Cheatography

Basic Circuit Analysis 2 Cheat Sheet (DRAFT) by Kevin694

AC and DC Circuit Analysis

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Basic Concepts (H1)

 Current I[A]=Q­[C]­/t[s] Voltage U[V]=W­[J]­/Q[C] Power P[W]= W / t = U * I Energy W = P * t Coulomb 1C = 6,241*1018 elek.

Resistance (H2)

 Ohm's Law I[A] = U[V] / R[Ohm] Resist­ivity R = rho * (l[m]/A[m2]) Power Absorbtion P = V2/R = I2R

DC Circuits (H3)

 Voltage Law (KVL): The sum of all voltage drops equals the sum of al voltage rises in a mesh. Current Law (KCL): The sum of all currents entering a closed surface equals the sum of all leaving one. Equivalent Resistor: Rt = (R1 * R2) / (R1+R2) (in case of 2 resistors paralllel)

DC Circuits Analysis (H4)

 Source Transf­orm­ation: Current and Voltage source with 1 resistor are interc­han­gable. I = V / R and U = I * R Mesh Analysis: Applying KVL to a mesh. Nodal Analysis: Applying KCL to a node.

Equivalent Circuits (H5)

 Thevenin Circuit: Circuits can be reduced to voltage source with resistor in serie. Rt = Rth (open circuit and indepe­ndent sources deacti­vated) Vth = open circuit voltage Isc = current in short-­circuit between a and b Norton Circuit: Found by source transf­orm­ation of Thevenin Isc equals In Maximum Power Transfer: Vth2 / 4Rth Milliman's Theorem: Multiple voltage sources with resistors can be combined into one by transf­orm­ations giving one voltage source. Vm = (G1V1 + .. + GnVn) / (G1 + .. + Gn) Rm = 1 / (G1 + .. + Gn) Delta-Y Transf­orm­ation: Ra = (R1 * R2) / (R1 +R2 + R3) Rb = (R2 * R3) / (R1+ R2 + R3) Rc = (R1 * R3) / (R1+ R2 + R3) R1 = (RaRb + RaRc + RbRc) / Rb R2 = (RaRb + RaRc + RbRc) / Rc R3 = (RaRb + RaRc + RbRc) / Ra

Operat­ional Amplifier (H6)

 U+ = U- and I+ = I- = 0 inverter: Vo=-(R­f/R­i)*Vi summer: Vo=-((­Rf/­Ra)­Va+­(Rf­/Rb­)Vb­+(R­f/R­c)Vc)

Capacitors (H8)

 Capaci­tance C = Q / U Capaci­tance C = e * (A/d) Capaci­tance parallel Ct = C1 + C2 + .. Capaci­tance series 1 / Ct = (1/C1) + (1/C2) etc. Energy Storage Wc = 0.5CV22 Time-v­arying Current i = dq/dt = C * dv/dt RC time constant tau = Rth * C RC expression voltage v(t) = v(oo) + [v(0+) - v(00)]e-t/tau V RC expression current i(t) = i(oo) + [i(0+) - i(00)]e-t/tau A

Inductors (H9)

 Flux v = N * dphi/dt Inductance L i = N phi Coil inductance L = (N2*mu*A)/l Inductor series Lt = L1+ L2 + Ln Inductor parallel 1 / Lt = (1/L1) + (1/L2) etc. Energy Storage Wl=0.5Li2 RC time constant tau = L / Rth

Altern­ating Current (H10)

 Frequency f [Hz] = 1 / T [s] Angular Velocity omega [rad/s] = 2*pi*f Average Value factor 2 / pi = 0.637 Resistor Power Pav = Vm2 / 2R = Im2R / 2 Effective Value (RMS) Veff = Vm / 20.5 Inductor Law Xl = omega*L and Im = Vm / Xl Capacitor Law Xc = -1/(om­ega*C)

Component Behavior (H10)

 Resistor: Current and Voltage in phase. v=Vm * sin(om­ega­*t+phi) i=Im * sin(omga * t+phi) Inductor: Voltage leads Current by 90 deg. v=Xl * Im*cos­(om­ega*t + phi) i=Im*s­in(­omega*t + phi) Capacitor: Current leadsV­oltage by 90 deg. v=Vm*s­in(­ome­ga*­t+phi) i=omega * C * Vm * cos(om­ega*t + phi)

AC Circuit Analysis (H12)

 Impedantie Z=V/I Impedantie (2) Z=R+jX Admitantie Y=1/Z AC Current I=(Im/20.5)*hoek AC Voltage V=((R * Im)/20.5)*hoek

AC Circuit Analysis (H13)

 Mesh Analysis: Transform current to voltage source Use of KVL Nodal Analysis: Transform voltage to current source Use of KCL

AC Y-Delta transf­orm­ation (H14)

 Delta-Y Transf­orm­ation: Za = (Z1 * Z2) / (Z1 +Z2 + Z3) Zb = (Z2 * Z3) / (Z1 +Z2 + Z3) Zc = (Z1 * Z3) /(Z1 +Z2 + Z3) Z1 = (ZaZb + ZaZc + ZbZc) / Zb Z2 = (ZaZb + ZaZc + ZbZc) / Zc Z3 = (ZaZb + ZaZc + ZbZc) / Za

Maximum Power Absorbed (H14)

 The load is the Zth conjungate Zl = Zth* Max. Power Absorbed Vth2/(4Rth) (Vth is RMS of Vth)

Power in AC circuits (H15)

 Instan­taneous Power: p = V * I cos(theta) cos(theta) = Power Factor (PF) theta = fase spanning - fase stroom Reactive Power: Q = V * I * sin(theta) Complex Power: S=P+jQ Apparent Power: S=VI 1hp = 745,7 W

Transf­ormers (H16)

 Ratio v1/v2 = N1/N2 = i2/i1 Reflected Impedance Zr = V1/I1 = a2Z2 Current rating kVA transf­ormer / voltage rating PhiMax PhiM = (sqrt(­2)*­Vrm­s)/(wN) coupling coeffi­cient k = M / sqrt(L­1*L2)

tijd-fase formules

 weerstand spoel conden­sator Z R jwL 1/(jwC) R R 0 0 X 0 wL -1/(wC) Y 1/R 1/(jwL) jwC G 1/R 0 0 B 0 -1/(wL) wC

3-Phase (H17)

 Vline = sqrt(3­)*V­phase I line = sqrt(3­)*I­phase

Dot rule transf­ormer

 Primary I into dot and secondary I out of dot: I1 and I2 both positive or negative.