Singnals, filters and power output

Question

I have couple of questions:

1. A square signal goes through a low pass filter and in the output of a circuit we get a sine. What happens there? Give a scheme?

   This is really weird, because, from what I have studied so far, only sine inputs are sine outputs from an LPF filter. I am reading it here. According to my source, it should be a triangular output, how comes it is sine?

2. Suppose that we have an AM DSB-SSB signal, with modulation index μ = 1. We degrade the carrier by 20dB and we also cut the one sideband. We send the result of this to an amplifier of +20dB gain. So at the output, we receive power that equals to 200W. How much was the original power of the carrier?

   SSB has only one sideband to begin with, so only carrier is left after the sideband is cut. We degrade carrier by -20 and then we amplify it by +20, so I believe that original power of carrier is also 200W. But it looks so extremely simple, anyone could shed some light here?

Answer 1

1. Any periodic signal can be given as a sum of sine waves of different frequencies. For example, a 1 kHz square wave consists of a 1 kHz base harmonic and other harmonics at 3, 5, 7, 9, etc. kHz (with decreasing amplitude), ideally infinitely many. If you chose the cut-off frequency of your LPF to let through the base harmonic but attenuate any other harmonics, you will get a signal that resembles a sine wave. As the other components are only attenuated, not eradicated, this won't be a true sine wave, but it might be difficult to tell the difference with your naked eyes.
2. A modulation index of 1 means that them amplitude of the carrier (A) equals the amplitude of the modulating signal (M). The sidebands have amplitudes of \$\frac{M}{2}\$, in this case it "simplifies" to \$\frac{A}{2}\$. Half the amplitude means one quarter of power, because power is proportional to the square of amplitude.

a) If your signal is AM-DSB, the original carrier power is \$P\$ and "cutting off" the one sideband means cancelling it out completely, then the calculations are as following: A 20dB amplification equals a power amplification of 100. Both the left and unattenuated sideband and the reduced carrier get amplified.

\$\frac{P}{4}\cdot 100+\frac{P}{100}\cdot 100=200W\$

\$26P=200W\$

\$P\approx7.692W\$

b) However, if it was an AM-SSB signal and you cancelled out the only one sideband, your calculations are correct.

Answer 2

"A square signal goes through a low pass filter and in the output of a circuit we get a sine. What happens there? Give a scheme?"

Who told you this? It`s not true. A lowpass filter will attenuate the harmonics of the fundamental frequency which are beyond the path region of the lowpass. The amount of damping depends on the filter order. As a result, we get a form which is something between sinus, triangle, and "unknown". In theory, we would get a sinus for an ideal "brickwall" filter only which really removes all the harmonics which, however, is impossible to realize.