电子科技大学：《现代网络理论与综合 Theory and Synthesize of Electric Network》课程教学资源（课件讲稿）第16讲 贝塞尔函数和频率变换

第16讲 贝塞尔逼近与频带变换 《网综》UESTC一陈会主讲

第16讲 贝塞尔逼近与频带变换 《网综》UESTC—陈会主讲

计算机辅助设计工具： Filter Solutions It is a tool,based on filter synthesis and analysis software package 集总电路的综合窗口： File Zmatch Data License Options Window Parts QuickFilter Help Filter Type Filter Attributes Ideal Filter Response Gaussian Set Order Standard Pass Band Atten Frequency Resp. Time Response S Parameters Bessel 3 Order Transfer Function Pole Zero Plots VSG Analysis I Butterworth 1H2 Legendre Pass Band Freq Chebyshev I Lumped Design Source Res Chebyshev lli 1st Ele Shunt Add Tx Zeros Hourglass 1st Ele Series Load Res Elliptic Min Inductors Custom Raised Cos Delay Equalize Matched Implementation Delav Lumpec●Distrib●Active●SwCap●Digital Filter Class门 Multiple Bands Freq Scale Graph Limits Complex Terminate Low Pass Band Pass ●Rad/Sec 200MH25GH2 0 10nS High Pass Band Stop Hertz Synthesize Filter Diplexer 1 Diplexer 2 Log Min Freq Max Freq Min Time Max Time Topology Parasitics 《网综》UESTC一F 陈会主讲

计算机辅助设计工具： Filter Solutions It is a tool, based on filter synthesis and analysis software package 集总电路的综合窗口： 《网综》UESTC—陈会主讲

集总和分布参数电路的综合窗口： Eile Zmatch Data License Options Window Parts Advanced Help U心Dsz.1 FilterQuick Shape Types Band Classes Update Topologies: Genera Requirements Vaue Low Pass Requitements Vale Mrimum Inductors: Pass Band Attenuation 301B Minimum Capacitors Pass Band Frequnecy 1 GHz Sngly Terminated at Load Stop Band Atterustion 40 cB Stop Band Frequency 2GHz Sngy Terminated at Source mpedance 50 0hme Inductor Q AddT装ZGos Capactor Q ■Force0rder Hin Freq Hax Fre View Group Delay Linoar Frequency Automate Min/Max 500 MH:4GHz Balarce 4D■Fm Plint Copy Limts Text cil S12/5217s11/522 Annete nds Select Lumped Filter S Parameters ■smth■Pcla Export 7th Order Low Pass Butterworth Caps Select 521512 511522 Pass Band Frequency-1.000 GHz 2 500089923nh1592nH 9923nH n 417 .736 417pf 50.00 789 121416182 Wed Nov200292018 7h Orcer Low Pass Butterworth Frequency (Hz) Wed Nov 208:29 2016 《网综》UESTC-一陈会主讲

集总和分布参数电路的综合窗口： 《网综》UESTC—陈会主讲

例：3阶butterworth LPF原型的综合一T型 fc=1 Hz File Zmatch Data Options Window arts Advanc Help PUuDsz.1 FilterQuick opolodies: Pa:o Band Asenustion 301d9 Pa Band Frequnecy 1Hz Sngy Terminated at Load 40d8 2Hz indy Terminated at Source Inductor Q Add Tx Zeros CapaciorD Foree Order 3 View Group Delay Lingac Frequency Automate Min/Mas500si4H: Bslence9oiom日 Pint Copz Linta Tesdi 5125217S11522 Ind:Select Lumped Filter S Parameters Smh■Pc Export 3rd Order Low Pass Butterworth 62112 511822 Pass Band Frequency a 1.009 Hz 10 5 100 1592ntH1592mh 20 25 25 3183F 100 3 39 121410182 Wy26542016 Frequency也 《网综》UESTC一陈会主讲

例：3阶butterworth LPF原型的综合—T型 fc=1 Hz 《网综》UESTC—陈会主讲

例：3阶outterworth LPF原型的综合一T型 fc=1 Hz File Zmatch Data License Options Window Parts Advanced Help FilterQuick Shape Types Band Classes Update Implementations 9egpaafiFean Topologies: General Requrements Value Low Pass Requitemenits Value oimmm-Induetor Pass Band Alteruation 301B Pass Band Frequnecy ngy Termna 40 dB 2H2 ngy lermnated at Source impedance 10hms inductor Q Ind Add Tx Zeros Capacitor Q Force Order:3 Min Freq Max Freg View Group Delay Linear Frequency Automate Min/Max 500 mHz 4Hz ■Balance 4D■Ft Prik Copy Limits TextihS12/S21 S11/S22 ￥d Copy Ind:Select Lumped Filter S Parameters Sma■Pals 3rd Order Low Pass Butterworth Capa Select S21312 Pass Band Frequency 1.000 Hz S11522 -10 15 15 1.c00R 318.3mH -20 20 1592mf 1592mF 1.000 35 -40 121416182 Wed Nov 2 08:50 2018 Frequency (Hz】 Va010w20850201g 《网综》UESTC 一陈会主讲

例：3阶butterworth LPF原型的综合—型 fc=1 Hz 《网综》UESTC—陈会主讲

fc=0.159Hz T型 File Zmatch Data License Options Window Parts Advanced Help small-号 FilterQuick Shape Types Band Classes Update FilterQuck Interlace Implementations Use Advanced Panel for Full Functionality Topologies: General Requirements Value Low Pass Requirements Value Minimum Inductors linimum●S0BCITO客 Pass Band Attenuation 3.01dB Pass Band Frequnecy 0.159H2z Singly Terminated at Load 40 dB 0.3Hz Singly Terminated at Source Impedance 10hms Inductor Q Inf Add Tx Zeros Capacitor Q Inf ☑Force Order:3 Min Freq Max Freq View Group Delay Linear Frequency Automate Min/Max 79.5 mH:636 mH2 Print NetList ■Balance 4 Digs Fit Print Copy Linits Texti VS12/521VS11S22 d8 Copy Annote Inds Select Lumped Filter S Parameters ■Smith■Polar Export 3rd Order Low Pass Butterworth Caps Select 0 S21S12 S11S22 Pass Band Frequency 159.0 mHz 5 10 10 15 -15 1.000 1.001H 1.001H -20 -20 25 2.002F 「1.000 -30 4 35 35 40 40 12141.6182 《网综》ESTC陈会主讲 cy (Hz) We0N0w208.572010

fc=0.159 Hz T型 《网综》UESTC—陈会主讲

Π型 File Zmatch Data License Options Window Parts Advanced Help FilterQuick Shape Types Band Classes Update F月ie0 ick inleiface Implementations Use Advanced Pane fo Ful Functionalty Topologies: General Requitements Value Low Pass Requitemerts Value Mnimun Inductors Minimum Caoacitors Pass Band Attenuation 3.01dB Pass Band Frequnecy 0.159Hz 40 dB 0.3Hz Singly Termnated at Source Impedance 10hms Inductor Q Ini Add Tx Zeros Capactor Q Ini Force Order:3 Hin Freg Max Freq View Group Delay Linear Fiequency Automate Min/Max 79.5 mHz636 mHz Print Belance4Dos■Fm Print Copy Limits Text S12/5217s11/522 dB Inds Select Lumped Filter S Parameters Smth■Palar 3rd Order Low Pass Butterworth Caps Select 0 S21/512 :S11/522 Pass Band Frequency 159.0 mHz 5 15 1.000g 2.002H 20 20 2 1.001f 1.001F 1.0002 30 40 121416182 100m Ved Nov209012018 3rd Order Low Pass Butterwortn Frequency (Hz) Wed Nov2090120t相 《网综》UESTC-一陈会主讲

型 《网综》UESTC—陈会主讲

幅频特性，已经在8-4至8-6节中讨论过。 相频特性？ 时延、波形失真问题、相位调制，影响参数。 u(t)=Ku;(t-To) 拉氏变换： U.(s)=KU,(s)e-sto 传输函数： T(S)= U。(S) =Ke-sTo U,(s) 《网综》UESTC-一陈会主讲

( ) ( ) T0 u t Ku t o  i  0 ( ) ( ) sT o i U s KU s e   0 ( ) ( ) ( ) sT i o Ke U s U s T s    幅频特性,已经在8-4至8-6节中讨论过。 相频特性? 时延、波形失真问题、相位调制，影响参数。 拉氏变换： 传输函数： 《网综》UESTC—陈会主讲

T(s)= U。(s) =Ke-sTo L U,(S) 令：s=jω T(jo)-Ke-joTo T(jω)=K 相位： (ω)=-ωT 群延迟为： ow）=- do(@)=To dw 《网综》UESTC一陈会主讲

0 ( ) ( ) ( ) sT i o Ke U s U s T s    令： s  j 0 ( ) j T T j Ke     T( j)  K 0 ()  T 0 ( ) ( ) T d d         群延迟为： 相位： 《网综》UESTC—陈会主讲

7(@)-- d(o=T。 dw 群延迟与频率无关，这是理想的群延迟特性。 简化，令： K=1 转移函数： H(S)= =e T(S) 归一化： T=1 有： H(s)=e 该函数非自然的s多项式，不 能直接综合 转移函数 《网综》UESTC一陈会主讲

0 ( ) 1 ( ) sT e T s H s   群延迟与频率无关，这是理想的群延迟特性。 K 1 简化，令： 归一化： 转移函数： T0 1 s H(s)  e 0 ( ) ( ) T d d         有： 该函数非自然的s多项式，不 能直接综合 转移函数 《网综》UESTC—陈会主讲