Amplitude Modulation. Amplitude Modulation. Amplitude Modulation. Amplitude Modulation. A. Introduction. A. Introduction

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Rosalyn Norman
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1 1. In AM modulation we impart the information of a message signal m(t) on to a sinusoidal carrier c(t). This results in the translation of the message signal to a new frequency range. The motivation for imparting the information of a message signal on to a sinusoidal carrier is to exploit the transmission properties of the channel at different frequencies. For example, in order to communicate with submarines it is necessary to use extremely low frequencies in order to get the signal to penetrate the ocean. Conversely, extremely high frequencies are needed to penetrate the atmosphere so that satellite communications are possible. The need for AM modulation first arose in connection with radio transmission of low frequency audio signals. For efficient transmission it was found that the antenna dimensions had to be of the same order of magnitude as the wavelength (λ) of the signal. = λ c=3x10 / For a typical audio signal of 10 khz, we would need an antenna of about λ= = ,000 =30,000 =17 Which is obviously impractical. 1

2 2. Consider a general sinusoid carrier = cos (2 + ) Within the broad category of AM there exists numerous techniques of implementation. The most popular include: Double Side Band Suppressed Carrier {DSB-SC} Double side Band Large Carrier {DSB-LC} Single Side Band {SSB} Vestigial Side Band {VSB} 3. AM Terminology and Fun Facts c(t)= carrier signal m(t) = message signal s(t) = modulated signal B. Double Side Band Suppressed Carrier {DSB-SC} B. Double Side Band Suppressed Carrier {DSB-SC} 2. DSB-SC in Time Domain = c(t) = cos (2 ) = carrier frequency = carrier amplitude m(t) = message signal 2

3 2. DSB-SC in Time Domain 3. DSB-SC in Frequency Domain 3. DSB-SC in Frequency Domain 4. DSB-SC in Pictures 3

4 4. DSB-SC Notes The message signal spectrum is even symmetric so that after translation the bandwidth is doubled. [From W to 2W]. The portion of the spectrum above + [and below ] is called the Upper Side Band {USB} The portion of the spectrum below + [and above ] is called the Lower Side Band {LSB} 4. DSB-SC Observations The message signal amplitude spectrum is scaled and translated, the shape is preserved. The carrier spectrum does NOT appear in the DSB-SC spectrum. AM thus consists of a frequency shift of the message. Thus AM process is also called, frequency shifting, frequency translation, frequency conversion, or heterodyning. Ex Single Tone Modulation Consider the single tone modulating signal = cos (2 ) Let the carrier signal be = cos (2 ) The DSBSC signal = c(t) = cos (2 ) cos (2 ) Ex Single Tone Modulation In time domain Using CosA CosB = ½[Cos(A-B) +Cos(A+B)] = 1 2 cos 2 [ + cos (2 [ + ] )} 4

5 Ex Single Tone Modulation In frequency domain Ex Multiple Tone Modulation A carrier at frequency =100 is DSBSC modulated by the multi-tone signal =10cos cos cos a) List the frequencies at the modulator output. b) What is the time domain expression for the DSBSC output? c) Plot the DSBSC spectrum? Ex Multiple Tone Modulation Solution : a) The message signal frequencies are 1 khz, 2kHz, and 3kHz Ex Multiple Tone Modulation Solution : b) = =[10cos cos cos 6 10 ][cos 2 10 ] So the DSBSC frequencies are USB s => 101, 102, 103 khz LSB s => 99, 98, 97 khz 5

6 5. DSB-SC Modulators A signals spectrum can be frequency translated by an amount +/-fc by multiplying the signal by ANY periodic waveform with fundamental frequency fc. Recall: Any period signal with finite average power can be represented by it s F.S. = ; = 1 Letting =, and multiplying by m(t), 5. DSB-SC Modulators = The Spectrum is thus; ; = ( ) Thus the new spectrum contains M(f) and translation at M(f +/- n fc). Once the spectral replica s are produced the frequency modulated copy is extracted via a band pass filter. 5.a Chopper /Switching DSB-SC Modulators Two steps I. Multiply by periodic wave at fc [ i.e. sample] II. Band pass filter at fc 5.a Chopper /Switching DSB-SC Modulators 6

7 5.a Chopper /Switching DSB-SC Modulators 5.a Chopper /Switching DSB-SC Modulators Notes: The gp(t) drives the switch and produces a periodic pulse train that multiples m(t) to produce ms(t). Thus ms(t) is a chopped version of m(t), which can be thought of as the product of the message signal with a pulse type signal that has levels of 0, 1, and a period of 1/fc. The resulting spectrum Ms(f) consists of scaled and translated copies of M(f). Scaled by the Cn of the pulses and translated by +/- n fc. 5.a Chopper /Switching DSB-SC Modulators Notes: The BPF extracts ± ± components. The are dependent on the periodic waveshape. For a square pulse w/ 50% duty cycle; So at = we have = ( ) ± = (1/2) b Ring modulator The ring modulator works on the same principal as the switch modulator with 2 exceptions. 1. uses diodes as switches 2. uses 4 diodes to act like two switches The diodes provide circuit reliability at reduced cost and weight, and permits higher frequency carrier operation. The use of two switches permits pulses to have negative and positive cycles available, this not only increases efficiency, but ensures no carrier frequencies appear in the DSB-SC output. 7

8 5.b Ring modulator 5.b Ring modulator 6. DSBSC Recovery and Demodulation Recovery of the original message signal {m(t)} from the DSBSC signal { }, requires another shift in frequency to shift the signal back to its original position. Schematic: 8

Amplitude Modulated Systems

Amplitude Modulated Systems Communication is process of establishing connection between two points for information exchange. Channel refers to medium through which message travels e.g. wires, links, or