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Простой транзисторный узкополосный фильтр
Схемотехника 2007 №8, стр. 40.

Рис. 1. Схема фильтра

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Рис. 2. Эквивалентная схема фильтра

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>    restart: with(MSpice): ESolve(`Equal/BJT-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`):

`Cистема Кирхгофа`

(V2-V1)*s*C2+(V3-V1)*s*C1+(Vin-V1)/R1-V1/R2 = 0

-VOUT/R5-(VOUT-V3)*s*C3 = 0

(V3-V2)*s*Cbc+(V3-V2)/R3-V2*s*Cbe-(V2-V3)/Rbc-(V2-V1)*s*C2-V2/Rbe = 0

(V2-V3)/Rbc+(VOUT-V3)*s*C3-55*V2-(V3-V2)*s*Cbc-V3/Rce-V3/R4-(V3-V2)/R3-(V3-V1)*s*C1 = 0

{VOUT, V1, V2, V3}

MSpice v8.96:   http://pspicelib.narod.ru

Заданы источники: [Vin]

Заданы узлы: {VINP}

Получены решения:

V_NET:=[VOUT, V1, V2, V3]:

J_NET:=[JC1, JR2, JR4, JR5, JR3, JCbe, JR1, JC3, JC2, JCbc, JRbc, JRbe, JVin, JRce]:

>    H:=simplify(VOUT/Vin,`size`);

H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...
H := R4*Rce*s^2*C3*R2*(((C1+Cbc)*C2+C1*(Cbe+Cbc))*Rbe*Rbc*R3*s+((-55*C2*R3+C2+C1)*Rbc+R3*(C2+C1))*Rbe+C1*Rbc*R3)*R5/(Rbe*Rbc*R4*Rce*Cbe*C3*R2*((C1+Cbc)*C2+Cbc*C1)*R3*R1*R5*s^4+(((((((((((55*Cbc+55*C1)*...

>    Values(AC,RLCVI,[]):
`\n Режимы транзисторов\n`;
Jэ:=10/2/2e3,`  ток эмиттера\n`; Jэ:=%[1]:    
Fт:=100e6,`  частота единичного усиления\n`; Fт:=%[1]:
'Rэб'=evalf(Rэб,3),'Cэб'=evalf(Cэб,3),`  параметры эквивалентной схемы\n`;

Номиналы компонентов:   

Cbe:=127e-12:  [127p]

Cbc:=3.5e-12:  [3.5p]

Rbc:=1e6:  [1MEG]

Rce:=26e3:  [26K]

R2:=1e3:  [1K]

R4:=22e3:  [22K]

R5:=100e3:  [100K]

R3:=680e3:  [680k]

C2:=6.8e-9:  [6.8n]

C1:=6.8e-9:  [6.8n]

C3:=15e-9:  [15n]

R1:=22e3:  [22K]

Rbe:=533:  [533]

AC источник: Vin:=1e-3:  AC: Vin:=1e-3:   Pfase(degrees):=0:

`\n Режимы транзисторов\n`
`\n Режимы транзисторов\n`
`\n Режимы транзисторов\n`

`Jэ` := .2500000000e-2, `  ток эмиттера\n`
`Jэ` := .2500000000e-2, `  ток эмиттера\n`

`Fт` := .100e9, `  частота единичного усиления\n`
`Fт` := .100e9, `  частота единичного усиления\n`

`Rэб` = `Rэб`, `Cэб` = `Cэб`, `  параметры эквивалентной схемы\n`
`Rэб` = `Rэб`, `Cэб` = `Cэб`, `  параметры эквивалентной схемы\n`

>    B:=55: H:=simplify(H);
s:=I*2*Pi*f:
Fo:=solve(diff(evalc(abs(H)),f)=0,f)[1]: print('Fo'=Fo,`  резонансная частота`):
F_3dB:=solve(evalc(abs(H))=limit(evalc(abs(H)),f=Fo)/sqrt(2),f):
BW:=abs(evalc(simplify(F_3dB[1]-F_3dB[2]))):
print(F_3dB_Low=F_3dB[1], F_3dB_Hig=F_3dB[2],'BW'=BW,`  полоса 3 dB`);
ploth([H],f=1e2..1e4,"3) semi фильтра");

H := 858000.*s^2*(1708948093.*s-.1355479238e20)/(4021744483.*s^4+.1741796594e22*s^3+.2574479207e25*s^2+.9825991794e29*s+.6486962856e32)

Fo = 1189.672839, `  резонансная частота`

F_3dB_Low = 1126.875856, F_3dB_Hig = 1256.027664, BW = 129.1518080, `  полоса 3 dB`

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