Lecture 6 and Demodulation
Agenda Introduction to and Demodulation Frequency and Phase Modulation Angle Demodulation FM Applications
Introduction The other two parameters (frequency and phase) of the carrier sinusoid can be varied by the message signal m(t) We will start by discussing the Frequency Modulation (FM) Previously, it was thought that the bandwidth required by the FM is less than the one needed by the AM bandwidth However, the bandwidth at FM is greater with several times than that of AM
Introduction While AM signals carry a message with their varying amplitude, FM signals can vary instantaneous frequency in proportion to the modulating signal m(t) The carrier frequency is changing continuously every instant Instantaneous frequency Consider a general sinusoid Conventional sinusoid
Introduction The relation between the instantaneous angular frequency and the generalized angle Now, at transmitting the information of m(t), the angle of the carrier varies (Phase Modulation or PM)
Introduction The resulting PM wave In PM, the instantaneous angular frequency is given by The instantaneous angular frequency varies linearly with the derivative of the modulating signal (FM) In FM, the instantaneous angular frequency is
Introduction The angle is now From The FM wave is
Introduction
Introduction In both PM and FM, the angle of the carrier is varied in proportion to some measure of m(t) In PM, it is directly proportional to m(t) In FM, it is proportional to the integral of m(t) As shown in the figure in the previous slide, A frequency modulator can be directly used to generate an FM signal or the message m(t) can be processed by a differentiator to generate PM signals
Introduction The generalized angle-modulated carrier can be The message m(t) can be recovered from by passing it through a system with transfer function
Bandwidth of Angle-Modulated Waves Unlike AM, angle modulation is nonlinear and no properties if Fourier transform can be directly applied for its bandwidth analysis To determine the bandwidth of an FM wave and define
Bandwidth of Angle-Modulated Waves Such that its relationship to the FM signal is Expanding the exponential series yields in power and
Bandwidth of Angle-Modulated Waves The modulated wave consists of an unmodulated carrier plus various amplitude-modulated terms The signal a(t) is an integral of m(t) If M(f) is bandlimited to B, A(f) is also bandlimited to B Integration is a linear operation equivalent to passing a signal through a transfer function The spectrum of is bandlimited to nb
Bandwidth of Angle-Modulated Waves Although the bandwidth of an FM wave is theoretically infinite, for practical signals with bounded will remain finite
Narrowband Approximation Unlike AM, angle modulations are nonlinear When Then, the equation becomes
Narrowband Approximation This approximation is a linear modulation that has an expression similar to that of the AM signal with message signal a(t) Because the bandwidth of a(t) is B Hz, the bandwidth of is 2B Hz according to the frequency-shifting property due to the term For this case, the FM signal at the case of is called narrowband FM (NBFM)
Wideband FM (WBFM) Bandwidth Analysis Note that an FM signal is meaningful only if its frequency deviation is large enough In other words, practical FM chooses the constant large enough that the condition is not satisfied At this case, we have Wideband FM (WBFM) The maximum and minimum carrier frequencies are
Wideband FM (WBFM) Bandwidth Analysis The peak frequency deviation from the carrier frequency The estimated FM bandwidth This estimated bandwidth is calculated based on the staircase approximation of m(t) This bandwidth is somewhat higher that the actual value
Wideband FM (WBFM) Bandwidth Analysis Better FM bandwidth approximation is between In case of very small is very small that we have NBFM So, However, we showed previously that for NBFM, the FM bandwidth is approximately 2B Hz
Wideband FM (WBFM) Bandwidth Analysis So, better estimate for bandwidth of FM In case We define a deviation ratio The bandwidth of FM β is called modulation index
Phase Modulation All results derived for FM can be directly applied to PM The instantaneous frequency The peak frequency deviation
Phase Modulation If we assume Then
Notes In FM, Depends only on the peak of m(t) not the spectrum of m(t) In PM, Depends on the peak of However, depends strongly on the spectral composition of m(t) PM depends on the spectral shape of m(t) [not in FM] So, for m(t) spectrum concentrated at lower frequencies, bandwidth of PM will be smaller than the one at case of m(t) spectrum concentrated at higher frequencies
Generating FM Waves There are two ways of generating FM waves Indirect Narrowband FM generator Direct Voltage-controlled oscillator
Narrowband FM (NBFM) Generation Indirect FM generators are used for generating wideband angle modulation signals For NBFM and NBPM signals In case of and the modulated signals can be approximated by Both approximations are linear and similar to the expression of the AM wave
NBFM Generation The equations Possible methods of generating narrowband FM and PM signals by using DSB-SC modulators
NBFM Generation Because the approximation in The NBFM generated by has some distortion and amplitude variations
NBFM Generation A nonlinear device designed to limit the amplitude of a bandpass signal can remove most of the distortion Bandpass Limiter The amplitude variations of an angle-modulated carrier can be eliminated by what is known as a bandpass limiter, consists of a hard limiter followed by a bandpass filter
NBFM Generation Bandpass Limiter The input output characteristic of a hard limiter is shown The limiter output will be a square wave of unit amplitude regardless of the incoming sinusoidal amplitude
NBFM Generation Angle-modulated sinusoidal input Results in a constant amplitude angle-modulated square wave
Indirect Method of Armstrong In this method, NBFM is generated as shown Then converted to WBFM by using additional frequency multipliers
Indirect Method of Armstrong A frequency multiplier can be realized by a nonlinear device followed by a bandpass filter For a nonlinear device with output y(t) and input x(t) If an FM signal passes through the device, the output signal will be
Indirect Method of Armstrong Simplified commercial FM transmitter using Armstrong s method
Direct Generation In a voltage-controlled oscillator (VCO), the frequency is controlled by an external voltage The oscillation frequency varies linearly with the control voltage An FM wave by using the modulating signal m(t), as a control signal, can be generated VCO can be built by varying one of the reactive parameters (C or L) of the resonant circuit
Features of The transmission bandwidth of AM systems cannot be changed In angle modulation, the transmission bandwidth can be adjusted by adjusting f AM systems do not have the feature of exchanging signal power for transmission bandwidth For angle-modulated systems, the SNR is roughly proportional to the square of the transmission bandwidth
Demodulation of FM Signals The information in an FM signal resides in the instantaneous frequency Frequency-selective network with a transfer function of the form Over the FM band would yield an output proportional to the instantaneous frequency Angle Demodulation
Demodulation of FM Signals FM demodulator frequency response Output of the differentiator to the input FM wave Angle Demodulation
Demodulation of FM Signals FM demodulation by direct differentiation. Ideal differentiator with transfer function is j2πf The output if we apply differentiator to the ideal
Demodulation of FM Signals Both the amplitude and the frequency of the signal are modulated Because, we have for all t Then, m(t) can be obtained by envelope detection The amplitude A of the carrier should be constant Channel noise and fading cause A to vary
Demodulation of FM Signals Practical Frequency Demodulators The differentiator is only one way to convert frequency variation of FM signals into amplitude variation [envelope detectors] Another method for detection using Operational amplifier differentiator The role of the differentiator can be replaced by any linear system (frequency response contains a linear segment of positive slope) [slope detection]
Demodulation of FM Signals Practical Frequency Demodulators One simple device for FM demodulation is an RC highpass filter The RC frequency response If the parameter RC << that The RC filter approximates a differentiator
Demodulation of FM Signals FM Demodulation via Phase Locked Loop (PLL) Voltage Controlled Oscillator Angle Demodulation
Demodulation of FM Signals FM Demodulation via Phase Locked Loop (PLL) Consider a PLL with input signal and output error signal When the input signal is an FM signal The loop filter output signal If the incoming signal is a PM wave, then Angle Demodulation
Effects of Nonlinear Distortion and Interference Immunity of to Nonlinearities Very useful feature of angle modulation is its constant amplitude, which makes it less susceptible to nonlinearities Amplifier with second order nonlinear distortion Clearly, the first term is the desired signal amplification term, the remaining terms are the unwanted nonlinear distortion
Effects of Nonlinear Distortion and Interference Immunity of to Nonlinearities For the angle modulated signal The nonideal system output A bandpass filter centered at with bandwidth equaling to can extract the desired FM signal component without any distortion For a DSB-SC signal passes through a nonlinearity, the output is
Effects of Nonlinear Distortion and Interference Interference Effect Angle modulation is also less vulnerable than AM to smallsignal interference from adjacent channels Let us consider the interference of an unmodulated carrier with another sinusoid The received signal where
Effects of Nonlinear Distortion and Interference Interference Effect When the interfering signal is small in comparison to the carrier then The output The interference output is inversely proportional to the carrier amplitude A The larger A, the smaller interference effect in FM
Effects of Nonlinear Distortion and Interference Interference due to Channel Noise The channel noise acts as interference in an anglemodulated signal We will consider the most common form of noise, white noise, which has a constant power spectral density Such noise may be considered as a sum of sinusoids of all frequencies in the band All components have the same amplitudes (uniform density) This means that the interference I is constant for all frequencies
Effects of Nonlinear Distortion and Interference Interference due to Channel Noise The amplitude spectrum of the interference at the receiver output is shown Effect of interference in PM, FM, and FM with preemphasis-deemphasis (PDE)
Effects of Nonlinear Distortion and Interference Interference due to Channel Noise Preemphasis and Deemphasis in FM Broadcasting In FM, interference increases linearly with frequency The noise power in the receiver output is concentrated at higher frequencies To consider this issue At the transmitter, the weaker high frequency components are boosted before modulation At the receiver, attenuating the higher frequency components
Effects of Nonlinear Distortion and Interference Interference due to Channel Noise Preemphasis and Deemphasis in FM Broadcasting
Effects of Nonlinear Distortion and Interference Interference due to Channel Noise Preemphasis and Deemphasis Filters Assignment Prepare a report about those filters discussing their comprising components and their works
Superheterodyne Analog AM/FM Receivers The radio receiver used in broadcast AM and FM systems is called superheterodyne receiver
Superheterodyne Analog AM/FM Receivers It consists of an RF (radio-frequency) section Tunable filter and an amplifier a frequency converter or mixer Translates the carrier from to a fixed IF frequency An intermediate-frequency (IF) amplifier An envelope detector An audio amplifier
Superheterodyne Analog AM/FM Receivers The importance of the superheterodyne receiver Used in radio and television broadcasting Adequate selectivity of frequencies Accommodate many carrier frequencies
FM Broadcasting System FM Transmitter The FCC has assigned a frequency range of 88 to 108 MHz for FM broadcasting with a separation of 200 KHz between adjacent stations
FM Broadcasting System Spectrum of a baseband stereo signal
FM Broadcasting System FM Stereo Receiver
Lecture Summary Covered material Introduction to and Demodulation Frequency and Phase Modulation Angle Demodulation FM Applications Material to be covered next lecture Performance Study of in the Existence of Noise