# Amplitude modulation

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Amplitude modulation (AM) is a modulation scheme, notably used in AM radio.

An amplitude transceiver modulates the amplitude of an sinusoid carrier signal using the incoming signal. The carrier signal is sinusoid with a fixed Frequency, usually much higher than the highest frequency occurring in the spectrum of the modulating signal.

## Mathematical setting

Base for transmission is a sinusoid carrier signal with continuous carrier frequency $f_c$:

$\omega_c := 2 \pi f_c$

This is modulated by the incoming signal, here modeled by a simple sine with frequency $f_m$:

$\omega_m := 2 \pi f_m$

The actual signal coming out of the AM modulator is simply the product of both functions $\omega_c \cdot \omega_m$. Evaluating this in detail leads to the expression:

$u_{AM}(t) = U_c \cdot cos(\omega_c \ t) \cdot [1 + m \cdot cos(\omega_m \ t)]$

where $U_c$ is the modulation amplitude and $m$ the modulation index.

The first formula describes what happens in time domain. It's basically multiplying of two cosine signals leading to the time domain picture in the example below.

The second formula describes the frequency response, the frequency spectrum consists of three spectrum lines at each time, t. The first term is the carrier, for sure the carrier is in the spectrum, the second and third terms describe two spectrum lines around the carrier, and their amplitude is dependent on the modulation index, m. As the modulating signal varies the lines around the carrier frequency are varying.

## Example

 Carrier signal in time domain File:AM picture4.jpg Carrier signal in frequency domain (to be added) Modulating signal in time domain File:AM picture5.jpg Modulating signal in frequency domain (to be added) AM signal File:AM picture6.jpg AM signal in frequency domain (to be added)

## Acquired bandwidth

An AM signal shows up as a single peak in the frequency spectrum.

## Noise sensitivity

Echoes, multipath signaling, atmospheric and meteorologic phenomenons like lightings and electrostatic discharges contribute noise that simply gets added to the transmitted signal. Most other Modulation Schemes are less sensitive to noise.