Disclaimer

This information HAS errors and is made available WITHOUT ANY WARRANTY OF ANY KIND and without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. It is not permissible to be read by anyone who has ever met a lawyer or attorney. Use is confined to Engineers with more than 370 course hours of engineering.
If you see an error contact:
+1(785) 841 3089
inform@xtronics.com

Electronic Formulas

Power

W = Watt
J = Joule
S = Second

, $W = \frac{J}{S}$

Transformer inductance and coupling

$M = k \sqrt{(L_1)(L_2}$

Where:

M = Mutual inductance in Henrys
k = coefficient of coupling
L_1 Inductance of first winding
L_2 Inductance of second winding

Turns ratio

For Iron Core , $\frac{N_s}{N_p} = \frac{E_s}{E_p} = \frac{I_p}{I_s}$

Where:

p subscript refers to Primary winding
s subscript refers to secondary winding
N = number of turns

Ohms law in magnetics

Where:

F = repulsive force
r = distance between poles
μ permeability ( μ of air = 1)
H = Magnetizing Force in Oersted
mmf = Magnetic Motive Force - in Gilberts
Orested = Gilberts/CM
β = Flux density in Gauss
φ = Total flux density in Maxwells
r = Reluctance
P = Permeance

$\mathcal{P} = \frac{1}{\mathcal{R}}$

mmf = φR

$F = \frac{m_1m_2}{\mu r^2}$

, $H = \frac{F}{m_2} = \frac{m_1}{\mu r^2}$

Impedance

Where

X_L refers to inductive reactance
X_C refers to capacitive reactance

$X_C = \frac{1}{2\pi Cf}$

$\,\! X_L = 2\pi Lf$

Impedance through a transformer

$\frac{Z_p}{Z_s} = \left(\frac{N_p}{N_s}\right)^2$

Series RCL

$Z = \sqrt{R^2 + \left(X_L -X_C\right)^2}$

Parallel RCL

$Z = \frac{1}{\sqrt{\frac{1}{R^2} +\left( \frac{1}{X_L} - \frac{1}{X_C}\right)^2}}$

Parallel LC Resonance

$f_r = \frac{1}{2\pi\sqrt{LC}}$

Q or Quality factor

$Q = \frac{X}{R}$

Time constance

Τ = time in seconds to 2/3 rise

Τ = RC

$\Tau = \frac{L}{R}$

Power factor

$P_f = \frac{True\;power}{apparent\;power} = \frac{I^2R}{VA} = \frac{R}{Z} = \cos\theta$

Standing Wave Ratio (SWR)

$SWR = \frac{E_{max}}{E_{min}} = \frac{I_{max}}{I_{min}} = \frac{Z_1}{Z_2}$

Modulation

$%Modulation = \frac{E_{max} - E_{min}}{2E_{carrier}}\left( 100% \right)$

$Deviation\ Ratio = \frac{Max\ Deviation}{Highest\ Modulating\ Frequency}$ Deviation = modulating index Deviation ratio = Deviation / highest modulating frequency

Transistors

Zero_Gain_Amps
Current gain

I_c = I_bβ

$I_b = \frac{I_c}{\beta}$

Where

β = beta </math> I_b = Base current I_c = Collector current

Transconductance: Transconductance is a contraction of transfer conductance. The old unit of conductance, the mho (ohm spelled backwards), was replaced by the SI unit, the siemens, with the symbol S (1 siemens = 1 ampere per volt).

$g_m = \frac{\Delta I_{out}}{\Delta V_{in}}$

For small signal alternating current, the Transconductance is estimated:

$g_m = {i_\mathrm{out} \over v_\mathrm{in}} = \frac{I_{cq}}{\frac{kT}{q}} = \frac{I_{cq}}{26mV} = \frac{\Delta I_{out}}{\Delta V_{in}}$

Where :

g_m = small signal transconductance
$\frac{kT}{q} = V_{T}$ Thermal voltage
k Boltzmann constant , $1.380 × 10^{−23} \frac{J}{K}$
I_cq = quiescent point, Q-point, or bias point

Distortion begins somewhere once the base voltage exceeds about 5 to 15mVp-p

If we look at large signals we must use

$G_m = {i_\mathrm{out} \over v_\mathrm{in}}$

Where :

G_m = Large signal Transconductance (not to be confused with g_m

Small-signal-input-resistance ( R_π )for a common emitter amp with the emitter AC grounded:

$R_\pi = \frac{\Delta V_{be}}{\Delta I_c} = \beta \left( \Delta \frac{V_{be}}{\Delta I_c} \right) = \frac{\beta }{g_m}$

Which means that input resistance goes up with β

Large-signal-Input-resistance ( R_Π )for a common emitter amp with the emitter AC grounded:

$R_\Pi = \frac{R_\pi G_m}{g_m}$

Ebers-Moll equation

$I_{E} = I_{ES} \left(e^{\frac{V_{BE}}{V_{T}}} - 1\right)$

$V_{T} = \frac{kT}{q}$ (approximately 26 mV at 300 K ≈ room temperature).

where

V_T is the Boltzmann constant kT / q
q Electronic Charge
TTemperature in K
I_E is the emitter current
I_C is the collector current
α_F is the common base forward short circuit current gain (0.98 to 0.998)
I_ES is the reverse saturation current of the base–emitter diode (on the order of 10⁻¹⁵ to 10⁻¹² amperes)
V_BE is the base–emitter voltage

ESR formulas

Capacitors_and_ESR

Top Page

wiki Index