Lecture 1.7. AM FM PM OOK BPSK FSK

AM, FM, and Digital Modulated Systems Amplitude Modulation (AM) Double Sideband Suppressed carrier (DSSC) Assymetric Sideband Signals Single sideband signals (SSB)

Bandpass Signaling Review The modulated bandpass signal can be described by Where Modulation Mapping function: Convert m(t) →g(t) Ref : Table 4-1 The voltage spectrum of the bandpass signal is The PSD of the bandpass signal is Where

Amplitude Modulation The Complex Envelope of an AM signal is given by Ac indicates the power level of AM and m(t) is the Modulating Signal Representation of an AM signal is given by Ac[1+m(t)] In-phase component x(t) If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated Envelope detection can be used if % modulation is less than 100%.

Amplitude Modulation An Example of a message signal m(t) Waveform for Amplitude modulation of the message signal m(t)

Carrier component together with the message Amplitude Modulation B An Example of message energy spectral density. Carrier component together with the message 2B Energy spectrum of the AM modulated message signal.

AM – Percentage Modulation Definition: The percentage of positive modulation on an AM signal is The percentage of negative modulation on an AM signal is The percentage of overall modulation is If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated

AM Signal Waveform % Positive modulation= 50% % Negative modulation =50% Overall Modulation = 50% Amax = 1.5Ac Amin = 0.5 Ac

AM – Percentage Modulation Under modulated (<100%) 100% modulated Envelope Detector Can be used Gives Distorted signal Over Modulated (>100%)

Discrete Carrier Power AM – Normalized Average Power The normalized average power of the AM signal is If the modulation contains no dc level, then The normalized power of the AM signal is Discrete Carrier Power Sideband power

AM – Modulation Efficiency Definition : The Modulation Efficiency is the percentage of the total power of the modulated signal that conveys information. Only “Sideband Components” – Convey information Modulation Efficiency: Highest efficiency for a 100% AM signal : 50% - square wave modulation Normalized Peak Envelope Power (PEP) of the AM signal: Voltage Spectrum of the AM signal: Unmodulated Carrier Spectral Component Translated Message Signal

Double Side Band Suppressed Carrier (DSBSC) Carrier Power Sideband power Power in a AM signal is given by DSBSC is obtained by eliminating carrier component If m(t) is assumed to have a zero DC level, then Spectrum  Power  Modulation Efficiency  Disadvantages of DSBSC: Less information about the carrier will be delivered to the receiver. Needs a coherent carrier detector at receiver

No Extra Carrier component DSBSC Modulation B An Example of message energy spectral density. No Extra Carrier component 2B Energy spectrum of the DSBSC modulated message signal.

Single Sideband (SSB) Modulation An upper single sideband (USSB) signal has a zero-valued spectrum for A lower single sideband (LSSB) signal has a zero-valued spectrum for SSB-AM – popular method ~ BW is same as that of the modulating signal. Note: Normally SSB refers to SSB-AM type of signal USSB LSSB

Single Sideband Signal Theorem : A SSB signal has Complex Envelope and bandpass form as: Upper sign (-)  USSB Lower sign (+)  LSSB – Hilbert transform of m(t)  Where and Hilbert Transform corresponds to a -900 phase shift H(f) f -j j

Single Sideband Signal Proof: Fourier transform of the complex envelope Upper sign  USSB Lower sign  LSSB Using Recall from Chapter 4 Upper sign  USSB If lower signs were used  LSSB signal would have been obtained

Single Sideband Signal

SSB - Power The normalized average power of the SSB signal Hilbert transform does not change power. SSB signal power is: Power of the modulating signal Power gain factor The normalized peak envelope (PEP) power is:

Generation of SSB Advantages of SSB SSB signals have both AM and PM. The complex envelope of SSB: For the AM component, For the PM component, Advantages of SSB Superior detected signal-to-noise ratio compared to that of AM SSB has one-half the bandwidth of AM or DSB-SC signals

Generation of SSB SSB Can be generated using two techniques Phasing method Filter Method This method is a special modulation type of IQ canonical form of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)

Generation of SSB Filter Method The filtering method is a special case in which RF processing (with a sideband filter) is used to form the equivalent g(t), instead of using baseband processing to generate g(m) directly. The filter method is the most popular method because excellent sideband suppression can be obtained when a crystal oscillator is used for the sideband filter. Crystal filters are relatively inexpensive when produced in quantity at standard IF frequencies.

Weaver’s Method for Generating SSB.

Generation of VSB

AM, FM, and Digital Modulated Systems Phase Modulation (PM) Frequency Modulation (FM) Generation of PM and FM Spectrum of PM and FM Carson’s Rule Narrowband FM

AM and FM Modulation (a) Carrier wave. (b) Sinusoidal modulating signal. (c) Amplitude-modulated signal. (d) Frequency modulated signal.

Angle Modulation Advantages: Disadvantages: Constant amplitude means Efficient Non-linear Power Amplifiers can be used. Superior signal-to-noise ratio can be achieved (compared to AM) if bandwidth is sufficiently high. Disadvantages: Usually require more bandwidth than AM More complicated hardware

Modulation Index The Peak Phase Deviation is given by: ∆θ is related to the peak modulating voltage by: Where The Phase Modulation Index is given by: Where ∆θ is the peak phase deviation The Frequency Modulation Index is given by: ∆F Peak Frequency Deviation B Bandwidth of the modulating signal

Spectra of Angle modulated signals Where Spectrum of Angle modulated signal Spectra for AM, DSB-SC, and SSB can be obtained with simple formulas relating S(f) to M(f). But for angle modulation signaling, because g(t) is a nonlinear function of m(t). Thus, a general formula relating G(f) to M(f) cannot be obtained. To evaluate the spectrum for angle-modulated signal, G(f) must be evaluated on a case-by-case basis for particular modulating waveshape of interest.

Spectrum of PM or FM Signal with Sinusoidal Modulating Signal Assume that the modulation on the PM signal is Then Where is the phase Modulation Index. Same θ(t) could also be obtained if FM were used where and The peak frequency deviation would be The Complex Envelope is: which is periodic with period

Spectrum of PM or FM Signal with Sinusoidal Modulating Signal Using discrete Fourier series that is valid over all time, g(t) can be written as Where Which reduces to Jn(β) – Bessel function of the first kind of the nth order Is a special property of Bessel Functions Taking the fourier transform of the complex envelope g(t), we get or

Bessel Functions of the First Kind J0(β)=0 at β=2.4, 5.52 & so on

Bessel Functions of the First Kind

Frequency spectrum of FM The FM modulated signal in time domain Observations: From this equation it can be seen that the frequency spectrum of an FM waveform with a sinusoidal modulating signal is a discrete frequency spectrum made up of components spaced at frequencies of c± nm. By analogy with AM modulation, these frequency components are called sidebands. We can see that the expression for s(t) is an infinite series. Therefore the frequency spectrum of an FM signal has an infinite number of sidebands. The amplitudes of the carrier and sidebands of an FM signal are given by the corresponding Bessel functions, which are themselves functions of the modulation index

Spectra of an FM Signal with Sinusoidal Modulation The following spectra show the effect of modulation index, , on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands 1.0 f BT

Spectra of an FM Signal with Sinusoidal Modulation J0(1.0) 1.0 J1(1.0) J2(1.0) f BT

Spectra of an FM Signal with Sinusoidal Modulation 1.0 f BT

Carson’s rule Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted. Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side. (1+b)fm

Carson’s rule Note: When β =0 i.e. baseband signals Therefore the Bandwidth required is given by β – phase modulation index/ frequency modulation index B – bandwidth of the modulating signal For sinusoidal modulation Carson’s rule : Bandwidth of an FM signal is given by Note: When β =0 i.e. baseband signals

AM, FM, and Digital Modulated Systems Binary Bandpass Signalling Techniques OOK BPSK FSK

Binary Bandpass Signaling techniques On–Off keying (OOK) [amplitude shift keying (ASK)] - Consists of keying (switching) a carrier sinusoid on and off with a unipolar binary signal. - Morse code radio transmission is an example of this technique. - OOK was one of the first modulation techniques to be used and precedes analog communication systems. Binary Phase-Shift Keying (BPSK) - Consists of shifting the phase of a sinusoidal carrier 0o or 180o with a unipolar binary signal. - BPSK is equivalent to PM signaling with a digital waveform. Frequency-Shift Keying (FSK) - Consists of shifting the frequency of a sinusoidal carrier from a mark frequency (binary 1) to a space frequency (binary 0), according to the baseband digital signal. - FSK is identical to modulating an FM carrier with a binary digital signal.

Binary Bandpass Signaling techniques

On-Off Keying (OOK) Also known as Amplitude Shift Keying (ASK) Carrier Cos(2fct) Message m(t) OOK output Acm(t)Cos(2fct) The complex envelope is The OOK signal is represented by The PSD of this complex envelope is given by where m(t) has a peak value of So that s(t) has an average normalized power of

Tb – bit period ; R – bit rate On-Off Keying (OOK) 1 0 1 0 1 0 1 Message Unipolar Modulation Bipolar OOK signal m(t) s(t) Tb – bit period ; R – bit rate

On-Off Keying (OOK) PSD of the bandpass waveform is given by Null-to-Null bandwidth is and absolute bandwidth is The Transmission bandwidth is Where B is the baseband bandwidth

Detection of OOK Non-Coherent Detection Binary output OOK in Envelope Detector Coherent Detection with Low-pass filter OOK in LPF Binary output

Binary Phase Shift Keying (BPSK) Generation: Carrier:Cos(2fct) Message: m(t) BPSK output AcCos(2fct+Dpm(t)) -90 Phase shift 1 0 1 0 1 0 1 Message Unipolar Modulation Bipolar BPSK output m(t) s(t)

Binary Phase Shift Keying (BPSK) The BPSK signal is represented by let pilot carrier term data term The level of the pilot carrier term is set by the value of the peak deviation The digital modulation index ‘h’ is given by 2∆θ – maximum peak-to-peak deviation during time Ts If Dp is small, then there is little power in data term & more in pilot term To maximize performance (minimum probability of error) Optimum case : BPSK signal :

Binary Phase Shift Keying (BPSK) The complex envelope for this BPSK is given by The PSD for this complex envelope is given by PSD of the bandpass waveform is given by Average normalized power of s(t) : Null-to-Null BW PSD of optimum BPSK

Binary Phase Shift Keying (BPSK) Power Spectral Density (PSD) of BPSK: fc 2R = 2/Tb If Dp  /2 Pilot exists

Frequency Shift Keying (FSK) Discontinuous FSK : Cos(2f1t) Message: m(t) FSK output AcCos(2f1t+1) or AcCos(2f2t+2) Osc. f2 Osc. f1 Cos(2f2t) The discontinuous-phase FSK signal is represented by for t during a binary ‘1’ signal for t during a binary ‘0’ signal

Frequency Shift Keying (FSK) Continuous FSK : Frequency Modulator fc FSK output Message: m(t) The Continuous-phase FSK signal is represented by or where for FSK

Frequency Shift Keying (FSK) 1 0 1 0 1 0 1 Message Unipolar Modulation Bipolar FSK output (Discontinuous) (Continuous) Mark(binary 1) frequency: f1 Space(binary 0) frequency: f2 m(t) s(t)

Frequency Shift Keying (FSK) Computer FSK modem (Originate) Center (Answer) Digital data PSTN Dial up phone line f1 = 1270Hz f2 = 1070Hz f1 = 2225Hz f2 = 2025Hz FSK modem with 300bps

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