# root-mean square value for sinusoidal signal that superimposed onto the dc signal

#### coolgirl

Joined Dec 17, 2009
1
hello....i have a problem in solving the questions related with the signal..Let, say a sinusoidal signal of magnitude A and period T is superimposed onto a dc signal of magnitude B to produce a resultant sine wave which have peak value as (B+A).The resultant wave start at B instead zero value..So,how to find root-mean-square value for the resultant wave???Please help me to solve this problem...

#### KL7AJ

Joined Nov 4, 2008
2,229
hello....i have a problem in solving the questions related with the signal..Let, say a sinusoidal signal of magnitude A and period T is superimposed onto a dc signal of magnitude B to produce a resultant sine wave which have peak value as (B+A).The resultant wave start at B instead zero value..So,how to find root-mean-square value for the resultant wave???Please help me to solve this problem...
You just add the DC value to each point, and then work the RMS from there. You have to add it BEFORE the averaging, though....you just can't tack it on at the end.

From a practical standpoint, you can get rid of superimposed DC by using capacitor coupling (or transformer coupling) in many cases. Then it's just the RMS value.

#### kdillinger

Joined Jul 26, 2009
141
It is the square root of the sum of the squares. Square the DC term and add it to the square of the RMS term then take the square root of that total.

#### Ron H

Joined Apr 14, 2005
7,014

$$\sqrt{\frac{2*B^2+A^2}{2}}$$.

I got this by squaring

$$B+Asin(w*T)$$

Discard the resulting purely AC terms (which average to zero), then take the square root of the remaining DC terms.
I verified this with several example simulations in LTspice.

#### t_n_k

Joined Mar 6, 2009
5,455
Which is the same as kdillinger's rendering .....

$$\sqrt{B^{2}+A_{rms}^{2}}$$

#### Ron H

Joined Apr 14, 2005
7,014
Which is the same as kdillinger's rendering .....

$$\sqrt{B^{2}+A_{rms}^{2}}$$
It was a homework problem. I was explaining how to get there mathematically.