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*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) |
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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 |
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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. |
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