Bikvad "JH" pro realizaci elipticke sekce

>    restart;

>    with(Syrup):

>    obvod:= TEXT(

>    `Bikvad "dva integratory ve slucke zapornej spetnej vazby"`,

>    `V1 1 0 `,

>    `R1  1 2 RD`,

>    `R2  1 4 RP`,

>    `R3  1 6 RH`,

>    `R4  3 4 R`,

>    `R5  5 6 R`,

>    `R6  6 7 R`,

>    `R7  7 2 R`,

>    `R8  2 3 RQ`,
`C1  2 3 C`,

>    `C2  4 5 C`,
`E1  3 0 0 2 A`,

>    `E2  5 0 0 4 A`,
`E3  7 0 0 6 A`,

>    `.end`):

>    AA:= syrup(obvod,ac):

parsedeck:   Analyzing SPICE deck "Bikvad \"dva integratory ve slucke zapornej spetnej vazby\"" (ignoring this line)

>    Hu:= collect(simplify(subs(AA, v[7]/V1)),[s,A],recursive,factor);

Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...
Hu := -A*R*((2*R^2*RP*A*C^2*RD*RQ+R^2*RP*C^2*RD*RQ+R^2*RP*A^2*C^2*RD*RQ)*s^2+(R*C*RD*(-RQ*RH+R*RP)*A^2+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*A+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s...

Normovany tvar pre menovatel prenosovej funkcie

>    DHu:= collect(simplify(denom(Hu)),s, recursive,factor):

>    DHu1:= collect(simplify(DHu/coeff(DHu,s,2)),s,recursive,factor);

DHu1 := s^2+1/R/C*(RD*R*A*RP+RP*RQ*R+RD*R*RQ+R*RP*RD+2*RP*RD*RQ)/(A+1)/RP/RD/RQ*s+(RD*R^3+R^3*RQ+R^2*RQ*A*RH+A^2*RH*RD*R^2+RD*RQ*RP*A*RH+R^2*RQ*RD+R*RQ*RD*A*RH+2*R*RQ*RD*RH+RD*R*A^2*RH*RP+2*R*RP*RH*RQ+...
DHu1 := s^2+1/R/C*(RD*R*A*RP+RP*RQ*R+RD*R*RQ+R*RP*RD+2*RP*RD*RQ)/(A+1)/RP/RD/RQ*s+(RD*R^3+R^3*RQ+R^2*RQ*A*RH+A^2*RH*RD*R^2+RD*RQ*RP*A*RH+R^2*RQ*RD+R*RQ*RD*A*RH+2*R*RQ*RD*RH+RD*R*A^2*RH*RP+2*R*RP*RH*RQ+...
DHu1 := s^2+1/R/C*(RD*R*A*RP+RP*RQ*R+RD*R*RQ+R*RP*RD+2*RP*RD*RQ)/(A+1)/RP/RD/RQ*s+(RD*R^3+R^3*RQ+R^2*RQ*A*RH+A^2*RH*RD*R^2+RD*RQ*RP*A*RH+R^2*RQ*RD+R*RQ*RD*A*RH+2*R*RQ*RD*RH+RD*R*A^2*RH*RP+2*R*RP*RH*RQ+...

>    Omega[ps]:= collect(simplify(coeff(DHu1,s,0)),A,recursive,factor);

Omega[ps] := (A^3*RQ*RD*RH*RP+R*RD*RH*(R+RP)*A^2+(R+RP)*(RD*R^2+RH*R*RQ+3*RH*RD*R+RH*RD*RQ)*A+(R+2*RH)*(R+RP)*(RD*R+R*RQ+RD*RQ))/R^2/RP/C^2/RD/RQ/(A+1)^2/(A*RH+R+2*RH)

Normovany tvar pre citatel prenosovej funkcie

>    NHu:= collect(simplify(numer(Hu)),s, recursive,factor);

>    NHu1:= collect(simplify(NHu/coeff(NHu,s,2)),s,recursive,factor);

NHu := -A*R^3*(A+1)^2*RP*C^2*RD*RQ*s^2-A*R^2*C*(A+1)*(-RQ*RD*A*RH+RD*R*A*RP+RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD)*s-A*R*(RP*RD*RQ+R^2*RQ+RD*R*RQ-A^2*RH*RD*R+RD*R^2*A-R*RQ*A*RH+R*RP*RD-A*RD*R*RH-RQ*RD*A*R...
NHu := -A*R^3*(A+1)^2*RP*C^2*RD*RQ*s^2-A*R^2*C*(A+1)*(-RQ*RD*A*RH+RD*R*A*RP+RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD)*s-A*R*(RP*RD*RQ+R^2*RQ+RD*R*RQ-A^2*RH*RD*R+RD*R^2*A-R*RQ*A*RH+R*RP*RD-A*RD*R*RH-RQ*RD*A*R...

NHu1 := s^2+(-RQ*RD*A*RH+RD*R*A*RP+RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD)/C/R/(A+1)/RP/RD/RQ*s+1/R^2*(RP*RD*RQ+R^2*RQ+RD*R*RQ-A^2*RH*RD*R+RD*R^2*A-R*RQ*A*RH+R*RP*RD-A*RD*R*RH-RQ*RD*A*RH+RD*R^2+RD*R*A*RP+R...
NHu1 := s^2+(-RQ*RD*A*RH+RD*R*A*RP+RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD)/C/R/(A+1)/RP/RD/RQ*s+1/R^2*(RP*RD*RQ+R^2*RQ+RD*R*RQ-A^2*RH*RD*R+RD*R^2*A-R*RQ*A*RH+R*RP*RD-A*RD*R*RH-RQ*RD*A*RH+RD*R^2+RD*R*A*RP+R...

>    Omega[ns]:= collect(simplify(coeff(NHu1,s,0)),A,recursive,factor);

Omega[ns] := 1/R^2*(-RH*(RD*R-RP*RQ)*A^2+(-RH*RD*R+RD*R^2-RH*R*RQ+R*RP*RD-RH*RD*RQ)*A+(R+RP)*(RD*R+R*RQ+RD*RQ))/(A+1)^2/RP/C^2/RD/RQ

Idealni prenos

>    Hi:= collect(limit(Hu,{A=infinity}),s,recursive,factor);

Hi := -R*(R^2*RP*s^2*C^2*RD*RQ+R*C*RD*(-RQ*RH+R*RP)*s-RH*(RD*R-RP*RQ))/RD/RH/RP/(s*C*R^2+R^2*s^2*C^2*RQ+RQ)

>    DHi1:= collect(simplify(denom(Hi)/coeff(denom(Hi),s,2)),s,recursive,factor);

DHi1 := s^2+1/C/RQ*s+1/(R^2*C^2)

>    NHi1:= collect(simplify(numer(Hi)/coeff(denom(Hi),s,2)),s,recursive,factor);

>    NHi2:= collect(simplify(numer(Hi)/coeff(numer(Hi),s,2)),s,recursive,factor);

NHi1 := -R/RH*s^2-1/C*(-RQ*RH+R*RP)/RP/RQ/RH*s+(RD*R-RP*RQ)/R/RP/C^2/RD/RQ

NHi2 := s^2+1/R/C*(-RQ*RH+R*RP)/RP/RQ*s-RH*(RD*R-RP*RQ)/R^2/RP/C^2/RD/RQ

>    PD:= solve({coeff(DHi1,s,0)=Omp^2,coeff(DHi1,s,1)=Omp/Qp},{Omp,Qp});

PD := {Omp = -1/(C*R), Qp = -1/R*RQ}, {Qp = 1/R*RQ, Omp = 1/(C*R)}

>    PN:= evalf(solve({coeff(NHi2,s,0)=Omz^2,coeff(NHi2,s,1)=Omz/Qz},{Omz,Qz}));

PN := {Omz = RootOf(RH*RD*R-RQ*RH*RP+RP*RD*RQ*_Z^2,label = _L4)/C/R, Qz = RootOf(RH*RD*R-RQ*RH*RP+RP*RD*RQ*_Z^2,label = _L4)*RQ*RP/(-1.*RQ*RH+R*RP)}

Frekvencne zavisle zesileni, zjednoduseny prenos

>    subs(A=B/s,Hu):

>    H1:= collect(simplify(%),[s,B],recursive,factor);

H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...
H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...
H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...
H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...
H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...
H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...
H1 := -B*R*(R^2*RP*s^4*C^2*RD*RQ+(2*R^2*RP*B*C^2*RD*RQ+R*C*(RP*RQ*R+RD*R*RQ+2*RP*RD*RQ+R*RP*RD))*s^3+(R^2*RP*B^2*C^2*RD*RQ+R*C*(-RH*RD*RQ+RD*R*RQ+2*RP*RD*RQ+2*R*RP*RD+RP*RQ*R)*B+(R+RP)*(RD*R+R*RQ+RD*RQ...

Navrhovy blok:

Zadana

 prenosova funkce  H(s) = h*(s^2 + omega[n]^2)/(s^2 + s*omega[p]/Q[p] + omega[p]^2)

Zadej:

>    unassign('omega','Q','omega','h','k','kd','kh');

>    omega[n]:= 2: omega[p]:= 1: Q[p]:= 5: h:= 0.25:

>    kd:= h*omega[p]^2/omega[n]^2:  kh:= h:

Pocatecni podminky:

>    unassign('R','RH','RP','RD','RQ','C');

>    k:= kh;

k := .25

Vypocet:

>    C:= 1.:

>    Rik:= solve({k*omega[n]^2=-coeff(NHi1,s,0),coeff(NHi1,s,1)=0,
k=-coeff(NHi1,s,2),omega[p]^2=coeff(DHi1,s,0),omega[p]/Q[p]=coeff(DHi1,s,1)}, {R,RH,RP,RD,RQ});

Rik := {RQ = 5., R = 1., RP = 20., RD = .9900990099, RH = 4.}, {RQ = 5., R = -1., RP = 20., RH = -4., RD = -.9900990099}

>    Rika:= Rik[1];

Rika := {RQ = 5., R = 1., RP = 20., RD = .9900990099, RH = 4.}

>    assign(Rika);

Vypocet Ri, Ci

>    'R'=evalf(R),' RQ'=evalf(RQ),' C'=evalf(C);

>    'RD'=evalf(RD),' RP'=evalf(RP),' RH'=evalf(RH);

R = 1., RQ = 5., C = 1.

RD = .9900990099, RP = 20., RH = 4.

Staticke parametry

>    evalf(Hi);

-.1262500000e-1*(99.00990100*s^2+396.0396040)/(1.*s+5.*s^2+5.)

Konecne zesileni

>    A:= 1000.0;

>    'Omega[ps1]'=evalf(Omega[ps]),'omega[ps1]'=evalf(sqrt(Omega[ps]));

>    'Omega[ns1]'=evalf(Omega[ns]),'omega[ns1]'=evalf(sqrt(Omega[ns]));

A := 1000.0

Omega[ps1] = .9959744265, omega[ps1] = .9979851835

Omega[ns1] = 3.991782764, omega[ns1] = 1.997944635

Frekvencne zavisle zesileni

>    B:= 200;

B := 200

>    Sold:= solve(evalf(denom(H1))=0,s);

Sold := -202.5284398, -200.5189168, -88.92442860, -.8855183344e-1-.9882939800*I, -.8855183344e-1+.9882939800*I

>    Sold1:= (Sold[5]):

>    Omega[dp]:= evalf((Re(Sold1))^2+(Im(Sold1))^2);

>    omega[dp]:= sqrt(Omega[dp]); Q[dp]:= evalf(omega[dp]/(-2*Re(Sold1)));

Omega[dp] := .9845664181

omega[dp] := .9922532026

Q[dp] := 5.602668880

Citatel

>    Soln:= solve(evalf(numer(H1))=0,s);

Soln := -201.6500799-1.956466683*I, -201.6500799+1.956466683*I, .2007985319e-1-1.983439229*I, .2007985319e-1+1.983439229*I

>    Soln1:= (Soln[4]):

>    Omega[np]:= evalf((Re(Soln1))^2+(Im(Soln1))^2);

>    omega[np]:= sqrt(Omega[np]); Q[np]:= evalf(omega[np]/(-2*Re(Soln1)));

Omega[np] := 3.934434376

omega[np] := 1.983540868

Q[np] := -49.39131898

frekvencne charakteristiky

>    'Hi'=Hi; 'H1'=H1;

>    ModI:= abs(subs(s=I*omega,Hi)): ModA:= abs(subs(s=I*omega,H1)):

Hi = -.1262500000e-1*(99.00990100*s^2+396.0396040)/(1.*s+5.*s^2+5.)

H1 = -200.*(99.00990100*s^4+39926.73268*s^3+4025180.247*s^2-4594.059406*s+15841584.16)/(891.0891090*s^5+438548.5149*s^4+68203651.94*s^3+3230478654.*s^2+636990099.1*s+3168316832.)

>    plot([20*log10(ModI),20*log10(ModA)],omega=0...4,color=[blue,red],thickness=[1,1]);

[Maple Plot]

>