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carg-polarform

polarform(3+%i);

carg(3+%i);

Calculate

carg-float-invert-matrix-polarform-ratsimp-rectform

a:matrix([9-%i*10,-5,...

b:matrix([0],[-10*%e^...

c:polarform(float(rec...

Calculate

carg

carg (1 + %i);

Calculate

carg-plot2d-sin
plot2d([5.958762397937049*sin(wt+carg(I2))], [wt,0,2*%pi],[y,-6,6]);

plot2d([5.95876239793...

Calculate

carg-float

float(carg(i*3));

Calculate

carg-linsolve

Z: %i*L*w + -%i/(C*w)...

eq: carg(Z) = %pi/4;

linsolve(eq,[w]);

Calculate

carg-linsolve

Z: %i*L*w + -%i/(C*w)...

eq: carg(Z) = %pi/4;

linsolve(eq,w);

Calculate

carg-numer-rectform

L: 3.1847e-2;

C: 3.1847e-7;

R: 10;

Calculate

carg-linsolve-plot3d-rhs
plot3d(   360/(2*%pi)*carg(eq7),   [f,1,100000],[k,0.01,0.1],   [logx],[nticks,1000]);

eq1: Vint=-Iint/(s*C);

eq2: Iint=k*Iin;

eq3: Iin=Vin/30000 + ...

Calculate

carg-imagpart-radcan-realpart-sqrt

realpart(((1-(%i)*sqr...

imagpart(((1-(%i)*sqr...

radcan(((1-(%i)*sqrt(...

Calculate

carg

Run Example
(%i1)H(z):=(z+1/3)*(z-3/2)*(z-2)/z^3;
                                     1       3
                                (z + -) (z - -) (z - 2)
                                     3       2
(%o1)                   H(z) := -----------------------
                                           3
                                          z
(%i2) Ha1(z):=(z-3/2)*(z-2)/((z-2/3)*(z-1/2));
                                          3
                                     (z - -) (z - 2)
                                          2
(%o2)                      Ha1(z) := ---------------
                                          2       1
                                     (z - -) (z - -)
                                          3       2
(%i3) Hm1(z):=(z+1/3)*(z-1/2)*(z-2/3)/z^3;
                                      1       1       2
                                 (z + -) (z - -) (z - -)
                                      3       2       3
(%o3)                  Hm1(z) := -----------------------
                                            3
                                           z
(%i4) Ha2(z):=(z+1/3)*(z-3/2)*(z-2)/((z+3)*(z-2/3)*(z-1/2));
                                      1       3
                                 (z + -) (z - -) (z - 2)
                                      3       2
(%o4)                  Ha2(z) := -----------------------
                                              2       1
                                 (z + 3) (z - -) (z - -)
                                              3       2
(%i5) Hm2(z):=(z+3)*(z-2/3)*(z-1/2)/(z^3);
                                              2       1
                                 (z + 3) (z - -) (z - -)
                                              3       2
(%o5)                  Hm2(z) := -----------------------
                                            3
                                           z
(%i6) l:solve(ratnumer(H(z)),z);
                                   1      3
(%o6)                       [z = - -, z = -, z = 2]
                                   3      2
(%i7) nullst:[];
(%o7)                                 []
(%i8) re(x):=abs(x)*cos(carg(x));
(%o8)                    re(x) := abs(x) cos(carg(x))
(%i9) im(x):=abs(x)*sin(carg(x));
(%o9)                    im(x) := abs(x) sin(carg(x))
(%i10) for i:1 thru length(l) step 1 do(    a:rhs(l[i]),    nullst:append(nullst,[[re(a),im(a)]]));
(%o10)                               done
(%i11) l:solve(denom(H(z)),z);
(%o11)                              [z = 0]
(%i12) pole:[];
(%o12)                                []
(%i13) for i:1 thru length(l) step 1 do(    a:rhs(l[i]),    pole:append(pole,[[re(a),im(a)]]));
(%o13)                               done
(%i14) concat("usprüngliche Funktion H(z)");
(%o14)                    uspr?ngliche Funktion H(z)
(%i15) plot2d([sqrt(1-x^2),-sqrt(1-x^2),[discrete,nullst],[discrete,pole]],[x,-3,3],[y,-3,3],[style,[lines,0.4],[lines,0.4],[points],[points]],[point_type, circle, circle,circle,times],[color,black,black,red,blue],[legend,false],[gnuplot_preamble, "set size ratio -1"],[adapt_depth,10]);
plotplot2d([sqrt(1-x^2),-sqrt(1-x^2),[discrete,nullst],[discrete,pole]],[x,-3,3],[y,-3,3],[style,[lines,0.4],[lines,0.4],[points],[points]],[point_type, circle, circle,circle,times],[color,black,black,red,blue],[legend,false],[gnuplot_preamble, "set size ratio -1"],[adapt_depth,10]);
Run Example
T1:1;
(%o1)                                  1
(%i2) declare([T1,w], real);
(%o2)                                done
(%i3) assume(T1>
0,w>
0);
(%o3)                         [redundant, w > 0]
(%i4) w:solve(T1^2*w^4-w^2-100=0,w);
             sqrt(sqrt(401) + 1)      sqrt(sqrt(401) + 1)
(%o4) [w = - -------------------, w = -------------------, 
                   sqrt(2)                  sqrt(2)
                            sqrt(sqrt(401) - 1) %i      sqrt(sqrt(401) - 1) %i
                      w = - ----------------------, w = ----------------------]
                                   sqrt(2)                     sqrt(2)
(%i5) w:w[2];
                                sqrt(sqrt(401) + 1)
(%o5)                       w = -------------------
                                      sqrt(2)
(%i6) carg(10/(%i*w*(1+%i*w*T1)));
                          %pi          sqrt(sqrt(401) + 1)    %pi
(%o6)         - atan(w) - --- = - atan(-------------------) - ---
                           2                 sqrt(2)           2
(%i7) 
Run Example
eq1: Vint=-Iint/(s*C);
                                          Iint
(%o1)                            Vint = - ----
                                          s C
(%i2) eq2: Iint=k*Iin;
(%o2)                            Iint = Iin k
(%i3) eq3: Iin=Vin/30000 + Vint/30000;
                                    Vint     Vin
(%o3)                         Iin = ----- + -----
                                    30000   30000
(%i4) eq4: Iout=Vint/15000+Vin/30000;
                                    Vint     Vin
(%o4)                        Iout = ----- + -----
                                    15000   30000
(%i5) eq5: linsolve([eq1,eq2,eq3,eq4],[Iin,Iout,Vint,Iint]);
                s Vin C             30000 s Vin C - k Vin
(%o5) [Iin = -------------, Iout = -----------------------, 
             30000 s C + k         900000000 s C + 30000 k
                                               k Vin               k s Vin C
                                  Vint = - -------------, Iint = -------------]
                                           30000 s C + k         30000 s C + k
(%i6) eq6: rhs(eq5[2]);
                             30000 s Vin C - k Vin
(%o6)                       -----------------------
                            900000000 s C + 30000 k
(%i7) eq7: 2*%pi*carg(eq6),C=220e-12,k=0.1,s=%i*2*%pi*f,Vin=1;
(%o7) 2 %pi (atan2(1.3199999999999999E-5 %pi f, - 0.1)
                                           - atan(1.3199999999999998E-4 %pi f))
(%i8) plot2d(eq7,[f,1,100000],[logx]);
plotplot2d(eq7,[f,1,100000],[logx]);
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