# Rectangular pulse waves AC-component

#### Marik

Joined Dec 15, 2005
4
Hello everyone.

I have a positive rectangular pulse wave with amplitude levels A (while up) and 0 (while) down. The duty cycle is given as x/T, where x is the uptime and T is the cycle time.

Could someone help me with calculating the absolute mean value of the signals AC-component?

Cheers,
Marik

#### n9352527

Joined Oct 14, 2005
1,198

#### Marik

Joined Dec 15, 2005
4
Originally posted by n9352527@Dec 15 2005, 09:31 AM
[post=12476]Quoted post[/post]​
I assume that youre referring to this information in Italic.

Square wave (positive only, duty cycle D) Vrms=Vp*√D

Yes i checked that post and they concern the RMS values. Or are the rectified mean values same as the RMS values? Im at a bit of a loss here.

This is what ive come up so far. I got the VrmsTOT formula from a datasheet and reverse engineered the VrmsDC and the VrmsAC formulas, hence the VrmsAC formula isn't that pretty. But the formulas seem to work when i tested them on some True RMS measurement data.

The RMS value of the DC component: VrmsDC = A*(d/T)
The RMS value of the AC component: VrmsAC = A* √ [(d/T)(1-d/T)]
Total RMS : VrmsTOT = A* √ (d/T)

Is there a way to derive the rectified mean value for the AC component from the VrmsAC formula?

Cheers,
Marik

#### n9352527

Joined Oct 14, 2005
1,198
I'm sorry I thought you were asking about RMS value. Can you explain more about what you are trying to calculate or do? I don't really get what you mean by rectified mean value or absolute mean value.

#### Marik

Joined Dec 15, 2005
4
Originally posted by n9352527@Dec 15 2005, 11:00 AM
I'm sorry I thought you were asking about RMS value. Can you explain more about what you are trying to calculate or do? I don't really get what you mean by rectified mean value or absolute mean value.
[post=12478]Quoted post[/post]​
By rectified mean i mean the mean value of the absolute value of the signal. Value=mean(abs(original_signal)

In the image below you can see the original signal in the first picture, the absolute value of the signal in the lower picture and its mean value represented by the straight line with a value 5*2/pi. So the straight line is the Absolute Mean Value.

I am basically trying to find a formula for the AC component of the positive rectangular wave. Because if i just calculate the absolute mean value for the original signal, any DC components would distort the results.

So if anyone has ideas on

1) How to represent a positive rectangular wave by using its DC and AC components
2) How to calculate the form factor of a positive rectangular wave

Or any better suggestions on how to approach the problem. '

Cheers,
Marik

#### n9352527

Joined Oct 14, 2005
1,198
If you have a rectangular AC pulse, you will end up with rectified mean value of exactly half Vpp irrespective of the duty cycle, assuming that the pulse is symmetrical. I think. At least that was what my poor convoluted brain came up with.

Taking out the offset from a rectangular DC pulse is not a matter of shifting the ground to halfway between Vpp. Duty cycle affects this.

If you approach it from delivered power angle, then what you have done Vrms(tot)=Vrms(ac) + Vrms(dc) is good. But checking your formulas for 0.5 duty cycle did not produce the expected result.

The relationship of the arithmetic mean and RMS is:

RMS^2=Mean^2+(standard deviation)^2

As you can see the reverse RMS function is not unique, but you can always solve for a few simple instances.

#### Marik

Joined Dec 15, 2005
4
Originally posted by n9352527@Dec 16 2005, 06:08 AM
If you have a rectangular AC pulse, you will end up with rectified mean value of exactly half Vpp irrespective of the duty cycle, assuming that the pulse is symmetrical. I think. At least that was what my poor convoluted brain came up with.

Taking out the offset from a rectangular DC pulse is not a matter of shifting the ground to halfway between Vpp. Duty cycle affects this.

If you approach it from delivered power angle, then what you have done Vrms(tot)=Vrms(ac) + Vrms(dc) is good. But checking your formulas for 0.5 duty cycle did not produce the expected result.

The relationship of the arithmetic mean and RMS is:

RMS^2=Mean^2+(standard deviation)^2

As you can see the reverse RMS function is not unique, but you can always solve for a few simple instances.
[post=12495]Quoted post[/post]​
After some pondering and consultation heres the results. The rectified mean value of the AC component is calculated like the rms value except instead of sqrt:ing the signal, the absolute value is used. Naturally. Then we just apply this to the rms ac value you will get Rectified_mean_value_AC = 2*A*(D-D^2).

In aftersight the solution was really simple but stupid people (referring to me ) can't always see the forest from the trees Cheers for the replies n9352527 ,
Marik