Physics · Modern Physics

Electronic Devices formulas for JEE

Every Electronic Devices formula you need for JEE, grouped by concept.

FormulasRevision notes
27 formulas2 concepts
01Semiconductors and Diodes02Logic Gates and Special Diodes
01

Semiconductors and Diodes

17 formulas

Semiconductor Conductivity

σ=e(neμe+nhμh)\sigma = e(n_e \mu_e + n_h \mu_h)

Electrical conductivity based on charge carrier concentrations and their mobilities.

conductivitymobilityjee-advanced

Shockley Diode Equation

I=Is(eqVηkT−1)I = I_s \left( e^{\frac{qV}{\eta kT}} - 1 \right)

Current-voltage relationship for a p-n junction diode.

applies whenV is positive for forward bias, negative for reverse bias.
diodecurrentjee-advanced

Dynamic Resistance

rd=ΔVΔIr_d = \frac{\Delta V}{\Delta I}

The resistance offered by a p-n junction diode to small changes in applied voltage.

applies whenNon-ohmic devices; evaluated at a specific operating point.
dioderesistance

Filter Circuit Time Constant

τ=RLC\tau = R_L C

Time constant determining the discharge rate and ripple voltage in a capacitor filter.

applies whenCapacitor filter connected in parallel to the load.
filtercapacitortime-constant

Full-Wave Rectifier Output Frequency

fout=2finf_{out} = 2f_{in}

The fundamental ripple frequency of a full-wave rectified output is double the input ac frequency.

applies whenFull-wave rectification.
rectifierfrequency

Full-Wave Rectifier Efficiency

ηFW=81.21+rfRL%\eta_{FW} = \frac{81.2}{1 + \frac{r_f}{R_L}} \%

Percentage efficiency of converting AC power to DC power in a full-wave rectifier.

rectifierefficiencyjee-advanced

Full-Wave Ripple Factor

γFW=(IrmsIdc)2−1≈0.48\gamma_{FW} = \sqrt{\left(\frac{I_{rms}}{I_{dc}}\right)^2 - 1} \approx 0.48

Measure of the fluctuating AC component present in the full-wave rectified output.

applies whenWithout filter circuits.
rectifierripplejee-advanced

Half-Wave Rectifier Output Frequency

fout=finf_{out} = f_{in}

The fundamental ripple frequency of a half-wave rectified output matches the input ac frequency.

applies whenHalf-wave rectification.
rectifierfrequency

Half-Wave Ripple Factor

γHW=(IrmsIdc)2−1≈1.21\gamma_{HW} = \sqrt{\left(\frac{I_{rms}}{I_{dc}}\right)^2 - 1} \approx 1.21

Measure of the fluctuating AC component present in the half-wave rectified output.

applies whenWithout filter circuits.
rectifierripplejee-advanced

Intrinsic Carrier Concentration

ne=nh=nin_e = n_h = n_i

Equality of electron and hole concentrations in an intrinsic semiconductor.

applies whenPure (undoped) semiconductor in thermal equilibrium.
intrinsiccarrier-concentration

Mass Action Law

nenh=ni2n_e n_h = n_i^2

The product of electron and hole concentrations is constant at a given temperature.

applies whenThermal equilibrium; not applicable if heavily illuminated or externally biased.
mass-actioncarrier-concentration

Majority Carrier Approx (n-type)

ne≈NDn_e \approx N_D

Electron concentration is approximately equal to the donor impurity concentration.

applies whenComplete ionization at room temperature; ND≫niN_D \gg n_i.
dopingapproximation

n-Type Carrier Condition

ne≫nhn_e \gg n_h

Electrons are majority carriers and holes are minority carriers in n-type material.

applies whenSemiconductor doped with pentavalent impurities.
extrinsicn-type

Majority Carrier Approx (p-type)

nh≈NAn_h \approx N_A

Hole concentration is approximately equal to the acceptor impurity concentration.

applies whenComplete ionization at room temperature; NA≫niN_A \gg n_i.
dopingapproximation

p-Type Carrier Condition

nh≫nen_h \gg n_e

Holes are majority carriers and electrons are minority carriers in p-type material.

applies whenSemiconductor doped with trivalent impurities.
extrinsicp-type

Half-Wave Rectifier Efficiency

ηHW=40.61+rfRL%\eta_{HW} = \frac{40.6}{1 + \frac{r_f}{R_L}} \%

Percentage efficiency of converting AC power to DC power in a half-wave rectifier.

rectifierefficiencyjee-advanced

Total Semiconductor Current

I=Ie+IhI = I_e + I_h

Total current is the sum of electron current in the conduction band and hole current in the valence band.

applies whenUnder an applied electric field.
currentdrift
02

Logic Gates and Special Diodes

10 formulas

Common-Base Current Gain

α=ICIE\alpha = \frac{I_C}{I_E}

Ratio of collector current to emitter current.

applies whenValue is always slightly less than 1.
transistorbjtjee-advanced

Common-Emitter Current Gain

β=ICIB\beta = \frac{I_C}{I_B}

Ratio of collector current to base current.

applies whenLarge value, typically 20 to 100+.
transistorbjtjee-advanced

BJT Current Gain Relation

β=α1−α\beta = \frac{\alpha}{1-\alpha}

Mathematical relationship between common-emitter gain and common-base gain.

transistorbjtjee-advanced

BJT Current Relationship

IE=IB+ICI_E = I_B + I_C

Emitter current is the sum of base and collector currents.

applies whenActive mode typical.
transistorbjtjee-advanced

AND Gate Boolean Expression

Y=A⋅BY = A \cdot B

Output is high only if all inputs are high.

logic-gatesbooleanjee-advanced

NAND Gate Boolean Expression

Y=A⋅B‾Y = \overline{A \cdot B}

Universal gate; logically equivalent to an AND gate followed by a NOT gate.

logic-gatesbooleanjee-advanced

NOR Gate Boolean Expression

Y=A+B‾Y = \overline{A + B}

Universal gate; logically equivalent to an OR gate followed by a NOT gate.

logic-gatesbooleanjee-advanced

NOT Gate Boolean Expression

Y=AˉY = \bar{A}

Output is the logical inversion of the input.

logic-gatesbooleanjee-advanced

OR Gate Boolean Expression

Y=A+BY = A + B

Output is high if any input is high.

logic-gatesbooleanjee-advanced

Zener Voltage Regulator Series Resistor

RS=Vin−VZIZ+ILR_S = \frac{V_{in} - V_Z}{I_Z + I_L}

Calculates the required series resistance for a Zener diode voltage regulator.

applies whenZener diode operating in the breakdown region (Vin>VZV_{in} > V_Z).
zenerregulationjee-advanced
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