Vmax(cos2pi F t + sin2pi F t)....

Hi guys,

Sorry but Can you guys help me out for the waveform of the following:

Vmax(cos2pi F t + sin2pi F t)
and:
Vmax(cos2pi F t - sin2pi F t)

Suppose that "Vmax" is 2V or something so, and "F" is 100KHz or so...

Thanks a bunch

P.s. What is the difference and what will happen If I use one of them as a replacement for a signal like "Vmax (cos2pi F t)" or a signal like "Vmax(sin2pi F t)"?

I myself think that the cos wave and the sine wave would be added (subtracted) in magnitude to each other while they are summed (subtracted). Am I right? If so how much of difference I would;d expect in comparison to a signal like "Vmax (cos2pi F t)" or a signal like "Vmax(sin2pi F t)"?

To be honnest, I am built a SSB modulator using PHASING method. The below picture shows the output result (LSB formula and USB formula). As I wanted to have the carrier at the output too then I decided to add a DC offset to the input so that I could simply have a carrier in the output. But you can simply conclude that adding a DC offset will yeald to have a carrier with the formulas of:
Vmax(cos2pi F t + sin2pi F t)
and:
Vmax(cos2pi F t - sin2pi F t)

which the first formula is for whiles that we have LSB and the second one is for whiles which we have USB...
For instance suppose that I want to have USB with the carrier, By adding a Dc ofset to the input the USB output signal would be as follows:

Em cos (Wm +Wc)t + Vmax(cos2pi F t - sin2pi F t)

I myself guess that the formula should be:
Em cos (Wm +Wc)t + Vmax(cos2pi F t)
or like this:
Em cos (Wm +Wc)t - Vmax( sin2pi F t).

Now I want to see if the said formula having both sin and cosine sammed as carrier is wrong? Or it can simply do what a carrier by having just a sine or just a cosine does???!!!

Thanks a bunch

dr.power,

Vmax(cos2pi F t + sin2pi F t)
and:
Vmax(cos2pi F t - sin2pi F t)

Click to expand...

Tsk, tsk. You should really review your trigonometric identities. I will do the first one, and you can easily do the second one. Using the sum of angles identity sin(A+B) = sin(A)cos(B)+cos(A)*sin(B), we can easily derive sin(ωt)+cos(ωt) = √2*sin(ωt+pi/4) = √2*cos(ωt-pi/4), take your choice.

What is the difference and what will happen If I use one of them as a replacement for a signal like "Vmax (cos2pi F t)" or a signal like "Vmax(sin2pi F t)"?

Click to expand...

They will show a pi/4 radian phase shift. and an amplitude increase of √2

Ratch

Thanks Ratch,

So for the LSB we'll get the below as the carrier:

Vc (cos2pi F t + sin2pi F t) = √2*Vc cos(ωt-pi/4)

Now can you guys please let me know if It is possible to use the above formula for the carrier? You know that the carrier normally has the forms of:
"Vc (cos2pi F t)"
or
"Vc (sin2pi F t)

So?...

No Idea please?