Amplitude Modulation (AM) Transmission

AM Transmission

• Signals are transmitted between a transmitter over some form of transmission medium

• But normally signals are not in the form that is suitable for transmission and need to be transformed

• Modulation is a process of impressing (applying) a low frequency information signals onto a relatively high frequency carrier signal

Principles of AM

• Amplitude Modulation - is a process of changing the amplitude of a relatively high frequency carrier signal with the instantaneous value of the modulating signal (information signal).

• 2 inputs to the modulation devise (modulator)

A single, high frequency RF carrier signal of constant amplitude.

Low frequency information signals that maybe a single frequency or a complex waveform made up of many frequencies.

• In the modulator, the information signal modulates the RF carrier signal to produce a modulated waveform made up of many frequencies. This modulated waveform also called as AM envelope.

AM Envelope The most commonly used AM

modulation technique is the AM double- sideband full carrier (DSBFC) scheme.

Given a signals representation as follow,

• Carrier signal = Vc sin [2 fc t ]

• Modulating signal = Vm sin [2 fm t ]

• Modulated wave = Vam [t ]

When a modulating signal (information signal) is applied to the carrier signal, the amplitude of the output wave varies in accordance with the modulating signal

AM Frequency Spectrum and Bandwidth • Output envelop is a complex wave made

up of a DC voltage, the carrier frequency, sum frequencies (fc + fm) and difference frequencies (fc -fm).

• The sum and difference frequencies are displaced from carrier frequency by an amount equal to modulating frequency.

• The AM signal spectrum contains frequency components spaced fm Hz on either side of the carrier as shown in figure 4-2.

The AM spectrum ranges from fc - fm(max) to fc + fm(max).

Parameters : Lower sideband (LSB) = band of frequencies between

fc -

fm(max) and fc Lower side frequency (LSF) = any frequency within LSB Upper sideband (USB) = band of frequencies between fc and fc +

fm(max) Upper side frequency (USF) = any frequencies within USB

Bandwidth : twice the highest modulating signal frequency

B = 2 fm(max)

Phasor Representation of an Amplitude-Modulation Wave

• AM envelope is produced from the vector addition of the carrier and the upper and lower side frequencies.

• The two side frequencies combine and produce a resultant components that combines with the carrier vector .

Coefficient of Modulation and Percent Modulation

Coefficient of Modulation is a term used to describe the amount of amplitude change presents in an AM waveform.

Percent Modulation is the coefficient of modulation stated as a percentage.

Mathematical representation :

• m= (1)

• M = ×100= m×100 (2)

Where:

m = modulation coefficient where usually

0 < m 1

M = percent modulation

= peak change in the amplitude of the

output waveform

= peak amplitude of the unmodulated

carrier waveform

Graphical representation of the relationship between m, and .

Based from the above figure, = ( ) (3) = ( + ) (4)

M = 100

= 100 (5)

can also be defined as the sum of voltages from upper and lower side frequencies.

= (6)

(7)

Therefore,

(8)

Where:

= peak amplitude of the upper side frequency (volts)

= peak voltage of the lower side frequency (volts)

Ex : For the AM waveform shown below, determine

a) Peak amplitude of the upper and lower side frequencies

b) Peak amplitude of the unmodulated carrier

c) Peak change in the amplitude of the envelope

d) Coefficient of modulation Percent modulation

AM Voltage Distribution and Analysis  The amplitude of the AM wave varies in proportional to the amplitude of the modulating signal and the maximum amplitude of the AM wave is + .

Given the unmodulated carrier signal as

(t) = sin (2t) (9)

Where:

(t) = time-varying voltage waveform for the carrier

= peak carrier amplitude (volts)

= carrier frequency (hertz)

Based on the following characteristics of the AM wave :

• the repetition rate of an AM envelope is equal to the frequency of the modulating signal

• the amplitude of the AM wave varies proportional to the amplitude of the modulating signal

• the maximum amplitude of the modulated wave is equal to +

therefore, the output modulated wave can be expressed as

(t ) = [ + sin ( 2t )][sin (2t )] (10)

Where:

[ + sin ( 2t )] = amplitude of the modulated wave

= peak carrier signal amplitude

= carrier signal frequency

= modulating signal frequency

= peak modulated output signal amplitude

substituting (1) into (10),

(t) = [+ sin(2t )][sin (2t )] (11)

rearranging equation (11), we get

(t) = [1 + m sin(2t )] [ sin (2t )] (12)

Where:

[1 + m sin(2t )] = constant + modulating signal

[ sin (2t )] = unmodulated carrer

(t) = sin (2t )+[ sin(2t)][sin(2t )] (13)

Then by using a trigonometric function, equation (13) can be represented as,  ( t ) = sin (2t ) cos [2 ( + )t ] + cos [2 ( )t ] (14)

Where:

sin (2t ) = carrier signal (volts)

cos [2 ( + )t ] = upper side frequency signal (volts)

+ cos [2 ( )t ] = lower side frequency signal (volts)

From equation (14) there are few characteristics of AM DSBFC that can be deduced as follow :

1. the amplitude of the carrier signal is unaffected by the modulation process.

2. the amplitude of USF and LSF depends on both the carrier amplitude and the coefficient of modulation.

3. for 100% modulation (m = 1) and from previous section,