that the Vcc supplied to it is constant over time? In that case, things are pretty simple. When either I(t) or V(t) is constant, Pavg will be equal to:
Pavg=Vavg*I for constant I
Pavg=V*Iavg for constant V.

 

[crutschow]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Your teacher is wrong. It may not be a sinewave, but it is still a time varying waveform. You need to use RMS to calculate the power of the waveform.

In the case of a pulse you can calculate the RMS value by calculating the power of each pulse and averaging that over the period of the pulse. if you used the average voltage value of the pulse over the period for the calculations, you will get an incorrect answer.

The Average (true) power (Pave) is the power calculated by using RMS current and voltage values to determine the power. Average power has no other correct definition. Prms is not a normal designation of true power.

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

You may undrstod me wrogn. My teacher said "when the waveform is a pulse and it is on the positive side (since it is the current required by the XBee module ) you should think only on average, rms uses only with AC voltage , current ..etc"

I am saying, even if the waveform is only on the positive part, still we need to use rms .. Average will give wrong results (in fact I don't know where to use average).

What I want to calculate is to say : XBee will consume x.xxx W in the AT Mode with sleep mode activated. This is what I am trying to measure and calculate.
As you can see, I don't know to which of the reading their in the figures above I trust and is correct ???

 

[Ratch]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Mariwan,

Still I don't get the point. Yesterday I tried to calculate and measure such a frequency (puls) using multiple multimeter with True RMS and without. Using Oscilliscope avg and rms. Each device gives a reading.

I can see the o'scope and it appears to be correct for RMS. It says the amplitude is 2.88 volts. I estimate the fractional part of the period the pulse is on as about 1/12. So using the formula I gave you previously, we get Vrms = 2.88*√(1/12) = 831 mv. The scope says Vrms = 823.65 mv. The Vave should be 2.88/12 = 0.24 volts, so I don't know why the scope says 80 mv.

I cannot see the rest of the instruments well enough to determine what is going on.

Ratch

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

You can click the figures to get full screen. It is very clear.
One of the multimeter says to calculate always True rms while it obviously it doesn't (the white one)
The red one I tried both, with true rms and without , that is why you have two figures.

---------- Post added at 20:33 ---------- Previous post was at 20:26 ----------

Generally, all multimeter measure only average values if it doesn't say it measure true rms .. (the white one is exception as it is lying .. )

 

[Ratch]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

View attachment RMS-1.pdfmtweig,

Of course there is such a thing as Prms. RMS is just a mathematical function which can be applied to anything. Though often people are more interested in Pavg than Prms, and therefore don't refer to Prms.

What does Prms mean? Can you explain it? Look at the second to the last sentence of the attachment. Then look at this link https://www.hifi-writer.com/he/misc/rmspower.htm

Ratch

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Ratch:
You say that there is no Prms.. Ok explain to me this equation.
VCC=3.3 this is a DC voltage goes to the XBee module
but the current is as the waveform shown in one of the figures, two way to calcualte the power.
1- using average equation --> you get I average
2- using rms equation --> you get I rms

now when you multiply I avg with 3.3 v ---> what is the result? what you call it (I call it Pavg)
Then if you multiply Irms with 3.3 V ---- > what is the result ? what you call this (I call it Prms)

it is confusing .. believe me

 

[Ratch]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Mariwan,

Why don't you produce a low frequency pulse with a half duty cycle with an amplitude of one, and see what your instruments say it is. It would be easy to figure out what each of those measurements should be, too.

Ratch

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

I cannot do it now but I will try it later (may be tomorrow).

 

[Ratch]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Mariwan,

now when you multiply I avg with 3.3 v ---> what is the result? what you call it (I call it Pavg)

I call it nothing meaningful.

Then if you multiply Irms with 3.3 V ---- > what is the result ? what you call this (I call it Prms)

Again, I call it nothing meaningful.

it is confusing .. believe me .

Only if you lose your focus on what the definition of average power is.

Vrms is a weighted average that takes into consideration that a voltage increase from 10 volts to 11 volts causes a larger power increase than a voltage increase from 1 to 2 volts.

Irms is the same thing, only with current.

Pave = Vrms * Irms. Pave ≠ (a intermittent constant voltage)*Irms. Prms = nonsense. See the link and attachment I sent to mtweig previously.

Ratch

 

[FvM]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

If I understand the problem correctly (constant battery voltage, time variable current), the below equation given by mtwieg is all you need:

Pavg=V*Iavg for constant V

For constant pulse current, Iavg can be also written as Ipeak*t1/T. In other words, to RMS calculation isn't required for constant supply voltage.

Of course there is such a thing as Prms. RMS is just a mathematical function which can be applied to anything.

Yes. But although you can apply RMS calculation (square root of averaged square value) to power quantities, it makes no technical sense.

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

Ok, lets talk about the instruments used to measure the voltage here .. which one is correct?

 

[FvM]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

It's not clear how the instruments are connected. Even the oscilloscope meaurement is unclear. You say, you measure the voltage across a series resistor. The shown voltage is 2.88 V peak, the supply voltage is said to be 3.3 V. So there would be only 0.42 V remaining for the RF module, rather unlikely.

Is the 2.88 V actually the voltage across the resistor? Or is it the module voltage and 0.42 V is the resistor voltage? In any case, a shunt resistor should be selected for a voltage drop that doesn't reduce the remaining supply voltage too much. But even 0.42 V voltage drop would be unwanted high.

 

[Ratch]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

FvM,

If I understand the problem correctly (constant battery voltage, time variable current), the below equation given by mtwieg is all you need:

How can the current change if the voltage is constant, unless the resistor changes value? That is not what the problem is about. You can never calculate average power from the average of either voltage or current. The only time AVE and RMS are equal is for constant value V or I with no pulsing. But the OP was referring to pulsing. I think maybe the OP's teacher told him that the average power for a positive pulse would be proportional the the average current, which is different than calculating the actual average power from the average current. If you can manufacture an example using a constant current/voltage pulse, and use its average value to find the average power, I would be interested.

Ratch

 

[Mariwan]

Re: Confiused abou how to calculate effective power/voltage/current of a pulse wave

It's not clear how the instruments are connected. Even the oscilloscope measurement is unclear. You say, you measure the voltage across a series resistor. The shown voltage is 2.88 V peak, the supply voltage is said to be 3.3 V. So there would be only 0.42 V remaining for the RF module, rather unlikely.

Is the 2.88 V actually the voltage across the resistor? Or is it the module voltage and 0.42 V is the resistor voltage? In any case, a shunt resistor should be selected for a voltage drop that doesn't reduce the remaining supply voltage too much. But even 0.42 V voltage drop would be unwanted high.

The figures are a simulation of the problem. I just give a pulse with the waveform shown to different multimeter and oscilloscope and I want to calculate the voltage. ON the xbee I have the same (almost) shape of waveform and the capture voltage was on the 7 ohm resistor


oscilloscope
|7 ohm|
+3.3 volt ----/\/\/\---XBEE MODULE
|
- ----------------------------|

I believe the only way to calculate the effective power consumption having such a waveform is to Fourier transform the waveform and choose n to some number of accuracy and find out the rms for the different part of the Fourier series and sum it .. this is the only way to get a correct effective power consumption.
Xbee is not a resistive load, it is a digital, and it varies as the sending takes much more power from the power supply (VCC) this is why when it wake up it takes much power than normal state. I upload the figure which I took for the XBee on the 7.3 ohm resistor so you can see the real problem I have, the uploaded figures in the beginning was to simulate the real problem I have.

XBee current captured over a 7.3 ohm resistor

The real waveform is a constant current and a pulse, the constant current is easy to find, it remains the pulse part which this discussion is about