started table
This commit is contained in:
alexander
@@ -920,11 +920,6 @@
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)
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]
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#bgBlock(fill: colorAllgemein)[
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#subHeading(fill: colorAllgemein)[Complex Zahlen]
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]
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// Complex AC
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#bgBlock(fill: colorComplexAC)[
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#subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung]
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@@ -970,6 +965,8 @@
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$P_w = U_m^2 / 2R = (I_m^2 R)/2$
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$P = 1/2 U I^* = 1/2 abs(U)^2 Y^* = 1/2 abs(I)^2 Z^*$
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$U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$
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]
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@@ -991,192 +988,303 @@
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#pagebreak()
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#bgBlock(fill: colorZweiTore, width: 100%)[
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#subHeading(fill: colorZweiTore)[Zwei-Tor-Übersichts]
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#table(
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fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow },
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columns: (auto, auto, auto, 1fr, 1fr, 1fr),
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[*Name*],
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[*Schaltbild*],
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[*Ersatz-Schaltbild*],
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[*Eigenschaften*],
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[*Beschreibung*],
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[*Knotenspannungs Analyse*],
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[Nullor],
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[],
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[],
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[],
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[$A = mat(0, 0; 0, 0)$],
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[],
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[OpAmp \ lin],
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[],
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[],
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[],
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[],
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[],
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[OpAmp \ $U_"sat+"$],
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[],
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[],
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[],
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[],
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[],
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[OpAmp \ $U_"sat-"$],
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[],
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[],
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[],
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[],
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[],
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[VCVS],
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[],
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[],
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[],
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[$H' = mat(0, 0; mu, 0) quad A = mat(1/mu 0; 0, 0)$],
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[],
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[VCCS],
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[],
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[],
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[],
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[$G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0)$],
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[],
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[CCVS],
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[],
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[],
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[],
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[$R = mat(0, 0, r, 0) quad A = mat(0, 0; 1/r, 0)$],
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[],
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[CCCS],
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[],
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[],
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[],
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[$H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta)$],
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[],
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[Übertrager],
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[],
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[],
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[],
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[],
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[],
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[Gyrator],
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[],
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[],
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[
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- Antireziprok, Antisymetrisch
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- Auch Positiv-Immitanz-Inverter
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],
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[$R = mat(0, -R_d; R_d, 0) quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) quad A' = mat(0, -R_d; -1/R_d, 0)$],
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[],
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[NIK],
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[],
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[],
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[],
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[
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- Akitv
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- Antireziprok
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- Symetrisch für $abs(k) = 1$
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],
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[$H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0); A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k)$],
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[T-Glied],
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[],
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[],
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[],
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[
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],
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[],
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[$pi$-Glied],
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[],
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[],
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[
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]
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)
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]
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// Tor Eigenschaften
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#place(
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bottom, float: true, scope: "parent",
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bgBlock(fill: colorEigenschaften, width: 100%)[
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#subHeading(fill: colorEigenschaften)[Tor Eigenschaften]
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#bgBlock(fill: colorEigenschaften, width: 100%)[
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#subHeading(fill: colorEigenschaften)[Tor Eigenschaften]
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#table(
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columns: (auto, auto, auto, auto),
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inset: 2mm,
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align: horizon,
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fill: (x, y) => if calc.rem(y, 2) == 1 { rgb("#c5c5c5") } else { white },
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table.header([], [*Ein-Tor*], [*Zwei-Tor*], [*Reaktive Elemente*]),
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[*passiv*\ (nimmt Energie auf)\ $not$aktiv],
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[$forall (u,i) in cal(F): u dot i >= 0$],
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[
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$jMat(U)^T jMat(I) + jMat(I)^T jMat(U)$\
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$forall vec(jVec(u),jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0$
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],
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[],
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[*verlustlos*],
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[
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$forall (u,i) in cal(F): u dot i = 0$\
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Kennline nur $u\/i$-Achsen
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],
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[$forall vec(jVec(u),jVec(v)) in cal(F) : jVec(u)^T jVec(i) = 0$],
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[
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$u\/q$-Plot: Wenn keine Schleifen \
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$i\/Phi$-Plot: Wenn keine Schleifen \
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$u\/i$-Plot: Wenn Auf Achse \
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$Phi\/q$-Plot: Wenn auf Achse \
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],
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[*linear*],
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[Kennline ist Gerade],
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[
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Darstellbar: Matrix $+$ Aufpunkt\
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$lambda_1 vec(jVec(u)_1, jVec(i)_1) + lambda_2 vec(jVec(u)_2, jVec(i)_2) in cal(F)$
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],
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[],
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[*quellenfrei*],
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[$(qty("0", "A"), qty("0", "V")) in cal(F)$],
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[$(qty("0", "A"), qty("0", "V")) in cal(F)$],
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[$(qty("0", "A"), qty("0", "V")) in cal(F)$],
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[*streng linear*],
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[linear UND quellenfrei],
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[linear UND quellenfrei\ Darstellbar: Nur Matrix],
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[],
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[*ungepolt* \ (Punkt sym.)],
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[$(u,i) in cal(F) <=> (-u, -i) in cal(F)\
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g(u) = i, r(i) = u
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$],
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[
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N/A
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],
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[],
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[*symetrisch*\ $<=>$ Umkehrbar],
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[N/A],
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[
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$jMat(A) = jMat(A')$\
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$jMat(G) = jMat(P) jMat(G) jMat(P), space jMat(R) = jMat(P) jMat(R) jMat(P), quad jMat(P) = mat(0, 1; 1, 0) \
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det(H) = 1, $
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],
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[],
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[*Reziprok*],
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[Immer Reziprok],
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[
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$cal(F)$ symetrisch $=> cal(F)$ reziprok
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$jMat(U)^T jMat(I) - jMat(I)^T jMat(U) = 0 \
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jMat(R)^T = jMat(R), quad jMat(G)^T = jMat(G) quad h_21 = -h_12 \ det(jMat(A)) = 1 quad det(jMat(A')) = 1 quad h'_21 = -h'_12$],
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[],
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[*$x$-gesteudert*], [Existiert $r(i) = u \/g(u) = i$], [Existiert die Matrix? siehe Tabelle],
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[],
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[Alle Beschreibung],
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[Klar],
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[$det(M) != 0$, Alle Eintrag $!= 0$]
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)
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]
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#bgBlock(fill: colorZweiTore)[
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#set text(size: 10pt)
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#subHeading(fill: colorZweiTore)[Umrechnung Zweitormatrizen]
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#table(
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columns: (12mm, 1fr, 1fr, 1fr, 1fr, 1fr, 1fr),
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align: center,
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inset: (bottom: 4mm, top: 4mm),
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gutter: 0.1mm,
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fill: (x, y) => if x != 0 and calc.rem(x, 2) == 0 { rgb("#c5c5c5") } else { white },
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table.cell(
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inset: 0mm,
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[
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#cetz.canvas(length: 12mm,{
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import cetz.draw : *
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||||
line((1,0), (0,1))
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||||
content((0.309, 0.25), "Out")
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content((0.75, 0.75), "In")
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||||
})
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||||
]),
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$bold(R)$,
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$bold(G)$,
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$bold(H)$,
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$bold(H')$,
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$bold(A)$,
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$bold(A')$,
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$bold(R)$,
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$mat(r_11, r_12; r_21, r_22)$,
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$jMat(G^(-1) =) 1/det(bold(G)) mat(g_22, -g_12; -g_21, g_11)$,
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$1/h_22 mat(det(bold(H)), h_12; -h_21, 1)$,
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$1/h'_11 mat(1, -h'_12; h'_21, det(bold(H')))$,
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$1/a_21 mat(a_11, det(bold(A)); 1, a_22)$,
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$1/a'_21 mat(a'_22, 1; det(bold(A')), a'_11)$,
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$bold(G)$,
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$jMat(R^(-1) =) 1/det(bold(R)) mat(r_22, -r_12; -r_21, r_11)$,
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$mat(g_11, g_12; g_21, g_22)$,
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$1/h_11 mat(1, -h_12; h_21, det(bold(H)))$,
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$1/h'_22 mat(det(bold(H')), h'_12; -h'_21, 1)$,
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$1/a_12 mat(a_22, -det(bold(A)); -1, a_11)$,
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$1/a'_12 mat(a'_11, -1; -det(bold(A')), a'_22)$,
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$bold(H)$,
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$1/r_22 mat(det(bold(R)), r_12; -r_21, 1)$,
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$1/g_11 mat(1, -g_12; g_21, det(bold(G)))$,
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$mat(h_11, h_12; h_21, h_22)$,
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$jMat(H')^(-1)= 1/det(bold(H')) mat(h'_22, -h'_12; -h'_21, h'_11)$,
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||||
$1/a_22 mat(a_12, det(bold(A)); -1, a_21)$,
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$1/a'_11 mat(a'_12, 1; -det(bold(A')), a'_21)$,
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$bold(H')$,
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$1/r_11 mat(1, -r_12; r_21, det(bold(R)))$,
|
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$1/g_22 mat(det(bold(G)), g_12; -g_21, 1)$,
|
||||
$jMat(H^(-1))= 1/det(bold(H)) mat(h_22, -h_12; -h_21, h_11)$,
|
||||
$mat(h'_11, h'_12; h'_21, h'_22)$,
|
||||
$1/a_11 mat(a_21, -det(bold(A)); 1, a_12)$,
|
||||
$1/a'_22 mat(a'_21, -1; det(bold(A')), a'_12)$,
|
||||
|
||||
$bold(A)$,
|
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$1/r_21 mat(r_11, det(bold(R)); 1, r_22)$,
|
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$1/g_21 mat(-g_22, -1; -det(bold(G)), -g_11)$,
|
||||
$1/h_21 mat(-det(bold(H)), -h_11; -h_22, -1)$,
|
||||
$1/h'_21 mat(1, h'_22; h'_11, det(bold(H')))$,
|
||||
$mat(a_11, a_12; a_21, a_22)$,
|
||||
$jMat(A'^(-1))= 1/det(bold(A')) mat(a'_22, a'_12; a'_21, a'_11)$,
|
||||
|
||||
$bold(A')$,
|
||||
$1/r_12 mat(r_22, det(bold(R)); 1, r_11)$,
|
||||
$1/g_12 mat(-g_11, -1; -det(bold(G)), -g_22)$,
|
||||
$1/h_12 mat(1, h_11; h_22, det(bold(H)))$,
|
||||
$1/h'_12 mat(-det(bold(H')), -h'_22; -h'_11, -1)$,
|
||||
$jMat(A^(-1))= 1/det(bold(A)) mat(a_22, a_12; a_21, a_11)$,
|
||||
$mat(a'_11, a'_12; a'_21, a'_22)$,
|
||||
)
|
||||
|
||||
#table(
|
||||
columns: (auto, auto, auto, auto),
|
||||
inset: 2mm,
|
||||
align: horizon,
|
||||
fill: (x, y) => if calc.rem(y, 2) == 1 { rgb("#c5c5c5") } else { white },
|
||||
columns: (12mm, 1fr, 1fr, 1fr, 1fr, 1fr, 1fr),
|
||||
align: center,
|
||||
inset: (bottom: 4mm, top: 4mm),
|
||||
gutter: 0.1mm,
|
||||
fill: (x, y) => if x != 0 and calc.rem(x, 2) == 0 { rgb("#c5c5c5") } else { white },
|
||||
|
||||
table.header([], [*Ein-Tor*], [*Zwei-Tor*], [*Reaktive Elemente*]),
|
||||
[*passiv*\ (nimmt Energie auf)\ $not$aktiv],
|
||||
[$forall (u,i) in cal(F): u dot i >= 0$],
|
||||
[
|
||||
$jMat(U)^T jMat(I) + jMat(I)^T jMat(U)$\
|
||||
$forall vec(jVec(u),jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0$
|
||||
],
|
||||
[],
|
||||
$bold(R) jVec(i) = jVec(u)$,
|
||||
$bold(G) jVec(u) = jVec(i)$,
|
||||
$bold(H) vec(i_1, u_2) = vec(u_1, i_2)$,
|
||||
$bold(H') vec(u_1, i_2) = vec(i_1, u_2)$,
|
||||
$bold(A) vec(u_2, -i_2) = vec(i_1, u_1)$,
|
||||
$bold(A') vec(u_1, -i_1) = vec(i_2, u_2)$,
|
||||
|
||||
[*verlustlos*],
|
||||
[
|
||||
$forall (u,i) in cal(F): u dot i = 0$\
|
||||
|
||||
Kennline nur $u\/i$-Achsen
|
||||
],
|
||||
[$forall vec(jVec(u),jVec(v)) in cal(F) : jVec(u)^T jVec(i) = 0$],
|
||||
[
|
||||
$u\/q$-Plot: Wenn keine Schleifen \
|
||||
$i\/Phi$-Plot: Wenn keine Schleifen \
|
||||
$u\/i$-Plot: Wenn Auf Achse \
|
||||
$Phi\/q$-Plot: Wenn auf Achse \
|
||||
],
|
||||
|
||||
|
||||
[*linear*],
|
||||
[Kennline ist Gerade],
|
||||
[
|
||||
Darstellbar: Matrix $+$ Aufpunkt\
|
||||
$lambda_1 vec(jVec(u)_1, jVec(i)_1) + lambda_2 vec(jVec(u)_2, jVec(i)_2) in cal(F)$
|
||||
],
|
||||
[],
|
||||
|
||||
[*quellenfrei*],
|
||||
[$(qty("0", "A"), qty("0", "V")) in cal(F)$],
|
||||
[$(qty("0", "A"), qty("0", "V")) in cal(F)$],
|
||||
[$(qty("0", "A"), qty("0", "V")) in cal(F)$],
|
||||
|
||||
[*streng linear*],
|
||||
[linear UND quellenfrei],
|
||||
[linear UND quellenfrei\ Darstellbar: Nur Matrix],
|
||||
[],
|
||||
|
||||
|
||||
[*ungepolt* \ (Punkt sym.)],
|
||||
[$(u,i) in cal(F) <=> (-u, -i) in cal(F)\
|
||||
g(u) = i, r(i) = u
|
||||
$],
|
||||
[
|
||||
N/A
|
||||
],
|
||||
[],
|
||||
|
||||
[*symetrisch*\ $<=>$ Umkehrbar],
|
||||
[N/A],
|
||||
[
|
||||
$jMat(A) = jMat(A')$\
|
||||
$jMat(G) = jMat(P) jMat(G) jMat(P), space jMat(R) = jMat(P) jMat(R) jMat(P), quad jMat(P) = mat(0, 1; 1, 0) \
|
||||
det(H) = 1, $
|
||||
|
||||
],
|
||||
[],
|
||||
|
||||
[*Reziprok*],
|
||||
[Immer Reziprok],
|
||||
[
|
||||
$cal(F)$ symetrisch $=> cal(F)$ reziprok
|
||||
|
||||
$jMat(U)^T jMat(I) - jMat(I)^T jMat(U) = 0 \
|
||||
jMat(R)^T = jMat(R), quad jMat(G)^T = jMat(G) quad h_21 = -h_12 \ det(jMat(A)) = 1 quad det(jMat(A')) = 1 quad h'_21 = -h'_12$],
|
||||
[],
|
||||
|
||||
[*$x$-gesteudert*], [Existiert $r(i) = u \/g(u) = i$], [Existiert die Matrix? siehe Tabelle],
|
||||
[],
|
||||
|
||||
[Alle Beschreibung],
|
||||
[Klar],
|
||||
[$det(M) != 0$, Alle Eintrag $!= 0$]
|
||||
)
|
||||
]
|
||||
)
|
||||
|
||||
#place(bottom+left, scope: "parent", float: true)[
|
||||
#bgBlock(fill: colorZweiTore)[
|
||||
#set text(size: 10pt)
|
||||
|
||||
#subHeading(fill: colorZweiTore)[Umrechnung Zweitormatrizen]
|
||||
#table(
|
||||
columns: (12mm, 1fr, 1fr, 1fr, 1fr, 1fr, 1fr),
|
||||
align: center,
|
||||
inset: (bottom: 4mm, top: 4mm),
|
||||
gutter: 0.1mm,
|
||||
fill: (x, y) => if x != 0 and calc.rem(x, 2) == 0 { rgb("#c5c5c5") } else { white },
|
||||
|
||||
table.cell(
|
||||
inset: 0mm,
|
||||
[
|
||||
#cetz.canvas(length: 12mm,{
|
||||
import cetz.draw : *
|
||||
line((1,0), (0,1))
|
||||
content((0.309, 0.25), "Out")
|
||||
content((0.75, 0.75), "In")
|
||||
})
|
||||
]),
|
||||
$bold(R)$,
|
||||
$bold(G)$,
|
||||
$bold(H)$,
|
||||
$bold(H')$,
|
||||
$bold(A)$,
|
||||
$bold(A')$,
|
||||
|
||||
$bold(R)$,
|
||||
$mat(r_11, r_12; r_21, r_22)$,
|
||||
$jMat(G^(-1) =) 1/det(bold(G)) mat(g_22, -g_12; -g_21, g_11)$,
|
||||
$1/h_22 mat(det(bold(H)), h_12; -h_21, 1)$,
|
||||
$1/h'_11 mat(1, -h'_12; h'_21, det(bold(H')))$,
|
||||
$1/a_21 mat(a_11, det(bold(A)); 1, a_22)$,
|
||||
$1/a'_21 mat(a'_22, 1; det(bold(A')), a'_11)$,
|
||||
|
||||
$bold(G)$,
|
||||
$jMat(R^(-1) =) 1/det(bold(R)) mat(r_22, -r_12; -r_21, r_11)$,
|
||||
$mat(g_11, g_12; g_21, g_22)$,
|
||||
$1/h_11 mat(1, -h_12; h_21, det(bold(H)))$,
|
||||
$1/h'_22 mat(det(bold(H')), h'_12; -h'_21, 1)$,
|
||||
$1/a_12 mat(a_22, -det(bold(A)); -1, a_11)$,
|
||||
$1/a'_12 mat(a'_11, -1; -det(bold(A')), a'_22)$,
|
||||
|
||||
$bold(H)$,
|
||||
$1/r_22 mat(det(bold(R)), r_12; -r_21, 1)$,
|
||||
$1/g_11 mat(1, -g_12; g_21, det(bold(G)))$,
|
||||
$mat(h_11, h_12; h_21, h_22)$,
|
||||
$jMat(H')^(-1)= 1/det(bold(H')) mat(h'_22, -h'_12; -h'_21, h'_11)$,
|
||||
$1/a_22 mat(a_12, det(bold(A)); -1, a_21)$,
|
||||
$1/a'_11 mat(a'_12, 1; -det(bold(A')), a'_21)$,
|
||||
|
||||
$bold(H')$,
|
||||
$1/r_11 mat(1, -r_12; r_21, det(bold(R)))$,
|
||||
$1/g_22 mat(det(bold(G)), g_12; -g_21, 1)$,
|
||||
$jMat(H^(-1))= 1/det(bold(H)) mat(h_22, -h_12; -h_21, h_11)$,
|
||||
$mat(h'_11, h'_12; h'_21, h'_22)$,
|
||||
$1/a_11 mat(a_21, -det(bold(A)); 1, a_12)$,
|
||||
$1/a'_22 mat(a'_21, -1; det(bold(A')), a'_12)$,
|
||||
|
||||
$bold(A)$,
|
||||
$1/r_21 mat(r_11, det(bold(R)); 1, r_22)$,
|
||||
$1/g_21 mat(-g_22, -1; -det(bold(G)), -g_11)$,
|
||||
$1/h_21 mat(-det(bold(H)), -h_11; -h_22, -1)$,
|
||||
$1/h'_21 mat(1, h'_22; h'_11, det(bold(H')))$,
|
||||
$mat(a_11, a_12; a_21, a_22)$,
|
||||
$jMat(A'^(-1))= 1/det(bold(A')) mat(a'_22, a'_12; a'_21, a'_11)$,
|
||||
|
||||
$bold(A')$,
|
||||
$1/r_12 mat(r_22, det(bold(R)); 1, r_11)$,
|
||||
$1/g_12 mat(-g_11, -1; -det(bold(G)), -g_22)$,
|
||||
$1/h_12 mat(1, h_11; h_22, det(bold(H)))$,
|
||||
$1/h'_12 mat(-det(bold(H')), -h'_22; -h'_11, -1)$,
|
||||
$jMat(A^(-1))= 1/det(bold(A)) mat(a_22, a_12; a_21, a_11)$,
|
||||
$mat(a'_11, a'_12; a'_21, a'_22)$,
|
||||
)
|
||||
|
||||
#table(
|
||||
columns: (12mm, 1fr, 1fr, 1fr, 1fr, 1fr, 1fr),
|
||||
align: center,
|
||||
inset: (bottom: 4mm, top: 4mm),
|
||||
gutter: 0.1mm,
|
||||
fill: (x, y) => if x != 0 and calc.rem(x, 2) == 0 { rgb("#c5c5c5") } else { white },
|
||||
|
||||
[],
|
||||
$bold(R) jVec(i) = jVec(u)$,
|
||||
$bold(G) jVec(u) = jVec(i)$,
|
||||
$bold(H) vec(i_1, u_2) = vec(u_1, i_2)$,
|
||||
$bold(H') vec(u_1, i_2) = vec(i_1, u_2)$,
|
||||
$bold(A) vec(u_2, -i_2) = vec(i_1, u_1)$,
|
||||
$bold(A') vec(u_1, -i_1) = vec(i_2, u_2)$,
|
||||
|
||||
)
|
||||
]
|
||||
]
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
#let bgBlock(body, fill: color, width: 100%) = block(body, fill:fill.lighten(80%), width: width, inset: (bottom: 2mm))
|
||||
#let bgBlock(body, fill: color, width: 100%) = block(body, fill:fill.lighten(80%), width: width, inset: (bottom: 2mm, left: 2mm, right: 2mm,))
|
||||
|
||||
#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm))
|
||||
#let MathAlignLeft(e) = {
|
||||
@@ -6,7 +6,7 @@
|
||||
}
|
||||
|
||||
#let subHeading(body, fill: color) = {
|
||||
box(
|
||||
move(dx: -2mm, dy: 0mm, box(
|
||||
align(
|
||||
top+center,
|
||||
text(
|
||||
@@ -17,10 +17,10 @@
|
||||
)
|
||||
),
|
||||
fill: fill,
|
||||
width: 100%,
|
||||
width: 100% + 4mm,
|
||||
inset: 1mm,
|
||||
height: auto
|
||||
)
|
||||
))
|
||||
}
|
||||
|
||||
#let MathAlignLeft(e) = {
|
||||
@@ -58,12 +58,14 @@
|
||||
#let ComplexNumbersSection(i: $i$) = [
|
||||
$1/#i = #i^(-1) = -#i quad quad #i^2=-1 quad quad sqrt(#i) = 1/sqrt(2) + 1/sqrt(2)#i$
|
||||
|
||||
$z in CC = a + b #i quad quad quad z = r dot e^(phi #i)$ \
|
||||
$z in CC = a + b #i quad quad quad z = r dot e^(#i phi)$ \
|
||||
$z_0 + z_1 = (a_0 + a_1) + (b_0 + b_1) #i$\
|
||||
$z_0 dot z_1 = (a_1 a_2 - b_1 b_2) + #i (a_1b_2 + a_2 b_1) = r_0 r_1 e^(#i (phi_0 + phi_1))$\
|
||||
$z^x = r^x dot e^(phi #i dot x) quad x in RR$ \
|
||||
$z_0/z_1 = r_0/r_1 e^(#i (phi_0 - phi_1)) quad quad quad$
|
||||
|
||||
$z^* = a - #i b = r e^(-#i phi)$
|
||||
|
||||
$r = abs(z) quad phi = cases(
|
||||
+ arccos(a/r) space : space b >= 0,
|
||||
- arccos(a/r) space : space b < 0,
|
||||
|
||||
Reference in New Issue
Block a user