precision sine wave reference

[mdanh2002]

Just tried again with 3V peak-to-peak 50Hz triangular wave.

With no DC offset, in AC coupling mode, oscilloscope measures Vrms = 879mV and the APPA 207 true RMS multimeter reads 0.8882V. When a 3V DC offset is added, the reading is 885mV on oscilloscope and 0.8932V on the Appa 207. The reading on the APPA 207 remains in agreement with the oscilloscope as the frequency increases to around 250kHz, after that the reading will decrease and eventually reaches 0. The oscilloscope of course is still able to measure Vrms until the frequency reaches its bandwidth limit.

So I guess the true RMS capability on the Appa 207 is quite good.

Interestingly, for both my Rigol DS1052E and HP 54600B oscilloscope, V(avg) of both square wave, sine wave, and triangular wave is measured to be approximate 20-30mV. I think that's due to the ADC errors and otherwise should have been zero. Is that expected? Your previous post says that the average value of a 3.906v peak to peak square wave is 1.953v (50% of the peak to peak).

Also if the oscilloscope is in DC coupling mode, Vrms will read incorrectly on both oscilloscopes and show 4.625V for a 3V peak-to-peak triangular waveform with around 3V DC offset. So in this aspect, both oscilloscopes are worse than the Appa 207, which knows how to exclude the DC offset and shows proper RMS value. Or am I missing something?

 

[MrAl]

Hi,

This is interesting.

The meter seems to be interpreting the wave as an AC only wave no matter what we do to the DC component.
Using a 3vpp triangle (1.5v peak above zero and -1.5v peak below zero), the true RMS voltage is 0.866 vrms.
Using the same wave with a +3v offset means the wave starts out at 1.5v, climbs to 4.5v, then back down to 1.5v then repeats. The true rms value of the AC part only is still 0.866v, but the true rms of the entire wave is now 3.12v. This last result of 3.12v reflects the true rms because that more or less reflects the power producing ability of the wave which must include the DC content unless it is to be used with some sort of capacitive coupling.

So apparently the meter only measures the AC part of the wave to get the AC RMS value. You'd have to calculate the true rms of the entire wave yourself with the square root of the sum of squares method, after measuring the DC value. You can try measuring the DC value with the meter on the DC scale if you like.

Additionally, the average value of the wave is considered to be zero when it varies above ground as much as it varies below ground and in the same way, but for a sine wave (and possibly other waves too) we would take the absolute value of the wave first before calculating the average value. This means if there is a large DC content and it measures 0v (or near 0v) average, then that means it is not accounting for the DC component.
10mv or 20mv is probably just noise.

BTW, the true rms value of a triangle or sawtooth wave when there is no DC content is:
Vrms=Vpp/(2*sqrt(3))
Vpp being the peak to peak value.
If there is DC content then it is:
Vrms=sqrt(12*Vdc^2+Vpp^2)/(2*sqrt(3))

 

[NorthGuy]

Also if the oscilloscope is in DC coupling mode, Vrms will read incorrectly on both oscilloscopes and show 4.625V for a 3V peak-to-peak triangular waveform with around 3V DC offset. So in this aspect, both oscilloscopes is worse than the Appa 207, which knows how to exclude the DC offset and shows proper RMS value. Or am I missing something?

Both 4.63V and 0.89V readings are correct. 4.63V simply takes into account 4.5V DC offset, and 0.89V doesn't. The meter should have an AC mode, where it removes DC offset, and DC mode, where the DC offset is not removed.

It is customary to measure average voltage in DC mode instead of RMS. However, even for DC, RMS may be more valuable than average, because it can be used for power calculations, such as P = V^2/R. When used in such formulae, average voltage gives a biased result.

 

[MrAl]

Both 4.63V and 0.89V readings are correct. 4.63V simply takes into account 4.5V DC offset, and 0.89V doesn't. The meter should have an AC mode, where it removes DC offset, and DC mode, where the DC offset is not removed.

It is customary to measure average voltage in DC mode instead of RMS. However, even for DC, RMS may be more valuable than average, because it can be used for power calculations, such as P = V^2/R. When used in such formulae, average voltage gives a biased result.

Hi,

Where are you getting 4.63v for the rms voltage of the triangle plus DC offset of 3v?
That's higher than the peak
Did you apply the offset to the lower peak of the triangle then (which gives 4.58v)?
The RMS is 3.12v and the peak is 4.5v. The average will be 3v.

mdanh2002:
Did you apply the 3v offset to the BOTTOM of the triangle (6v peak), or to the zero center of the triangle (4.5v peak)?
The DC offset is almost always taken to be the "DC component", which means it gets applied to the zero center of the AC component, not some arbitrary point on the waveform

 

[NorthGuy]

Where are you getting 4.63v for the rms voltage of the triangle plus DC offset of 3v?
That's higher than the peak
Did you apply the offset to the lower peak of the triangle then (which gives 4.58v)?
The RMS is 3.12v and the peak is 4.5v. The average will be 3v.

The OP is using 3V triangular wave (0 to 3V) + 3V DC offset (resulting in 3V to 6V wave). It gives 4.5V DC. The OP's scope measures 4.63V.

 

[mdanh2002]

Hi,

Sorry, I guess I am confusing the terms here The 3V DC is applied to the bottom of the waveform and that gives a 4.5V peak. If "DC offset" is the term used for the voltage being applied to the zero center of the AC component, then I should say it's 4.5V DC offset, not 3V.

There is no DC offset or AC amplitude display on my function generator, so I need to count the squares on the oscilloscope display to get the DC component, resulting in the inaccuracies.

I just tested again. If fed in a 3V triangular wave with 3V DC applied to the bottom of the waveform, the Appa 207 reads 0.88V true-RMS in AC mode and 4.63V in DC mode, which is in agreement with the oscilloscope Vrms measurement. So I guess the oscilloscope rms measurement simply includes the DC component as part of the measurement and is also correct.

 

[MrAl]

Hi,

Yes that sounds better now.

Yes, it is erroneous to say that the DC offset starts from the bottom of the waveform as the DC offset is the same as the DC component which is relative to zero, which is the value of the Fourier DC component. Doing it any other way means we would have more to calculate and keep track of and it would get confusing fast.
For example, for the 3vpp triangle and 3vdc taken to be at the BOTTOM of the waveform, the average DC is then not equal to the DC offset. Specifying the DC offset as 4.5v, then it is.
For another kind of funny example, if we always applied the "DC offset" to the bottom of the wave then we would have to specify an ordinary 3vpp triangle that is vertically centered at zero volts as having "-1.5 volt DC offset". You can see how this messes things up.
And since the average voltage is the DC offset, we know right away what the DC offset is if we specify the average, and we can then also say we have "3vpp riding on 4.5v DC" which is a typical description of the wave we're talking about, but we could not say "3vpp riding on 3v DC" because that would not be true.

Here's a quote from the web:
"When describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean value of the waveform. If the mean amplitude is zero, there is no DC offset. In contrast, various other frequencies are analogous to superimposed AC voltages or currents, hence called AC components or AC coefficients."

 

[mdanh2002]

Hi,

Yes that sounds better now.

Yes, it is erroneous to say that the DC offset starts from the bottom of the waveform as the DC offset is the same as the DC component which is relative to zero, which is the value of the Fourier DC component. Doing it any other way means we would have more to calculate and keep track of and it would get confusing fast.
For example, for the 3vpp triangle and 3vdc taken to be at the BOTTOM of the waveform, the average DC is then not equal to the DC offset. Specifying the DC offset as 4.5v, then it is.
For another kind of funny example, if we always applied the "DC offset" to the bottom of the wave then we would have to specify an ordinary 3vpp triangle that is vertically centered at zero volts as having "-1.5 volt DC offset". You can see how this messes things up.
And since the average voltage is the DC offset, we know right away what the DC offset is if we specify the average, and we can then also say we have "3vpp riding on 4.5v DC" which is a typical description of the wave we're talking about, but we could not say "3vpp riding on 3v DC" because that would not be true.

Here's a quote from the web:
"When describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean value of the waveform. If the mean amplitude is zero, there is no DC offset. In contrast, various other frequencies are analogous to superimposed AC voltages or currents, hence called AC components or AC coefficients."

Thanks for the detailed explanation

 

[MrAl]

Hi again,

You're welcome. And it's interesting that we have the other phrase that is used sometimes, "3 vpp riding on 4.5vdc" or the other form, "x volts AC riding on y volts DC". This i think is a less well defined way to describe it but it is used from time to time. It makes sense with something like a rectifier circuit, where we might say 1vac "riding" on 20vdc which of course is describing the ripple voltage, even though the ripple is not a pure sine. Doing it this way means we know the average DC and the amount of ripple on that waveform.

 

[NorthGuy]

The 3V DC is applied to the bottom of the waveform and that gives a 4.5V peak. If "DC offset" is the term used for the voltage being applied to the zero center of the AC component, then I should say it's 4.5V DC offset, not 3V. .

You cannot apply an offset to the bottom or to the top, you apply the offset to the entire signal. Both peaks and the average get changed by the same amount.

You had a triangular wave from 0V to 3V. Average was 1.5V. You then applied 3V offset. All these numbers grew by 3V. Minimum became 0+3=4V, maximum became 3+3=6V. Average (or DC offset if you want to call it so) became 1.5+3=4.5V.

 

[MrAl]

Hi,

It is also interesting that when we measure the average value of a typical sine wave that varies plus and minus we usually take the average of the absolute value of the wave rather than the average value of the wave itself. The average value of a sine is zero (the DC offset is zero), but if we take the absolute value first we get what we usually call the 'average value' of the sine. So we do have two different ways of measuring a sine wave. We usually dont do this with any other type of wave but i guess it is possible.

 

[NorthGuy]

I think they get AC-coupled signal, then just dismiss everything negative and calculate average of the positive half.