Adding two signals with different or the same frequency

im rather confused about adding two signals which have same freq or different.

No 1.
i have 2 signals V1 = A sin ωt volt and V2 = A sin 2ωt volt
the power of V1 = A²/2 and power V2= A²/2 , note that R normalized to 1
are those right ?

if i add V1 to V2, these two signals become V3=V1+V2 = A (sin ωt + sin 2ωt) volt
can i say that the power of V3 is sum of each signal power ?
Power V3 = power V1 + power V2 = A² ?????


No 2
i have two signals V1 = V2 = A sin ωt volt
the power of each signal PV1 = PV2 = A²/2.
V3 = V1 + V2 = 2A sin ωt volt , is it right??
Power of V3 = (2A)² / 2 = 4A²/2 = 2A²

I think it's absurd because i add two signals which each signal has power A²/2 and how come the result signal has power 2A²?? in my mind, it doest satisfy the law of energy conservation, because from where the difference power A² comes.
A²/2 + A²/2 should be A² not 2A².

it seems trivia problem but it's really confusing for me.
can anyone explain about that or tell me from where i went wrong in understanding it?

Thanks 4 ur helps

regard

masadi

how to add two signals

I think you r right .
Lets see what others say

adding two signal sources

No1:
No you can not add 2 signal power.
for example, supose [V=Asin ωt] and [V2=-Asin ωt] or [V2=Asin(ωt+Π)] and when we add
two signal Vsum=V1+V2=Asinωt+(-Asinωt)=0

No2:
yes your formula is correct.

but i think it is not absurd because power is proporatinal to power2 of voltage or current !

Regards
Davood Amerion

assign phase to signal power

the power is equal to :
t-final=T
1/T * ∫((sinwt+sin2wt)^2 dt)=A^2/2+A^2/2=A^2
t-initial=0

w=2π/T

adding two signal

i am sorry, i am not sure that i understand your perdicament.

the signals are sinusoidal, which of course means that the coefficent is a multiple of 1 or less, correct, well that number will be dependent on the argument, which
is dependent on the freq correct, so

basically if you add two sinusoids you can have 2*A at a location or the negative or any combo in between based on where the maxima of one and the minima of the other fall

i may have not understood your question correctly

Added after 2 minutes:

sorry, i see, yes that is voltage, what you where looking at, but power
uses the formula posted by the other gentelman, sorry

add two signals

Adding two sinusoids of same frequency follow linearity property. But power does not follow linearity property because power is proportional to the square of sinusiods amplitude.( P∞ A²)
If signal3 = signal1 + signal2, both signal1&2 being sinusoids of same freq,then
Amp(signal3) = Amp(signal1) + Amp(signal2). But

Power(signal3) ≠ Power(signal1) + Power(signal2)

So the resultof adding two signals each signal having power A²/2 and the resulting signal having power 2A² shouldn't be surprising.

Regards
Magnetra

addition of two sinusoidal signals

adding of two signals doent mean that we are adding their powers.

thnx

purna

adding signal powers

no 2
adding two signals means nothing but putting them in series.
consider this example
suppose u have two different sources of voltages v and v
u connected both of them individually
them current given out by each of them is i(say)
v.i+v.i=2.v.i
then if you connected them in series then each will be forced to give a current of
2i. Thats why the power dissipated by each source is doubled
v.2i+v.2i= 4.v.i
thank u