C06-OTA.html

Synteza filtru C 06 20 b , Theta=49.

Realizace s OTA , funkcni simulace

LC prototyp

Prvky LC prototypu:

> restart;

> rg:= 1: c1:= 1.09341: l2:= 1.094878: c2:= 0.279112: c3:= 1.645566: l4:= 0.950813: c4:= 0.544587:

> c5:= 1.668723: l6:= 0.892775: r2:= 2/3:

Simulace

> with(Syrup);

> obvod:= TEXT(

> `LC Cauer C06`,

> `V1 1 0 V1`,
`Rg 1 2 rg`,

> `C1 2 0 c1`,

>    `C2 2 3   c2`,
`L2 2 3   l2`,
`C3 3 0   c3`,
`C4 3 4   c4`,
`L4 3 4   l4`,
`C5 4 0   c5`,
`L6 4 5   l6`,

> `RL 5 0 r2`,

> `.end`) :

> AA:= syrup(obvod, ac):

Syrup/parsedeck:   Analyzing SPICE deck "LC Cauer C06" (ignoring this line)

> HLC:= collect(simplify(subs(AA, v[5]/V1)),s,recursive,factor);

póly:

> XLC:= evalf(solve(denom(HLC)=0,s));

> MHLC:= evalc(abs(subs(s=I*omega, HLC))):
MHLCd:= 20*log10(MHLC):

> with(plots):

Warning, the name changecoords has been redefined

> plot(MHLCd, omega=0....4, thickness=2);

Popis prototypu - obvodové rovnice

Rovnice "zdrojové" větve:

ig:= 1/rg*(ug - u1); -> vg:= R/rg*(ug - u1);

Rovnice 1.větve:

u1:= 1/(p*c1*R)*(vg - vl2 - p*c2*R*(u1 - u3));

Rovnice 2.větve:

vl2:= R/(p*l2)*(u1 - u3);

Rovnice 3.větve:

u3:= 1/(p*c3*R)*(vl2 - vl4 + p*c2*R*(u1-u3) - p*c4*R*(u3-u5));

Rovnice 4.větve:

vl4:= R/(p*l4)*(u3 - u5);

Rovnice 5.větve:

u5:= 1/(p*c5*R)*(vl4 - v6 + p*c4*R*(u3 - u5));

Rovnice 6.větve:

v6:= R/(p*l6)*(u5 - u7);

Rovnice 7.větve:

u7:= r2/R*v6;

Návrh

Výpočet integrátorů:

> R:= r2; gm1:= 1; ci1:= solve(1/(c1*R)=gm1/ci1, ci1);

> gm2:=1; ci2:= solve(R/l2=gm2/ci2, ci2);

> gm3:=1; ci3:= solve(1/(c3*R)=gm3/ci3, ci3);

> gm4:= 1; ci4:= solve(R/l4=gm4/ci4, ci4);

> gm5:=1; ci5:= solve(1/(c5*R)=gm5/ci5, ci5);

> gm6:= 1; ci6:= solve(R/l6=gm6/ci6, ci6);

Výpočet koncových větví:

vstupní větev:

> gmo2:= 1; gmo1:= solve(R/rg=gmo1/gmo2, gmo1);

výstupní větev:

> gmo4:= 1; gmo3:= solve(r2/R=gmo3/gmo4, gmo3);

Vazební kondenzátory:

> c2n:= c2*R*gm2; c4n:= c4*R*gm4;

Simulace

> obvod2:= TEXT(

> `FS C06 - VM`,

> `V1 1 0 V1`,

> `Go1 2 0 1 3 -gmo1`,

> `Go2 2 0 0 2 -gmo2`,

>    `G1   3 0 2 4 -gm1`,
`C1   3 0           ci1`,
`G2   4 0 3 5 -gm2`,
`C2   4 0           ci2`,
`C22 3 5          c2n`,
`G3   5 0 4 6 -gm3`,
`C3   5 0           ci3`,
`G4   6 0 5 7 -gm4`,
`C4   6 0           ci4`,
`C44 5 7           c4n`,
`G5   7 0 6 8 -gm5`,
`C5   7 0           ci5`,
`G6   8 0 7 9 -gm6`,
`C6   8 0           ci6`,
`Go3 9 0 8 0 -gmo3`,
`Go4 9 0 0 9 -gmo4`,

> `.end`) :

> AB:= syrup(obvod2, ac):

Syrup/parsedeck:   Analyzing SPICE deck "FS C06 - VM" (ignoring this line)

syrup:   There may be an unconnected component.


The following component(s) have zero current: {V1}.

> H:= collect(simplify(subs(AB, v[9]/V1)),s,recursive,factor);

póly:

> XH:= evalf(solve(denom(H)=0,s));

> XLC;

Dynamika:

> H2:= collect(simplify(subs(AB, v[2]/V1)),s,recursive,factor): MH2:= evalc(abs(subs(s=I*omega, H2))):

> H3:= collect(simplify(subs(AB, v[3]/V1)),s,recursive,factor): MH3:= evalc(abs(subs(s=I*omega, H3))):

> H4:= collect(simplify(subs(AB, v[4]/V1)),s,recursive,factor): MH4:= evalc(abs(subs(s=I*omega, H4))):

> H5:= collect(simplify(subs(AB, v[5]/V1)),s,recursive,factor): MH5:= evalc(abs(subs(s=I*omega, H5))):

> H6:= collect(simplify(subs(AB, v[6]/V1)),s,recursive,factor): MH6:= evalc(abs(subs(s=I*omega, H6))):

> H7:= collect(simplify(subs(AB, v[7]/V1)),s,recursive,factor): MH7:= evalc(abs(subs(s=I*omega, H7))):

> H8:= collect(simplify(subs(AB, v[8]/V1)),s,recursive,factor): MH8:= evalc(abs(subs(s=I*omega, H8))):

Grafy:

> with(plots):

> MH:= evalc(abs(subs(s=I*omega, H))):

> MHd:= 20*log10(MH):

> plot([MHLCd,MHd], omega=0....1.1, thickness=2, color=[blue,red]);

> plot([MH,MH2,MH3,MH4,MH5,MH6,MH7,MH8], omega=0....1.1, thickness=2);

>

Kmitočtové a impedanční odnormování:

Normovací kmitočet

> fn:= 4*10^6:

> omega[n]:= 2*Pi*fn;

> gmn:= 0.30*10^(-3);

> Ci1:= ci1*gmn/omega[n]; evalf(Ci1*1e12);

> Ci2:= ci2*gmn/omega[n]; evalf(Ci2*1e12);

> Ci3:= ci3*gmn/omega[n]; evalf(Ci3*1e12);

> Ci4:= ci4*gmn/omega[n]; evalf(Ci4*1e12);

> Ci5:= ci5*gmn/omega[n]; evalf(Ci5*1e12);

> Ci6:= ci6*gmn/omega[n]; evalf(Ci6*1e12);

> C2:= c2n*gmn/omega[n]; evalf(C2*1e12);

> C4:= c4n*gmn/omega[n]; evalf(C4*1e12);

> Gmi:= gm1*gmn; # i=1,2,..,6;

> Gmo1:= gmo1*gmn; Gmo2:= gmo2*gmn; Gmo3:= gmo3*gmn; Gmo4:= gmo4*gmn;

>