Cheatography
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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*10^{18} elek. 
Resistance (H2)
Ohm's Law 
I[A] = U[V] / R[Ohm] 
Resistivity 
R = rho * (l[m]/A[m^{2}]) 
Power Absorbtion 
P = V^{2}/R = I^{2}R 
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 shortcircuit between a and b
Norton Circuit:
Found by source transformation of Thevenin
Isc equals In
Maximum Power Transfer:
Vth^{2} / 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)
DeltaY 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 = 0.5CV^{2}2 
Timevarying 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 = (N^{2}*mu*A)/l 
Inductor series 
Lt = L1+ L2 + Ln 
Inductor parallel 
1 / Lt = (1/L1) + (1/L2) etc. 
Energy Storage 
Wl=0.5Li^{2} 
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 = Vm^{2} / 2R = Im^{2}R / 2 
Effective Value (RMS) 
Veff = Vm / 2^{0.5} 
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/2^{0.5})*hoek 
AC Voltage 
V=((R * Im)/2^{0.5})*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 YDelta transformation (H14)
DeltaY 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 
Vth^{2}/(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 = a^{2}Z2 
Current rating 
kVA transformer / voltage rating 
PhiMax 
PhiM = (sqrt(2)*Vrms)/(wN) 
coupling coefficient 
k = M / sqrt(L1*L2) 
tijdfase 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 
3Phase (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. 
