Communication Systems/Amplitude Modulation

This page will talk about Amplitude modulation.

Amplitude Modulation

Amplitude modulation (AM) occurs when the amplitude of a carrier wave is modulated, to correspond to a source signal. In AM, we have an equation that looks like this:

$F_{signal}(t)=A(t)\sin (\omega t)$

We can also see that the phase of this wave is irrelevant, and does not change (so we dont even include it in the equation).

AM Double-Sideband (AM-DSB for short) can be broken into two different, distinct types: Carrier, and Suppressed Carrier varieties (AM-DSB-C and AM-DSB-SC, for short, respectively). This page will talk about both varieties, and will discuss the similarities and differences of each.

AM-DSB-SC

AM-DSB-SC is characterized by the following transmission equation:

$v(t)=As(t)\cos (2\pi f_{c}t)$

It is important to notice that s(t) can contain a negative value. AM-DSB-SC requires a coherent receiver, because the modulation data can go negative, and therefore the receiver needs to know that the signal is negative (and not just phase shifted). AM-DSB-SC systems are very susceptable to frequency shifting and phase shifting on the receiving end. In this equation, A is the transmission amplitude.

AM Transmitter

A typical AM-DSB-SC transmitter looks like this:

          cos(...)
             |
Signal ---->(X)----> AM-DSB-SC

AM Receiver

To demodulate AM-DSB-SC, you need to have a correlation receiver, with a tightly synchronized reference signal.

AM-DSB-C

In contrast to AM-DSB-SC is AM-DSB-C, which is categorized by the following equation:

$v(t)=A[s(t)+c]\cos (2\pi f_{c}t)$

Where c is a positive term representing the carrier. If the term $[s(t)+c]$ is always non-negative, we can receive the AM-DSB-C signal non-coherently, using a simple envelope detector to remove the cosine term. The +c term is simply a constant DC signal and can be removed by using a blocking capacitor.

It is important to note that in AM-DSB-C systems, a large amount of power is wasted in the transmission sending a "boosted" carrier frequency. since the carrier contains no information, it is considered to be wasted energy. The advantage to this method is that it greatly simplifies the receiver design, since there is no need to generate a coherent carrier signal at the receiver. For this reason, this is the transmission method used in conventional AM radio.

AM-DSB-SC and AM-DSB-C both suffer in terms of bandwidth from the fact that they both send two identical (but reversed) frequency "lobes", or bands. These bands (the upper band and the lower band) are exactly mirror images of each other, and therefore contain identical information. Why can't we just cut one of them out, and save some bandwidth? The answer is that we can cut out one of the bands, but it isn't always a good idea. The technique of cutting out one of the sidebands is called Amplitude Modulation Single-Side-Band (AM-SSB). AM-SSB has a number of problems, but also some good aspects. A compromise between AM-SSB and the two AM-DSB methods is called Amplitude Modulation Vestigial-Side-Band (AM-VSB), which uses less bandwidth then the AM-DSB methods, but more than the AM-SSB.

Transmitter

A typical AM-DSB-C transmitter looks like this:

             c    cos(...)
             |       |
Signal ---->(+)---->(X)----> AM-DSB-C

which is a little more complicated than an AM-DSB-SC transmitter.

Receiver

An AM-DSB-C receiver is very simple:

AM-DSB-C ---->|Envelope Filter|---->|Capacitor|----> Signal

The capacitor blocks the DC component, and effectively removes the +c term.

AM-SSB

To send an AM-SSB signal, we need to remove one of the sidebands from an AM-DSB signal. This means that we need to pass the AM-DSB signal through a filter, to remove one of the sidebands. The filter, however, needs to be a very high order filter, because we need to have a very agressive roll-off. One sideband needs to pass the filter almost completely unchanged, and the other sideband needs to be stopped completely at the filter.

To demodulate an AM-SSB signal, we need to perform the following steps:

1. Low-pass filter, to remove noise
2. Modulate the signal again by the carrier frequency
3. Pass through another filter, to remove high-frequency components
4. Amplify the signal, because the previous steps have attenuated it significantly.

AM-SSB is most efficient in terms of bandwidth, but there is a significant added cost involved in terms of more complicated hardware to send and receive this signal. For this reason, AM-SSB is rarely seen as being cost effective.

SSB Transmitter

AM-SSB transmitters are a little more complicated:

          cos(...)
             |
Signal ---->(X)---->|Low-Pass Filter|----> AM-SSB

The filter must be a very high order, for reasons explained in that chapter.

SSB Receiver

An AM-SSB receiver is a little bit complicated as well:

          cos(...)
             |
AM-SSB ---->(X)---->|Low-Pass Filter|---->|Amplifier|----> Signal

This filter doesnt need to be a very high order, like the transmitter has.

AM-VSB

As a compromise between AM-SSB and AM-DSB is AM-VSB. To make an AM-VSB signal, we pass an AM-DSB signal through a lowpass filter. Now, the trick is that we pass it through a low-order filter, so that some of the filtered sideband still exists. This filtered part of the sideband is called the "Vestige" of the sideband, hence the name "Vestigial Side Band".

AM-VSB signals then can get demodulated in a similar manner to AM-SSB. We can see when we remodulate the input signal, the two vestiges (the positive and negative mirrors of each other) over-lap each other, and add up to the original, unfiltered value!

AM-VSB is less expensive to implement then AM-SSB because we can use lower-order filters.

Transmitter

here we will talk about an AM-VSB transmitter circuit.

Receiver

here we will talk about an AM-VSB receiver circuit.

AM Demodulation

When trying to demodulate an AM signal, it seems like good sense that only the amplitude of the signal needs to be examined. By only examining the amplitude of the signal at any given time, we can remove the carrier signal from our considerations, and we can examine the original signal. Luckily, we have a tool in our toolbox that we can use to examine the amplitude of a signal: The Envelope Detector.