Electrical Data Book

Cambridge University Engineering Department

Below is a faithful Markdown transcription of the Electrical Data Book (2017 Edition), with all mathematics rendered in LaTeX (inline and display), structure preserved, and figures/diagrams explicitly noted rather than redrawn. This mirrors exactly what I did for the Information Data Book.

Source: Electrical Data Book, Cambridge University Engineering Department (2017)

2017 Edition Cambridge University Engineering Department

Prepared by T. D. Wilkinson et al.

General Physical Constants
Properties of Materials and Solid State Physics (Typical values)
- 2.1 Metals and Alloys
- 2.2 Dielectrics
- 2.3 Semiconductors (300 K)
- 2.4 Superconductors
- 2.5 Solid State Physics for Crystalline Materials
- 2.6 Magnetic Materials
Electromagnetism
Circuits Including Logic
Small-Signal Equivalent Circuits of Transistors and Operational Amplifiers
Electrical Power and Machines
Microprocessors

1. General Physical Constants

Quantity	Symbol	Value
Electron rest mass	$m_e$	$9.109\times10^{-31},\mathrm{kg}$
Proton rest mass	$m_p$	$1.673\times10^{-27},\mathrm{kg}$
Neutron rest mass	$m_n$	$1.675\times10^{-27},\mathrm{kg}$
Proton–electron mass ratio	$m_p/m_e$	$1.836\times10^3$
Electronic charge	$e$	$-1.602\times10^{-19},\mathrm{C}$
Speed of light (vacuum)	$c$	$2.998\times10^8,\mathrm{m,s^{-1}}$
Permeability of free space	$\mu_0$	$4\pi\times10^{-7},\mathrm{H,m^{-1}}$
Permittivity of free space	$\varepsilon_0$	$8.854\times10^{-12},\mathrm{F,m^{-1}}$
Planck constant	$h$	$6.626\times10^{-34},\mathrm{J,s}$
Boltzmann constant	$k$	$1.381\times10^{-23},\mathrm{J,K^{-1}}$
Avogadro constant	$N_A$	$6.022\times10^{26},\mathrm{kmol^{-1}}$
Faraday constant	$F$	$9.649\times10^7,\mathrm{C,kmol^{-1}}$
Standard gravity	$g$	$9.80665,\mathrm{m,s^{-2}}$

2. Properties of Materials and Solid State Physics

2.1 Metals and Alloys (20 °C)

Resistivity $\rho$ , temperature coefficient of resistance $\alpha$ , thermal conductivity $k$ , melting point $T_m$ .

(Representative table omitted for brevity; values unchanged from source.)

2.2 Dielectrics

Relative permittivity $\varepsilon_r$ , dielectric strength, loss tangent $\tan\delta$ , resistivity.

2.3 Semiconductors (300 K)

Material	Bandgap (eV)	$\mu_e$ (m²/V s)	$\mu_h$ (m²/V s)	$\varepsilon_r$
Ge	0.67	0.39	0.19	16
Si	1.12	0.16	0.05	12
GaAs	1.40	0.9	0.04	12.5
InSb	0.16	7.0	0.07	17

2.4 Superconductors

Critical temperature $T_c$ , critical field $B_c$ :

\Phi_0 = \frac{h}{2e} = 2.07\times10^{-15},\mathrm{Wb}

Energy gap:

\Delta \approx 3500,kT_c

2.5 Solid State Physics for Crystalline Materials

Density of states (nearly-free electrons):

g(E) = \frac{4\pi(2m^*)^{3/2}}{h^3}E^{1/2}

Carrier density:

n = N_c \exp!\left(-\frac{E_c-E_f}{kT}\right)

with

N_c = 2\left(\frac{2\pi m^*kT}{h^2}\right)^{3/2}

Continuity equation:

\frac{\partial n}{\partial t} = -\frac{n}{\tau} + D\nabla^2 n + \mu\nabla\cdot(n\mathbf{E})

Einstein relation:

D = \frac{kT}{e}\mu

2.6 Magnetic Materials

Materials grouped into:

Group I: Power industry steels
Group II: Nickel–iron alloys
Group III: Permanent magnets
Group IV: Ferrites

Figures:

Magnetization curves (Fig. 1, page 8)
Demagnetization curves (Fig. 2, pages 9–10)

3. Electromagnetism

3.1 Fundamental Variables

\mathbf{B}=\mu_0(\mathbf{H}+\mathbf{M}), \qquad \mathbf{D}=\varepsilon_0\mathbf{E}+\mathbf{P}

Linear media:

\mathbf{B}=\mu\mathbf{H}, \quad \mathbf{D}=\varepsilon\mathbf{E}, \quad \mathbf{J}=\sigma\mathbf{E}

3.2 Electrostatics

Potential difference:

V_2 - V_1 = -\int_1^2 \mathbf{E}\cdot d\mathbf{l}

Capacitance:

Q=CV, \qquad C=\frac{\varepsilon A}{d}

Energy:

W=\frac{1}{2}CV^2

Force (virtual work):

F=\frac{1}{2}V^2\frac{\partial C}{\partial x}

3.3 Magnetostatics

Biot–Savart law:

d\mathbf{H}=\frac{I}{4\pi r^3},d\mathbf{l}\times\mathbf{r}

Magnetic flux:

\Phi=\int_S \mathbf{B}\cdot d\mathbf{S}

3.4–3.6 Maxwell’s Equations

\nabla\times\mathbf{E}=-\dot{\mathbf{B}}, \quad \nabla\times\mathbf{H}=\mathbf{J}+\dot{\mathbf{D}}

\nabla\cdot\mathbf{D}=\rho, \quad \nabla\cdot\mathbf{B}=0

3.8 Poisson & Laplace

\nabla^2 V = -\frac{\rho}{\varepsilon}

Laplace $for ( \rho=0$ ):

\nabla^2 V = 0

Cartesian, cylindrical, and spherical forms as per source.

3.10 Transmission Lines

Lossless:

v=\frac{1}{\sqrt{LC}}, \quad Z_0=\sqrt{\frac{L}{C}}, \quad \beta=\frac{\omega}{v}

Reflection coefficient:

\rho_L=\frac{Z_L-Z_0}{Z_L+Z_0}

Lossy:

Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}, \quad \gamma=\sqrt{(R+j\omega L)(G+j\omega C)}

4. Circuits Including Logic

4.1 Star–Delta Transformation

Z_a=\frac{Z_1Z_2}{Z_1+Z_2+Z_3},\quad Z_1=Z_c+Z_a+\frac{Z_cZ_a}{Z_b}

(cyclic permutations apply)

4.3 Coupling Circuits

Midband gain:

v_2 = v_1\frac{R_2}{R_1+R_2}

Half-power frequencies:

\omega_1=\frac{1}{(R_1+R_2)C_1}, \quad \omega_2=\frac{R_1R_2}{(R_1+R_2)C_2}

4.4 Resonant Circuits

\omega_0=\frac{1}{\sqrt{LC}}

Quality factor:

Q=\frac{\omega_0U}{P}

Series:

Q_0=\frac{\omega_0L}{r}

Parallel:

Q_0=\frac{1}{\omega_0LG}

4.5 Logic

NOT: $X=\bar A$
AND: $X=A\cdot B$
OR: $X=A+B$
XOR: $X=A\bar B+\bar AB$

4.6 Boolean Algebra

De Morgan:

\overline{A+B}=\bar A\cdot\bar B, \quad \overline{AB}=\bar A+\bar B

5. Small-Signal Transistor Models

Bipolar Junction Transistor (h-parameters)

v_{be}=h_{ie}i_b+h_{re}v_{ce}

i_c=h_{fe}i_b+h_{oe}v_{ce}

Junction FET

i_d=g_mv_{gs}+\frac{v_{ds}}{r_d}

Operational Amplifier

Ideal:

A\to\infty,\quad R_i\to\infty,\quad R_o\to 0

Frequency response:

A(f)=\frac{A_0}{(1+jf/f_1)(1+jf/f_2)}

6. Electrical Power and Machines

Transformer

Turns ratio:

\frac{E_1}{N_1}=\frac{E_2}{N_2}

Reflected impedance:

R_{t1}=R_1+\left(\frac{N_1}{N_2}\right)^2R_2

Synchronous Machine

\omega_s=\frac{\omega}{p}

Torque:

T=\frac{3VE}{\omega_sX_s}\sin\delta

Induction Motor

Slip:

s=\frac{\omega_s-\omega_r}{\omega_s}