# Correct Peak-Peak but Wrong RMS?

#### Elhassan

Joined Jul 17, 2022
7
Hello, I am working on a High-Frequency Pure Sine Wave Inverter Project, Everything is going well Until I've got the output.
as shown here

peak to peak voltage is fine [316 VDC], but the RMS Voltage is too low, about 101 Volt RMS?
I've checked with Volt-Meter, and the same Result was given to me.
I want to get 220VAC RMS @50Hz
so what do you think is wrong?

#### Papabravo

Joined Feb 24, 2006
21,225
316 V P-P is ±158 V
158/√2 is 111.7 V RMS
That is not as far off as it seems given the scale of the measurements and the 8 V average as opposed to an average of 0 V.

#### Elhassan

Joined Jul 17, 2022
7
316 V P-P is ±158 V
158/√2 is 111.7 V RMS
That is not as far off as it seems given the scale of the measurements and the 8 V average as opposed to an average of 0 V.
Oh, I'll try to fix the Voltage
Thanks very much

#### crutschow

Joined Mar 14, 2008
34,406
There appears to be some high-frequency ripple on the waveform, so that is perhaps giving a slightly higher peak-to-peak than if that ripple were filtered out.
Can you use two oscilloscope cursors to measure the pk-pk from the middle of the trace thickness and see what that gives?

Also if you can use a 50V vertical scale sensitivity instead of 100V, that should improve the measurement accuracy slightly.

#### MrAl

Joined Jun 17, 2014
11,453
Hello, I am working on a High-Frequency Pure Sine Wave Inverter Project, Everything is going well Until I've got the output.
as shown here
View attachment 271812
peak to peak voltage is fine [316 VDC], but the RMS Voltage is too low, about 101 Volt RMS?
I've checked with Volt-Meter, and the same Result was given to me.
I want to get 220VAC RMS @50Hz
so what do you think is wrong?

Hello,

Is 316 really the peak to peak, why does it state 'peak' on the scope?

Anyway, if that really is the peak to peak then with 8v offset the peak of a zeroed sine may only be 150 volts.

[Updated formula here]
The RMS of a sine wave with a DC offset is:
Vrms=sqrt(A^2/2+vos^2)

where
A is the amplitude peak (not peak to peak) of the zeroed sine, and
vos is the DC offset in volts, and
pi is the constant 3.14159... (the ratio of the circumference of a circle to it's diameter).

Now given 316 is the vpp then the peak is 158 volts so if we set A=158 and vos=8 we get:
Vrms=112 volts
which is still not very close to the scope reading.
If possible, also use an RC low pass filter to filter the waveform or see if the scope has one built in.
Also check the DC offset of the scope itself sometimes you have to adjust that. You can check a line voltage sine wave if your scope allows measuring the line with because you have to be careful about that you cant do that with many USB scopes for example.

Last edited:

#### crutschow

Joined Mar 14, 2008
34,406
Is 316 really the peak to peak, why does it state 'peak' on the scope?
Good question.
But the vertical scale is 100V/div so it must be pk-pk.

#### MrAl

Joined Jun 17, 2014
11,453
Good question.
But the vertical scale is 100V/div so it must be pk-pk.
Hi,

Yes and that to me indicates something isnt quite right maybe in the measurements. I kept looking at the scope pic and the readings and just had to wonder what is going on there. It could be the scope too i've seen some shady scope software in the past.
I guess we wont know until the TS comes back with some answers.

#### MrChips

Joined Oct 2, 2009
30,794
I had a similar problem on 15 brand new Siglent oscilloscopes. They all had to be reprogrammed with the latest firmware in order to correct the problem.

#### MrAl

Joined Jun 17, 2014
11,453
Hello, I am working on a High-Frequency Pure Sine Wave Inverter Project, Everything is going well Until I've got the output.
as shown here
View attachment 271812
peak to peak voltage is fine [316 VDC], but the RMS Voltage is too low, about 101 Volt RMS?
I've checked with Volt-Meter, and the same Result was given to me.
I want to get 220VAC RMS @50Hz
so what do you think is wrong?

Hello again,

I made an error when i posted the formula for the RMS of a sine wave with a DC offset voltage. The formula i gave was for a very specific case which does not match up well with this application. So here is the more general formula, and it is very simple so that's nice.

Vrms=sqrt(A^2/2+vos^2)
where
A is the peak amplitude in volts (taken to be 158vac for the example below),
vos is the DC offset voltage in volts (taken to be 8vdc for the example below).

Using that formula, we get a value very very close to 112 volts RMS. That's not that close to 101.74 so the scope calibration is still an issue and also the peak vs peak to peak issue we talked about before that needs to be corrected. The 101.74 volts may get better with a filter though.