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abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1000,100000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp-d*(t...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1,1000000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp+d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([log(abs(eq7))],[f,1,100000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp-d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1,1000000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp+d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,8000,30000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp+d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1000,1000000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp+d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([log(abs(eq7))],[f,1,100000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp-d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,8000,30000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp+d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1,1000000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp-d*(V...

eq2: Vbp1=I(Vhp);

Calculate

abs-linsolve-log-plot2d-rhs
plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1,1000000],[logx]);

I(i):=-i/(s*R*C);

eq1: Vhp=Vin+Vlp-d*(t...

eq2: Vbp1=I(Vhp);

Calculate

[abs,linsolve,log,plot2d,rhs]

Run Example
(%i1)I(i):=-i/(s*R*C);
                                          - i
(%o1)                            I(i) := -----
                                         s R C
(%i2) eq1: Vhp=Vin+Vlp-d*(tilt*Vbp1-0.5*Vbp2+(1/tilt)*Vbp3);
                                    Vbp3
(%o2)          Vhp = Vlp + Vin - d (---- - 0.5 Vbp2 + tilt Vbp1)
                                    tilt
(%i3) eq2: Vbp1=I(Vhp);
                                          Vhp
(%o3)                           Vbp1 = - -----
                                         s C R
(%i4) eq3: Vbp2=I(Vbp1);
                                         Vbp1
(%o4)                           Vbp2 = - -----
                                         s C R
(%i5) eq4: Vbp3=I(Vbp2);
                                         Vbp2
(%o5)                           Vbp3 = - -----
                                         s C R
(%i6) eq5: Vlp=I(Vbp3);
                                         Vbp3
(%o6)                            Vlp = - -----
                                         s C R
(%i7) eq6: linsolve([eq1,eq2,eq3,eq4,eq5],[Vhp,Vbp1,Vbp2,Vbp3,Vlp]);

rat: replaced -0.5 by -1/2 = -0.5
(%o7) [Vhp = 
                              4           4  4
                           2 s  tilt Vin C  R
- ---------------------------------------------------------------------, 
             4  4  4      2  2  2             3     2  3  3
  tilt (- 2 s  C  R  + d s  C  R  + 2) + 2 d s  tilt  C  R  + 2 d s C R
                                   3           3  3
                                2 s  tilt Vin C  R
Vbp1 = ---------------------------------------------------------------------, 
                  4  4  4      2  2  2             3     2  3  3
       tilt (- 2 s  C  R  + d s  C  R  + 2) + 2 d s  tilt  C  R  + 2 d s C R
Vbp2 = 
                              2           2  2
                           2 s  tilt Vin C  R
- ---------------------------------------------------------------------, 
             4  4  4      2  2  2             3     2  3  3
  tilt (- 2 s  C  R  + d s  C  R  + 2) + 2 d s  tilt  C  R  + 2 d s C R
                                 2 s tilt Vin C R
Vbp3 = ---------------------------------------------------------------------, 
                  4  4  4      2  2  2             3     2  3  3
       tilt (- 2 s  C  R  + d s  C  R  + 2) + 2 d s  tilt  C  R  + 2 d s C R
                                     2 tilt Vin
Vlp = - ---------------------------------------------------------------------]
                   4  4  4      2  2  2             3     2  3  3
        tilt (- 2 s  C  R  + d s  C  R  + 2) + 2 d s  tilt  C  R  + 2 d s C R
(%i8) eq7: (eq6),s=%i*2*%pi*f,R=100000,C=100e-12,d=1,Vin=1.0,tilt=0.667;
                                          4  4
(%o8) [Vhp = - (2.1344000000000005E-19 %pi  f )
                                     4  4                             2  2
/(0.667 (- 3.2000000000000003E-19 %pi  f  - 4.0000000000000001E-10 %pi  f  + 2)
                                3  3
 - 7.1182240000000016E-15 %i %pi  f  + 4.0000000000000003E-5 %i %pi f), 
                                       3  3
Vbp1 = - (1.0672000000000001E-14 %i %pi  f )
                                     4  4                             2  2
/(0.667 (- 3.2000000000000003E-19 %pi  f  - 4.0000000000000001E-10 %pi  f  + 2)
                                3  3
 - 7.1182240000000016E-15 %i %pi  f  + 4.0000000000000003E-5 %i %pi f), 
                                 2  2
Vbp2 = (5.336000000000001E-10 %pi  f )/(0.667
                              4  4                             2  2
 (- 3.2000000000000003E-19 %pi  f  - 4.0000000000000001E-10 %pi  f  + 2)
                                3  3
 - 7.1182240000000016E-15 %i %pi  f  + 4.0000000000000003E-5 %i %pi f), 
Vbp3 = (2.6679999999999999E-5 %i %pi f)
                                     4  4                             2  2
/(0.667 (- 3.2000000000000003E-19 %pi  f  - 4.0000000000000001E-10 %pi  f  + 2)
                                3  3
 - 7.1182240000000016E-15 %i %pi  f  + 4.0000000000000003E-5 %i %pi f), 
                                                  4  4
Vlp = - 1.334/(0.667 (- 3.2000000000000003E-19 %pi  f
                             2  2                                     3  3
 - 4.0000000000000001E-10 %pi  f  + 2) - 7.1182240000000016E-15 %i %pi  f
 + 4.0000000000000003E-5 %i %pi f)]
(%i9) db(v):=20*log(abs(v))/log(10);
                                     20 log(abs(v))
(%o9)                       db(v) := --------------
                                        log(10)
(%i10) plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,8000,80000],[logx]);
plotplot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,8000,80000],[logx]);
Run Example
I(i):=-i/(s*R*C);
                                          - i
(%o1)                            I(i) := -----
                                         s R C
(%i2) eq1: Vhp=Vin+Vlp-d*(tilt*Vbp1-0.8*Vbp2+(1/tilt)*Vbp3);
                                    Vbp3
(%o2)          Vhp = Vlp + Vin - d (---- - 0.8 Vbp2 + tilt Vbp1)
                                    tilt
(%i3) eq2: Vbp1=I(Vhp);
                                          Vhp
(%o3)                           Vbp1 = - -----
                                         s C R
(%i4) eq3: Vbp2=I(Vbp1);
                                         Vbp1
(%o4)                           Vbp2 = - -----
                                         s C R
(%i5) eq4: Vbp3=I(Vbp2);
                                         Vbp2
(%o5)                           Vbp3 = - -----
                                         s C R
(%i6) eq5: Vlp=I(Vbp3);
                                         Vbp3
(%o6)                            Vlp = - -----
                                         s C R
(%i7) eq6: linsolve([eq1,eq2,eq3,eq4,eq5],[Vhp,Vbp1,Vbp2,Vbp3,Vlp]);

rat: replaced -0.8 by -4/5 = -0.8
(%o7) [Vhp = 
                               4           4  4
                            5 s  tilt Vin C  R
- -----------------------------------------------------------------------, 
             4  4  4        2  2  2             3     2  3  3
  tilt (- 5 s  C  R  + 4 d s  C  R  + 5) + 5 d s  tilt  C  R  + 5 d s C R
Vbp1 = 
                             3           3  3
                          5 s  tilt Vin C  R
-----------------------------------------------------------------------, 
           4  4  4        2  2  2             3     2  3  3
tilt (- 5 s  C  R  + 4 d s  C  R  + 5) + 5 d s  tilt  C  R  + 5 d s C R
Vbp2 = 
                               2           2  2
                            5 s  tilt Vin C  R
- -----------------------------------------------------------------------, 
             4  4  4        2  2  2             3     2  3  3
  tilt (- 5 s  C  R  + 4 d s  C  R  + 5) + 5 d s  tilt  C  R  + 5 d s C R
Vbp3 = 
                           5 s tilt Vin C R
-----------------------------------------------------------------------, 
           4  4  4        2  2  2             3     2  3  3
tilt (- 5 s  C  R  + 4 d s  C  R  + 5) + 5 d s  tilt  C  R  + 5 d s C R
                                 4  4  4        2  2  2
Vlp = - (5 tilt Vin)/(tilt (- 5 s  C  R  + 4 d s  C  R  + 5)
        3     2  3  3
 + 5 d s  tilt  C  R  + 5 d s C R)]
(%i8) eq7: (eq6),s=%i*2*%pi*f,R=100000,C=100e-12,d=1,Vin=1.0,tilt=0.667;
                                          4  4
(%o8) [Vhp = - (5.3360000000000009E-19 %pi  f )
                                     4  4                            2  2
/(0.667 (- 8.0000000000000008E-19 %pi  f  - 1.6000000000000001E-9 %pi  f  + 5)
                                3  3
 - 1.7795560000000005E-14 %i %pi  f  + 1.0E-4 %i %pi f), 
                                       3  3
Vbp1 = - (2.6680000000000006E-14 %i %pi  f )
                                     4  4                            2  2
/(0.667 (- 8.0000000000000008E-19 %pi  f  - 1.6000000000000001E-9 %pi  f  + 5)
                                3  3
 - 1.7795560000000005E-14 %i %pi  f  + 1.0E-4 %i %pi f), 
                                 2  2
Vbp2 = (1.3340000000000001E-9 %pi  f )/(0.667
                              4  4                            2  2
 (- 8.0000000000000008E-19 %pi  f  - 1.6000000000000001E-9 %pi  f  + 5)
                                3  3
 - 1.7795560000000005E-14 %i %pi  f  + 1.0E-4 %i %pi f), 
Vbp3 = (6.6699999999999995E-5 %i %pi f)
                                     4  4                            2  2
/(0.667 (- 8.0000000000000008E-19 %pi  f  - 1.6000000000000001E-9 %pi  f  + 5)
                                3  3
 - 1.7795560000000005E-14 %i %pi  f  + 1.0E-4 %i %pi f), 
                                                  4  4
Vlp = - 3.335/(0.667 (- 8.0000000000000008E-19 %pi  f
                            2  2                                     3  3
 - 1.6000000000000001E-9 %pi  f  + 5) - 1.7795560000000005E-14 %i %pi  f
 + 1.0E-4 %i %pi f)]
(%i9) db(v):=20*log(abs(v))/log(10);
                                     20 log(abs(v))
(%o9)                       db(v) := --------------
                                        log(10)
(%i10) plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1000,100000],[logx]);
plotplot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1000,100000],[logx]);
Run Example
I(i):=-i/(s*R*C);
                                          - i
(%o1)                            I(i) := -----
                                         s R C
(%i2) eq1: Vhp=Vin+Vlp+d*(Vbp1+Vbp3-0.354*Vbp2);
(%o2)           Vhp = Vlp + Vin + d (Vbp3 - 0.354 Vbp2 + Vbp1)
(%i3) eq2: Vbp1=I(Vhp);
                                          Vhp
(%o3)                           Vbp1 = - -----
                                         s C R
(%i4) eq3: Vbp2=I(Vbp1);
                                         Vbp1
(%o4)                           Vbp2 = - -----
                                         s C R
(%i5) eq4: Vbp3=I(Vbp2);
                                         Vbp2
(%o5)                           Vbp3 = - -----
                                         s C R
(%i6) eq5: Vlp=I(Vbp3);
                                         Vbp3
(%o6)                            Vlp = - -----
                                         s C R
(%i7) eq6: linsolve([eq1,eq2,eq3,eq4,eq5],[Vhp,Vbp1,Vbp2,Vbp3,Vlp]);

rat: replaced -0.354 by -177/500 = -0.354
                                          4      4  4
                                     500 s  Vin C  R
(%o7) [Vhp = ----------------------------------------------------------------, 
                  4  4  4           3  3  3        2  2  2
             500 s  C  R  + d (500 s  C  R  + 177 s  C  R  + 500 s C R) - 500
                                      3      3  3
                                 500 s  Vin C  R
Vbp1 = - ----------------------------------------------------------------, 
              4  4  4           3  3  3        2  2  2
         500 s  C  R  + d (500 s  C  R  + 177 s  C  R  + 500 s C R) - 500
                                    2      2  2
                               500 s  Vin C  R
Vbp2 = ----------------------------------------------------------------, 
            4  4  4           3  3  3        2  2  2
       500 s  C  R  + d (500 s  C  R  + 177 s  C  R  + 500 s C R) - 500
                                  500 s Vin C R
Vbp3 = - ----------------------------------------------------------------, 
              4  4  4           3  3  3        2  2  2
         500 s  C  R  + d (500 s  C  R  + 177 s  C  R  + 500 s C R) - 500
                                  500 Vin
Vlp = ----------------------------------------------------------------]
           4  4  4           3  3  3        2  2  2
      500 s  C  R  + d (500 s  C  R  + 177 s  C  R  + 500 s C R) - 500
(%i8) eq7: (eq6),s=%i*2*%pi*f,R=100000,C=100e-12,d=1,Vin=1.0,tilt=1;
                                        4  4
(%o8) [Vhp = (8.0000000000000006E-17 %pi  f )
                            4  4                                3  3
/(8.0000000000000006E-17 %pi  f  - 3.9999999999999999E-12 %i %pi  f
                            2  2
 - 7.0800000000000012E-8 %pi  f  + 0.01 %i %pi f - 500), 
                                     3  3
Vbp1 = (3.9999999999999999E-12 %i %pi  f )
                            4  4                                3  3
/(8.0000000000000006E-17 %pi  f  - 3.9999999999999999E-12 %i %pi  f
                            2  2
 - 7.0800000000000012E-8 %pi  f  + 0.01 %i %pi f - 500), 
                                   2  2
Vbp2 = - (2.0000000000000002E-7 %pi  f )
                            4  4                                3  3
/(8.0000000000000006E-17 %pi  f  - 3.9999999999999999E-12 %i %pi  f
                            2  2
 - 7.0800000000000012E-8 %pi  f  + 0.01 %i %pi f - 500), 
                                                    4  4
Vbp3 = - (0.01 %i %pi f)/(8.0000000000000006E-17 %pi  f
                                3  3                            2  2
 - 3.9999999999999999E-12 %i %pi  f  - 7.0800000000000012E-8 %pi  f
                                                                4  4
 + 0.01 %i %pi f - 500), Vlp = 500.0/(8.0000000000000006E-17 %pi  f
                                3  3                            2  2
 - 3.9999999999999999E-12 %i %pi  f  - 7.0800000000000012E-8 %pi  f
 + 0.01 %i %pi f - 500)]
(%i9) db(v):=20*log(abs(v))/log(10);
                                     20 log(abs(v))
(%o9)                       db(v) := --------------
                                        log(10)
(%i10) plot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1,1000000],[logx]);
plotplot2d([db(rhs(eq7[1])),db(rhs(eq7[2])),db(rhs(eq7[3])),db(rhs(eq7[4])),db(rhs(eq7[5]))],[f,1,1000000],[logx]);
[abs,acos,asin,atan2,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [abs,acos,asin,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [abs,append,carg,cos,denom,do,plot2d,ratnumer,rhs,sin,solve,sqrt] [abs,carg,linsolve,log,plot2d,rhs] [abs,cos,plot2d,sin] [abs,define,diff,expand,find_root,float,plot2d,realroots] [abs,define,diff,find_root,float,pi,plot2d] [abs,define,find_root,plot2d] [abs,define,plot2d,realroots] [abs,define,plot2d] [abs,diff,log,plot2d] [abs,draw,draw2d,load,log] [abs,ev,eval,plot2d,sin] [abs,ev,load,log,plot2d] [abs,exp,float,plot2d] [abs,exp,plot2d] [abs,expand,plot2d,solve,tex] [abs,linsolve,log,plot2d,rhs] [abs,linsolve] [abs,log,matrix,plot2d,ratsimp] [abs,log,plot2d] [abs,plot2d,simpsum,sin,sum] [abs,plot2d,sin] [abs,plot2d,sqrt] [abs,plot2d] [acos,asin,atan,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [asin,atan,expand,float,linsolve,pi,rhs,sqrt,time] [bc2,diff,numer,ode2,plot2d,rhs,solve,subst] [cabs,carg,ev,load,log,numer,plot2d] [cos,define,diff,expand,find_root,float,log,plot2d] [cos,diff,float,ic2,ode2,plot2d,rhs,sqrt] [cos,diff,ic2,ode2,plot2d,rhs] [cos,fortran,log,plot2d,taylor,tex] [cos,globalsolve,linsolve,plot2d,sin,true] [cos,log,plot2d] [diff,exp,ic2,ode2,plot2d,rhs] [diff,exp,log,plot2d,realpart] [diff,ic1,ode2,plot2d,rhs] [diff,ic2,ode2,plot2d,rhs] [diff,log,plot2d] [diff,ode2,plot2d,rhs] [exp,float,globalsolve,linsolve,plot2d,true] [exp,log,plot2d] [expand,float,linsolve,matrix,rhs,time] [expand,float,linsolve,rhs,time] [factor,kill,length,makelist,map,plot2d,rhs,solve,sum] [fortran,log,plot2d,taylor,tex] [globalsolve,linsolve,plot2d,true] [integrate,log,plot2d] [log,plot2d,rhs,solve]

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