Chapter 5. Angle Modulation Husheng Li The University of Tennessee Phase and Frequency Modulation Consider the standard CW signal We define the total instantaneous angle Phase and Frequency Modulation Phase modulation (PM) Frequency modulation (FM) Characteristics of Angle Modulation The amplitude of an angle modulated wave is constant. The message resides in the zero crossings alone, providing the carrier frequency is large. The modulated wave does not resemble the message waveform. Narrowband PM and FM We can expand the signal (using Taylor’s expansion) The spectrum is given by Hence, the signal has a bandwidth of 2W. Example of Narrow Band Angle Modulation Both PM and FM have carrier component. Tone Modulation We can allow a 90 degree difference in the modulating tones: Βis called the modulation index for PM or FM with tone modulation. Spectrum of Narrowband Tone Modulation When the modulation index is very small, we have The spectrum is given by Spectrum of Arbitrary Modulation Index For a single tone signal with arbitrary modulation index, the modulated signal can be written as where j_n(β) is the Bessel function. Bessel Functions Characteristic of FM Spectrum Homework 5 Deadline Oct. 14, 2013 Spectrum with Different Modulation Indices We can either fix fmor fix Am fD Multi-tone Consider the case of multiple tones, e.g., x(t) = A1 cosw1t + A2 cosw2t The modulated signal can be written as Periodic Modulation When the signal is periodic, the Fourier series are given by The modulated signal can be written as Transmission Bandwidth The generation and transmission of pure FM requires infinite bandwidth. Hence, our questions is: how much of the modulated signal spectrum is significant? The Bessel function falls off rapidly for n / b >1 There are M significant sideband pairs and 2M+1 significant lines all told. The bandwidth can be given by Illustration Arbitrary Modulated Signal Bandwidth For arbitrary modulating signal, the required bandwidth is given by (deviation ratio) An approximation: Carson’s rule Case of Phase Modulation We can also define the phase deviation. We have Linear Distortion We consider an angle-modulated bandpass signal applied to a linear system: The lowpass equivalent output spectrum is Nonlinear Distortion The output of signal through a nonlinear system is given by Example: Clipper A clipper has only two outputs The output signal is given by Procedure of Clipper Direct FM In direct FM, we use VCO to generate the frequency modulated by the signal. Phase Modulator Although we seldom transmit a PM wave, we are still interested in phase modulators because (1) the implementation is relatively easy; (2) the carrier can be supplied by a stable frequency source; (3) integrating the input signal to a phase modulator produces an FM output. Switching-circuit Modulator Larger phase shifts can be achieved by the switching-circuit modulator: Indirect FM Transmitter The integrator and phase modulator constitute a narrowband frequency modulator that generates an initial NBFM signal with instantaneous frequency: Triangular-Wave FM Triangular-wave FM is a modern and rather novel method for frequency modulation that overcomes the inherent problems of conventional CVOs and indirect FM systems. Frequency Detection A frequency detector, often called a discriminator, produces an output voltage that should vary linearly with the instantaneous frequency of the input. Almost every circuit falls into one of the following four categories: FM-to-AM conversion Phase-shift discrimination Zero-crossing detection Frequency feedback FM-to-AM Conversion Any device of circuit whose output equals the time derivative of the input produces FM-to-AM conversion: PHASE-SHIFT Discriminators Phase-shift discriminators involve circuits with linear phase response, in contrast to the linear amplitude response for slope detection: Quadrature Detector A phase-shift discriminator built with a network having group delay and carrier delay: Zero Crossing Detector Interference Interference refers to the contamination of an information-bearing signal by another similar signal, usually from a human source. Interfering sinusoids: consider a receiver tuned to some carrier frequency. The total received signal is Demodulated Output Consider a weak interference. The demodulated output is Deemphasis The fact that detected FM interference is most severe at large values of |f_i| suggests a method for improving system performance with selective postdetection filtering, called deemphasis filtering.