display pyq solutions

KUET ECE 1209: Display & Optoelectronics PYQ Answers (2022 - 2024)

This note compiles, merges, and answers all questions from the 2022, 2023, and 2024 KUET ECE Term Exams regarding CRT Deflection & Electron Ballistics, Display Technologies (LCD, OLED, QLED, Plasma), and Optoelectronic Devices.

Section 1: CRT Deflection & Electron Ballistics

1.1 Electrostatic Deflection Sensitivity & Proportionality

📝 Merged KUET Exam Questions (2024, 2022):

• Prove that the deflection on the screen of a Cathode Ray Tube (CRT) is directly proportional to the deflecting voltage applied between the plates.

• Show that the electrostatic deflection sensitivity of a CRT is given by $S=\frac{lL}{2d{V}_a}$, defining all the symbols used.

Physical Model & Geometry

An electron of mass $m$ and charge $e$ enters a set of parallel deflecting plates of length $l$ separated by a distance $d$. The distance from the center of these plates to the screen is $L$.

                  Deflection Plates (Length = l, Spacing = d)
                         ┌───────────────────────┐  ▲
                         │                       │  │
                         │    Electric Field (Ey)│  │
   ─── Electron Beam ──> ┼───────────────────────┼  │ d  [ Deflecting Voltage = Vd ]
      (Velocity = vx)    │          ─ ─ ─ ─ ─ ─ ─│  │
                         │                       │  │
                         └───────────────────────┘  ▼
                         |<────────── l ────────>|
                         |<───────────────── L ─────────────────>|  (To Screen)
                                                                 ▼
                                                                 Screen Deflection (D)

Step-by-Step Derivation

Step 1: Axial Velocity ($v_x$) The electron is accelerated from rest toward the anode by the accelerating potential $V_a$. The work done on the electron equals its kinetic energy gain:

$e{V}_a=\frac{1}{2}m{v}_x^2⟹v_x^2=\frac{2e{V}_a}{m}$

Step 2: Transit Time ($t$) The time spent by the electron traveling through the deflecting plates of length $l$ at constant horizontal velocity $v_x$ is:

$t=\frac{l}{v_x}$

Step 3: Vertical Acceleration ($a_y$) The deflecting voltage $V_d$ applied across the plates produces a uniform vertical electric field:

$E_y=\frac{V_d}{d}$

The vertical force is $F_y=e{E}_y$. According to Newton’s Second Law:

$a_y=\frac{F_y}{m}=\frac{e{V}_d}{md}$

Step 4: Exit Velocities & Angled Trajectory At the exit of the plates, the vertical velocity component $v_y$ gained by the electron is:

$v_y=a_{y}t=\left(\frac{e{V}_d}{md}\right)\left(\frac{l}{v_x}\right)=\frac{e{V}_{d}l}{md{v}_x}$

The deflection angle $\theta$ of the electron beam as it exits the plates is:

$\tan \theta =\frac{v_y}{v_x}=\frac{e{V}_{d}l}{md{v}_x^2}$

Step 5: Total Screen Deflection ($D$) After exiting the plates, the electron travels in a straight line. Assuming the beam projects as if it originated from the physical center of the plates, the deflection $D$ on the screen at distance $L$ is:

$D=L\tan \theta =L\left(\frac{e{V}_{d}l}{md{v}_x^2}\right)=\frac{elL{V}_d}{md{v}_x^2}$

Substituting the expression for $v_x^2$ from Step 1:

$D=\frac{elL{V}_d}{md\left(\frac{2e{V}_a}{m}\right)}=\frac{lL{V}_d}{2d{V}_a}$

Deflection Sensitivity ($S$)

By definition, deflection sensitivity $S$ is the deflection per unit deflecting voltage:

$S=\frac{D}{V_d}=\frac{lL}{2d{V}_a}$

Where:

• $D$ = Deflection on screen (m)

• $V_d$ = Deflecting voltage (V)

• $l$ = Length of the deflecting plates (m)

• $L$ = Distance from the center of the plates to the screen (m)

• $d$ = Distance of separation between the plates (m)

• $V_a$ = Accelerating anode voltage (V)

Proof of Direct Proportionality ($D\propto V_d$)

Since the physical dimensions of the tube ($l,L,d$) are fixed during manufacturing, and the accelerating voltage $V_a$ is maintained at a constant regulated DC value, the term $\frac{lL}{2d{V}_a}$ is a constant ($K$):

$D=\left[\frac{lL}{2d{V}_a}\right]V_d=K\cdot V_d⟹D\propto V_d$

Thus, the vertical deflection of the electron spot on the screen is directly proportional to the applied deflecting voltage, enabling the CRT to function as a linear voltage indicator.

1.2 Motion of a Charged Particle in Crossed Fields

📝 KUET Exam Question (2024):

Describe the motion of a charged particle in a constant perpendicular (crossed) electric and magnetic field. Derive the equations of motion.

Physical Setup

Let a constant electric field $\vec{E}$ act along the y-axis and a constant magnetic field $\vec{B}$ act along the z-axis:

$\vec{E}=E_y\hat{j},\vec{B}=B_z\hat{k}$

Let a particle of mass $m$ and charge $q$ enter the field at the origin ($x=0,y=0,z=0$) at $t=0$ with an initial velocity ${\vec{v}}_0=v_{x0}\hat{i}+v_{y0}\hat{j}+v_{z0}\hat{k}$.

Equations of Motion

The Lorentz force acting on the particle is:

$\vec{F}=q(\vec{E}+\vec{v}\times \vec{B})=m\frac{d\vec{v}}{dt}$

Expressing the cross product $\vec{v}\times \vec{B}$:

$\vec{v}\times \vec{B}=\det \left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ v_x& v_y& v_z\\ 0& 0& B_z\end{array}\right|=(v_y{B}_z)\hat{i}-(v_x{B}_z)\hat{j}$

Substituting this into the force equation:

$m\left(\frac{d{v}_x}{dt}\hat{i}+\frac{d{v}_y}{dt}\hat{j}+\frac{d{v}_z}{dt}\hat{k}\right)=q\left[(v_y{B}_z)\hat{i}+(E_y-v_x{B}_z)\hat{j}\right]$

Equating the vector components:

1. Along x-axis: $\frac{d{v}_x}{dt}=\frac{q{B}_z}{m}{v}_y\text{— (Eq 1)}$

2. Along y-axis: $\frac{d{v}_y}{dt}=\frac{q{E}_y}{m}-\frac{q{B}_z}{m}{v}_x\text{— (Eq 2)}$

3. Along z-axis: $\frac{d{v}_z}{dt}=0\text{— (Eq 3)}$

Let ${\omega }_c=\frac{q{B}_z}{m}$ define the cyclotron frequency. The equations simplify to:

\frac{dv_x}{dt} = \omega_c v_y \quad \text{--- (Eq 4)}$$$$\frac{dv_y}{dt} = \frac{q E_y}{m} - \omega_c v_x \quad \text{--- (Eq 5)}

Mathematical Solution

Differentiating Eq 5 with respect to time $t$:

$\frac{d^2{v}_y}{d{t}^2}=-{\omega }_c\frac{d{v}_x}{dt}$

Substitute Eq 4 into this relation:

$\frac{d^2{v}_y}{d{t}^2}+{\omega }_c^2{v}_y=0$

This is a standard second-order linear differential equation. Its general solution is:

$v_y(t)=C_1\cos ({\omega }_{c}t)+C_2\sin ({\omega }_{c}t)$

Assuming the particle starts from rest at the origin ($v_{x0}=0,v_{y0}=0$):

• At $t=0$, $v_y(0)=0⟹C_1=0$.

• Therefore, $v_y(t)=C_2\sin ({\omega }_{c}t)$.

To find $C_2$, solve for $\frac{d{v}_y}{dt}$ at $t=0$ using Eq 5:

$\frac{d{v}_y}{dt}{|}_{t=0}=\frac{q{E}_y}{m}-{\omega }_c(0)=\frac{q{E}_y}{m}$

Differentiating our expression for $v_y(t)$:

$\frac{d{v}_y}{dt}=C_2{\omega }_c\cos ({\omega }_{c}t)⟹\frac{d{v}_y}{dt}{|}_{t=0}=C_2{\omega }_c$

Equating the two:

$C_2{\omega }_c=\frac{q{E}_y}{m}⟹C_2=\frac{q{E}_y}{m{\omega }_c}=\frac{E_y}{B_z}$

Thus, the velocity components are:

v_y(t) = \frac{E_y}{B_z} \sin(\omega_c t)$$$$v_x(t) = \frac{E_y}{B_z} \left(1 - \cos(\omega_c t)\right)

Integrating these equations with respect to time ($t$) to find the position coordinates ($x(t),y(t)$) with boundary conditions $x(0)=0,y(0)=0$:

x(t) = \frac{E_y}{B_z \omega_c} \left(\omega_c t - \sin(\omega_c t)\right)$$$$y(t) = \frac{E_y}{B_z \omega_c} \left(1 - \cos(\omega_c t)\right)

Trajectory Analysis

These equations describe a cycloid in the xy-plane. The particle executes a circular rolling motion superimposed on a net linear drift along the positive x-axis at a constant drift velocity of:

$v_d=\frac{E_y}{B_z}$

Section 2: Display Technologies

2.1 Operation & Applications of Twisted Nematic (TN) LCDs

📝 Merged KUET Exam Questions (2024, 2023, 2022):

Describe the basic operating principle of an LCD panel and write down its applications.

Basic Operation (Twisted Nematic Mode)

An LCD controls light transmission rather than emitting light itself. It is a transmissive display.

       [Backlight] ──> [Vertical Polarizer] ──> [Glass Plate with Vert. Grooves]
                                                           │
       [Horizontal Polarizer] <── [Glass with Horiz. Grooves] <── [Liquid Crystals (90° twist)]

• OFF State (No Voltage Applied): Unpolarized light from a backlight is vertically polarized by a rear polarizing filter. It then enters a liquid crystal (LC) layer. Because the bounding glass substrates are rubbed in perpendicular directions (vertical on the rear, horizontal on the front), the LC molecules naturally form a 90° helical twist. As the vertically polarized light passes through, its polarization plane is guided and rotated by 90°. It emerges horizontally polarized, allowing it to pass through the horizontal front polarizer, creating a bright (white) state.

• ON State (Voltage Applied): When an electrical potential is applied across the transparent Indium Tin Oxide (ITO) electrodes, the liquid crystal molecules untwist and align parallel to the electric field. This destroys the helical structure. The vertically polarized light now passes through the LC layer without rotation. Because its polarization remains vertical, it is blocked by the horizontal front polarizer, creating a dark (black) state.

Applications:

1. Industrial Instruments: Displays on digital multimeters (DMMs), oscilloscopes, and function generators.

2. Consumer Electronics: Laptop screens, computer monitors, digital watches, and calculators.

3. Automotive Systems: Digital speedometers and dashboard navigation interfaces.

2.2 LCD vs. CRT & QLED vs. OLED Displays

📝 Merged KUET Exam Questions (2024, 2023, 2022):

• Write down the advantages of LCD displays over older CRT displays.

• Differentiate clearly between QLED and OLED display technologies.

Advantages of LCD over CRT:

1. Low Power Consumption: LCDs require microwatts to milliwatts because they do not utilize power-intensive thermionic electron guns or deflection coils.

2. Compact Form Factor: They are thin and lightweight, requiring very little desk depth.

3. Perfect Geometry: They do not suffer from pincushion, barrel, or trapezoidal geometric distortions.

4. No Burn-In & Long Lifespan: Unlike CRTs, LCDs are highly resistant to permanent phosphorescent screen burn-in.

5. Safety: LCDs generate no dangerous ionizing X-ray radiation or electromagnetic interference (EMI).

Comparison: QLED vs. OLED

Feature	OLED (Organic Light-Emitting Diode)	QLED (Quantum Dot LED)
Light Emission	Self-Emissive: Every pixel generates its own light via organic semiconductor compounds.	Transmissive: Uses an inorganic blue LED backlight shining through a Quantum Dot enhancement layer.
Backlight (BLU)	No backlight required.	Requires a continuous LED backlight.
Black Levels	Absolute/True Black ($0\text{ nits}$): Pixels can turn off completely.	Dark Gray: Some light leakage from the active backlight always remains.
Contrast Ratio	Infinite ($\infty :1$): Because black levels are absolute.	Limited: Typically ranges from $1,000:1$ to $5,000:1$.
Response Time	Extremely fast (down to $0.1\text{ ms}$), eliminating ghosting.	Slower (typically $1\text{ ms}$ to $5\text{ ms}$).
Burn-In Risk	Susceptible: Prolonged static images can cause uneven organic compound decay.	No risk of burn-in: Built from stable, long-lasting inorganic crystals.

2.3 Plasma Display Technology

📝 KUET Exam Question (2023):

Write short notes on plasma display technology.

Definition & Construction

A Plasma Display Panel (PDP) is an emissive flat-panel display. It consists of a matrix of tiny cells sandwiched between two glass plates, filled with a mixture of noble gases (typically Xenon and Neon).

       Front Glass ──> [Dielectric Layer] ──> [Display Electrode] ──> [Gas Chamber: Xe + Ne]
                                                                               │ (UV Release)
       Rear Glass <── [Phosphor: R, G, B] <── [Dielectric Layer] <── [Address Electrode] 

Operating Principle

1. Gas Ionization: When a high voltage is applied between the address and display electrodes, an electric field is established across the cell. This field ionizes the noble gas mixture, turning it into a gas discharge plasma containing free electrons and positive ions.

2. UV Light Generation: Free electrons collide with gas atoms, exciting their orbital electrons to higher energy bands. When these excited electrons return to their ground states, they emit ultraviolet (UV) light photons.

3. Visible Color Conversion: The emitted UV photons strike red, green, or blue phosphors coated on the inner walls of the sub-pixel cell. The phosphors absorb the UV radiation and re-emit visible red, green, or blue light via photoluminescence.

4. Additive Mixing: By controlling the driving duty cycle of each sub-pixel, millions of colors can be synthesized at each pixel location.

Section 3: Optoelectronic Devices

3.1 Solar Cells: Construction & Working Principle

📝 Merged KUET Exam Questions (2024, 2022):

Describe the construction and basic operating principle of a solar cell. Mention its applications.

Construction

A solar cell is a large-area semiconductor p-n junction diode designed to absorb light.

       Incoming Photons (hν ≧ Eg)
               │   │   │
       ┌───────▼───▼───▼───────┐  <── Anti-Reflective Coating
       ├─┐   ┌─┐   ┌─┐   ┌─┐   ┤  <── Front Metal Finger Contacts (-)
       └───▒───▒───▒───▒───▒───┘  <── Thin n-Type Layer
       =========================  <── p-n Junction Depletion Region (Field = Ebi)
       ┌───────────────────────┐
       │      p-Type Base      │
       └───────────────────────┘
       =========================  <── Back Metal Contact Plate (+)

It consists of:

• A thick p-type silicon wafer base ($100-300\mu \text{m}$).

• A thin n-type layer ($<1\mu \text{m}$) diffused on top to create the junction, keeping it close to the surface for maximum light penetration.

• An anti-reflective coating (ARC) to minimize photon reflection loss.

• A front metal contact grid (fingers) to collect electrons while allowing light to pass, and a continuous rear metal contact plate to collect holes.

Operating Principle

1. Photogeneration: Incoming solar photons with energy greater than the bandgap of silicon ($h\nu \ge E_g\approx 1.1\text{ eV}$) are absorbed. This excites electrons from the valence band to the conduction band, generating free electron-hole pairs (EHPs).

2. Charge Separation: The built-in electric field (${\vec{E}}_{bi}$) across the depletion region sweeps minority carriers across the junction before they can recombine:

   • Electrons are swept to the n-side.

   • Holes are swept to the p-side.

3. Collection: This charge accumulation creates an open-circuit photovoltage ($V_{oc}$) across the terminals. Connecting an external electrical load allows a photocurrent ($I_L$) to flow.

Practical Applications:

• Utility-scale grid-tied solar farms and residential rooftop arrays.

• Primary electrical power systems for satellites and spacecraft.

• Off-grid power for water pumps, weather monitoring stations, and telecommunications yokes.

3.2 Operating Principle of Photoconductive Cells (LDRs)

📝 KUET Exam Question (2024):

Explain the operating principle and mention applications of photo-conductive cells.

Operating Principle

A photoconductive cell, or Light Dependent Resistor (LDR), relies on the phenomenon of photoconductivity. It is typically constructed by depositing a zigzag track of Cadmium Sulfide (CdS) onto a ceramic substrate.

               [ Dark State ]                      [ Illuminated State (hν ≧ Eg) ]
       Conduction Band  [ No Electrons ]           Conduction Band  [  e-   e-   e-  ]
                             ▲                                           ▲  (Generation)
                        Band Gap (Eg)                                    │
                             │                                           │
       Valence Band     [  h+   h+   h+  ]         Valence Band     [  h+   h+   h+  ]
       Result: Resistance is extremely High        Result: Resistance Drops Drastically

• Dark Resistance: In the absence of light, the material has very few free charge carriers at room temperature, resulting in a high dark resistance ($R_{\text{dark}}\approx 1\text{ M}\Omega -10\text{ M}\Omega$).

• Light Resistance: When light with photon energy $h\nu \ge E_g$ strikes the CdS track, valence electrons are excited across the bandgap into the conduction band. This creates free electron-hole pairs, causing a sharp drop in the device’s electrical resistance ($R_{\text{light}}\approx 100\Omega -1\text{ k}\Omega$).

Practical Applications:

• Automatic dusk-to-dawn street lighting switches.

• Security systems (light-beam alarm triggers).

• Camera exposure meters to measure ambient light levels.