Maharashtra State Board · Class 12 · Physics · Chapter 16

Semiconductor Devices — Formula Sheet

Board Formulas

12 formulas

1.Ripple Frequency of Rectifier Output
$f_{o u t} = f_{in} (half-wave), f_{o u t} = 2 f_{in} (full-wave)$
$f_{in}$ : Frequency of the AC input (Hz) · $f_{o u t}$ : Frequency of the ripple in the output (Hz)
A half-wave rectifier gives one output pulse per input cycle; a full-wave rectifier gives two. With 50 Hz mains, the ripple frequency is 50 Hz (half-wave) or 100 Hz (full-wave).
2.Ripple Factor
$γ = \frac{V _{a c, r m s}}{V _{d c}} = \frac{rms value of AC component}{value of DC component}$
Ratio of the rms value of the AC component (ripple) left in the rectifier output to the DC component. A smaller ripple factor means a more effective rectifier: a full-wave rectifier has less ripple than a half-wave one, and a capacitor filter reduces the ripple further.
3.Zener Regulator — Current Through Series Resistor★
$I_{s} = \frac{V _{in} - V _{Z}}{R _{s}}$
$V_{in}$ : Unregulated input voltage (V) · $V_{Z}$ : Zener breakdown voltage = regulated output (V) · $R_{s}$ : Series resistance (Ω) · $I_{s}$ : Current through the series resistor (A)
The Zener holds the output at V_Z, so the series resistor R_s drops the rest of the input voltage. R_s also limits the current through the Zener so it is not damaged.
4.Zener Regulator — Load and Zener Currents
$I_{L} = \frac{V _{Z}}{R _{L}}, I_{Z} = I_{s} - I_{L}$
$R_{L}$ : Load resistance (Ω) · $I_{L}$ : Load current (A) · $I_{Z}$ : Zener current (A)
The load is in parallel with the Zener, so it sees V_Z. The Zener carries whatever current the load does not take. If the input rises, I_s rises and the extra flows through the Zener.
5.Photon Energy and Band Gap (LED, Photodiode, Solar Cell)
$E_{g} = h ν = \frac{h c}{λ} \Rightarrow λ = \frac{h c}{E _{g}}$
$E_{g}$ : Band gap energy (J or eV) · $h$ : Planck's constant = 6.63×10⁻³⁴ J s · $c$ : Speed of light = 3×10⁸ m s⁻¹ · $λ$ : Wavelength of emitted or absorbed light (m)
An LED emits photons of energy close to its band gap, so E_g decides the colour. A photodiode or solar cell responds only to photons with hν ≥ E_g. Shortcut: λ (nm) ≈ 1240 / E_g (eV).
6.Transistor Currents★
$I_{E} = I_{B} + I_{C}$
$I_{E}$ : Emitter current (A) · $I_{B}$ : Base current (A) · $I_{C}$ : Collector current (A)
Kirchhoff's current law applied to the transistor. The emitter current is the largest. The base is thin and lightly doped, so I_B is only a small fraction of I_E.
7.Common-Base DC Current Gain
$α_{d c} = \frac{I _{C}}{I _{E}}$
Always slightly less than 1, typically 0.95 to 0.99, because I_C < I_E. No unit.
8.Common-Emitter DC Current Gain
$β_{d c} = \frac{I _{C}}{I _{B}}$
Much greater than 1, typically several tens to a few hundred. A small base current controls a much larger collector current, which is the basis of amplification. No unit.
9.Relation Between α and β★
$β = \frac{α}{1 - α}, α = \frac{β}{1 + β}$
As α approaches 1, β becomes very large. Example: α = 0.98 gives β = 49.
10.OR, AND and NOT Gates
$OR: Y = A + B, AND: Y = A \cdot B, NOT: Y = A$
OR: output 1 if at least one input is 1. AND: output 1 only if all inputs are 1. NOT: output is the complement of the input. Here + and · are logical operations, not arithmetic.
11.NAND and NOR Gates
$NAND: Y = A \cdot B, NOR: Y = A + B$
NAND = AND followed by NOT; its output is 0 only when all inputs are 1. NOR = OR followed by NOT; its output is 1 only when all inputs are 0. Both are universal gates: any other gate can be built from either one alone.
12.XOR (Exclusive-OR) Gate
$Y = A \oplus B = A B + A B$
Output is 1 when the inputs are different and 0 when they are the same. Unlike OR, 1 ⊕ 1 = 0.