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Electronic Formulas



,  W = \frac{J}{S}

Transformer inductance and coupling

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


Turns ratio

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


Ohms law in magnetics


\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}



 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 = \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


Ic = Ibβ


I_b = \frac{I_c}{\beta}

β = beta </math> Ib = Base current Ic = Collector current

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 :

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 :

Gm = Large signal Transconductance (not to be confused with gm
 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

 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).


ESR formulas

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