### Related

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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

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

eq2: Vbp1=I(Vhp);

Calculate

##### abs-linsolve-log-plot2d-rhs

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]);
plot```
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]);
plot```
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]);
plot```

### Related Help

Help for Abs

Help for Linsolve

Help for Log

Help for Plot2d

Help for Rhs