Fatih University Electrical and Electronics Engineering Department EEE Communications I EXPERIMENT 5 FM MODULATORS

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1 Fatih University Eletrial and Eletronis Engineering epartent EEE 36 - Couniations I EXPERIMENT 5 FM MOULATORS 5. OBJECTIVES. Studying the operation and harateristis of a varator diode.. Understanding the operation of voltage-ontrolled osillator in frequeny odulators. 3. Ipleenting a frequeny odulator with a varator diode and a voltage-ontrolled osillator (MC648). 5. PRELIMINARY WORK Read hapter 5 in the textbook. 5.3 EQUIPMENT AN MATERIALS The equipent list that will be used in this experient is shown in Table 5.. Before starting the experient, reord the odel, serial nuber and offie stok nuber of the equipent that will be used throughout the experient. Also, reord any daages. Table 5. Equipent list for experient 5. Ite No Equipent Model Serial No Offie Stok No igital Osillosope (O) Funtion Generator () 3 Funtion Generator () 4 C Power Supply 5 Conneting Probes and Cables 6 MC648 FM Modulator Unit Reord of daages or other oents: 5.4 THEORY Frequeny odulation (FM) is a proess in whih the arrier frequeny is varied by the aplitude of the odulating signal (i.e., intelligene signal). The FM signal an be expressed by the following equation. x FM [ ] ( t) A t + K x( t) = os dt (5.) EEE 36 - Couniations I Experient 5 Page of 8

2 where, x ( t) A os t = (5.) is the unodulated arrier, and ( t) x is the odulating signal. The instantaneous frequeny of the FM signal an be obtained by taking the derivative of the angle of os funtion in Eq. (5.). The result is [ dt] = + Kx( t) d ( t) = t + K x( t) dt. (5.3) Hene, the instantaneous frequeny of the FM signal is hanging in proportional with the odulating x t, K being the proportionality onstant. signal ( ) When the odulating signal is a pure sinusoid with the peak value x ( t) A os t, A and frequeny, i.e., = (5.4) the FM signal and the instantaneous frequeny an be found by using Eqs. (5.), (5.3), and (5.4). as follows: x FM KA (5.5) = + KA os (5.6) ( t) = A os t + sin t, ( t) t The frequeny deviation is obtained fro Eq. (5.6) to be = KA (5.7) Hene, the instantaneous frequeny varies in [ + ] +]. The deviation ratio β of an FM signal is defined as, sine os t varies between [-, B β = (5.8) where, is the frequeny deviation and is the highest frequeny oponent of the intelligene. Using Eqs. (5.7) and (5.8), the relation between the odulation onstant K and the deviation ratio β is found to be KA β β or K = A 5.4. Varator iode =, (5.9) The varator diode soeties alled the tuning diode is the diode whose apaitane is proportional to the aount of the reverse bias voltage aross the p-n juntion. Inreasing the reverse bias voltage applied aross the diode dereases the apaitane sine the depletion EEE 36 - Couniations I Experient 5 Page of 8

3 region width beoes wider. Conversely, when the reverse bias voltage is dereased, the depletion region width beoes narrower and the apaitane is inreased. When an AC voltage is applied aross the diode, the apaitane varies with the hange of the AC voltage. A d Figure 5. Relationship between a varator diode and a parallel plate apaitor. A relationship between a varator and a onventional apaitor is shown in Figure 5.. In fat, a reverse-biased varator diode is siilar to a apaitor. When p and n juntions are obined together, a sall depletion region is fored beause of the diffusion of inority arriers. The positive and negative harges oupy n and p sides of the juntion, respetively. This is just like a apaitor. The aount of the internal apaitane of the diode an be alulated by the apaitane forula εa C =, (5.) d where, ε =.8ε = dieletri onstant, ε = 8.85 x F/, A = Cross setional area of the apaitor, d = The width of the depletion region. Aording to the above forula, the varator apaitane is inversely proportional to the width of the depletion region (or the distane between plates) if the area A is onstant. Therefore, a sall reverse voltage will produe a sall depletion and a large apaitane. Conversely, an inrease in reverse bias will result in a large depletion region and a sall apaitane. C R Figure 5. Equivalent iruit of a varator diode. EEE 36 - Couniations I Experient 5 Page 3 of 8

4 A varator diode an be onsidered as a apaitor and resistor onneted in series as shown in Figure 5.. C is the juntion apaitane between p and n juntions. R is the su of bulk resistane and ontat resistane, approxiately several ohs, whih is an iportant paraeter deterining the quality of a varator diode. Tuning ratio (TR) is defined as the ratio of the apaitane of varator diode at the reverse voltage V to another reverse voltage V, and an be expressed as C, V TR = (5.) C, V where TR = Tuning ratio, C,V = Capaitane of varator diode at V, C,V = Capaitane of varator diode at V. TR is usually expressed as a nuber greater than, hene C, V > C, V whih iplies that V < V. SV55 varator diode is used in our experient and its ajor harateristis are C, 3 V = 4 pf (apaitane of varator diode at 3V), TR =.65 (at 3V~3V) Frequeny Modulator Based on MC648 VCO In this experient the frequeny odulator is ipleented with MC648 VCO hip as shown in Figure 5.3. Basially, this iruit is an osillator, and the tuning iruit at the input end deterines its osillating frequeny. In this iruit, apaitors C and C 3 are the bypass apaitors for filtering noise. When operating at a high frequeny (for exaple.4 MHz), the apaitane reatane of these two apaitors are very sall and an be negleted in the LC loop fored by C 3, L,, C for pratial purposes. This akes possible to assue be in parallel with L. Therefore, the AC equivalent iruit is a tuning tank whih onsists of a parallel LC resonant iruit as shown in Figure 5.4. C an be onsidered as the su of the apaitane of SV55 ( C ) and the input apaitane of MC648 ( C ) onneted in parallel, i.e., C = C + Cin. The value of C in is approxiately 6 pf. If the stray apaitane is negleted, the osillating frequeny an be alulated by the forula in f = π LC = π ( + 6x ) L C (Hz) (5.) EEE 36 - Couniations I Experient 5 Page 4 of 8

5 Figure 5.3 MC648 FM odulator iruit. As entioned above, the apaitane C of the varator diode varies with the aount of its reverse voltage. It is known that the hange of C will ause the hange of osillating frequeny. In the iruit of Figure 5.3, a sall C bias will produe a large C and a low frequeny output. On the other hand, an inrease in C bias will result in a sall C and a high frequeny output. Therefore, if the C bias is fixed and an audio signal is applied to the audio input to hange the bias voltage around the fixed value, the VCO output signal will be a frequeny-odulated signal of the audio input. Figure 5.4 AC equivalent iruit of the tuning tank. 5.5 EXPERIMENTAL PROCEURE AN RESULTS Note: When using digital osillosope (O), reord the ritial data related with any observation on O, for exaple C level, peak values, period and frequeny for different regions; then draw the wavefor based on this data on sale. The ritial data should appear just below the assoiated figure. You an take the O display by holding and taking it in storage. EEE 36 - Couniations I Experient 5 Page 5 of 8

6 5.5. Charateristi Measureents on MC648. Take MC648 FM Modulator Unit supplied at your experient table and onnet +5 V supply voltage to it. Use the swith SW to set the indutor L to µ H.. Connet V C bias input and observe the output wavefor by using the osillosope. Adjust R v until a sine wave appears at the output. Reord the frequeny in Table Repeat the above step for all the C bias input voltages shown in Table 5.. Table 5. Change of the free osillation frequeny of MC648 VCO with the bias voltage. C Bias input (V) Output frequeny f MHz. (experiental) Frequeny Modulation by MC648 FM Modulator Unit. Repeat the first step of setion Connet a 5 V C bias input and observe the output wavefor using the seond hannel of O. Adjust R until a sine wave appears at the output. Reord the v unodulated arrier frequeny f and the pp value of the output on the legend of Table Connet 3 khz. sine wave to the audio input and adjust its aplitude to V pp by using the first hannel of O. Plot this input on Table 5.3 at the appropriate plae on sale. Indiate the frequeny and the peak value expliitly. 4. With the above input still onneted, observe and plot the FM output signal observed on hannel-ii. Plot this wavefor on Table 5.3 at the appropriate plae on sale. Measure and reord the pp value and the axiu and iniu frequenies of the FM output signal. Use the hold and eory ontrol of O. 5. Observe the spetru of the FM signal output on the spetru analyzer. Reord the frequeny and aplitude of eah oponent in Table Repeat steps 3-5 for 5 khz and 8 khz audio frequenies. EEE 36 - Couniations I Experient 5 Page 6 of 8

7 Audio input frequeny f (khz) Table 5.3 The input intelligene and FM Output signals of the MC648 FM Modulator Audio input:.5 V pp ; Unodulated arrier: V pp, f =..khz. Audio wavefor (Intelligene or essage signal) FM output signal (FM odulated arrier) Spetru of FM signal Freq. Ap. 3 peak value: f =, f = in o ax Freq. Ap. 5 peak value: f =, f = in o ax Freq. Ap. 8 peak value: f =, f = in o ax EEE 36 - Couniations I Experient 5 Page 7 of 8

8 5.6 RESULTS AN ISCUSSIONS. Using the experiental results in Table 5., plot the frequeny versus voltage urve in Figure 5.6. f C bias voltage (V) Figure 5.6 Variation of the osillation frequeny of the VCO MC 648 shown in Fig. 5.3 with the C bias voltage; L = µ H.. For eah of the input signal frequenies f = 3, 5, 8 khz. appearing in Table 5.3, opute the approxiate frequeny deviations by the forula f f ax f in = (5.3) and find the deviation ratio using Eq. (5.8). Enter the results in Table 5.4. Coent on the results. Table 5.4 Change of the deviation ratio in FM by MC648. Audio input frequeny f (khz.) Frequeny deviation f (khz.) eviation ratio β = f / f EEE 36 - Couniations I Experient 5 Page 8 of 8