# Why is the modulating shape appear in both sides of the carrier signal in AM?

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

• Are you talking about side-bands or the top and bottom waveform halves of the carrier due to sinewave modulation? Commented Jan 4, 2016 at 15:27
• Top and bottom waveform halves! Commented Jan 4, 2016 at 15:37
• Are you sure you understand Olin's answer? Commented Jan 4, 2016 at 15:47
• Yea kind of. And also I found out that it is the property of a cosine wave form and AC coupling is the reason for this to happen :) Commented Jan 4, 2016 at 15:50
• Olin is talking about sidebands (as far as I can tell) and not talking about the top and bottom of the waveform. Commented Jan 4, 2016 at 15:52

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.

• So single sided modulation is also possible? I didn't mean the SSB Modulating. Commented Jan 4, 2016 at 15:07
• Single sided modulation would just be the sum of pure AM and the modulating signal. After a high pass filter - i.e. before it reached the antenna - it would revert to pure AM again.
– user16324
Commented Jan 4, 2016 at 16:32