EE 255 ELECTRONICS I LABORATORY EXPERIMENT 1 RESONANT CIRCUITS

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1 EE 255 EETNIS I ABATY EXPEIMENT 1 ESNANT IUITS BJETIVES In this exeriment yu will earn hw resnant circuits can be used t make bandass and band-reject filters. Gain exerience in measuring the frequency resnse f a simle netwrk. Becme familiar with the labratry layut and equiment. INTDUTIN Befre rceeding with the electrnics exeriments, we will briefly exlre simle series- and arallel-resnant circuits. As yu knw, resnance is an imrtant henmenn in many fields. esnant circuits are used extensively in cmmunicatin and wireless circuits, energy and wer electrnics circuits, audi and vide equiment, and ther circuits. ead thrugh this exeriment befre class and reare as much as yu can befre yur lab sessin. This will make things g quickly and smthly. Yu may als want t refer t yur circuits textbk. This material is nt in the 253 text. INTEPETING INDUT SPEIFIATINS Figure 1 shws tw simle mdels fr a ractical inductr. The mdel in Fig. 1(a) is used feries-resnant cases, while the mdel in Fig. 1(b) is used fr arallel-resnant cases. (a) (b) Fig. 1. Tw ways f mdeling a ractical inductr.

2 esistances r and s reresent the lsses in a real inductr (cil). Nte that the value is nt the same as the dc resistance f cil. The questin nw is hw can we btain these resistance values frm the manufacturers data. The inductr we will use in this exeriment has the fllwing secificatins: Inductance Qmin Test Freq. Min. SF Max. D es. Max. D urrent 220µΗ 10% MHz 9 MHz 21 Ω 52 ma In this case, we have a cil with an inductance f 220µ H with 10% tlerance. When measured at a test frequency f 790 khz, the cil Q is guaranteed t be at least 30. This means that if the cil is resnated at 790 khz with an ideal caacitr, it will exhibit an effective quality factr f Q c > 30. Due t the distributed caacitance f the winding, the cil will exhibit a self-resnance int at f = 9 MHz. We usually want t use the inductr at a frequency << this self-resnant frequency (SF). The maximum dc resistance is 21 hms and any dc current flwing thrugh the inductr must be limited t 52 ma. We can btain the value f by nting that the cil Q is defined as Q c = ω/ s that = ω/q c If Q c is high, it can be shwn by equating the tw netwrks f Fig. 1 that arximated as can be = r s Q 2 c = ωq c Thus, given the test frequency in the data sheet, we can calculate estimates f lss resistances and. EXPEIMENT 1. Using the equatins given abve, calculate the values f r and s inductr. fr the 220µ H 2. The series-resnant circuit in Fig. 2 is cnfigured t erfrm a bandass functin. That is, at resnance, the reactance f will cancel the reactance f, leaving nly a resistive circuit. This will rvide maximum culing at f. alculate the caacitance needed fr a resnant frequency f f 400 khz.

3 = 100 Ω () V t Fig. 2. A simle bandass filter. 3. alculate the laded Q f the circuit at f : Q = ω ο / where is the effective series resistance in the circuit. 4. alculate the bandwidth f the filter: BW = f /Q 5. Using a breadbard and arts in the lab, cnstruct the circuit f Fig. 2. Yu may have t use a cmbinatin f caacitrs t get the required value f. 6. Set the signal generatr utut t abut 1 vlt eak-t-eak. With the yur scillsce rbe cnnected t the utut, adjust the signal frequency t find the center (resnant) frequency f. Nte this value. Adjust the signal amlitude fr full scale (8 divisins) n the sce at the circuit utut, then vary the frequency abve and belw f t btain the 3dB (i.e., the 0.707) ints. Hw des yur measured center frequency and bandwidth cmare with thse calculated abve? What factrs culd have cntributed t the differences? 7. Next, recnfigure the circuit t make a band-reject filter f Fig. 3. Set the signal frequency at least 20 times greater r 20 times less than f and set the amlitude f the circuit s utut t full scale n the sce. Vary the frequency t determine the center (resnant) int. Nw, vary the frequency abve and belw f, taking amlitude data. Plt a sketch f amlitude vs frequency. Determine the bandwidth f this filter.

4 1 =100 V () t Fig. 3. A simle band - reject filter. 8. Next, we will cnstruct a bandass filter using a arallel-resnant circuit as shwn in Fig. 4. Use the same and values. alculate the required circuit Q fr a bandwidth f 50 khz: Q = f /BW alculate the required arallel resistance t btain this Q: = ω Q What value is needed fr 1 t btain this equivalent? (Hint: What is the equatin fr when Nrtn s therem is alied t the surce?) 9. nstruct the circuit and determine the center (resnant) frequency and 3dB ints. Hw d these measured frequencies cmare with yur desired design frequencies? What wuld haen if yu interchanged the arallel resnant circuit and 1? 1 V () t Fig. 4. A arallel-resnant circuit cnfigured as a bandass filter.

5 MMENTAY Generally seaking, yu will use series resnant circuits in lw-imedance circuits and arallel resnant circuits in high-imedance circuits. This will make it ssible t btain a reasnable circuit Q and BW. The series-resnant circuit in Fig. 5(a) erfrms a bandass functin in the lw-imedance inut circuit f a cmmnbase amlifier. The high-imedance inut f the JFET amlifier f Fig. 5(b) revents lading f the arallel resnant bandass filter. If this filter had been cnnected t the inut f a BJT, the effective resistance wuld have been lwered, and the circuit Q wuld be lw. This wuld result in a very brad bandwidth which may nt be desired. Higher-rder filters with mre-ideal characteristics can als be designed. These are cvered in ther curses and reference bks. E S S V EE (a) V Fig. 5. Bandass filters fr lw- and high-imedance level circuits. (b)