CPE351 A Communication Principles PDF

Communication Principles Part A (CPE351) compiled by ISI EDEOGHON ( P H. D. ) 2021 Part One Analog Modulation [email protected] 2 Modulation Modulation is the alteration or modification of a signal (known as a carrier) to behave analogously like another signal (baseband signal) in order...

Communication Principles Part A (CPE351) compiled by ISI EDEOGHON ( P H. D. ) 2021 Part One Analog Modulation [email protected] 2 Modulation Modulation is the alteration or modification of a signal (known as a carrier) to behave analogously like another signal (baseband signal) in order to convey and transmit information. Why the need for Modulation? The message or baseband signal is often times a weak signal and we therefore need to make use of another signal called the carrier, which is stronger and more resistant to noise to encode the information contained in the baseband signal for transmission. At the receiver, the original signal can be obtained through the use of what is known as a low pass filter. [email protected] 3 Key terms Baseband, Message or Modulating Signal A signal which contains information to be transmitted, is called a baseband signal, it goes through the process of modulation to be transmitted. It is also called a modulating signal. Carrier Signal A high frequency signal carrying no information is called a carrier signal. It is empty signal but is used to carry the signal to the receiver after modulation with the baseband signal. It is the modulated signal. Modulated Signal The resultant signal after the process of modulation is called as a modulated signal. This signal is a combination of baseband or message signal and carrier signal. [email protected] 4 Amplitude Modulation It is often referred to as AM and is used in transmitting a piece of information through a radio carrier wave. Amplitude modulation is a process by which the wave signal (representing the information) is transmitted by modulating the amplitude of a carrier signal. This technique is used as a modulation scheme for portable two-way radios; citizens band radio, VHF aircraft radio and in modems for computers. [email protected] 5 Baseband vs Carrier Wave [email protected] 6 Modulated Carrier Wave [email protected] 7 Amplitude Modulated waves in time domain 𝑚 𝑡 = 𝐴𝑚𝑐𝑜𝑠 2𝜋𝑓𝑚𝑡 modulating signal (eq 1) 𝑐 𝑡 = 𝐴𝑐𝑐𝑜𝑠 2𝜋𝑓𝑐𝑡 carrier signal (eq 2) s 𝑡 = [𝐴𝑐 + 𝐴𝑚𝑐𝑜𝑠(2𝜋𝑓𝑚𝑡)]𝑐𝑜𝑠 2𝜋𝑓𝑐𝑡 Amplitude modulated signal (eq 3) Where, Am: amplitude of modulating signal Ac: amplitude of carrier signal fm: frequency of modulating signal fc: frequency of carrier signal Therefore, above is the derivation of Amplitude Modulation [email protected] 8 Modulation index derivation Modulation index μ is also known as modulation depth and is defined for a carrier wave to describe the modulated variable of carrier signal varying with respect to its unmodulated level. It states the level of modulation that a carrier wave undergoes. It is represented as follows: 𝐴𝑚 𝜇= (eq 4) 𝐴𝑐 It is also given as : 𝐴𝑚𝑎𝑥 −𝐴𝑚𝑖𝑛 𝜇= 𝐴𝑚𝑎𝑥+𝐴𝑚𝑖𝑛 (eq 5) where 𝐴𝑚𝑎𝑥 = 𝐴𝑐 + 𝐴𝑚 𝑎𝑛𝑑 𝐴𝑚𝑖𝑛 = 𝐴𝑐 − 𝐴𝑚 [email protected] 9 Modulation index of 0.5 and 1.5 [email protected] 10 Bandwidth of a signal Bandwidth (BW) refers to the difference between the highest and lowest frequencies of a signal. Mathematically, it is represented as: BW=fmax−fmin (eq5) Applying to Eq 3 s(t)=Ac[1+μcos(2πfmt)]cos(2πfct) ⇒s(t)=Accos(2πfct)+Acμcos(2πfct)cos(2πfmt) We obtain: ⇒s(t)=Accos(2πfct)+Acμ2cos[2π(fc+fm)t]+Acμ2cos[2π(fc−fm)t] (eq6) [email protected] 11 Bandwidth of a signal Following from Eq 5 Recall: fmax = fm + fc fmin = fm -fc We obtain: BW =2fm (eq7) [email protected] 12 Illustration of Bandwidth Upper Side Band (USB) = fm + fc LSB USB Lower Side Band (LSB) = fm -fc Thus: BW =2fm fm -fc fm + fc [email protected] 13  Power of an AM wave Power of an AM wave refers to the total power transmitted by an AM signal. Mathematically, it is represented as: 𝜇2 ⇒𝑃𝑡 = 𝑃𝑐(1 + 2 ) (eq8) Where Pc = Carrier Power, μ = Modulation index and Pt = Total AM power 𝜇2 And PsB (sideband power ) ⇒𝑃𝑐( 2 ) (eq9) Note that when the modulation index μ=1 then the power of an AM wave 1.5 times greater than the carrier power. This is known as perfect modulation. Exercise: Show the derivation steps for Pt [email protected] 14 Exercise The equation of amplitude wave is given by s(t)=50[1+0.7cos(2π×𝟏𝟎𝟒 t)]cos(4π×𝟏𝟎𝟓 t). Find the carrier power, the total sideband power, and the band width of the AM wave. [email protected] 15 Types of Amplitude Modulation (1) Double sideband-suppressed carrier modulation (DSB-SC). Single Sideband Modulation (SSB). Vestigial Sideband Modulation (VSB). [email protected] 16 Types of Amplitude Modulation (2) Double sideband-suppressed carrier modulation (DSB-SC). It has lower power consumption and it is simple technique of modulation. But it is complex to detect at the AM receiver. It is used in analog TV transmission systems to transmit color information. Single Sideband Modulation (SSB). It is has efficient spectrum management capabilities. But generation of SSB modulation is difficult and it is complex to detect at the receiver. It is used for 2-way radio Frequency Division Multiplex [email protected] 17 Types of Amplitude Modulation (3) Vestigial Sideband Modulation (VSB). It compromises of DSB and SSB types of AM. Demodulation is however complex at the receiver. It has a 25% higher bandwidth compared to SSB-SC. It is used for analog TV broadcast systems. [email protected] 18 Types of Amplitude Modulation Double sideband-suppressed carrier modulation (DSB-SC). The carrier frequency (fc) is suppressed and is not transmitted in order to save power and the sidebands are transmitted instead. [email protected] 19 Double sideband-suppressed carrier modulation (DSB-SC). Mathematically, s(t)=Am Accos(2πfmt)cos(2πfct) for a DSB-SC AM wave Eliminating fc we have:- AmAc AmAc ⇒s(t)= 2 cos[2π(fc + fm)t] + 2 cos[2π(fc − fm)t] [email protected] 20  Double sideband-suppressed carrier modulation (DSB-SC). Mathematically Power Combining the upper and lower side bands of DSB-SC, together we have: Pt=PUSB+PLSB 𝑃𝑡 = 𝑃𝑈𝑆𝐵 + 𝑃𝐿𝑆𝐵 𝑣𝑟𝑚𝑠 2 (𝑣𝑚 Τ√2)2 P= = 𝑅 𝑅 (𝐴𝑚 𝐴𝑐 )2 (𝐴𝑚 𝐴𝑐 )2 (𝐴𝑚 𝐴𝑐)2 𝑝𝑡 = + 8𝑅 8𝑅 (2√2)2 𝑝𝑈𝑆𝐵 = 𝑅 (𝐴𝑚 𝐴𝑐 )2 (𝐴𝑚 𝐴𝑐 )2 𝑝𝑈𝑆𝐵 = 𝑝𝑡 = 8𝑅 4𝑅 Where R = 1 (In most (𝐴𝑚 𝐴𝑐 )2 𝑝𝑡 = as the power of a DSB-SC cases) 4𝑅 [email protected] 21 Types of Amplitude Modulation Single Sideband Modulation (SSB). This involves suppressing the carrier and a sideband and transmitting one sideband only. Either the upper sideband or the lower sideband can be transmitted. [email protected] 22 Single Sideband Modulation (SSB) Mathematically, s(t)=Am Accos(2πfmt)cos(2πfct) for a SSB-SC AM wave Eliminating fc and fc+fm or fc-fm we have:- AmAc ⇒s(t)= 2 cos[2π(fc + fm)t] for upper sideband AmAc ⇒s(t)= 2 cos[2π(fc − fm)t] for lower side band [email protected] 23  Single sideband-suppressed carrier modulation (SSB-SC). Mathematically Power Since only one side band is transmitted in SSB- of DSB-SC, SC 𝑃𝑡 = 𝑃𝑈𝑆𝐵 Pt=PUSB+PLSB 𝑣𝑟𝑚𝑠 2 (𝑣𝑚 Τ√2)2 PUSB= = (𝐴𝑚 𝐴𝑐 )2 𝑅 𝑅 𝑝𝑡 = 8𝑅 (𝐴𝑚 𝐴𝑐)2 (2√2)2 𝑝𝑈𝑆𝐵 = (𝐴𝑚 𝐴𝑐 )2 𝑅 𝑝𝑡 = 8𝑅 (𝐴𝑚 𝐴𝑐 )2 𝑝𝑈𝑆𝐵 = 8𝑅 (𝐴𝑚 𝐴𝑐 )2 𝑝𝑡 = as the power of a SSB-SC Where R = 1 (In most 8𝑅 cases) [email protected] 24 Exercise Explain the mechanism behind Vestigial Sideband Modulation (VSB). [email protected] 25 Types of AM Modulators Square law modulator Switching modulator [email protected] 26 Square Law Modulator (1) A square law modulator is a device that is used to modulate a signal in order to produce an output proportional to the square of the input signal. [email protected] 27 Square Law Modulator (2) Schematic of a Square Law Modulator Here, V1(t) =m(t)+Accos(2πfct) (eq 9) [email protected] 28 Square Law Modulator (3) Equation of a square law modulator V1(t) = m(t) + Accos(2πfct) (eq 9) Substitute Eq 9 into Eq 10 as the value for V1(t) V2(t) = k1V1(t) + k2𝑽𝟏𝟐 (t) (eq 10) Thus: = [email protected] 29 Square Law Modulator (4) After filtering the other terms with a bandpass filter we obtain: As the equation for the output of a square law modulator [email protected] 30 Switching Modulator Exercise Sketch the circuit for a switching modulator and explain its working principle (Mathematically or otherwise) [email protected] 31 Angle Modulation Angle Modulation is the process in which the frequency or the phase of a carrier signal varies with a baseband (message) signal. It can be mathematically represented thus: s(t)=Ac cos(θi(t)) Where, Ac is the amplitude of the modulated wave, which is the same as the amplitude of the carrier signal θi(t) is the angle of the modulated wave [email protected] 32 Angle Modulation A signal can be expressed mathematically as: 𝑠 𝑡 = 𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜃𝑖 Note that mathematically : 𝜃𝑖 𝑡 = 2𝜋 ‫𝑡𝑑 𝑖𝑓 ׬‬ Where, 𝜔𝑡 is the phase of the signal, 𝜃 represents the angle of the signal in this case a phase fi(t) is the instantaneous frequency. [email protected] 33 Angle Modulation Angle modulation is divided into frequency modulation (FM) and phase modulation (PM). Frequency Modulation is the process of varying the frequency of a carrier signal linearly with that of the baseband or message signal. Phase Modulation is the process of varying the phase of a carrier signal linearly with that of the baseband or message signal. [email protected] 34 Frequency Modulation Let us denote the instantaneous frequency of FM as: fi(t) And 𝑓𝑖 𝑡 = 𝑓𝑐 + 𝑚(𝑡) To obtain the value of the angle (𝜃𝑖 ) we integrate the instantaneous frequency (𝑓𝑖 ) , Thus: 𝜃𝑖 𝑡 = 2𝜋 ‫𝑡𝑑 𝑖𝑓 ׬‬ 𝜃𝑖 𝑡 = 2𝜋(𝑓𝑐 +𝑆 ‫)𝑡𝑑 )𝑡(𝑚 ׬‬ Where S is known as the frequency sensitivity [email protected] 35 Frequency Modulation Putting it all together we obtain: 𝑠 𝑡 = 𝐴𝑐 cos(2𝜋(𝑓𝑐 +𝑆 ‫))𝑡𝑑 )𝑡(𝑚 ׬‬ If the modulating signal is 𝑚 𝑡 = 𝐴𝑚 cos(2𝜋𝑓𝑚 𝑡) then the equation of FM wave will be 𝑠 𝑡 = 𝐴𝑐 cos(2𝜋(𝑓𝑐 +𝑆 ‫ 𝑚𝐴 ׬‬cos(2𝜋𝑓𝑚 𝑡)𝑑𝑡)) 𝑠 𝑡 = 𝐴𝑐 cos(2𝜋(𝑓𝑐 +𝑆 𝐴𝑚 sin 2𝜋𝑓𝑚 𝑡 𝑑𝑡 ) Replacing S*Am =β 𝒔 𝒕 = 𝑨𝒄 𝐜𝐨𝐬(𝟐𝝅(𝒇𝒄 +𝜷 𝒔𝒊𝒏 𝟐𝝅𝒇𝒎 𝒕 𝒅𝒕 ) as the equation for an FM wave [email protected] 36 Frequency Modulation [email protected] 37 Wideband FM This frequency modulation has infinite bandwidth. The modulation index β is large, i.e., higher than 1. Its spectrum consists of a carrier and infinite number of sidebands, which are located around it. This is used in entertainment, broadcasting applications such as FM radio, TV, etc. [email protected] 38 Narrow Band FM This frequency modulation has a small bandwidth when compared to wideband FM. The modulation index β is small, i.e., less than 1. Its spectrum consists of the carrier, the upper sideband and the lower sideband. This is used in mobile communications such as police wireless, ambulances, taxicabs, etc. [email protected] 39 Phase Modulation Let us denote the instantaneous phase of PM as: θm(t) And θ𝑚 𝑡 = 𝑆𝑚(𝑡) Where S is known as the phase sensitivity and m(t) the baseband(message) signal Thus if: s 𝑡 = 𝐴𝑐 cos(ϑ(𝑡)) ⇒ 𝐴𝑐 cos(𝜔𝑐 𝑡 + ϑ𝑚 (𝑡)) And 𝜃 𝑡 = 2𝜋𝑓𝑐 + 𝑆𝑚 𝑡 𝑑𝑡 [email protected] 40 Phase Modulation s 𝑡 = 𝐴𝑐 cos(ϑ(𝑡)) s 𝑡 = 𝐴𝑐 cos(2𝜋𝑓𝑐 + 𝑆𝑚 𝑡 𝑑𝑡)) s 𝑡 = 𝐴𝑐 cos(2𝜋𝑓𝑐 + 𝑆𝐴𝑚 cos2π𝑓𝑚(𝑑𝑡)) Replacing S*Am with α Then: s 𝒕 = 𝑨𝒄 𝐜𝐨𝐬(𝟐𝝅𝒇𝒄 + 𝜶𝐜𝐨𝐬𝟐𝝅𝒇𝒎(𝒅𝒕)) As the equation for a PM wave [email protected] 41 Phase Modulation [email protected] 42 PM and FM side by side [email protected] 43 References 2021 https://www.tutorialspoint.com/analog_communication.htm 2021 A practical guide to Radio Frequency Analysis and Design, © ETECH Media [email protected] 44