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Дифференциальный усилитель

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Рис. 1. Схема модели дифференциального усилителя на BJT транзисторах

[Maple Bitmap]

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

`Cистема Кирхгофа`

-VOUT2/Rbc2+B/Rbe2*VE-VOUT2/R2-VOUT2*s*Cbc2-(VOUT2-VE)/Rce2 = 0

-VOUT1/R1+(Vin-VOUT1)/Rbc1-B/Rbe1*(Vin-VE)-(VOUT1-VE)/Rce1-(VOUT1-Vin)*s*Cbc1 = 0

(VOUT1-VE)/Rce1-Ie-VE*s*Cbe2-VE/Rbe2+(Vin-VE)*s*Cbe1+(VOUT2-VE)/Rce2+(Vin-VE)/Rbe1+B/Rbe1*(Vin-VE)-B/Rbe2*VE = 0

{VE, VOUT1, VOUT2}

MSpice v8.92:   http://pspicelib.narod.ru

Заданы источники: [Vin, Ie]

Заданы узлы: {VINP1}

Получены решения:

V_NET:=[VE, VOUT1, VOUT2]:

J_NET:=[JRce2, JRbe1, JR1, JVin, JCbc2, JRbc2, JRce1, JCbe2, JCbc1, JRbe2, JRbc1, JR2, Je, JCbe1]:

>    Rbc1:=Rbc: Rbc2:=Rbc: Rbe1:=Rbe: Rbe2:=Rbe:  Rce1:=Rce: Rce2:=Rce:

>    Cbc1:=Cbc: Cbc2:=Cbc:Cbe1:=Cbc: Cbe2:=Cbc: R1:=R: R2:=R:

>    VOUT:=simplify(VOUT1);

VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...
VOUT := 1/2*(4*s*Rce^2*Cbc*Rbc*Rbe*Vin*R+2*Rce*Rbe^2*Vin*R+7*Rbe^2*Rbc*R*s*Cbc*Rce*Vin-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin+2*s*Cbc*Rbe^2*Vin*Rbc^2*R-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*V...

На постоянном токе

>    VOUT:=subs(s=0,VOUT);

VOUT := 1/2*(2*Rce*Rbe^2*Vin*R-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*Vin-Rce*Rbc^2*Rbe^2*Ie+2*Rce*Rbe^2*Vin*Rbc+Rce*Rbc^2*Vin*Rbe+Rbe^2*Vin*Rbc*R+2*Rce^...
VOUT := 1/2*(2*Rce*Rbe^2*Vin*R-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*Vin-Rce*Rbc^2*Rbe^2*Ie+2*Rce*Rbe^2*Vin*Rbc+Rce*Rbc^2*Vin*Rbe+Rbe^2*Vin*Rbc*R+2*Rce^...
VOUT := 1/2*(2*Rce*Rbe^2*Vin*R-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*Vin-Rce*Rbc^2*Rbe^2*Ie+2*Rce*Rbe^2*Vin*Rbc+Rce*Rbc^2*Vin*Rbe+Rbe^2*Vin*Rbc*R+2*Rce^...
VOUT := 1/2*(2*Rce*Rbe^2*Vin*R-Rbc^2*Rbe^2*R*Ie+Rbc^2*Rbe*R*Vin-B^2*Rce^2*Rbc^2*Vin-B^2*Rce^2*Rbc*Vin*R-B*Rce^2*Rbc^2*Vin-Rce*Rbc^2*Rbe^2*Ie+2*Rce*Rbe^2*Vin*Rbc+Rce*Rbc^2*Vin*Rbe+Rbe^2*Vin*Rbc*R+2*Rce^...

>    VOUT := limit(VOUT,Rbc = infinity)

VOUT := -1/2*(Rbe^2*R*Ie-Rbe*R*Vin+B^2*Rce^2*Vin+B*Rce^2*Vin+Rce*Rbe^2*Ie-Rce*Vin*Rbe+B*Rce*Rbe*R*Ie+B*Rce*Vin*Rbe+B*Rce*Vin*R+B*Rce^2*Rbe*Ie)*R/Rbe/(Rce*Rbe+R*Rbe+R^2+2*R*Rce+Rce^2*B+Rce^2+R*Rce*B)

>    VOUT := limit(VOUT,Rce = infinity)

VOUT := -1/2*B*(B*Vin+Vin+Rbe*Ie)*R/Rbe/(1+B)

>    K_DC := VOUT/Vin

K_DC := -1/2*B*(B*Vin+Vin+Rbe*Ie)*R/Rbe/(1+B)/Vin

>    Values(AC,RLCVI,[]):

Номиналы компонентов:   

Rce1:=26e3:  [26K]

Cbe2:=127e-12:  [127p]

R1:=2.2e3:  [2.2k]

Cbc1:=3.5e-12:  [3.5p]

Rbe2:=533:  [533]

R2:=2.2e3:  [2.2k]

Cbe1:=127e-12:  [127p]

Cbc2:=3.5e-12:  [3.5p]

Rbc1:=1e6:  [1MEG]

Rbc2:=1e6:  [1MEG]

Rce2:=26e3:  [26K]

Rbe1:=533:  [533]

AC источник: Vin:=1:  AC: Vin:=1:   Pfase(degrees):=0:

DC источник: Ie:=2.7e-3:  AC: Ie:=0:

>    B:=55: VOUT:=simplify(VOUT1); Rbe:=533:R:=2.2e3: K_DC:=K_DC;
ploth([VOUT],f=1..1e9,"2) semi");

VOUT := 1.100000000*(-.4655987792e28*s+328649979.*s^3-.4524471538e19*s^2-.5226282960e36)/(.8843031532e26*s+361514977.*s^3+.4012387002e18*s^2+.5504591708e34)

K_DC := -113.5084428

[Maple Plot]

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