Thông tin thiết kế mạch P4

FREQUENCY MODULATED RADIO TRANSMITTERIn Chapter 2, the amplitude of a high-frequency (carrier) sinusoidal signal was varied in accordance with the waveform of an audio-frequency (modulating) signal to give an amplitude modulated (AM) wave which could be transmitted, received, and demodulated to recover the original audio frequency signal. In frequency modulated (FM) radio, the frequency of the carrier is varied about a fixed value in accordance with the amplitude of the audio frequency.
Nội dung trích xuất từ tài liệu:
Thông tin thiết kế mạch P4 Telecommunication Circuit Design, Second Edition. Patrick D. van der Puije Copyright # 2002 John Wiley & Sons, Inc. ISBNs: 0-471-41542-1 (Hardback); 0-471-22153-8 (Electronic) 4 FREQUENCY MODULATED RADIO TRANSMITTER4.1 INTRODUCTIONIn Chapter 2, the amplitude of a high-frequency (carrier) sinusoidal signal was variedin accordance with the waveform of an audio-frequency (modulating) signal to givean amplitude modulated (AM) wave which could be transmitted, received, anddemodulated to recover the original audio frequency signal. In frequency modulated (FM) radio, the frequency of the carrier is varied about afixed value in accordance with the amplitude of the audio frequency. The amplitudeof the carrier is kept constant. The waveform of a sinusoidal carrier modulated by asaw-tooth wave is shown in Figure 4.1. All signals carried on any transmission system will sooner or later be contami-nated by noise so the susceptibility of the communication system to noise is animportant consideration. The noise can be defined as a random variation super-imposed on the signal. In AM systems, the information to be transmitted iscontained in the envelope of the carrier signal. The noise therefore appears on theenvelope and has a direct role in corrupting the signal. In FM systems theinformation to be transmitted is contained in the variation of the frequency of thecarrier about a pre-set value. The amplitude of the FM signal is kept constant and,indeed, if there are changes in the amplitude of the FM signal, they are removed byclipping before demodulation. By comparison, FM systems are less susceptible todegradation by noise.4.2 FREQUENCY MODULATION THEORYWhile a saw-tooth modulating signal provides a simple picture of the FM signal, asinusoidal modulating signal is the simplest for the derivation of the mathematicalexpressions to describe the FM signal. 111112 FREQUENCY MODULATED RADIO TRANSMITTERFigure 4.1. The sawtooth waveform vs frequency modulates a carrier to give the output vfm .Note that the relative change in frequency has been exaggerated for clarity. In normal FM radio,the change in frequency relative to the carrier is less than 0.15% A sinusoidal voltage can be expressed as: v ¼ A sin ot ð4:2:1Þ v ¼ A sin yðtÞ ð4:2:2Þwhere o is a constant representing the angular velocity of the sinusoid and y is aphase angle with respect to an arbitrary datum. In general, the relationship betweenthe phase angle and the angular velocity is given by dyðtÞ ¼ oðtÞ: ð4:2:3Þ dtIn a frequency modulated system, o is varied about a fixed value oc , in accordancewith the modulating signal which is assumed in this case also to be a sinusoid: vs ¼ B cos os t: ð4:2:4ÞThe instantaneous angular velocity oi ¼ oc þ Doc cos os t ð4:2:5Þwhere oc is the long-term mean angular velocity, Do ( o, and Doc is themaximum deviation of the angular velocity about oc . 4.2 FREQUENCY MODULATION THEORY 113 Substituting instantaneous values into Equation (4.2.3) dyi ðtÞ oi ðtÞ ¼ : ð4:2:6Þ dtSubstituting Equation (4.2.5) into Equation (4.2.6) and integrating ðt ðt yi ðtÞ ¼ f þ oc dt þ Doc cos os tdt ð4:2:7Þ 0 0where f is the initial value of the phase angle which without loss of generality canbe set equal to zero. Then substituting Equation (4.2.7) into Equation (4.2.2) gives koc vfm ðtÞ ¼ A sinðoc t þ sin os tÞ ð4:2:8Þ oswhere kDoc ¼ B, the amplitude of the modulating signal. The term koc =os is called the modulation index, where max: frequency deviation of the carrier mf ¼ ð4:3:9Þ modulating signal frequency vfm ðtÞ ¼ A sinðoc t þ mf sin os tÞ: ð4:2:10ÞExpanding, vfm ðtÞ ¼ A½sin oc t cosðmf sin os tÞ þ cos oc t sinðmf sin os tފ: ð4:2:11ÞThe terms cosðmf sin os tÞ and sinðmf sin os tÞ can be expanded in the form of Fourierseries with coefficients which are Bessel functions of the first kind Jn ðmf Þ where n isthe order and mf is the argument, to give P cosðmf sin os tÞ ¼ J0 ðmf Þ þ 2 J2n ðmf Þ cos 2nos t ð4:2:12Þand P sinðmf cos os tÞ ¼ 2 J2nþ1 ðmf Þ sinð2n þ 1Þos t: ð4:2:13ÞSubstituting Equations (4.2.12) and (4.2.13) into Equation (4.2.11) and using cos x sin y ¼ 1 ½cosðx þ yÞ þ cosðx À yފ ...