Understanding Angle Modulation: FM and PM Signals, Lab Reports of Computer Science

Download Understanding Angle Modulation: FM and PM Signals and more Lab Reports Computer Science in PDF only on Docsity! Part-I Experiment 6:-Angle Modulation 1. Introduction 1.1 Objective This experiment deals with the basic performance of Angle Modulation - Phase Modulation (PM) and Frequency Modulation (FM). The student will learn the basic differences between the linear modulation methods (AM DSB SSB). Upon completion of the experiment, the student will: * Understand ANGLE modulation concept. * Learn how to generate FM signal. * Learn how to generate PM signal. * Learn how to build FM demodulator. * Get acquainted with Bessel Function. * Understand the difference between the linear and nonlinear modulation. 1.1.1 Prelab Exercise 1.Find the maximum frequency deviation of the following signal; and verify your results in the laboratory. Carrier sinewave frequency 10.7 MHz, amplitude 1 V p-p with frequency deviation constant 10.7 kHz/V ,modulated by sinewave frequency 10 kHz amplitude 1 V p-p . 2. Explain what is Carson’s rule. 3. What is the difference between NBFM and wideband FM refer to the Spectral component of the two. 4. Print a graphwithMatlab or other software of the followingFMsignal: wc = 15MHz,A=5, Am=1, wm=1KHz, Kf=7.5, t=0 to 12 seconds. Show a. Modulation frequency versus time. b. FM signal. c. Differentiated FM signal. d. Differentiated FM signal followed by LPF . 1.1.2 Necessary Background To understand the properties of angle-modulatedwaveforms (FM andPM), you need aworking knowledge of Fourier transform theory. We will also use the Bessel function, but will present the basic theory as it is needed. Finally, the actual systems for modulating and demodulating angle modulated waveforms require a knowledge of linear sys- tems,oscillators and phase-locked loops. 1.1.3 Background Theory An angle modulated signal, also referred to as an exponentially modulated signal, has the form Sm(t) = A cos[wt+ φ(t)] = Re{A exp[jwt+ jφ(t)]} (1) The instantaneous phase of Sm(t) is defined as φi(t) = wt+ φ(t) and the instantaneous frequency of the modulated signal is defined as wi(t) = d dt [wt+ φ(t)] = w + d(φ) dt (2) The functions φ(t) and d(φ)dt are referred to as the instantaneous phase and frequency deviations, respectively. The phase deviation of the carrier φ(t) is related to the baseband message signal s(t). Depending on the nature of the relationship between φ(t) and s(t) we have different forms of angle modulation. In phase modulation, the instantaneous phase deviation of the carrier is linearly proportional to the input message signal, that is, φ(t) = kps(t) (3) where kp is the phase deviation constant (expressed in radians/volt or degrees/volt). For frequency modulated signals, the frequency deviation of the carrier is proportional to the message signal, that is, d(φ) dt = kfs(t) (4) 2 assume s(t) to be sinusoidal then s(t) = Am coswmt (10) then the instantaneous phase deviation of the modulated signal is φ(t) = kfAm wm sinwmt For FM (11) φ(t) = kpAm coswmt For PM (12) The modulated signal, for the FM case, is given by Sm(t) = A cos(wt+ β sinwt) (13) where the parameter β is called the modulation index defined as β = kfAm wm For FM (14) β = kpAm For PM The parameter β is defined only for sinewave modulation and it represents the maximum phase deviation produced by the modulating signal. If we want to compute the spectrum of Sm(t) given in Equation 11, we can express Sm(t) as Sm(t) = Re{A exp(jwt) exp(jβ sinwmt)} (15) In the preceding expression, exp(jβ sinwmt) is periodic with a period Tm = 2πwm . Thus, we can represent it in a Fourier series of the form exp(jβ sinwmt) = ∞X −∞ Cx(nfm) exp(j2πnf) (16) Where Cx(nfm) = wm 2π Z π wM − πwM exp(jβ sinwmt) exp(−jwmt)dt (17) = 1 2π Z π −π exp[j(β sin θ − nθ)]dθ = jn(β) Where jn(β) known as Bessel functions. Combining Equations 14, 15 and 13, we can obtain the following ex- pression for the FM signal with tone modulation: Sm(t) = A ∞X −∞ jn(β) cos[(w + nwm)t] (18) The spectrum of Sm(t) is obtained from the preceding equation. An example is shown in Figure- 3 The spectrum of an FM signal has several important properties: A m pl itu de f c β=0.4 f c+ f m Am pl itu de f c β=2 f c+ f m f c+2 f m f c-3 f m FM spectrum Fig - 3 - : FM spectrum 1. The FM spectrum consists of a carrier component plus an infinite number of sideband components at fre- quencies f ± nfm (n = 1, 2, 3...). But the number of significant sidebands depend primarily on the value of β. In comparison, the spectrum of an AM signal with tone modulation has only three spectral components (at frequencies f , f + fm, and f − fm ). 2. The relative amplitude of the spectral components of an FM signal depend on the values of jn(β). The relative amplitude of the carrier depends on j0(β) and its value depends on the modulating signal (unlike AM modulation where the amplitude of the carrier does not depend on the value of the modulating signal). 5 1.1.6 Power and Bandwidth of FM Signals In the previous section we saw that a tone modulated FM signal has an infinite number of sideband components and hence the FM spectrum seems to have infinite spectrum. Fortunately, it turns out that for any β a large portion of the power is contained in finite bandwidth. . Hence the determination of FM transmission bandwidth depends to the question of how many significant sidebands need to be included for transmission, if the distortion is to be within certain limits. The answer to this question is based on experimental fact that indicates that baseband signal distortion is negligible if 98% or more of the FM signal power is contained within the transmission band. This rule of thumb based on experimental studies, leads to useful approximate relationships between transmission bandwidth, message signal bandwidth, and modulation index. To determine FM transmission bandwidth, let us define a power ratio Sn. as the fraction of the total power contained in the carrier plus n sidebands on each side of the carrier . That is, define Sn to be Sn = 1 2A nP k=−n j2k(β) 1 2A ∞P k=−∞ j2k(β) (19) The denominator of the preceding equation represents the average transmitted power ST . Now the amplitude of an angle modulated waveform is always constant. Therefore, regardless of the message s(t), the average transmitted power is ST = 1 2 A2 = 1 2 A2 ∞X k=−∞ j2k(β) (20) Substituting Equation-18 into 17, we have Sn = nX k=−n j2k(β) To find the transmission bandwidth of the FM signal for a given modulation index β, we have to find the smallest value of n that yields Sn > 0.98. We note that the underlines in Table- 1, which indicate the value of n for which Sn > 0.98, always occur just after n = β + 1. Thus, for tone modulation, the bandwidth of the FM signal is given by BT ≈ 2(β + 1)fm (21) For an arbitrary message s(t), we cannot use the preceding expression to determine BT since β is defined only for tone modulation. For arbitrary message signals bandlimited to fm we can define a deviation ratio D (which is analogous to the modulation index β) as D = peak frequency deviation bandwidth of s(t) = kf max[s(t)] 2πfm = ∆f fm (22) UsingD in place of β in Equation-23 results in the generally accepted expression for bandwidth: BT = 2(D + 1)fm = 2(∆f + fm) (23) Where ∆f = Dfm, is the maximum frequency deviation. The preceding expression for bandwidth is referred to as Carson’s rule, which indicates that the FM bandwidth is twice the sum of the maximum frequency deviation and the bandwidth of the message signal. FM signals are classified into two categories based on the value of D (or β). IfD (or β)¿ 1, the FM signal is called a Narrow Band FM (NBFM) signal and the bandwidth of the NBFM signal is equal to 2fm which is the same as the bandwidth of the AM signal. When D (or β)À 1, the FM signal is called a wideband FM (WBFM) signal and its bandwidth is approximately 2∆f. Narrowband FM is in many ways similar to DSB or AM signals. By way of illustration let us consider the NBFM signal Sm(t) = A cos[wt+ φ(t)] (24) 6 Where φ(t) = kf Z t −∞ s(τ)dτ (25) For NBFM , the maximum value of |φ(t)| is much less than one (another definition for NBFM ) and hence we can write s(t) as Sm(t) = A[cosφ(t) coswt− sinφ(t) sinwt] (26) ≈ A coswt−Aφ(t) sinwt Using the approximations cosφ = 1 and sinφ ≈ φ, when φ is very small. Equation-26 shows that a NBFM signal contains a carrier component and a quadrature carrier linearly modulated by (a function of) the baseband signal. Since s(t) is assumed to be bandlimited to fm therefore φ(t) is also bandlimited to fm,. Hence, the bandwidth of NBFM is 2fm, and the NBFM signal has the same bandwidth as an AM signal. 1.1.7 Narrow Band FM Modulator According to Equation-22, it is possible to generate NBFM using a system such as the one shown in Fig-4 . The signal is integrated prior to modulation and a DSB modulator is used to generate the quadrature component of the NBFM signal. The carrier is added to the quadrature component to generate an approximation to a true NBFM signal. The output of the modulator can be approximated by Sm(t) ≈ A cos[wt+ φ(t)] (27) Integrator DSBModulator + 90 Shift NBFM S(t) φ (t) Aφ( t)sinwt Acoswt NBFM Modulator Fig - 4 - : NBFM modulator Voltage Control Oscillator S(t) Acos[wt+ φ (t)] Wideband FM modulator Fig - 5 - : FM modulator The approximation is good as long as the deviation ratio D = ∆ffm , is very small. 1.1.8 Wide Band FM Modulator There are two basic methods for generating FM signals known as direct and indirect methods. The direct method makes use of a device called voltage controlled oscillator (V CO)whose oscillation frequency depends linearly on the modulation voltage. A system that can be used for generating a PM or FM signal is shown in Figure-5. The combination of message differentiation that drive a V CO produces a PM signal. The physical device that generates the FM signal is the V CO whose output frequency depends directly on the applied control voltage of the message signal. V CO0s are easily implemented up to microwave frequencies using the reflex klystron.. Integrated circuit V CO0s are also used at 7 Fig - 8 - : First Null Am pl itu de fc A m pl itu de Frequency 2∆ f fm Measurement of fm and frequency deviation Fig - 9 - : 5. In that state you tune the system to accurate frequency deviation ∆f = β ∗ fm = 2.4 ∗ fm. now calculate ∆f print the results. 6. Repeat the above procedure for ∆f = 50, 100 kHz and compare your measurement to the specification of the signal generatorHP − 8647A. Another way to approximately measure∆f with spectrum analyzer is to find carrier frequency, then measuring the sideband spacing using a sufficiently small IF filter and then the peak frequency deviation is measured by selecting an IF bandwidth wide enough to cover all major sidebands. 1. Set the IF bandwidth of the spectrum analyzer to 1 kHz and measure the modulation frequency. 2. Set the IF bandwidth of the spectrum analyzer to 100 kHz and measure the frequency deviation (see figure 9) print the results. 1.3.3 FM Spectrum and Bessel Function FM spectrum based on properties of Bessel function. We start to verify FM spectrum according to Equations-7,8 and 9. 1.Set the signal generatorHP−8647A to frequency 10.7MHz , amplitude 0 dBm, externalAC FM modulation, FM-2 kHz. 2. Set the AWG to sinewave frequency 10 kHz, amplitude As necessary to proper external FM modulation (about 530 mv). 3. Set the spectrum analyzer to 10.7MHz, span 200 kHz, bandwidth 1 kHz. 4. The spectrum of the signal look like AM-modulation, set marker on the carrier and two sidebands, print the results. what is the value of β? And what is the bandwidth of the FM signal? Is it narrow or wideband FM ? 5. Change FM deviation to 50 kHz , record the amplitude of every spectral line, pressMOD − OFF on Signal generator and measure the amplitude of the carrier without modulation. 6. Calculate β,and verify Equations-7,8 and 9 with carrier and sidebands what is the bandwidth of the FM signal? Is it narrow or wideband FM ? How many sidebands contains 98% of signal energy? 7. Set the AWG to triangle wave frequency 10 kHz, amplitude As necessary to proper external FM modulation (about 530 mv). 8. Measure and record with spectrum analyzer the highest spectral component of the triangle signal (fm). 9. Connect the AWG to signal generator as indicated in Figure-7- and measure the bandwidth of the modulated signal,print the results and compare them to Carson’s rule 1.3.4 Narrow Band FMModulator In this part of the experiment, we generate NBFM signal, without the first stage- integrator, since our input signal will be the integral of the modulating signal. 1. Connect the Test and Measurement (T&M) equipment according to Fig.-10. 2. Adjust the T&M equipment as follow: AWG LO- Sinewave frequency 10.7 MHz amplitude 7dbm. AWG R- Sinewave frequency 10 kHz amplitude -10dbm.(integral of the cosine input wave). 10 15.000,000 MHz LPF 10.7 MHz NBFM MODULATOR HP-33120A R L I 15.000,000 MHz HP-33120A + 90 Shift NBFM Spectrum analyzer HP-8590 Communication Test Set 1.000Sinad 0 24 Fig - 10 - : 3. Set the spectrum analyzer to 10.7 MHz span 50kHz , watch the FM signal at spectrum analyzer, change the amplitude and frequency of the modulating frequency generator, which component of the FM signal changed? n\β 0 0.1 0.15 0.2 0 0.00(Ref.) 0.00(Ref.) 0.00(Ref) 0.00(Ref.) 1 -∞ -26.0(dB) -22.5(dB) -19.95(dB) Table-3 Small β logarithmic values for NBFM 4. Change the amplitude and frequency of the local oscillator , which component of the FM signal changed? 5. According to table-3 set the system toNBFM β = 0.1, calculate the frequency deviation and print the results. 6. Calculate the proper DC voltage that cause the same frequency deviation. 7. Verify your results by setting the AWG to the calculated DC voltage and measure on spectrum analyzer the frequency difference of the signal, with and without DC signal. 1.3.5 Power and Bandwidth of FM Signal Set the spectrum to single sweep and make the measurement of the above signal as follow 1. Measure the power of each component of the FM above signal (signal with null carrier), measure the total bandwidth of the FM signal (signal with all the sidebands). 2. According to the criterion of 98% power calculate the power of the FM signal and the bandwidth of the signal. 3. what is the difference in percent between the measured and calculated power and bandwidth? 1.3.6 IF Filter as FM Discriminator In this part of the experiment you demodulate FM signal using the linear region of the IF filter of the spectrum analyzer as frequency discriminator. You have to choose If bandwidth and video bandwidth wide enough to pass all sidebands of the signal, but with proper slope so the amplitude of the demodulated signal will be measurable. 1. Connect the AWG directly to spectrum analyzer as shown in figure-11. 15.000,000 MHz FM Discriminator HP-33120A Spectrum analyzer HP-8590 Fig - 11 - : 2. Set the AWG to frequency 10.7 MHz, amplitude 0 dBm, FM modulation frequency 1 kHz, deviation 4 kHz. 3. Set the spectrum analyzer to Center frequency 10.7 MHz, Span 100 kHz, Bandwidth as necessary to pass all the signal B = 2 ∗ (∆f + fm), Amplitude linear (why) ? 4. Place the signal near the top of the screen and in the center of the screen. 5. Set the span to 0 kHz, and sweeptime to 20 ms, you see the time domain of modulation frequency near the top of the screen. 11 6. Change slightly clockwise the center frequency (center frequency>10 MHz) until you see in the middle of the screen sinewave demodulated by the negative slope of the IF filter, change the sweep to single sweep and measure the frequency of the signal. 7. Change slightly counterclockwise the center frequency (center frequency<10 MHz)until you see on the middle of the screen sinewave demodulated by the positive slope of the IF filter, change the sweep to single sweep andmeasure the frequency of the signal, print the results. 12