Electronic Devices

Complete Formula Sheet & Shortcut Bible · BITSAT 2026

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Energy Bands & Semiconductors

Mass-Action Law

nₑ nₕ = nᵢ²

Product of electron (nₑ) and hole (nₕ) concentration is constant for a given temperature, equal to the square of intrinsic carrier concentration (nᵢ).

Conductivity (σ)

σ = e (nₑμₑ + nₕμₕ)

For intrinsic: σᵢ = nᵢe(μₑ + μₕ)
For n-type: σ ≈ nₑeμₑ
For p-type: σ ≈ nₕeμₕ

Current Density (J)

J = σE = (nₑeμₑ + nₕeμₕ)E

Ohm's law in microscopic form. E is the electric field.

Semiconductor Diodes & Rectifiers

Diode Current Equation

I = I₀ (e^eV/ηkT - 1)

I₀: Reverse saturation current
η: Ideality factor (1 for Ge, 2 for Si)
V: Voltage across diode

Half-Wave Rectifier

V_dc = V_m/π
I_dc = I_m/π
Ripple Factor (r) = 1.21

Efficiency (η) is 40.6%. Only one half of the AC cycle is used.

Full-Wave Rectifier

V_dc = 2V_m/π
I_dc = 2I_m/π
Ripple Factor (r) = 0.48

Efficiency (η) is 81.2%. Both halves of the AC cycle are used.

Zener Diode Voltage Regulator

V_out = V_Z
I_S = I_Z + I_L

Operates in reverse breakdown. Maintains constant voltage V_Z across the load. I_S is source current, I_Z is Zener current, I_L is load current.

Junction Transistors (CE Configuration)

Current Relation

I_E = I_B + I_C

Emitter current is the sum of base and collector currents.

Current Gain (α & β)

α = I_C / I_E
β = I_C / I_B

α is for Common Base (CB), β is for Common Emitter (CE). α is always < 1, β is > 1.

Relation between α & β

β = α / (1 - α)
α = β / (1 + β)

This is a very frequently tested conversion. Memorize it.

Voltage Gain (Aᵥ)

Aᵥ = -β (R_out / R_in)

Also, Aᵥ = -gₘ Rₗ, where gₘ is transconductance. Negative sign indicates 180° phase shift.

Power Gain (Aₚ)

Aₚ = Aᵥ × β

It is the product of voltage gain and current gain.

Oscillators & Special Diodes

Barkhausen Criterion

|Aβ'| = 1
Total Phase Shift = 2nπ

Condition for sustained oscillations. A is amplifier gain, β' is feedback factor. The loop gain must be unity.

Light Emitting Diode (LED)

E_g ≈ hc/λ

Operates in forward bias. Band gap energy (E_g) determines the color (wavelength λ) of emitted light.

Photodiode & Solar Cell

I ∝ Intensity (Photodiode)
FF = (VₘIₘ)/(VₒₒIₛₒ)

Photodiode works in reverse bias. Solar cell works on photovoltaic effect. FF is Fill Factor.

Logic Gates & Transistor as a Switch

De Morgan's Theorems

(A + B)' = A' · B'
(A · B)' = A' + B'

Break the line, change the sign. Crucial for simplifying Boolean expressions.

Universal Gates

NAND & NOR

Any basic gate (AND, OR, NOT) can be constructed using only NAND gates or only NOR gates.

Transistor Switch: Cut-off

V_in < 0.7V
I_B ≈ 0, I_C ≈ 0
V_out ≈ V_CC (HIGH)

The transistor acts as an open switch.

Transistor Switch: Saturation

V_in > 0.7V
I_B > I_C(sat)/β
V_out ≈ 0 (LOW)

The transistor acts as a closed switch.

BITSAT Shortcuts & Tricks

For CE amplifiers, output is always 180° out of phase with input. This is the source of the negative sign in the voltage gain formula.

Ripple Factor order: Half-Wave (1.21) > Full-Wave (0.48). Lower is better, so FWR is more efficient at smoothing DC.

The relation β = α/(1-α) is a favorite. Since α is always just under 1 (e.g., 0.98), β will be a large number (e.g., 49).

NAND and NOR are 'Universal Gates'. BITSAT may ask how many NAND gates are needed to make an EX-OR gate (Answer: 4).

In Zener regulator problems, always check if the Zener is 'ON'. Calculate the voltage across the load without the Zener. If V_load > V_Z, the Zener is ON and regulates the voltage to V_Z.

For LEDs, remember the band gap order for colors: Infrared < Red < Green < Blue < UV. Higher energy (E_g) means shorter wavelength (λ).

Energy Band Comparison

Property	Conductors	Insulators	Semiconductors
Energy Gap (E_g)	≈ 0 eV (Overlapping)	> 3 eV	< 3 eV (Si: 1.1eV, Ge: 0.7eV)
Resistivity (ρ) at 300K	10⁻² - 10⁻⁸ Ωm	> 10⁸ Ωm	10⁻⁵ - 10⁶ Ωm
Temp. Coeff. of Resistance (α)	Positive	Negative	Negative
Charge Carriers	Free electrons	Almost none	Electrons and Holes

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