模拟高通滤波器设计*模拟高通滤波器的设计步骤(1)由频率映射将高通设计指标转换为原型低通设计指标の, =1 / o@, =1 / (2)设计满足指标の,のs，A,,A的原型低通滤波器H,(s)(3)由复频率转换将原型低通转换为高通HHp(s)Hμp(s)= H,(s)
模拟高通滤波器设计 ❖ 模拟高通滤波器的设计步骤 (1)由频率映射将高通设计指标转换为原型低通设计指标 p p ω = 1 / ω s s ω = 1/ ω (3)由复频率转换将原型低通转换为高通HHP(s) p s p s L (2) , , , ( ) 设计满足指标ω ω A A H s 的原型低通滤波器 HP L ( ) ( ) s s H s H s = = 1
[例】试设计满足下列指标的BW型模拟高通滤波器f,=5kHz,f=1kHz, A,≤1dB,A,≥40dB解：（1）将高通滤波器设计指标转换为原型低通设计指标,=1 / 0,=1/(2元×5000),@,=1 / 0,=1 / (2元×1000)A,≤1dB,A,≥40dB2)设计BW型原型低通滤波器100.1lg(100.14,取N=4N≥=3.282 lg(可, /可,)0=5.033×10-50(10014 -1)/(2N)
[例] 试设计满足下列指标的BW型模拟高通滤波器 f p=5kHz, f s=1kHz, Ap≤1dB, As≥40dB 解： (1) 将高通滤波器设计指标转换为原型低通设计指标 Ap1dB, As 40dB (2) 设计BW型原型低通滤波器 3.28 2lg( / ) ) 10 1 10 1 lg( s p 0.1 0.1 p s = − − A A N 取N=4 5 0.1 1/( 2 ) s c 5.033 10 (10 1) s − = − = A N p p s s ω = = = = 1/ 1/ (2 ω π 5000), 1/ 1/ (2 ω ω π 1000)
[例试设计满足下列指标的BW型模拟高通滤波器f,=5kHz,f=1kHz, A,≤1dB,A,≥40dB解：BW型原型低通滤波器的系统函数为1H,(3)=[(s /@.) +0.7654s /w。+1][(s /)2 +1.8478s /。+1]6.4166x10-184+1.3152×10-4g3+8.6485×10-g+3.3315×10-13+6.4166×10-18(3）由复频率转换Hμp(s)-H.(1/s)获得高通滤波器系统函数ASHμp(s)= H(3)I-1= -s4+5.192×10*s3+1.3478×10°s2+2.0497×1013s+1.5585×1017
解： 4 4 3 9 2 1 3 1 8 1 8 1.3152 10 8.6485 10 3.3315 10 6.4166 10 6.4166 10 − − − − − + + + + = s s s s (3) 由复频率转换HHP(s)=HL (1/s) 获得高通滤波器系统函数 BW型原型低通滤波器的系统函数为 [( / ) 0.7654 / 1][( / ) 1.8478 / 1] 1 ( ) c 2 c c 2 c L + + + + = s ω s ω s ω s ω H s [例] 试设计满足下列指标的BW型模拟高通滤波器 f p=5kHz, f s=1kHz, Ap≤1dB, As≥40dB 4 HP L 1 4 4 3 9 2 13 17 5.192 10 1.3478 10 2.0497 10 1.5 5 ( ) ( 0 | 58 ) s 1 s H s s s s H s s s = = + + = + +
[例】试设计满足下列指标的BW型模拟高通滤波器f,=5kHz,J=1kHz, A,≤1dB,A,≥40dBfp=5000;fs=-1000;Ap=1;As=40;%AFspecificationswLp-1/(2*pi*fp);wLs=1/(2*pi*fs);%HPspecificationstoLP's[N,Wc]-buttord(wLp,wLs,Ap,As,'s');%ComputerAForder[num,den]=butter(N,Wc,'s');%ComputeAFcoefficients[numt,dent]=lp2hp(num,den,1);%LPtoHP%displayApandAsomega=[2*pi*fp,2*pi*fs];h =freqs(numt, dent, omega);fprintf(Ap= %.4fln',-20*log10(abs(h(1));fprintf(As= %.4fln',-20*log10(abs(h(2)));%plotthegainomega =[0:200:6000*2*pi];h =freqs(numt, dent, omega), % Compute the frequency response of the AFgain=20*log10(abs(h); plot(omega/(2*pi),gain);xlabel(Frequency in Hz), ylabel(Gain in dB')
fp=5000;fs=1000; Ap=1;As=40; % AF specifications wLp=1/(2*pi*fp); wLs=1/(2*pi*fs); % HP specifications to LP’s [N,Wc]=buttord(wLp,wLs,Ap,As,'s'); % Computer AF order [num,den] = butter(N,Wc,'s'); % Compute AF coefficients [numt,dent] = lp2hp(num,den,1); % LP to HP % display Ap and As omega=[2*pi*fp, 2*pi*fs]; h = freqs(numt, dent, omega); fprintf('Ap= %.4f\n',-20*log10(abs(h(1)))); fprintf('As= %.4f\n',-20*log10(abs(h(2)))); % plot the gain omega = [0: 200: 6000*2*pi]; h = freqs(numt, dent, omega); % Compute the frequency response of the AF gain=20*log10(abs(h)); plot(omega/(2*pi),gain); xlabel('Frequency in Hz'); ylabel('Gain in dB'); [例] 试设计满足下列指标的BW型模拟高通滤波器 f p=5kHz, f s=1kHz, Ap≤1dB, As≥40dB
[例l试设计满足下列指标的BW型模拟高通滤波器f,=5kHz,f=1kHz, A,≤1dB,A,≥40dB0-10A,=0.1098dB-20-30e-40-50A,=40.0000dB-60-700200030004000100050006000Frequency in Hz
0 1000 2000 3000 4000 5000 6000 -70 -60 -50 -40 -30 -20 -10 0 Frequency in Hz Gain in dB As=40.0000dB Ap=0.1098dB [例] 试设计满足下列指标的BW型模拟高通滤波器 f p=5kHz, f s=1kHz, Ap≤1dB, As≥40dB