ece 402 midterm II equations

resistance

R = ρL/A
R = L/σA ohms

→ σ = S/cm (S = ohm^-1)
→ ρ = ohm*cm

resistivity

how strongly a material resists the flow of charges
ρ = 1/σ ohm*cm

Drift Current Density

J = σE A/cm² (in eq. booklet)
J = I/A → A/cm² is unit
amount of current flowing per cross sectional area

Drift Velocity

V_^d = μ_n/pE cm/S
avg velocity of charge carriers moving under the influence of an electric field

n-type doping

DONOR (P or As: 5 val. electrons)
electrons floating around
electrons » holes

n = n_i + N_D
n ≈ N_D
np = n_i²

p-type doping

ACCEPTORS (B: 3 val. electrons)
protons taken as part of a bond

electrons « holes

p = n_i + N_A
p ≈ N_A
n = n_i²/p

Electric Field

V/cm

E = V/L

in capacitors…
E = q/(εA) → E = V/d

Diffusion current

I = AqD_n(dn/dx)
→ A = cross sectional area

Capacitance

Farads = coulomb/V

C = q/V → C = (εA)/d

→ ε = total electrical permittivity = ε₀ε_r

C_ox = ???

(ε₀ε_r)/t_ox

Mobile electron charge density

C_ox(V_G - V_Th) C/cm²

Number Density (electron sheet density)

For V_G > V_Th:
(C_ox(V_G - V_Th)) / q cm^-2
For V_G < V_Th:
C_ox*V_G / q cm^-2

Op-Amps: Inverting vs. Non-Inverting

calc/have gain (G)

G > 0 → non-inverting
G < 0 → inverting

Power

P_L = (V_s²R_L) / (R_s + R_L)²
P_{L, max} = V_s² / 4R_s
→ R_L = R_s = R_Th

→ R_Th = set all independent sources to 0 → i_test to find V_test → (V_test)/(i_test)

Ohm’s Law: other ways to say

J =