ECE Course Cheatsheet

ece-1109 ECE-1109 Introduction to ECE

---

ECE 1109: Analog Electronics Cheatsheet

I. Semiconductor Fundamentals & Energy Bands

Concept	Definition/Condition	Classification/Parameters
Semiconductor	Elements with conductivity $\text{Conductor}>\sigma >\text{Insulator}$.	Types: Single-crystal (Ge, Si) or Compound (GaAs, CdS).
Energy Bands	Energy range an electron can occupy within a solid.	Valence Band ($E_V$): Filled (or partially filled) with valence electrons. Conduction Band ($E_C$): Normally empty/unfilled, higher permitted energy band.
Forbidden Band ($E_g$)	Region with no allowed energy levels, separating CB and VB.	Conductor: CB/VB overlap ($E_g=0$). Semiconductor: Small $E_g$ ($\le 2\text{ eV}$). Insulator: Large $E_g$ ($\le 15\text{ eV}$).
Fermi Level ($E_F$)	The highest energy level an electron can occupy at $0\text{ K}$.	At $T>0\text{ K}$, probability of occupancy at $E_F$ is $1/2$.
Intrinsic SC	Pure semiconductor, no intentional dopant atoms.	$E_F$ lies in the middle of the forbidden energy gap at $0\text{ K}$.
Extrinsic SC	Intentionally doped to increase conductivity.	Doping: Process of adding impurity to change characteristics.
N-type SC	Doped with Pentavalent impurity (Group V: P, As, Sb).	Majority Carrier: Electrons. $E_F$ is closer to the Conduction Band. Impurity: Donor atoms.
P-type SC	Doped with Trivalent impurity (Group III: B, Ga, In, Al).	Majority Carrier: Holes. $E_F$ is closer to the Valence Band. Impurity: Acceptor atoms.
Neutrality	Both n-type and p-type materials are electrically neutral.	This is because the immobile ionized donor/acceptor atoms balance the charge of the excess mobile carriers.
Current Flow	Drift Current: Caused by applied Electric Field ($E$). Diffusion Current: Caused by concentration gradient ($\frac{dn}{dx}$ or $\frac{dp}{dx}$).

---

II. P-N Junction Diodes

A. Static and Dynamic Characteristics

Concept	Description	Formulas/Constants
Junction Formation	Diffusion of majority carriers leaves behind fixed positive ions (N-side) and fixed negative ions (P-side), creating a Depletion Region.	-
Forward Bias (FB)	Positive terminal $\to$ P-side, Negative terminal $\to$ N-side.	Depletion Width ($W_D$) decreases. Barrier Potential decreases. $I_D$ rises exponentially.
Reverse Bias (RB)	Positive terminal $\to$ N-side, Negative terminal $\to$ P-side.	Depletion Width ($W_D$) increases. Barrier Potential increases. Current is small/constant (Reverse Saturation Current, $I_s$).
Diode Current ($I_D$)	Shockley Diode Equation: ${\mathbf{I}}_{\mathbf{D}}={\mathbf{I}}_{\mathbf{s}}({\mathbf{e}}^{{\mathbf{V}}_{\mathbf{D}}/\eta {\mathbf{V}}_{\mathbf{T}}}-1)$.	$V_T=\frac{kT}{e}\approx 0.026\text{ V}$ at $27^{\circ }\text{C}$. $\eta$: Identity factor ($\approx 1$ for Si/Ge in FB).
Static (DC) Resistance	Resistance under steady-state condition.	${\mathbf{R}}_{\mathbf{DC}}={\mathbf{V}}_{\mathbf{D}}/{\mathbf{I}}_{\mathbf{D}}$. High at reverse bias.
Dynamic (AC) Resistance	Resistance defined by a tangent to the curve at the Q-point.	${\mathbf{r}}_{\mathbf{d}}=\frac{\mathbf{\Delta }{\mathbf{V}}_{\mathbf{D}}}{\mathbf{\Delta }{\mathbf{I}}_{\mathbf{D}}}\approx \frac{\eta V_T}{I_D}$. For $\eta =1$, $r_d\approx \frac{26\text{ mV}}{{\mathbf{I}}_{\mathbf{D}}}$.

B. Capacitance & Switching Time

Type	Bias Condition	Mechanism	Characteristic
Transition Capacitance ($C_T$)	Reverse Bias.	Depletion region (free of carriers) acts like an insulator separating the conducting P and N regions.	$C_T$ decreases as reverse bias voltage increases (width increases).
Diffusion Capacitance ($C_D$)	Forward Bias.	Storage of minority carriers near the junction due to concentration gradient.	$C_D$ increases as forward bias voltage increases (depletion region width decreases).
Reverse Recovery Time ($t_{rr}$)	Time taken to switch from forward-biased conducting state to the reverse-biased blocking state.	$t_{rr}=t_s+t_t$ ($t_s$ = storage time, $t_t$ = transition time). Occurs due to large number of minority charge carriers.

---

III. Special Diodes

Diode	Function/Doping/Operation	Key Features/Applications
Zener Diode	Highly doped diode used as a voltage regulator in reverse bias. Breakdown mechanism is primarily Zener Breakdown (direct bond rupture) for low voltage/highly doped diodes.	High power dissipation capability. Used for maintaining constant voltage across a load.
Tunnel Diode	Highly doped p-n diode. Exhibits negative resistance region.	Used as amplifier, high-frequency oscillators, logic elements.
Varactor Diode	Designed to function as a voltage-variable capacitor. Used in reverse bias to control capacitance electrically.	Used in tuners, filters, and voltage-controlled capacitors.
PIN Diode	P-type, Intrinsic layer, N-type sandwich structure.	Used for high speed switching and RF switching due to low noise characteristics.
Photo Diode	Light sensitive semiconductor. Region of operation is typically reverse bias.	Used as light detectors and optical sensors. Dark Current: Current existing with no applied illumination.

---

IV. Rectifiers and Power Supplies

Rectifier Type	Output Parameters (Ideal Diode/Center-Tap FWR)	Notes
Half-Wave Rectifier (HWR)	${\mathbf{I}}_{\mathbf{dc}}=I_m/\pi$ \mathbf{I_{rms}} = I_m / 2$$$$\mathbf{V_{rms}} = V_m / 2 $\mathbf{PIV}=V_m$ (Peak inverse voltage).	Efficiency ($\eta$): $40.56\%$ (Low). Ripple Factor ($r_f$): $1.21$ (High).
Full-Wave Rectifier (FWR)	${\mathbf{I}}_{\mathbf{avg}}=2I_m/\pi$. ${\mathbf{I}}_{\mathbf{rms}}=I_m/\sqrt{2}$. ${\mathbf{V}}_{\mathbf{avg}}=2V_m/\pi$. ${\mathbf{V}}_{\mathbf{rms}}=V_m/\sqrt{2}$.	Efficiency ($\eta$): $81.12$. Ripple Factor ($r_f$): $0.481$. Types: Center-Tap or Bridge Type.
Regulation	The variation of DC output voltage as a function of DC load current.	\mathbf{%\ Regulation} = \frac{V_{no_load} - V_{full_load}}{V_{full_load}} \times 100%.
Load-Line Analysis (Diode)	Intersection of the load line and the diode characteristics defines the Operating Point (Q-point).	Load line slope: $m=-1/R_L$.

V. Transistors (BJT and FET)

A. Bipolar Junction Transistor (BJT)

Configuration	Controlling Quantity	Current Relationships	Amplification Factor
General	Current-Controlled Device (Difference from FET).	${\mathbf{I}}_{\mathbf{E}}={\mathbf{I}}_{\mathbf{B}}+{\mathbf{I}}_{\mathbf{C}}$.	-
Common Base (CB)	Input: $I_E$; Output: $I_C$.	$I_C=\alpha I_E+I_{CBO}$. $I_C\approx I_E$.	$\alpha$ (Common Base Current Gain): ${\alpha }_{dc}=I_C/I_E$.
Common Emitter (CE)	Acts as a current amplifier.	$I_C=\beta I_B+(\beta +1)I_{CBO}=\beta I_B+I_{CEO}$. $I_C\approx \beta I_B$.	$\beta$ (Common Emitter Current Gain): ${\beta }_{dc}=I_C/I_B$.
Relationship	-	-	$\beta =\frac{\alpha }{1-\alpha }$.

B. Field-Effect Transistor (FET)

Feature	JFET/FET	BJT
Control Mechanism	Voltage-Controlled Device.	Current-Controlled Device.
Carrier Type	Unipolar (electron or hole dependent).	Bipolar (both electron and hole transport).
Input Impedance	High Input Impedance.	Relatively low input impedance.
JFET Key Voltages	Pinch-off Voltage ($V_P$): Level of $V_{DS}$ where depletion regions appear to touch.	-
JFET Current	$I_{DSS}$: Maximum drain current occurring when $V_{GS}=0$.	-
JFET Drain Current Equation (Shockley): ${\mathbf{I}}_{\mathbf{D}}={\mathbf{I}}_{\mathbf{DSS}}{\left(1-\frac{{\mathbf{V}}_{\mathbf{GS}}}{{\mathbf{V}}_{\mathbf{P}}}\right)}^2$.	-

---

VI. Key Equations (Summary)

Equation	Symbol Definitions	Context
$\mathbf{n}\cdot \mathbf{p}={\mathbf{n}}_{\mathbf{i}}^2$	$n$: free electron conc., $p$: free hole conc., $n_i$: intrinsic carrier conc.	Mass Action Law (Thermal Equilibrium).
${\mathbf{P}}_{\mathbf{n}}=\frac{{\mathbf{n}}_{\mathbf{i}}^2}{{\mathbf{N}}_{\mathbf{D}}}$	$P_n$: Hole conc. (minority) in n-type, $N_D$: Donor conc.	Hole concentration in n-type semiconductor (if $N_A=0$).
${\mathbf{n}}_{\mathbf{p}}=\frac{{\mathbf{n}}_{\mathbf{i}}^2}{{\mathbf{N}}_{\mathbf{A}}}$	$n_p$: Electron conc. (minority) in p-type, $N_A$: Acceptor conc.	Electron concentration in p-type semiconductor (if $N_D=0$).
${\mathbf{V}}_{\mathbf{B}}={\mathbf{V}}_{\mathbf{T}}\ln \left(\frac{{\mathbf{N}}_{\mathbf{A}}{\mathbf{N}}_{\mathbf{D}}}{{\mathbf{n}}_{\mathbf{i}}^2}\right)$	$V_B$: Barrier potential, $V_T$: Thermal voltage, $N_A,N_D$: Doping conc., $n_i$: Intrinsic conc.	Potential barrier across P-N junction.
${\mathbf{r}}_{\mathbf{f}}=\sqrt{{\left(\frac{I_{rms}}{I_{dc}}\right)}^2-1}$	$I_{rms}$: RMS value of total current, $I_{dc}$: Average DC current.	General Ripple Factor Calculation.
${\mathbf{I}}_{\mathbf{D}}={\mathbf{I}}_{\mathbf{s}}({\mathbf{e}}^{{\mathbf{V}}_{\mathbf{D}}/\eta {\mathbf{V}}_{\mathbf{T}}}-1)$	$I_D$: Diode current, $I_s$: Reverse saturation current, $V_D$: Diode voltage, $\eta$: Identity factor.	Diode current-voltage relation.
$\beta =\frac{\alpha }{1-\alpha }$	$\alpha$: Common Base current gain, $\beta$: Common Emitter current gain.	Relationship between BJT amplification factors.