Ohm's Law
Solve
I Current
A
R Resistance
Ω
V Result
V
V = I × R
Power (DC)
V Voltage
V
I Current
A
R Resistance
Ω
P Power
W
P = V×I = I²R = V²/R
Voltage Divider
Vin Input
V
R1 Top
Ω
R2 Bottom
Ω
Vout Output
V
Vout = Vin × R2 / (R1 + R2)
Current Divider
Iin Input
A
R1 Branch 1
Ω
R2 Branch 2
Ω
I1 Current 1
A
I2 Current 2
A
I1 = Iin × R2/(R1+R2)
Parallel Resistance
R1
Ω
R2
Ω
R3
Ω
R4
Ω
Rt Total
Ω
1/Rt = 1/R1 + 1/R2 + ...
Capacitor Series / Parallel
Mode
C1
µF
C2
µF
C3
µF
C4
µF
Ct Total
µF
Parallel: Ct = C1+C2+...
Delta-Wye Transform
Mode
Ra Delta
Ω
Rb Delta
Ω
Rc Delta
Ω
Out1
Ω
Out2
Ω
Out3
Ω
D→Y: R1=Rb·Rc/(Ra+Rb+Rc)
Common Resistor Values (E12 Series)
1.0 1.2 1.5 1.82.2 2.7 3.3 3.94.7 5.6 6.8 8.2Multipliers: ×1, ×10, ×100, ×1k, ×10k
Capacitive Reactance (Xc)
f Frequency
Hz
C Capacitance
µF
Xc Result
Ω
Xc = 1 / (2πfC)
Inductive Reactance (XL)
f Frequency
Hz
L Inductance
mH
XL Result
Ω
XL = 2πfL
Impedance (Z)
R Resistance
Ω
X Reactance
Ω
|Z| Magnitude
Ω
θ Phase
deg
|Z| = √(R² + X²), θ = atan(X/R)
LC Resonance
L Inductance
µH
C Capacitance
pF
f₀ Resonance
Hz
f₀ = 1 / (2π√LC)
RC Time Constant
R Resistance
Ω
C Capacitance
µF
τ Time Const
s
fc Cutoff
Hz
τ = RC, fc = 1/(2πRC)
RL Time Constant
R Resistance
Ω
L Inductance
mH
τ Time Const
s
fc Cutoff
Hz
τ = L/R, fc = R/(2πL)
VSWR / Return Loss
From
Γ Refl Coeff
Γ Result
VSWR
:1
RL Ret Loss
dB
ML Mis Loss
dB
Γ=(Z-Z0)/(Z+Z0), VSWR=(1+Γ)/(1-Γ)
Skin Depth
f Frequency
Hz
Mat Material
δ Depth
µm
δ = √(2ρ / ωµ₀µr)
Transmission Line Z0
Type
W Trace
mm
H Dielectric
mm
T Copper
mm
εr Dk
Z0 Impedance
Ω
εeff
Hammerstad-Jensen (IPC-2141), valid to ~10 GHz
Filter Response Reference
-3dB Cutoff frequency (fc), 70.7% amplitude-6dB/oct First-order filter rolloff-12dB/oct Second-order filter rolloff5τ Time to 99.3% of final valueOp-Amp Gain
Config
Rf Feedback
Ω
Rin Input
Ω
Av Gain
V/V
dB Gain
dB
Inv: −Rf/Rin | Non-inv: 1+Rf/Rin
Wheatstone Bridge
Mode
Vs Supply
V
R1
Ω
R2
Ω
R3
Ω
R4
Ω
Result
V
Status
Vout = Vs(R3/(R3+R1) − R4/(R4+R2))
555 Timer
Mode
Ra
Ω
Rb
Ω
C
µF
f Frequency
Hz
D Duty
%
tH High
ms
tL Low
ms
f = 1.44/((Ra+2Rb)C)
Op-Amp Configuration Reference
Inverting Av = −Rf/Rin, input at inverting (−)Non-Inv Av = 1+Rf/Rin, input at non-inverting (+)Differential Vout = Rf/Rin × (V2−V1)Unity Gain Buffer, Av = 1 (Rf=0, Rin=∞)Junction Temperature
Mode
Pd Power
W
Ta Ambient
°C
Rja Junc-Amb
°C/W
Tjmax
°C
θtot Total
°C/W
Tj Junction
°C
Margin
°C
Status
Tj = Ta + Rja × Pd
Fuse Selection
P Power
W
V Voltage
V
SF Safety
×
I Operating
A
If Fuse Size
A
Fuse = (P/V) × SF, next std size
Wire Current Capacity (AWG)
AWG Gauge
d Diameter
mm
A Area
mm²
R Resistance
Ω/m
I Max Current
A
Chassis wiring @ 30°C rise
Resistor Code Decoder
Mode
1st
2nd
Mult
Tol
R Value
Ω
Capacitor Energy
C Capacitance
µF
V Voltage
V
E Energy
mJ
E = ½CV²
Inductor Energy
L Inductance
mH
I Current
A
E Energy
mJ
E = ½LI²
SNR / Noise Floor
Mode
Ps Signal
dBm
Pn Noise
dBm
SNR Result
dB
Lin Ratio
SNR = Ps − Pn | Friis: Ft = F1+(F2−1)/G1+...
Standard Capacitor Values (E12)
1.0 1.2 1.5 1.8 pF/nF/µF2.2 2.7 3.3 3.9 pF/nF/µF4.7 5.6 6.8 8.2 pF/nF/µF10 22 47 100 common µFdB (Power Ratio)
P1 Reference
W
P2 Measured
W
dB Result
dB
dB = 10 × log₁₀(P2/P1)
dB (Voltage Ratio)
V1 Reference
V
V2 Measured
V
dB Result
dB
dB = 20 × log₁₀(V2/V1)
dBm ↔ Watts
dBm
dBm
P Power
mW
P(mW) = 10^(dBm/10)
Watts → dBm
P Power
mW
dBm
dBm
dBm = 10 × log₁₀(P/1mW)
Frequency ↔ Wavelength
f Frequency
MHz
λ Wavelength
m
λ/4 Quarter
m
λ = c/f (c = 299,792,458 m/s)
Period ↔ Frequency
T Period
ms
f Frequency
Hz
f = 1/T
Common dB Values
+3 dB = 2× power, 1.41× voltage+6 dB = 4× power, 2× voltage+10 dB = 10× power, 3.16× voltage+20 dB = 100× power, 10× voltage-3 dB = 0.5× power, 0.707× voltage0 dBm = 1 mW into 50ΩRadio Frequency Bands
VLF 3-30 kHz (λ 100-10 km)LF 30-300 kHz (λ 10-1 km)MF 300-3000 kHz (λ 1000-100 m)HF 3-30 MHz (λ 100-10 m)VHF 30-300 MHz (λ 10-1 m)UHF 300-3000 MHz (λ 1-0.1 m)2.4 GHz WiFi (λ 12.5 cm)5.8 GHz WiFi (λ 5.2 cm)