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Electronic Formulas
Power
- W = Watt
- J = Joule
- S = Second
,
![W = \frac{J}{S}](images/bbec364d3bba4d025e19da00971a102b.png)
Transformer inductance and coupling
![M = k \sqrt{(L_1)(L_2}](images/9bfb804358264f590b7165214d317f77.png)
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}](images/63d1a80cab839c31b6f432205d53dab2.png)
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}}](images/35a567e0da042b50d6ec3dd6d22593ac.png)
mmf = φR
![F = \frac{m_1m_2}{\mu r^2}](images/9cc4ca3c1a1a009fc3739cf2d9f8458e.png)
,
![H = \frac{F}{m_2} = \frac{m_1}{\mu r^2}](images/4d5a58e34ddfde96498840c9c9a255d3.png)
Impedance
Where
- XL refers to inductive reactance
- XC refers to capacitive reactance
![X_C = \frac{1}{2\pi Cf}](images/fa35a08e076d8328902c4778e2474661.png)
![\,\! X_L = 2\pi Lf](images/115842c6f053d0c77fff021126d2a073.png)
Impedance through a transformer
![\frac{Z_p}{Z_s} = \left(\frac{N_p}{N_s}\right)^2](images/f620e88ec1fb01ea12cb19d12c843757.png)
Series RCL
![Z = \sqrt{R^2 + \left(X_L -X_C\right)^2}](images/2f4f0619b2b1e22b52bf83bffbe53add.png)
Parallel RCL
![Z = \frac{1}{\sqrt{\frac{1}{R^2} +\left( \frac{1}{X_L} - \frac{1}{X_C}\right)^2}}](images/41578e7e3aa4918d121defb153b90e34.png)
Parallel LC Resonance
![f_r = \frac{1}{2\pi\sqrt{LC}}](images/ed53c939fba615d029181c9248fc5284.png)
Q or Quality factor
![Q = \frac{X}{R}](images/c1dec8b6d28e17d499bd104477390f02.png)
Time constance
Τ = time in seconds to 2/3 rise
Τ = RC
![\Tau = \frac{L}{R}](images/788d1ed3df1d63d2ca78562ecf3483b2.png)
Power factor
![P_f = \frac{True\;power}{apparent\;power} = \frac{I^2R}{VA} = \frac{R}{Z} = \cos\theta](images/2032657f8b1a0fb391eac394b4fbc8ca.png)
Standing Wave Ratio (SWR)
![SWR = \frac{E_{max}}{E_{min}} = \frac{I_{max}}{I_{min}} = \frac{Z_1}{Z_2}](images/97a935feb6af8a664cc28ec5472d368c.png)
Modulation
![%Modulation = \frac{E_{max} - E_{min}}{2E_{carrier}}\left( 100% \right)](images/7dfa5f02a27cc0799071e295ccb2f7f4.png)
Deviation = modulating index Deviation ratio =
Deviation / highest modulating frequency
Transistors
- Ic = Ibβ
or
-
![I_b = \frac{I_c}{\beta}](images/5e571979967a2994e1342315c053a6d6.png)
β = beta </math> Ib = Base current Ic = 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}}](images/e920b4d00fb2069e52a3e1002cf0806f.png)
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}}](images/f868e3d6f82c2dfbfba566c9dafcf294.png)
Where :
- gm = small signal transconductance
-
Thermal voltage
- k Boltzmann constant ,
![1.380 × 10^{−23} \frac{J}{K}](images/e551d4c363f1023c8b046a94e956a0d2.png)
- Icq = 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}}](images/a0546eac0e149ed32d2894d0a2fd729c.png)
Where :
- Gm = Large signal Transconductance (not to be confused with gm
- Small-signal-input-resistance ( Rπ )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}](images/04c039656b7ea2032d56d8e1ede8a9ab.png)
Which means that input resistance goes up with β
- Large-signal-Input-resistance ( RΠ )for a common emitter amp with the emitter AC grounded:
-
![R_\Pi = \frac{R_\pi G_m}{g_m}](images/b1b707704e3aa31f0c65147ec16f4955.png)
Ebers-Moll equation
-
![I_{E} = I_{ES} \left(e^{\frac{V_{BE}}{V_{T}}} - 1\right)](images/55c368fee056b64494cd60dc4af8449b.png)
-
(approximately 26 mV at 300 K ≈ room temperature).
where
- VT is the Boltzmann constant kT / q
- q Electronic Charge
- TTemperature in K
- IE is the emitter current
- IC is the collector current
- αF is the common base forward short circuit current gain (0.98 to 0.998)
- IES is the reverse saturation current of the base–emitter diode (on the order of 10−15
to 10−12 amperes)
- VBE is the base–emitter voltage
ESR formulas
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