Class 12 · Chapter 14
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
11 formulas across 4 topics in Semiconductor Electronics.
Updated 2026-07-09 · v1.0.0
Doping deliberately unbalances a semiconductor's electron and hole populations — but their PRODUCT stays fixed at a given temperature, a constraint that underlies almost every device calculation in this chapter.
σ = e(n μ(e) + p μ(h))
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n, p | electron and hole concentrations | m⁻³ | [L⁻³] |
| μ(e), μ(h) | mobilities of electrons and holes | m²/(V·s) | [M⁻¹T²A] |
Valid when
n·p = n(i)²
At thermal equilibrium, the product of electron and hole concentrations depends only on temperature, not on the doping level
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n(i) | intrinsic carrier concentration (equal electron and hole density in pure semiconductor) | m⁻³ | [L⁻³] |
Valid when
Common mistakes
A p-n junction conducts easily in one direction and barely at all in the other — the ideal diode equation captures this asymmetry in a single exponential expression.
I = I₀ (e^(eV/kT) − 1)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I | diode current | A | [A] |
| I₀ | reverse saturation current | A | [A] |
| V | applied voltage across the diode (positive for forward bias) | V | [ML²T⁻³A⁻¹] |
Valid when
Common mistakes
A rectifier converts AC to (pulsating) DC using diodes' one-way conduction — a full-wave design uses the negative half-cycle too, doubling the theoretical maximum efficiency of a half-wave rectifier.
η(max) = 40.6%
Ratio of DC output power to total AC input power, maximised over one full input cycle where only one half is utilised
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| η | rectification efficiency | dimensionless (%) | [M⁰L⁰T⁰] |
Valid when
η(max) = 81.2%
Both half-cycles of the input are utilised (via a centre-tapped transformer or bridge configuration), exactly doubling the half-wave result
Valid when
Common mistakes
A transistor's three currents are locked together by simple conservation, and the ratios between them (α and β) are the single numbers that determine how much an amplifier circuit boosts a signal.
I(E) = I(B) + I(C)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I(E), I(B), I(C) | emitter, base, and collector currents | A | [A] |
Valid when
α = I(C)/I(E) (common-base current gain)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| α | common-base current gain, always slightly less than 1 | dimensionless | [M⁰L⁰T⁰] |
Valid when
β = I(C)/I(B) (common-emitter current gain)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| β | common-emitter current gain, typically large (tens to hundreds) | dimensionless | [M⁰L⁰T⁰] |
Valid when
β = α/(1−α) , α = β/(1+β)
Combining I(E)=I(B)+I(C) with the definitions of α and β algebraically
Valid when
Common mistakes
A(v) = β (R(C)/R(in))
Output voltage change (ΔI(C)·R(C)) divided by input voltage change (ΔI(B)·R(in)), using β = ΔI(C)/ΔI(B)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| A(v) | voltage gain | dimensionless | [M⁰L⁰T⁰] |
| R(C) | collector (output) resistance | Ω | [ML²T⁻³A⁻²] |
| R(in) | input resistance of the base circuit | Ω | [ML²T⁻³A⁻²] |
Valid when
A(p) = A(v) × A(i) = β² (R(C)/R(in))
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| A(p) | power gain | dimensionless | [M⁰L⁰T⁰] |
| A(i) | current gain, equal to β for this configuration | dimensionless | [M⁰L⁰T⁰] |
Valid when
Boards frequently ask to sketch input and output waveforms for a CE amplifier showing the 180° phase inversion alongside these gain formulas — know the diagram as well as the numbers.
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