Communication Part 3

ece-1109 ECE-1109 Introduction to ECE

1. Basic Logic Gates

The following table summarizes the fundamental logic gates, their algebraic expressions, and truth table behavior.

Name	Algebraic Expression	Output ($X$) Behavior (Truth Table Summary)
NOT	$X=\bar{A}$	Output is 1 if Input $A$ is 0; Output is 0 if Input $A$ is 1.
AND	$X=AB$	Output is 1 only if both $A$ and $B$ are 1.
NAND	$X=\overline{AB}$	Output is 0 only if both $A$ and $B$ are 1.
OR	$X=A+B$	Output is 1 if either $A$ or $B$ (or both) are 1.
NOR	$X=\overline{A+B}$	Output is 1 only if both $A$ and $B$ are 0.
XOR	$X=A\oplus B$	Output is 1 if $A$ and $B$ are different.
XNOR	$X=\overline{A\oplus B}$	Output is 1 if $A$ and $B$ are the same.

Universal Gates

• NAND as a Universal Gate: NAND gates can be arranged to function as NOT (Inverter), AND, OR, NOR, Exclusive-OR (XOR), and Exclusive-NOR (XNOR) gates.
• NOR as a Universal Gate: Similarly, NOR gates can be configured to function as NOT (Inverter), OR, AND, NAND, Exclusive-OR, and Exclusive-NOR gates.

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2. Boolean Algebra

Summary

• Boolean Variable: A variable whose value can be either 1 or 0.
• Basic Operations: AND, OR, and NOT.
• Expression to Circuit: Every Boolean expression can be converted into a circuit.
• Notation:
  • AND: Denoted by a dot ($\cdot$).
  • OR: Denoted by a plus ($+$).
  • NOT: Denoted by an overbar ($\bar{A}$), a single quote mark ($A^{\prime }$), or a tilde ($\sim A$).

Postulates

• Commutative Law:
  • $x\cdot y=y\cdot x$
  • $x+y=y+x$
• Identity Element:
  • $x\cdot 1=x$
  • $x+0=x$
• Complement:
  • $x\cdot x^{\prime }=0$
  • $x+x^{\prime }=1$

Theorems

1. Theorem 1: $x\cdot x=x$ and $x+x=x$.
2. Theorem 2: $x\cdot 0=0$ and $x+1=1$.
3. Theorem 3 (Involution): $(x^{\prime }{)}^{\prime }=x$ or $(\overline{\bar{x}})=x$.
4. Theorem 4:
   • Associative: $(x\cdot y)\cdot z=x\cdot (y\cdot z)$ and $(x+y)+z=x+(y+z)$.
   • Distributive: $x\cdot (y+z)=(x\cdot y)+(x\cdot z)$ and $x+(y\cdot z)=(x+y)\cdot (x+z)$.
5. Theorem 5 (DeMorgan):
   • $(x\cdot y{)}^{\prime }=x^{\prime }+y^{\prime }$ or $\overline{x\cdot y}=\bar{x}+\bar{y}$.
   • $(x+y{)}^{\prime }=x^{\prime }\cdot y^{\prime }$ or $\overline{x+y}=\bar{x}\cdot \bar{y}$.
6. Theorem 6 (Absorption): $x\cdot (x+y)=x$ and $x+(x\cdot y)=x$.

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3. Field Effect Transistor (FET)

Comparison to BJT

• FET: A voltage-controlled three-terminal device.
• BJT: A current-controlled three-terminal device.

Types of FET

1. JFET: Junction Field Effect Transistor.
2. MOSFET: Metal Oxide Semiconductor Field Effect Transistor.

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4. JFET (Junction Field Effect Transistor)

Construction and Terminals

• Terminals: Drain (D), Source (S), and Gate (G).
• Types: $n$-Channel JFET and $p$-Channel JFET.

Working Principle

• JFET operates as a voltage-controlled device when a reverse bias voltage ($-V_{GS}$) is applied.
• Changing the magnitude of the Gate-Source voltage ($V_{GS}$) varies the width of the conducting channel, thereby changing its resistance and controlling the Drain current ($I_D$),.

Characteristics

• Output Characteristics: The curve plotting Drain Current ($I_D$) versus Drain-Source Voltage ($V_{DS}$) at a constant $V_{GS}$.
• Pinch-off Voltage ($V_P$): The minimum drain-source voltage at which the current levels off (or the $V_{GS}$ that cuts off current).
• Shockley’s Equation: The relationship between $I_D$ and $V_{GS}$ is defined by: $I_D=I_{DSS}{\left(1-\frac{V_{GS}}{V_P}\right)}^2$.
  • At $V_{GS}=0$, $I_D=I_{DSS}$.
  • At $V_{GS}=V_P$, $I_D=0\text{ A}$.

Calculation Example Given a JFET with $I_D=5\text{ mA}$, $I_{DSS}=10\text{ mA}$, and $V_P=-6\text{ V}$, find $V_{GS}$:

1. $5=10{\left(1-\frac{V_{GS}}{-6}\right)}^2$
2. $0.5={\left(1+\frac{V_{GS}}{6}\right)}^2$
3. Solving yields $V_{GS}=-1.76\text{ V}$.

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5. MOSFET (Metal Oxide Semiconductor FET)

Types

1. Depletion-type (D-MOSFET):

   • Sub-types: $n$-channel and $p$-channel,.
   • Working Principle: A negative potential at the gate repels electrons from the channel toward the substrate and attracts holes, causing recombination. This reduces the number of free electrons, lowering the drain current,. The more negative the bias, the higher the recombination rate.
   • Transfer Characteristics Example: For an n-channel D-MOSFET with $I_{DSS}=10\text{ mA}$ and $V_P=-4\text{ V}$:
     • At $V_{GS}=0\text{ V}$, $I_D=10\text{ mA}$.
     • At $V_{GS}=-4\text{ V}$, $I_D=0\text{ mA}$.
     • At positive bias $V_{GS}=+1\text{ V}$, $I_D$ increases to $15.6\text{ mA}$,.

2. Enhancement-type (E-MOSFET):

   • Sub-types: $n$-channel and $p$-channel.
   • Structure: It has no physical channel initially. A channel is induced by applying voltage to the gate.
   • Output Characteristics: Current ($I_D$) increases as $V_{DS}$ increases until saturation, controlled by $V_{GS}$ above a threshold voltage ($V_T$). The source provides diagrams for biasing and output characteristics for both n-channel and p-channel E-MOSFETs.