ECE Derivations List

ece-1109 ECE-1109 Introduction to ECE

Comprehensive Derivation List

Topic	Question / Formula to Prove	Years of Appearance
Conductivity	Explain free electron theory and prove: $\sigma =\frac{n{e}^2\tau }{m}$	2015, 2017, 2021
Resistivity	State Matthiessen’s rule and show that: $\rho ={\rho }_T+\alpha T$	2018
Continuity	Derive the continuity equation of charge in a semiconductor.	2016, 2019, 2021
Diffusion	Using the continuity equation, show that diffusion length is: $L_p=\sqrt{D_p{\tau }_p}$	2017
Diffusion	Derive the expression for the rate of change of electron concentration where diffusion is small.	2015
Fermi Level	Show that the Fermi level in an n-type semiconductor is: $E_F=E_c-KT\ln (\frac{N_c}{N_D})$	2019
Atomic Spacing	Find out the expression of equilibrium spacing between atoms.	2017
P-N Potential	Show that the contact potential of a p-n junction is: $V_0=\frac{KT}{q}\ln (\frac{N_D{N}_A}{n_i^2})$	2015, 2016, 2018, 2020
Depletion Width	Show that the width of the space charge region is: $W=\sqrt{\frac{2ϵV_0}{q}(\frac{1}{N_d}+\frac{1}{N_a})}$	2017, 2018, 2021
Diode Current	Establish the diode current relation: $I=I_0(e^{V/\eta V_T}-1)$	2015, 2016
Diode Resistance	Show that dynamic resistance of a diode is: $r=\frac{\eta V_T}{I}$	2023
Diode Capacitance	Find an expression for the diffusion capacitance of an ideal p-n junction diode.	2015, 2016
BJT Current	Prove the collector current expression for Common Base: $I_c=\frac{\alpha }{1-\alpha }{I}_B+\frac{I_{CBO}}{1-\alpha }$	2015, 2016, 2017, 2018, 2022, 2023
BJT Parameters	Find the relationship between $\alpha$ and $\beta$.	2021, 2024
BJT Leakage	Show that in Common Emitter, $I_C$ is not zero even if $I_B$ is zero (Derive $I_{CEO}$).	2019, 2021
JFET	Derive the relationship between $I_D$ and $V_{GS}$ (Shockley’s Equation).	2022, 2023
Zener Limits	Determine the relations for min/max Load Resistance: (i) $R_{Lmin}=\frac{R{V}_z}{V_i-V_z}$ (ii) $R_{Lmax}=\frac{V_z}{I_{Lmin}}$	2016, 2017
Rectifier Efficiency	Show that for half-wave rectification, maximum efficiency is 40.6%.	2016, 2018, 2020
Rectifier PIV	Show that PIV in a center-tapped full wave rectifier is double that of a bridge: $PIV=2V_m$	2016, 2018, 2019, 2021
Filter Ripple	Show that ripple voltage for an RC filter is: $V_r=\frac{I_{dc}}{2fC}$	2022, 2023

Memorization Priority Tip

Based on the data, if you have limited time, ensure you memorize these three first as they appear most frequently:

1. BJT Collector Current Formula (6 appearances)
2. Contact Potential ($V_0$) (4 appearances)
3. Rectifier PIV & Efficiency (Combined 7 appearances)