PASSIVE FILTERS (LCR BASED)

Transcription

1 EXPEIMENT PAIVE FILTE (LC BAED) (IMULATION) OBJECTIVE T build highpass, lwpass and bandpass LC filters using circuit simulatin tls. INTODUCTION Ladder netwrks are filters f the first kind, built in the early part f last century, befre p-amp technlgy was available. The lssless, r reactance ladder, shwn in Fig., is still used tday in applicatins where p-amp are nt suited. Fr example, if the required pwer is beynd the capability f the p-amp, r fr high frequency applicatins. The ladder circuit shwn here is cnsidered a prttype lwpass filter, and therefre frequency transfrmatins may be applied t this structure t btain different respnses, and hence mre cmplicated ladder structures. The synthesis f a passive filter can be accmplished via many different methds. In this lab, yu will design lwpass, highpass and bandpass lssless ladder filters using the frequency transfrmatin techniques. The circuits will exhibit Butterwrth and Chebyshev respnses, in singly and dubly terminated cnfiguratins. The vltage transfer functins are all-ple functins and are characterized by: H V ut ( n n Vin bns bn s... k b THE LOWPA LOLE LADDE L0 L8 L6 L L V C9 C7 C C C V ' ' Fig. Please cnsult the text bk, Ch. fr yur understanding.

2 In the lw-pass ladder netwrk all the series elements are inductrs and the shunt elements are capacitrs. The synthesis fr a singly terminated ladder netwrk is utlined here. INGLY TEMINATED NETWOK Given a singly terminated netwrk with a transfer functin which represents a Butterwrth r V Chebyshev respnse, we can express ut as a rati f plynmials Q(, M( and N(. V in Vut Q(, if the degree f M( > the degree N(, r, Vin M ( N ( Vut Q(, if the degree f N( > the degree M( Vin N ( M ( Where M( = even prtin f the denminatr, and N( = dd prtin f the denminatr. If the degree f M( > degree f N(, we synthesize Y = M( / N(, and the first element f the ladder is a capacitr in shunt. Otherwise we synthesize Z = N( / M( and the first element is an inductr in the series ( where Y and Z are tw-prt netwrk parameter. The plynmial divisin can be dne by lng divisin, the divisin algrithm are capable f perfrming plynmial divisin. The nrmalized design is perfrmed fr a hm lad and a cut-ff frequency f rad/sec. Then the circuit is scaled accrdingly. If the denminatr has a degree n then there are a ttal f n L & C elements. EXAMPLE: ynthesize the functin; H ( s.6s.s.6s As a singly terminated LC ladder netwrk. By inspectin, M ( s.s and N(.6s. 6s ince the degree f M( > the degree f N( we synthesize Y. Therefre, s.s Y.6s.6s The results f the divisin algrithm are; 0.8s.08s.77s..6.6.

3 .s. ince M( > N( the first element in the ladder netwrk is a capacitr in shunt, and the element values crrespnd t the results in the divisin algrithm. These elements are cnsidered frm the lad lking tward the surce (hence Z r Y). LN/ L L CN/ C C Y L(N+)/ L L C(N+)/ C Fig. Z Fig.

4 DOUBLY TEMINATED NETWOK The dubly terminated netwrks are similar t the singly terminated netwrks in their synthesis. We always design a nrmalized filter ( hm resistrs and a cut-ff frequency f rad/sec). And then magnitude and frequency scale the cmpnents. With dubly terminated netwrks we synthesize Zin. If the rder f the numeratr is smaller than the rder f the denminatr, the netwrk starts with a capacitr in shunt, therwise if the rder f the numeratr is greater than the rder f the denminatr, the ladder starts with an inductr in series. The mst mechanical prcess invlved in these designs is btaining Zin. This prcedure will be cvered in yur lectures. We will wrk frm the assumptin that yu are given Zin. L L L(N-)/ Zin C C C(N+)/ (N<D) L L L(N+)/ Zin C C(N-)/ (N>D) Fig. Given: Z IN.6s.6s.6s.6s s.6s.6s.6s.6s Plynmial divisin yields the fllwing cmpnents, fr the nminal lw-pass transfer functin. Ln. 0 Ohm C n 0. 68F L n. 68H C n F L n. 68H

5 C n 0. 68F Using a terminatin f L 00 Ohm and w 0 rad/sec, K m 00 and K f 0, and the circuit is shwn in Fig. ( L Ln Km / K f, C Cn / K mk f, nk m). Nte that K m = f / i and K f = ω f /ω i. Here the subscript f stands fr the final value and the subscript I stands fr the initial value t which the scaling is applied u u 0.68 u 00 Fig. FEQUENCY TANFOMATION The nrmalized, dubly-terminated, lwpass filter, (== and w rad/sec ) can be transfrmed int a highpass r bandpass filter. HIGHHPA TANFOMATION With the nrmalized circuit; eplace the inductrs by capacitrs with the values /L. eplace the capacitrs by inductrs with the values /C. Once the transfrmatin is dne, magnitude and frequency scaling is applied. BANDPA TANFOMATION A bandpass filter can be realized by synthesizing a nrmal lwpass ladder circuit, and then appling the fllwing transfrmatins. eries inductrs are replaced by a series cmbinatin f L p an inductrand a capacitr, with the values Lbp and C. BW. bp BW as ( LP )( w ) shwn in Fig. 6.

6 hunt capacitrs are replaced by a parallel cmbinatin f a capacitr and an inductr, with the C values C lp bp BW and L bp BW as shwn in Fig. 7. Here ω is the ( C )( w ) center frequency f the band-pass filter. lp Nte that the bandwidth (BW) is calculated in Hz and the center-frequency (ω ) is calculated in rad/s. PE-LAB. ynthesize the fllwing transfer functin, f a singly terminated netwrk, fr a K lad resistr. The nrmalized circuit perates at rad/sec. cale the circuit fr a cut-ff frequency f 0KHz. T ( s.6s.6s.6s.6s. ynthesize the transfer functin, f a dubly terminated netwrk terminated in 00 hm resistrs, using Zin given belw. Use the clsest available capacitrs. The nrmalized circuit perates at rad/sec. cale the cicuit fr a cut-ff frequencyf 8.6KHz. ( s.7s.87s.096s.06s Z in.7s 0.687s.096s 0.s Cnvert the lwpass filter designed in part f the prelab t a highpass filter using the frequency transfrmatin techniques. 6

7 . Cnvert the LPF in step t a BPF with a bandwidth (BW) f KHz. Assume that the center frequency (ω ) fr the BPF is 0 KHz (ω =π x 0x0 rad/. All the resistrs are Ω. POCEDUE - imulate the circuit in part f the pre-lab using sinusidal signal with V peak-t-peak and frequency sweep frm 00Hz t 0 KHz. - epeat step fr the circuit in part f the pre-lab. - epeat step fr the circuit in part, and f the pre-lab. D the simulatin.while simulating part f pre-lab, it is better t sweep between 0 KHz and 0 KHz. In the simulatin settings use 00 pints per decade t get a smth curve. Verify the functinality. In all these cases attach the circuits and the utput with yur lab reprt. 7