216 formulas
Ohm's Law ECE-CA-1 V = I * R
V volts, I amps, R ohms
Electrical Power ECE-CA-1 P = V * I
P watts, V volts, I amps
Power (I^2 R) ECE-CA-1 P = I^2 * R
P watts, I amps, R ohms
Series Resistance ECE-CA-2 Req = R1 + R2
ohms
Parallel Resistance ECE-CA-2 Req = (R1*R2)/(R1+R2)
ohms
Capacitive Reactance ECE-CA-3 Xc = 1/(2*pi*f*C)
Xc ohms, f Hz, C farads
Inductive Reactance ECE-CA-3 Xl = 2*pi*f*L
Xl ohms, f Hz, L henries
Real Power (1-phase) ECE-PS-1 P = V * I * pf
P watts, V volts, I amps, pf dimensionless
Apparent Power (1-phase) ECE-PS-1 S = V * I
S VA, V volts, I amps
Reactive Power (1-phase) ECE-PS-1 Q = V * I * sqrt(1 - pf^2)
Q VAR, V volts, I amps, pf dimensionless
Real Power (3-phase) ECE-PS-1 P = sqrt(3) * VL * IL * pf
P watts, VL volts, IL amps, pf dimensionless
Voltage Divider ECE-CA-2 Vout = Vin * R2/(R1+R2)
volts; R ohms
Parallel Resistance (n resistors) ECE-CA-2 1/Req = 1/R1 + 1/R2 + 1/R3
ohms
RL Time Constant ECE-EL-1 tau = L / R
tau seconds, L henries, R ohms
Percent Change MATH-1 %change = (b - a)/a * 100
dimensionless
Quadratic Discriminant MATH-1 D = b^2 - 4*a*c
dimensionless
RMS of a Sinusoid MATH-1 Vrms = Vp / sqrt(2)
Vrms, Vp volts
Arithmetic Mean MATH-1 mean = (x + y)/2
any
Frequency and Period MATH-1 f = 1 / T
f Hz, T seconds
RC Time Constant ECE-EL-1 tau = R * C
tau seconds, R ohms, C farads
Coulomb's Law ECE-EM-1 F = k*q1*q2/r^2
F newtons, q coulombs, r meters
Current Divider (two branches) ECE-CA-2 I1 = It * R2/(R1+R2)
I amps, R ohms
Conductance ECE-CA-2 G = 1 / R
G siemens, R ohms
Kirchhoff's Current Law ECE-CA-1 Iout = Iin1 + Iin2 - Iknown
I amps
Kirchhoff's Voltage Law ECE-CA-1 Vx = Vs - V1 - V2
V volts
Energy Stored in a Capacitor ECE-CA-3 W = 0.5 * C * V^2
W joules, C farads, V volts
Energy Stored in an Inductor ECE-CA-3 W = 0.5 * L * I^2
W joules, L henries, I amps
Capacitor Charge ECE-CA-3 Q = C * V
Q coulombs, C farads, V volts
Capacitors in Series ECE-CA-3 Ceq = (C1 * C2)/(C1 + C2)
C farads
Capacitors in Parallel ECE-CA-3 Ceq = C1 + C2
C farads
Inductors in Series ECE-CA-3 Leq = L1 + L2
L henries
Impedance Magnitude (R, X) ECE-CA-3 Z = sqrt(R^2 + X^2)
Z ohms, R ohms, X ohms
Impedance Angle ECE-CA-3 theta = atan(X / R)
theta deg, R ohms, X ohms
Admittance Magnitude ECE-CA-3 Y = 1 / Z
Y siemens, Z ohms
Angular Frequency ECE-CA-3 omega = 2 * pi * f
omega rad/s, f Hz
Resonant Frequency (LC) ECE-CA-3 f0 = 1 / (2 * pi * sqrt(L * C))
f0 Hz, L henries, C farads
Quality Factor (series RLC) ECE-CA-3 Q = (1/R) * sqrt(L / C)
Q dimensionless, R ohms, L henries, C farads
Bandwidth from Q ECE-CA-3 BW = f0 / Q
BW Hz, f0 Hz, Q dimensionless
Maximum Power Transfer ECE-CA-2 Pmax = Vth^2 / (4 * Rth)
P watts, Vth volts, Rth ohms
Thevenin Load Current ECE-CA-2 IL = Vth / (Rth + RL)
I amps, V volts, R ohms
RC Charging Voltage ECE-EL-1 Vc = Vs * (1 - exp(-t/(R*C)))
V volts, t seconds, R ohms, C farads
Power Factor ECE-PS-1 pf = P / S
pf dimensionless, P watts, S VA
Apparent Power from P and Q ECE-PS-1 S = sqrt(P^2 + Q^2)
S VA, P watts, Q VAR
Transformer Turns Ratio (voltage) V2 = V1 * (N2 / N1)
V volts, N turns
Transformer Current Ratio I2 = I1 * (N1 / N2)
I amps, N turns
Reflected Impedance Zp = Zs * (N1 / N2)^2
Z ohms, N turns
Energy Cost ECE-PS-1 cost = P * h * rate
cost dollars, P kW, h hours, rate $/kWh
Efficiency ECE-PS-1 eta = Pout / Pin
eta dimensionless, P watts
Power Loss ECE-PS-1 Ploss = Pin - Pout
P watts
Per-Unit Value pu = actual / base
dimensionless
Base Impedance Zbase = Vbase^2 / Sbase
Z ohms, V volts, S VA
Three-Phase Real Power (line) ECE-PS-1 P = sqrt(3) * VL * IL * pf
P watts, VL volts, IL amps, pf dimensionless
Reactive Power from P and S ECE-PS-1 Q = sqrt(S^2 - P^2)
Q VAR, S VA, P watts
Power Angle from pf ECE-PS-1 theta = acos(pf)
theta rad, pf dimensionless
Reactive Power for PF Correction ECE-PS-1 Qc = P * (tan(acos(pf1)) - tan(acos(pf2)))
Q VAR, P watts, pf dimensionless
Capacitance for PF Correction ECE-PS-1 C = Qc / (2 * pi * f * V^2)
C farads, Q VAR, f Hz, V volts
Three-Phase Line Current ECE-PS-1 IL = P / (sqrt(3) * VL * pf)
I amps, P watts, VL volts, pf dimensionless
Line Voltage (Wye) ECE-PS-1 VL = sqrt(3) * Vp
V volts
Energy Consumed ECE-PS-1 E = P * t
E Wh, P watts, t hours
Voltage Regulation VR = (Vnl - Vfl) / Vfl * 100
VR percent, V volts
Diode Series Current I = (Vs - Vd) / R
I amps, V volts, R ohms
Voltage After Diode Drop Vout = Vs - Vd
V volts
Half-Wave Rectifier DC Output Vdc = Vm / pi
V volts
Full-Wave Rectifier DC Output Vdc = 2 * Vm / pi
V volts
BJT Collector Current Ic = beta * Ib
I amps, beta dimensionless
BJT Emitter Current Ie = (beta + 1) * Ib
I amps, beta dimensionless
BJT Alpha from Beta alpha = beta / (beta + 1)
dimensionless
MOSFET Saturation Current Id = 0.5 * k * (Vgs - Vt)^2
I amps, k A/V^2, V volts
Op-Amp Inverting Gain Av = -Rf / Rin
Av dimensionless, R ohms
Op-Amp Non-Inverting Gain Av = 1 + Rf / Rin
Av dimensionless, R ohms
Op-Amp Output (Non-Inverting) Vout = Vin * (1 + Rf / Rin)
V volts, R ohms
Op-Amp Summing Amplifier Vout = -Rf * (V1 / R1 + V2 / R2)
V volts, R ohms
Voltage Gain in Decibels GdB = 20 * log10(Vout / Vin)
G dB, V volts
Power Gain in Decibels GdB = 10 * log10(Pout / Pin)
G dB, P watts
Cascaded Stage Gain Atotal = A1 * A2
dimensionless
RC Filter Cutoff Frequency fc = 1 / (2 * pi * R * C)
f Hz, R ohms, C farads
RL Filter Cutoff Frequency fc = R / (2 * pi * L)
f Hz, R ohms, L henries
Zener Regulator Series Current Is = (Vin - Vz) / Rs
I amps, V volts, R ohms
Capacitor Ripple Voltage Vr = Iload / (f * C)
V volts, I amps, f Hz, C farads
Slope Between Two Points m = (y2 - y1)/(x2 - x1)
dimensionless
Distance Between Two Points d = sqrt((x2-x1)^2 + (y2-y1)^2)
dimensionless
Midpoint (x-coordinate) xm = (x1 + x2)/2
dimensionless
Quadratic Root (+) x = (-b + sqrt(b^2 - 4*a*c))/(2*a)
dimensionless
Logarithm Change of Base y = log(x)/log(b)
dimensionless
Logarithm Power Rule y = n * log10(x)
dimensionless
Exponential Growth y = A * exp(k * t)
dimensionless
Law of Cosines (side) a = sqrt(b^2 + c^2 - 2*b*c*cos(C))
lengths, C radians
Law of Sines (side) a = b * sin(A)/sin(B)
lengths, angles radians
Pythagorean Identity (sin) s = sqrt(1 - c^2)
dimensionless
Power Rule Derivative (at x) dy = n * x^(n-1)
dimensionless
Radius of Curvature (simplified) R = (1 + d1^2)^(3/2) / abs(d2)
dimensionless
Arithmetic Series Sum S = n * (a1 + an)/2
dimensionless
Geometric Series Sum S = a1 * (1 - r^n)/(1 - r)
dimensionless
Infinite Geometric Series S = a1/(1 - r)
dimensionless
Complex Magnitude r = sqrt(a^2 + b^2)
dimensionless
Complex Argument theta = atan(b / a)
dimensionless, theta radians
2D Dot Product d = ax*bx + ay*by
dimensionless
2x2 Determinant det = a*d - b*c
dimensionless
2D Vector Magnitude mag = sqrt(x^2 + y^2)
dimensionless
Weighted Mean m = (w1*x1 + w2*x2)/(w1 + w2)
dimensionless
Sample Variance (2 pts) s2 = ((x1-m)^2 + (x2-m)^2)/(n-1)
dimensionless
Sample Standard Deviation s = sqrt(v)
dimensionless
Range R = xmax - xmin
dimensionless
Permutations P = factn / factnr
dimensionless
Combinations C = perm / factr
dimensionless
Probability of Union P = pa + pb - pab
dimensionless
Conditional Probability P = pab / pb
dimensionless
Complement Probability P = 1 - p
dimensionless
Joint Probability (Independent) P = pa * pb
dimensionless
Bayes' Theorem P = (pba * pa)/pb
dimensionless
Expected Value (2 outcomes) E = x1*p1 + x2*p2
dimensionless
Binomial Probability P = comb * exp(k*log(p)) * exp((n-k)*log(1-p))
dimensionless
Binomial Mean mu = n * p
dimensionless
Binomial Variance v = n * p * (1 - p)
dimensionless
Standard Error of the Mean sem = sd / sqrt(n)
dimensionless
Least-Squares Slope (2 pts) b = (y2 - y1)/(x2 - x1)
dimensionless
Least-Squares Intercept a = ybar - b*xbar
dimensionless
Z-Score z = (x - mu)/sd
dimensionless
Nyquist Rate fs = 2 * fmax
f Hz
Folding (Nyquist) Frequency ff = fs / 2
f Hz
Period from Frequency T = 1 / f
T seconds, f Hz
Duty Cycle D = ton / period * 100
percent, seconds
Average of Half-Wave Rectified Sine avg = Vm / pi
V volts
Average of Full-Wave Rectified Sine avg = 2 * Vm / pi
V volts
Peak-to-Peak from Amplitude vpp = 2 * Vm
V volts
Crest Factor cf = Vpeak / Vrms
dimensionless
Harmonic Frequency fn = n * f0
f Hz
Wavelength lambda = v / f
lambda meters, v m/s, f Hz
Settling Time (first-order, ~4 tau) ts = 4 * tau
seconds
System DC Gain K = yss / xss
dimensionless
First-Order Roll-Off Attenuation atten = 20 * ndec
dB, decades
Phasor Magnitude mag = sqrt(re^2 + im^2)
dimensionless
Electric Field of a Point Charge ECE-EM-1 E = k*q/r^2
E V/m, q C, r m
Force from Field ECE-EM-1 F = q*E
F N, q C, E V/m
Potential of a Point Charge ECE-EM-1 V = k*q/r
V volts, q C, r m
Electric Flux (uniform field) flux = E*A
flux V*m, E V/m, A m^2
Gauss's Law (enclosed charge) qenc = eps0 * flux
q C, flux V*m
Field from Flux Density E = D / eps0
E V/m, D C/m^2
Parallel-Plate Capacitance C = epsr * eps0 * A / dgap
C F, A m^2, d m
Energy Stored in a Capacitor W = 0.5 * C * V^2
W J, C F, V volts
Charge on a Capacitor Q = C * V
Q C, C F, V volts
Energy Stored in an Inductor W = 0.5 * L * I^2
W J, L H, I A
Inductance of a Coil L = mu0 * N2 * A / len
L H, A m^2, len m
Faraday's Law (induced EMF) emf = N * dflux / dt
emf V, flux Wb, t s
Magnetic Force on a Charge F = q*v*B
F N, q C, v m/s, B T
Force on a Current-Carrying Wire F = B*I*len
F N, B T, I A, len m
Radius of Charged Particle in B Field r = m_kg*v / (q*B)
r m, v m/s, q C, B T
Electromagnetic Wave Speed v = f * lambda
v m/s, f Hz, lambda m
Intrinsic Impedance (ratio form) eta = E / H
eta ohms, E V/m, H A/m
Single Payment Compound Amount (F/P) ECE-EE-1 F = P * (1 + i)^n
F future, P present, i rate, n periods
Single Payment Present Worth (P/F) ECE-EE-1 P = F / (1 + i)^n
P present, F future, i rate, n periods
Uniform Series Compound Amount (F/A) ECE-EE-2 F = A * ((1 + i)^n - 1) / i
F future, A annuity, i rate, n periods
Capital Recovery (A/P) ECE-EE-2 A = P * (i * (1 + i)^n) / ((1 + i)^n - 1)
A annuity, P present, i rate, n periods
Straight-Line Depreciation ECE-EE-3 D = (C - S) / N
D annual, C cost, S salvage, N life
Benefit-Cost Ratio ECE-EE-4 BCR = B / Cost
BCR ratio, B benefits, Cost costs
Binary-to-Decimal (positional weights) ECE-DS-1 D = b3*8 + b2*4 + b1*2 + b0
D decimal, b3..b0 bits
Binary-to-Decimal (8-bit) ECE-DS-1 D = b7*128 + b6*64 + b5*32 + b4*16 + b3*8 + b2*4 + b1*2 + b0
D decimal, b7..b0 bits
Hex-to-Decimal (2 digits) ECE-DS-1 D = h1*16 + h0
D decimal, h1 high digit, h0 low digit
Binary Addition (value) ECE-DS-1 S = A + B
S sum, A addend, B addend
Full Adder Sum (numeric value) ECE-DS-2 S = a + b + cin
S sum value, a bit, b bit, cin carry-in
Positional Bit Weight ECE-DS-1 W = 2^n
W weight, n bit position
2:1 Multiplexer Output ECE-DS-3 Y = s*d1 + (1 - s)*d0
Y output, s select, d0 input0, d1 input1
Maximum Clock Frequency ECE-DS-3 f = 1000 / (n * tpd)
f MHz, n stages, tpd ns per stage
Power Gain in Decibels ECE-COMM-2 G = 10 * log10(Pout / Pin)
G dB, Pout output power, Pin input power
Voltage Gain in Decibels ECE-COMM-2 G = 20 * log10(Vout / Vin)
G dB, Vout output, Vin input
Decibels to Power Ratio ECE-COMM-2 R = 10^(G / 10)
R ratio, G dB
Shannon Channel Capacity ECE-COMM-2 C = B * log10(1 + SNR) / log10(2)
C bps, B bandwidth, SNR linear ratio
Nyquist Sampling Rate ECE-COMM-1 fs = 2 * fmax
fs sample rate, fmax max frequency
Nyquist Maximum Data Rate ECE-COMM-1 C = 2 * B * log10(L) / log10(2)
C bps, B bandwidth, L signal levels
Bandwidth (frequency span) ECE-COMM-1 BW = fhigh - flow
BW bandwidth, fhigh upper freq, flow lower freq
Signal-to-Noise Ratio in dB ECE-COMM-2 SNRdb = 10 * log10(Psig / Pnoise)
SNRdb dB, Psig signal power, Pnoise noise power
Closed-Loop DC Gain ECE-CTRL-1 T = G / (1 + G * H)
T closed-loop gain, G forward gain, H feedback gain
Open-Loop Gain ECE-CTRL-1 L = G * H
L loop gain, G forward gain, H feedback gain
First-Order Time Constant ECE-CTRL-2 tau = 1 / a
tau time constant, a pole magnitude
Percent Overshoot ECE-CTRL-2 PO = 100 * exp(-zeta * pi / sqrt(1 - zeta^2))
PO percent, zeta damping ratio
Settling Time (2%) ECE-CTRL-2 ts = 4 / (zeta * wn)
ts settling time, zeta damping ratio, wn natural frequency
Steady-State Error (step, type 0) ECE-CTRL-3 ess = 1 / (1 + Kp)
ess error, Kp position error constant
Gain Margin (dB) ECE-CTRL-4 GM = 20 * log10(1 / g)
GM dB, g gain at phase crossover
Phase Margin ECE-CTRL-4 PM = 180 + phase
PM degrees, phase angle at gain crossover
Usable Hosts per Subnet ECE-NET-2 H = 2^(32 - prefix) - 2
H usable hosts, prefix CIDR prefix length
Total Addresses in Subnet ECE-NET-2 A = 2^(32 - prefix)
A total addresses, prefix CIDR prefix length
Host Bits from Prefix ECE-NET-2 hb = 32 - prefix
hb host bits, prefix CIDR prefix length
Bandwidth-Delay Product ECE-NET-3 BDP = rate * delay
BDP bits, rate bandwidth, delay round-trip time
Packet Transmission Time ECE-NET-3 tt = size / rate
tt time, size packet size, rate link rate
Throughput (data over time) ECE-NET-3 TP = data / time
TP throughput, data bits transferred, time seconds
Average CPI (two instruction classes) ECE-COMP-1 CPI = (n1 * c1 + n2 * c2) / (n1 + n2)
CPI cycles per instruction, n1/n2 counts, c1/c2 class CPIs
CPU Execution Time ECE-COMP-1 T = IC * CPI * Tc
T time, IC instruction count, CPI cycles per instruction, Tc cycle time
Clock Cycle Time ECE-COMP-4 Tc = 1 / f
Tc cycle time, f clock frequency
Amdahl's Law Speedup ECE-COMP-4 S = 1 / ((1 - p) + p / k)
S speedup, p enhanced fraction, k enhancement factor
Memory Address Bits ECE-COMP-2 b = log10(N) / log10(2)
b address bits, N number of locations
Addressable Memory Locations ECE-COMP-2 N = 2^b
N locations, b address bits
Average Memory Access Time ECE-COMP-2 AMAT = ht + mr * mp
AMAT avg access time, ht hit time, mr miss rate, mp miss penalty
Data Transfer Rate ECE-COMP-3 R = bytes / time
R rate, bytes data size, time seconds
Simple Loop Operation Count ECE-SOFT-1 ops = c * n
ops operations, c ops per iteration, n iterations
Nested Loop Operation Count ECE-SOFT-1 ops = n * m
ops operations, n outer iterations, m inner iterations
Binary Search Maximum Comparisons ECE-SOFT-1 C = log10(n) / log10(2) + 1
C comparisons, n sorted elements (power of two)
Worst-Case Comparison Count (quadratic sort) ECE-SOFT-1 C = n * (n - 1) / 2
C comparisons, n elements
Array Element Memory Offset ECE-SOFT-2 addr = base + index * size
addr address, base base address, index element index, size element size
Stack Final Size ECE-SOFT-2 s = init + pushes - pops
s final size, init initial size, pushes count, pops count
Queue Final Size ECE-SOFT-2 q = init + enq - deq
q final size, init initial size, enq enqueues, deq dequeues
Resistivity from Resistance ECE-MAT-1 rho = R * A / L
rho resistivity, R resistance, A area, L length
Conductivity (reciprocal of resistivity) ECE-MAT-1 sigma = 1 / rho
sigma conductivity, rho resistivity
Resistance from Material Properties ECE-MAT-1 R = rho * L / A
R resistance, rho resistivity, L length, A area
Absolute Permittivity ECE-MAT-2 eps = epsr * eps0
eps permittivity, epsr relative permittivity, eps0 vacuum permittivity
Magnetic Flux Density from Permeability ECE-MAT-3 B = mur * mu0 * H
B flux density, mur relative permeability, mu0 vacuum permeability, H field strength
Minority Carrier Concentration ECE-MAT-4 p = ni2 / nd
p minority concentration, ni2 intrinsic squared, nd donor concentration
Drift Current Density ECE-MAT-4 J = sigma * E
J current density, sigma conductivity, E electric field
Laplace of Scaled Step (final value) ECE-LIN-1 F = a / s0
F value, a step amplitude, s0 evaluation point
Inverse Laplace Time Constant ECE-LIN-1 tau = 1 / a
tau time constant, a pole magnitude
Transfer Function DC Gain ECE-LIN-2 K = b0 / a0
K DC gain, b0 numerator constant, a0 denominator constant
First-Order Pole Location ECE-LIN-6 p = -a0 / a1
p pole, a0 constant term, a1 first-order coefficient
First-Order Zero Location ECE-LIN-6 z = -b0 / b1
z zero, b0 constant term, b1 first-order coefficient
First-Order Time Constant ECE-LIN-3 tau = 1 / wc
tau time constant, wc corner frequency
Damping Ratio from Coefficients ECE-LIN-3 zeta = b / (2 * sqrt(k * m))
zeta damping ratio, b damping coeff, k stiffness, m mass
First-Order Magnitude Response ECE-LIN-4 M = K / sqrt(1 + (w / wc)^2)
M magnitude, K DC gain, w frequency, wc corner frequency
Discrete Convolution Sample (two-tap) ECE-LIN-5 y = x0 * h1 + x1 * h0
y output sample, x0/x1 input samples, h0/h1 impulse taps