An AM radio transmitter operating on 3.9 MHz. what are the maximum upper and lower side frequencies? what is the total bandwidth of the AM signal?
Answers
Answer:
A spectrum represents the relative amounts of different frequency components in any signal. Its like the display on the graphic-equalizer in your stereo which has leds showing the relative amounts of bass, midrange and treble. These correspond directly to increasing frequencies (treble being the high frequency components). It is a well-know fact of mathematics, that any function (signal) can be decomposed into purely sinusoidal components (with a few pathological exceptions) . In technical terms, the sines and cosines form a complete set of functions, also known as a basis in the infinite-dimensional vector space of real-valued functions (gag reflex). Given that any signal can be thought to be made up of sinusoidal signals, the spectrum then represents the "recipe card" of how to make the signal from sinusoids. Like: 1 part of 50 Hz and 2 parts of 200 Hz. Pure sinusoids have the simplest spectrum of all, just one component:
In this example, the carrier has 8 Hz and so the spectrum has a single component with value 1.0 at 8 Hz.
Now, the most basic amplitude modulated signal has a pretty simple spectrum. In this example, a pure sinusoid is used as the information signal (like the EBS test signal).
The carrier has a frequency of 65 Hz, and the information signal is at 5 Hz. The modulation index is 0.5. The spectrum reveals that there are so-called side-bands on either side of the carrier. This is known as the beat effect where two frequencies mix to produce the sum and difference frequencies. An example is when you tune a guitar string against another by playing the same note simultaneously. If they are not in tune, you can hear the "beat frequency" which is actually the difference between the two. AM works the opposite way: the "beat frequency" is the information which produces the side-bands. One can show the equivalence of these two approaches mathematically (but is slightly boring, so we won't do it).
It is useful to measure the range of frequencies that the entire signal occupies. This is known as the bandwidth (BW). In this example the bandwidth would be 10 Hz (70 Hz - 60 Hz). You can predict the bandwidth in this case using the simple formula: BW = 2fm where fm is the frequency of the simple sine wave used to modulate with.