20 lines
1.1 KiB
Markdown
20 lines
1.1 KiB
Markdown
# Suppressed Carrier Wave
|
|
Derive expressions from which it will be evident whether the
|
|
communication channel has more power as an AM signal with
|
|
a suppressed carrier wave or as an AM signal with the carrier
|
|
wave present. Assume the voltage signal, $v(t)$ and $m(t)$, as in
|
|
the previous figure. Modulating (LF) sinusoidal signal has
|
|
amplitude $A$ and frequency $f_{LF}$ Hz, cosine wave RF carrier has
|
|
amplitude $1$ and frequency $f_{VF}$.
|
|
|
|
|
|
According to $P_t = P_c + P_{USB} + P_{LSB} $ the total transmitting power has to be split among carrier, upper and lower side band.
|
|
With the carrier wave suppressed, the modulating signal will take up all of the available transmission power instead.
|
|
|
|
For a standard AM signal with the above requirements, the formula is:
|
|
$$ s(t) = (1+A \cos(2\pi f_{LF}t)) \cdot \cos(2\pi f_{VF} t)$$
|
|
|
|
With the power of a wave signal given by $P=\frac{(v_m/\sqrt{2})^2}{2}$ (where $v_m$ is max of cosine signal),
|
|
our sideband power is $2* \frac{(A/\sqrt{2})^2}{2} = \frac{A^2}{2}$
|
|
and our carrier power $\frac{1}{2}$, equal to the power gained in DSB-SC.
|