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)  Frequency Division Multiplexing (FDM)

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

Amplitude Modulation  The Complex Envelope of an AM signal is given by A c indicates the power level of AM and m(t) is the Modulating Signal  A c [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  Representation of an AM signal is given by  Envelope detection can be used if % modulation is less than 100%.

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

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

 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 AM – Percentage Modulation If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated

AM Signal Waveform A max = 1.5A c A min = 0.5 A c % Positive modulation= 50% % Negative modulation =50% Overall Modulation = 50%

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

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 PowerSideband power

AM – Modulation Efficiency Translated Message Signal  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

Example 5-1. Power of an AM signal Suppose that a 5000-W AM transmitter is connected to a 50 ohm load; Then the constant A c is given by Without Modulation If the transmitter is then 100% modulated by a 1000-Hz test tone, the total (carrier + sideband) average power will be The peak voltage (100% modulation) is (2)(707) = 1414 V across the 50 ohm load. The peak envelope power (PEP) is The modulation efficiency would be 33% since =1/2

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

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

Carrier Recovery for DSBSC Demodulation  Coherent reference for product detection of DSBSC can not be obtained by the use of ordinary PLL because there are no spectral line components at f c.

Carrier Recovery for DSBSC Demodulation  A squaring loop can also be used to obtain coherent reference carrier for product detection of DSBSC. A frequency divider is needed to bring the double carrier frequency to f c.

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 phase shift H(f) f -j j

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

Single Sideband Signal

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

Generation 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 1.Phasing method 2.Filter Method Phasing 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

Frequency Divison Multiplexing

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  We have seen that an AM signal can be represented as  Now we will see that information can also be carried in the angle of the signal as Note that in this type of modulation the amplitude of signal carries information. Here the amplitude A c remains constant and the angle is modulated. This Modulation Technique is called the Angle Modulation Angle modulation: Vary either the Phase or the Frequency of the carrier signal  Phase Modulation and Frequency Modulation are special cases of Angle Modulation

Angle Modulation Representation of PM and FM signals: The Complex Envelope for an Angle Modulation is given by Is a constant Real envelope, θ(t) - linear function of the modulating signal m(t) The Angle-modulated Signal in time domain is given by g(t) - Nonlinear function of the modulation. Special Case 1: For PM the phase is directly proportional to the modulating signal. i.e.; Where D p is the Phase sensitivity of the phase modulator, having units of radians/volt. Special Case 2: For FM, the phase is proportional to the integral of m(t) so that where the frequency deviation constant D f has units of radians/volt-sec.

Angle Modulation Resulting PM wave:  Phase Modulation occurs when the instantaneous phase varied in proportion to that of the message signal. Dp is the phase sensitivity of the modulator  Frequency Modulation occurs when the instantaneous frequency is varied linearly with the message signal. Resulting FM wave: D f is the frequency deviation constant  Instantaneous Frequency (f i ) of a signal is defined by

Phase and Frequency Modulations Phase Modulation Frequency Modulation Comparing above two equations, we see that if we have a PM signal modulated by m p (t), there is also FM on the signal, corresponding to a different modulation wave shape that is given by: Similarly if we have a FM signal modulated by m f (t), the corresponding phase modulation on this signal is: Where f and p denote frequency and phase respectively.

Integrator Phase Modulator (Carrier Frequency fc) Differentiator Frequency Modulator (Carrier Frequency fc) Generation of FM from PM and vice versa FM Signal PM signal Generation of FM using a Phase Modulator: Generation of PM using a Frequency Modulator:

FM with sinusoidal modulating signal  The Instantaneous Frequency of the FM signal is given by:  The Peak Frequency Deviation is given by:  The Frequency Deviation from the carrier frequency:  The Peak-to-peak Deviation is given by ∆F is related to the peak modulating voltage by Where If a bandpass signal is represented by:

FM with sinusoidal modulating signal But,  VpVp BW   Average Power does not change with modulation

Angle Modulation Advantages:  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  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. Where Spectrum of Angle modulated signal

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 The Complex Envelope is: and The peak frequency deviation would be which is periodic with period

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

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

Bessel Functions of the First Kind

 The FM modulated signal in time domain  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 Observations: Frequency spectrum of FM

Spectra of an FM Signal with Sinusoidal Modulation BTBT f 1.0  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

BTBT J 0 (1.0) J 1 (1.0) J 2 (1.0) f 1.0 Spectra of an FM Signal with Sinusoidal Modulation

BTBT f 1.0 Spectra of an FM Signal with Sinusoidal Modulation

 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. Carson’s rule (1+  f m

Carson’s rule  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

Narrowband Angle Modulation  Narrowband Angle Modulation is a special case of angle modulation where θ(t) is restricted to a small value.  The complex envelope can be approximated by a Taylor's series in which only first two terms are used. becomes  The Narrowband Angle Modulated Signal is  The Spectrum of Narrowband Angle Modulated Signal is where PM FM

Indirect method of generating WBFM Balanced Modulator

Wideband Frequency modulation

FM Stero System

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

 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 0 o or 180 o 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

 The complex envelope is Carrier Cos(2  f c t) Message m(t) OOK output A c m(t)Cos(2  f c t)  The OOK signal is represented by On-Off Keying (OOK)  Also known as Amplitude Shift Keying (ASK)  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

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

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

Carrier:Cos(2  f c t) Message: m(t) BPSK output A c Cos(2  f c t+D p m(t)) -90  Phase shift Binary Phase Shift Keying (BPSK) Message Unipolar Modulation Bipolar Modulation BPSK output m(t) s(t) Generation:

 The BPSK signal is represented by pilot carrier termdata 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  If D p 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 : 2∆θ – maximum peak-to-peak deviation during time T s let 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)

fcfc 2R = 2/T b If D p   /2 Pilot exists Power Spectral Density (PSD) of BPSK: Binary Phase Shift Keying (BPSK)

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

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

Message Unipolar Modulation Bipolar Modulation FSK output (Discontinuous) FSK output (Continuous) Mark(binary 1) frequency: f 1 Space(binary 0) frequency: f 2 m(t)m(t) m(t)m(t) s(t)s(t) s(t)s(t) Frequency Shift Keying (FSK)

Computer FSK modem (Originate) Computer Center FSK modem (Answer) Digital data PSTN Dial up phone line f 1 = 1270Hz f 2 = 1070Hz f 1 = 2225Hz f 2 = 2025Hz FSK modem with 300bps Frequency Shift Keying (FSK)

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