modulation fundamentals

In AM what should be the typical ratio of message signal to carrier. Let us say carrier is 1KHz, now can the message signal be 500 Hz?

When you modulate signal of (B) bandwidth on carrier (Fc) the modulated signal will be of (2B) bandwidth centred on (Fc).
so your Fc and sampling rate must accommodate the double band as minimum. so yes 500Hz signal will fit around carrier at 1KHz tightly. normally you need extra for guard band and filtering requirements.

Minimal requirement for standard double-sideband amplitude modulation: Modulation signal bandwidth < carrier frequency

Everything else is set by the application.

Only for sake of academics, can the message signal be the same as the carrier? I mean taking a theoretical case that no other signal is in place. My question is oriented towards the effort for demodulation when the message signal gets closer to the carrier frequency

Hi,

From the theory I'd say yes.
But I think there often are practical problems when the lower sideband becomes very low frequency ... even DC.

When I see a 1MHz carrier and 1kHz modulation, then the lower sideband is 1MHz - 1kHz = 999kHz
And the upper is 1MHz + 1kHz = 1001kHz.

This looks symmetric. But for filters you need to think "logarithmic" means not "+" or "-", but as factor.
The factors are 0.999 and 1.001. There is a slight deviation, because 1/0.999 is not exactly 1.001.
But here it is no problem ....

Lowering the carrier to 10kHz:
--> 9kHz and 11kHz. --> 0.9 and 1.1, --> 1/0.9 = 1.111

3kHz:
--> 2kHz and 4kHz. --> 0.6667 and 1.25, --> 1/0.6667 = 1.3333 (not 1.25)

2kHz:
--> 1kHz and 3kHz. --> 0.5 and 1.5, --> 1/0.5 = 2.0 (not 1.5)

Going to the extreme 1kHz:
--> 0kHz and 2kHz. --> 0.0 and 2.0, --> 1/0.0 = infinite (far away from 2.0)

The usually use bandpass becomes a low pass. Any magnetics will saturate because of DC.

Klaus

The modulation signal frequency can be equal to the carrier, but then it can't be demodulated by a simple envelope detector.

What are you trying to achieve?

gary36 said:

Only for sake of academics, can the message signal be the same as the carrier? I mean taking a theoretical case that no other signal is in place. My question is oriented towards the effort for demodulation when the message signal gets closer to the carrier frequency

Click to expand...

Let us use practical figures. If your signal bandwidth is 10MHz and your carrier is 10MHz then that is possible but you will have your signal extending from dc to 20 MHz so you are back at baseband and I don't see what could be the purpose of such upconversion . Remember final bandwidth is across 20MH but carrier at 10MHz is a spot frequency at 10MHz.