Electronic – Why is the modulating shape appear in both sides of the carrier signal in AM
Modulation
It's about Amplitude Modulation. Can anyone tell me why is this signal wave or modulating waveform shape appears in both sides of the carrier sine wave? Why not in one side only?
$$x_c(t) = A_c[1 + \mu x_m(t)]\cos(\omega_ct)$$
I copied this image from Wikipedia
Best Answer
First let's clarify what you are asking about. I take your question to mean that you are looking at the carrier on a scope and notice that both the bottom and top of the amplitude envelope get modulated. You are asking why that is done, and why not just one "side", meaning either the top or the bottom. This has nothing to do with single-sideband modulation.
Think about what it would mean for only "one side" to be modulated. That's just the right amount of the modulating signal added to the modulated signal. The frequency of the modulating signal is much lower than the carrier, so is removed by anything that is narrow-band filtering around the carrier. Now consider that is exactly what radio receivers do.
Even if a transmitter did add the modulating signal to the carrier, it wouldn't propagate out since its frequency is way too low for the antenna, and receivers would ignore it anyway.
To use typical commercial broadcast AM as example, let's say the modulating signal is 3 kHz and the carrier 1 MHz. The antenna can't meaningfully radiate 3 kHz, and the circuit in AM radios tuned to this station go to great lengths to reject anything more than about ±10 kHz from the carrier (990 kHz to 1.01 MHz). Even if 3 kHz got radiated, it would be completely irrelevant to the AM radios picking up the 1 MHz station.
So to answer your question more directly, modulating "both sides" of the carrier is what pure AM modulation is. Possibly some transmitters do modulate the top of the envelope with the bottom fixed. However, the added modulation signal on the carrier this represents is quickly eliminated by various inherent filters between the internal signal generator and the receivers.
Your perfectly single-sideband suppressed-carrier modulated sinusoid certainly has a phase which can be measured. However, what you cannot tell is what the contributions of that measured phase from the audio input and the RF oscillator were.
There is another form of single-sideband modulation, in which not only one sideband but also the carrier component is transmitted. This provides a reference which can be used to synchronize the receive LO to the transmit one - normally done to insure exact tuning, but it would also give you the ability to recover the original audio phase.
It is also quite possible, especially with modern DSP gear, to transmit two separate audio channels, one on each side band. This is commonly called independent sideband modulation (ISB).
Many spread spectrum implementations are DSP based and capable of receiving multiple channels at once - GPS being a good example.
M is the amplitude of the modulating cosine (or sine to answer your
question)
A is the amplitude of the carrier sine (or cosine to reinforce the
answer!!)
φ is the phase displacement of the modulating sinewave but is
irrelevant all but mathematically
ωm and ωc are the frequencies of modulation and carrier.
Maybe I just don't recognize your formula but the answer is, like Jim Dearden implies swap them up or use the same because carrier and modulator are not going to be the same frequency when dealing with AM.
Best Answer
First let's clarify what you are asking about. I take your question to mean that you are looking at the carrier on a scope and notice that both the bottom and top of the amplitude envelope get modulated. You are asking why that is done, and why not just one "side", meaning either the top or the bottom. This has nothing to do with single-sideband modulation.
Think about what it would mean for only "one side" to be modulated. That's just the right amount of the modulating signal added to the modulated signal. The frequency of the modulating signal is much lower than the carrier, so is removed by anything that is narrow-band filtering around the carrier. Now consider that is exactly what radio receivers do.
Even if a transmitter did add the modulating signal to the carrier, it wouldn't propagate out since its frequency is way too low for the antenna, and receivers would ignore it anyway.
To use typical commercial broadcast AM as example, let's say the modulating signal is 3 kHz and the carrier 1 MHz. The antenna can't meaningfully radiate 3 kHz, and the circuit in AM radios tuned to this station go to great lengths to reject anything more than about ±10 kHz from the carrier (990 kHz to 1.01 MHz). Even if 3 kHz got radiated, it would be completely irrelevant to the AM radios picking up the 1 MHz station.
So to answer your question more directly, modulating "both sides" of the carrier is what pure AM modulation is. Possibly some transmitters do modulate the top of the envelope with the bottom fixed. However, the added modulation signal on the carrier this represents is quickly eliminated by various inherent filters between the internal signal generator and the receivers.