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Basic Circuit Analysis 2 Cheat Sheet (DRAFT) by

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

Y-Delta Transf­orm­ation

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.