ADVANCED CONTROL SYSTEM (EC-503 (C)) - Unit 5 Short Notes

UNIT 5: ADVANCED CONTROL SYSTEM - SHORT NOTES

Focus: Cellular Mobile Communication & Transmission Lines/Network Synthesis (Based on RGPV Past Papers)

PART A: CELLULAR MOBILE COMMUNICATION

1. Cellular Fundamentals & Frequency Reuse

• Concept: A geographic area is divided into small regions called cells. Each cell has a base station (BS). Users (Mobile Stations, MS) within a cell connect to its BS. Frequency reuse allows the same radio channel to be used in geographically separated cells, increasing system capacity.

• Frequency Reuse Factor (N): The number of cells in a cluster after which frequencies are reused. N = i² + ij + j² (i, j are integers).

• Need: To support a large number of users with limited spectrum.

• 19-Cell Cluster (i=3, j=2): Most common for hexagonal grid.

  • Co-channel cells are those using the same frequency band. They are separated by distance D = √(3N) * R, where R is cell radius.

  • DiagramSEARCH: "19 cell cluster frequency reuse hexagonal diagram co-channel cells"

• Merits of Cellular System:

  • Increased capacity (frequency reuse).

  • Reduced transmitter power (small cell size).

  • Improved battery life for mobiles.

  • Localized traffic handling.

• Evolution (1G to 5G):

  | Generation | Technology | Key Feature | | :--- | :--- | :--- | | 1G | Analog (AMPS) | Voice only | | 2G | Digital (GSM, CDMA) | Voice + SMS, circuit data | | 3G | CDMA2000, UMTS | Mobile broadband (video call, internet) | | 4G | LTE, WiMAX | IP-based, high-speed data | | 5G | NR (New Radio) | Ultra-low latency, massive IoT, mmWave |

• Performance Criteria: Coverage (area served), Capacity (number of users/channels), Quality (BER, call drop rate, speech quality).

[!TIP] Exam Focus: Be prepared to draw and label a 19-cell cluster, identifying co-channel cells (same letter/color) and calculating reuse distance D.

2. Propagation Models

• Free Space Propagation: Ideal model. Path loss: L(dB) = 32.45 + 20log₁₀(f[MHz]) + 20log₁₀(d[km]).

  DiagramSEARCH: "free space propagation model diagram"

• Two-Ray Ground Reflection Model: Considers direct ray + ground-reflected ray. More accurate for longer distances. Path loss ∝ d⁴. Critical distance d_c = (4πh_t h_r)/λ.

• Foliage Losses: Additional attenuation when signal penetrates trees/vegetation. Empirical models exist (e.g., loss ∝ f^0.5 * depth).

• Near-In-Distance (Near-Field) Propagation: Region very close to transmitter (d < 2D²/λ). Field strength decreases more slowly (1/d² or 1/d³) than far-field (1/d).

• Mobile-to-Mobile Propagation: Both antennas are low, near ground. No fixed BS. More severe fading due to multipath from surrounding objects.

• Hilly Terrain Angles:

  • Incident Angle (θᵢ): Angle between incident wave and horizontal at the receiver.

  • Slope Angle (θₛ): Angle of the hill slope relative to horizontal.

  • Calculation: tan(θₛ) = (H_t - H_r) / d (for simple slope).

3. Fading and Multipath

• Small-Scale Multipath Propagation: Rapid fluctuations in signal amplitude/phase over short distances (λ/2) or time due to constructive/destructive interference of multiple delayed copies.

• Fading Types:

  | Type | Cause | Time/Frequency Domain | | :--- | :--- | :--- | | Slow Fading | Shadowing (large obstacles) | Slow amplitude changes over distance | | Fast Fading | Multipath delay spread | Rapid fluctuations | | Flat Fading | B_s << B_c (Signal BW << Coherence BW) | All freq components fade equally | | Frequency-Selective Fading | B_s > B_c | Different freq components fade differently → ISI |

• Clarke's Model for Flat Fading:

  • Assumes a single incident plane wave + many scattered waves with uniform azimuth.

  • Received signal: r(t) = Re{ A(t) e^(j(2πf_c t + θ(t)) }

  • Envelope (A(t)) follows Rayleigh distribution (no LOS) or Rician distribution (with LOS).

  • Phase (θ(t)) is uniform [0, 2π].

  • Level Crossing Rate (LCR): Average rate at which fading envelope crosses a specified level R in positive direction. N_R ≈ √(2πf_d) e^(-R²/(2σ²)) for Rayleigh, where f_d is max Doppler shift.

• Dispersion Parameters (Time Domain):

  • Mean Excess Delay (τ̄): τ̄ = Σ(P_i * τ_i) / ΣP_i (power-weighted average of delays).

  • RMS Delay Spread (σ_τ): σ_τ = √(τ̄² - (τ̄)²). Key parameter for frequency-selective fading.

4. Channel Characterization

• Coherence Bandwidth (B_c): Frequency range over which channel impulse response is highly correlated. Approx: B_c ≈ 1/(50σ_τ) (for 50% correlation). Relation to Symbol Rate (R_s): For minimal ISI, need R_s << B_c (flat fading) or use equalizer if R_s > B_c.

• Coherence Time (T_c): Time duration over which channel impulse response is invariant. Approx: T_c ≈ 9/(16πf_d) (for 50% correlation). f_d = v/λ (max Doppler shift).

• Doppler Spread (B_d): Spectrum of Doppler shifts seen by the receiver. B_d ≈ 2f_d.

• Doppler Shift (f_d): f_d = (v/λ) cos(θ) where θ is angle between user direction and wave arrival.

[!TIP] Exam Focus: Direct formula application: Max Symbol Rate for minimal ISI ≈ B_c. Given B_c = 100 kHz, R_s,max ≈ 100 ksym/s.

5. Handoff and Mobility Management

• Necessity: When an MS moves out of its current cell's coverage area to maintain call continuity.

• Mechanism: MS measures signal strength (RSSI) of serving & neighboring BSs. Thresholds trigger handoff request.

• MAHO (Mobile Assisted Handoff): MS continuously monitors BSs and reports to network. Network makes handoff decision. Reduces network load, used in GSM.

• Queuing Concept: Handoff requests have higher priority than new call requests. Handoff requests can be queued if no channel available, but queue time must be < T_c to avoid drop.

• Types of Handoff:

  1. Hard Handoff (Break-before-make): MS releases old channel before acquiring new (FDMA/TDMA like GSM).

  2. Soft Handoff (Make-before-break): MS acquires new channel before releasing old (CDMA, dual receiver).

  3. Mobile-Assisted (MAHO): MS assists in measurement.

  4. Network-Controlled (NCHO): Network controls measurement & decision.

• CDMA Handoff: Softer Handoff (within same BS sector), Soft Handoff (between BSs). MS can be in communication with multiple BSs simultaneously (macro-diversity). Call Processing: Uses power control (reverse link) to manage interference; handoff based on E_b/N_0 or RSSI.

6. Multiple Access Techniques

• FDMA (Frequency Division Multiple Access):

  • Principle: Each user gets a dedicated frequency band (channel).

  • Channel Allocation: Total BW B_T, Guard Band B_g, Channel BW B_c.

  • Number of Channels: N = (B_T - B_g) / B_c.

    DiagramSEARCH: "FDMA channel allocation diagram"

• CDMA (Code Division Multiple Access) - Direct Sequence:

  • Principle: All users share same frequency/time. Separated by unique pseudo-noise (PN) codes.

  • Forward Channel (BS→MS): Uses Walsh codes for channelization + PN for spreading.

  • Reverse Channel (MS→BS): Uses PN codes only for spreading (orthogonal property lost due to asynchronous users).

  • Power Control (Vital): Near-far problem. BS controls MS transmit power to equalize received E_b/N_0 at BS. Reduces interference.

  • Processing Gain (PG): PG = (Chip Rate) / (Data Rate) = B_channel / R_b. Measures interference rejection capability.

  • Bit Error Probability (IS-95 Example): For K users, P_b ≈ (1/2) erfc(√(PG * E_b/N_0 / K)). (Simplified for BPSK in AWGN).

• FHSS (Frequency Hopped Spread Spectrum):

  • Principle: Carrier frequency changes rapidly ("hops") according to PN sequence.

  • Slow FH: Symbol duration T_s >> T_hop (multiple symbols per hop).

  • Fast FH: T_s << T_hop (multiple hops per symbol).

• Spread Spectrum Multiple Access (SSMA): General term for CDMA & FHSS. Provides interference rejection, security, and multiple access.

• OFDM (Orthogonal Frequency Division Multiplexing): High data rate stream split into many parallel low-rate streams, each modulating an orthogonal subcarrier. Resistant to frequency-selective fading (each subcarrier sees flat fading). Used in 4G/5G, Wi-Fi.

  DiagramSEARCH: "OFDM block diagram subcarriers"

• Advantages of CDMA over FDMA/TDMA:

  • Soft capacity: Graceful degradation beyond design load.

  • Soft handoff: Seamless, reduces drop rate.

  • 抗干扰能力 (Interference rejection): Via processing gain.

  • Universal frequency reuse: All cells use all frequencies (1-reuse).

  • Better security: Spread spectrum.

  • Higher capacity in many scenarios.

[!TIP] Exam Focus: FDMA Channel Calculation: N = (B_T - B_g) / B_c. CDMA PG: PG = Chip Rate / Data Rate. CDMA BER: Know formula P_b ≈ (1/2) erfc(√(PG * E_b/N_0 / K)). Be ready to plug numbers.

7. GSM System

• Architecture (Block Diagram):

  DiagramSEARCH: "GSM network architecture MSC BSC BTS MS HLR VLR block diagram"

  • MS (Mobile Station): Mobile phone + SIM.

  • BSS (Base Station Subsystem): BTS (transceiver), BSC (controls BTSs, handoff, frequency management).

  • NSS (Network Switching Subsystem): MSC (switching center), HLR (home location register), VLR (visitor location register), AUC (authentication), EIR (equipment identity).

• Interface Standards:

  • A interface: MSC ↔ BSC (circuit-switched).

  • Abis interface: BSC ↔ BTS (proprietary, usually).

  • Um interface: Air interface (MS ↔ BTS).

• Channels:

  • Traffic Channels (TCH): Carry voice/data (TCH/F, TCH/H).

  • Control Channels (CCH):

    • BCCH: Broadcast from BTS (cell info).

    • CCCH: Common control (paging, access grant).

    • DCCH: Dedicated control (SDCCH for call setup, SACCH for associated control).

• Frame Structure (TDMA):

  • TDMA Frame: 8 time slots (TS0-TS7), duration 4.615 ms.

  • Multiframe:

    • 26-Multiframe (TCH): 26 TDMA frames → 120 ms. Carries traffic.

    • 51-Multiframe (CCH): 51 TDMA frames → 235.39 ms. Carries control.

  • Burst: Information in one time slot. Types: Normal, Synchronization, Frequency Correction, Access.

• GSM Radio Subsystem: Comprises MS and BSS (BTS + BSC). Handles all radio-related functions (modulation, channel allocation, handover, transmission).

[!TIP] Exam Focus: Draw & label GSM architecture. Know 26 vs 51 multiframe purpose and duration. Distinguish TCH vs CCH.

8. Capacity and Interference Management

• Capacity (Erlang B Formula): E = (A^N / N!) / Σ_{k=0}^{N} (A^k / k!)

  • A = Offered traffic intensity (Erlangs).

  • N = Number of channels per cell.

  • Grade of Service (GoS): Probability of call blocking, P_b = E(A, N).

• Capacity Enhancement Techniques:

  • Cell Splitting: Divide congested cells into smaller cells (microcells/picocells). Increases channels per unit area.

  • Sectoring: Replace omni-directional antenna with directional antennas (e.g., 120° for 3-sector). Reduces co-channel interference, allows smaller N.

  • Microcells: Very small cells (radius < 1 km) for high-density areas.

• Channel Assignment Strategies:

  • Fixed Channel Assignment (FCA): Channels permanently assigned to cell. Simple, but inefficient under dynamic traffic.

  • Dynamic Channel Assignment (DCA): Channels allocated on demand from a pool. More flexible, complex. Requires signaling.

  • Borrowing: Non-fixed. Cell in need can "borrow" channel from neighbor (with coordination).

• Co-channel Interference (CCI):

  • Cause: Reuse of same frequency in nearby cells (N small).

  • Reduction Methods:

    1. Increase Reuse Distance (N): Reduces capacity.

    2. Power Control: Reduce BS/MS transmit power.

    3. Antenna Tilting/Down-tilt: Focus signal downward, reduce spillover.

    4. Sectoring: Reduces number of co-channel cells in interference path.

    5. Frequency Planning: Optimize channel allocation.

• Trunking & GoS: Cellular systems use trunking (pool of channels shared). GoS (P_b) is the blocking probability. Design trade-off: More channels → lower P_b but higher cost.

9. Antennas

• Cell-Site Antennas:

  • Types: Omni-directional (low capacity, rural), directional (3-sector 120°, 6-sector 60°).

  • Height: Typically 30-100m. Higher → larger coverage but more CCI.

  • Radiation Pattern: Vertical plane pattern (tilt) crucial for interference control.

  • Unique Situations: Hilltops, buildings (rooftop), towers. Need careful site survey.

• Mobile Antennas: Typically λ/4 monopole (quarter-wave), λ/2 dipole. Omnidirectional in horizontal plane. Diversity (space/pattern) often used.

10. Advanced Topics (Short Notes)

• MIMO (Multiple Input Multiple Output): Uses multiple antennas at both transmitter and receiver. Provides:

  • Spatial Multiplexing: Higher data rate (parallel streams).

  • Diversity: Improved reliability (space-time coding).

  • Beamforming: Directional transmission, reduces interference.

• Diversity Techniques (Spatial): Use multiple antennas separated by > λ/2 to receive independent fading copies. Types: selection combining, equal gain combining, maximal ratio combining. Combats fast fading.

PART B: TRANSMISSION LINES AND NETWORK SYNTHESIS

1. Two-Port Network Parameters

• Symmetrical Networks: Ports are interchangeable. Characterized by:

  • Z-Parameters (Impedance): V₁ = Z₁₁I₁ + Z₁₂I₂, V₂ = Z₂₁I₁ + Z₂₂I₂. For symmetrical: Z₁₁ = Z₂₂, Z₁₂ = Z₂₁.

  • Y-Parameters (Admittance): I₁ = Y₁₁V₁ + Y₁₂V₂, I₂ = Y₂₁V₁ + Y₂₂V₂. Symmetrical: Y₁₁ = Y₂₂, Y₁₂ = Y₂₁.

  • ABCD Parameters (Transmission): V₁ = A V₂ + B I₂, -I₁ = C V₂ + D I₂. For symmetrical: A = D.

  • Image Impedance (Zᵢ): Input impedance when network is terminated in its image impedance at other port. For symmetrical network, Zᵢ₁ = Zᵢ₂ = Zᵢ.

  • Characteristic Impedance (Z₀): For infinite cascade of identical symmetrical networks, Z₀ = Zᵢ.

• Asymmetrical Networks: Ports not interchangeable (e.g., T, π networks). Need image impedances Zᵢ₁ and Zᵢ₂ separately.

  • Image Impedance Calculation (T-network): Zᵢ₁ seen into port 1 with port 2 terminated in Zᵢ₂. Zᵢ₁ = Z₁ + (Z₂ || Zᵢ₂). Solve simultaneously.

  • Image Impedance Calculation (π-network): Zᵢ₁ seen into port 1 with port 2 terminated in Zᵢ₂. Zᵢ₁ = (Z₁ || (Z₂ + Zᵢ₂)). Solve simultaneously.

• Lattice Network: Symmetrical bridge network. Zᵢ = √(Z_a Z_b).

• Bridged T-Network: T-network with a bridge impedance across series arms.

• T and π Equivalent Circuits: Conversion formulas:

  • T → π: Z_A = (Z₁Z₃ + Z₂Z₃ + Z₁Z₂)/Z₂, Z_B = (Z₁Z₃ + Z₂Z₃ + Z₁Z₂)/Z₁, Z_C = (Z₁Z₃ + Z₂Z₃ + Z₁Z₂)/Z₃.

  • π → T: Z₁ = (Z_A Z_C)/(Z_A + Z_B + Z_C), Z₂ = (Z_A Z_B)/(Z_A + Z_B + Z_C), Z₃ = (Z_B Z_C)/(Z_A + Z_B + Z_C).

• Image Transfer Coefficient (θᵢ): For symmetrical network, θᵢ = cosh⁻¹(A) = cosh⁻¹(D). For cascade: θ_total = N θᵢ.

2. Filter Design

• Constant-K Filters:

  • Design: K = √(Z₁ Z₂). Series arm Z₁ = jωL or 1/(jωC), shunt arm Z₂ = 1/(jωC) or jωL.

  • LPF: Z₁ = jωL, Z₂ = 1/(jωC). f_c = 1/(2π√(LC)).

  • HPF: Z₁ = 1/(jωC), Z₂ = jωL.

  • BPF: Series L, shunt C in a T/π section.

  • Reactance Curves: X₁(ω) and X₂(ω) are odd/even functions. Limitation: Poor stopband attenuation (roll-off ~ 20 dB/dec).

• m-Derived Filters:

  • Design: Modify constant-K by adding a m-section (series/parallel) to create pole of attenuation at f_in > f_c.

  • m-derived LPF (T-section): L' = mL, C' = C/m, L_m = (1-m²)L, C_m = C/(1-m²).

  • Composite Filters: Combine constant-K and m-derived sections to improve stopband performance.

  • Frequency Transformation: From LPF prototype (Ω_c = 1) to HPF/BPF/BSF using s → Ω_c/s (HPF), s → (s² + Ω₀²)/(B s) (BPF), etc.

• Chebyshev Approximation:

  • LPF: Equiripple in passband, monotonic stopband. Ripple factor ε controls passband ripple.

  • HPF: Equiripple in passband (high freq), monotonic stopband. s → Ω_c/s transformation of LPF prototype.

  • Better roll-off than Butterworth for given order, at cost of passband ripple.

• Band-Pass Filter Resonance Frequency: f₀ = √(f₁ f₂), where f₁, f₂ are lower/upper cut-off frequencies.

• Filter Approximation Techniques Summary:

  | Type | Passband | Stopband | Roll-off | Use | | :--- | :--- | :--- | :--- | :--- | | Butterworth | Maximally flat | Monotonic | Moderate (20n dB/dec) | General purpose | | Chebyshev | Equiripple | Monotonic | Steeper (for same n) | Sharp cutoff needed | | Elliptic | Equiripple | Equiripple | Steepest | Very sharp cutoff |

3. Network Synthesis

• Realizability Conditions (For F(s) as impedance/admittance):

  1. Hurwitz Polynomial: Denominator D(s) must have roots in LHP (Re(s) < 0).

  2. Positive Real Function (PRF): Re[F(s)] ≥ 0 for Re(s) ≥ 0. Necessary & sufficient.

     • Necessary Conditions: D(s) Hurwitz, N(s), D(s) have same coefficients signs, degree N(s) ≤ degree D(s), F(s) real for real s.

• Foster Synthesis:

  • Form I: Partial fraction expansion of impedance Z(s) = K_∞ s + Σ (K_i s)/(s² + ω_i²) + Σ (K_i)/(s² + ω_i²). Realizes as parallel LC branches.

  • Form II: Partial fraction expansion of admittance Y(s). Realizes as series LC branches.

  • Steps: Expand Z(s) or Y(s) into partial fractions with simple poles on jω axis.

• Cauer Synthesis:

  • Form I (Ladder): Continued fraction expansion of impedance Z(s). Series-parallel LC ladder starting with series element.

  • Form II: Continued fraction expansion of admittance Y(s). Shunt-series ladder starting with shunt element.

  • Steps: Long division of N(s) by D(s) (or vice versa) to extract first element.

• Brune's Method: For synthesis of any PRF (not just LC). Uses:

  1. Removal of a pole at infinity (series impedance or shunt admittance).

  2. Removal of a finite pole (via Brune section: transformer + 2 impedances).

  3. Repeat until constant remainder.

• Bott-Duffin Method: General synthesis for any PRF using positive real functions and lossless two-ports. Ensures realizability with minimum number of elements.

  • Minimum Positive Real Function: A PRF that cannot be expressed as sum/product of simpler PRFs. Building block.

[!TIP] Exam Focus: Synthesis Problems: Given F(s), first test for PRF (Hurwitz, etc.). Then choose Foster (partial fractions) or Cauer (continued fraction) based on pole locations. Brune/Bott-Duffin are for general PRFs.

4. Transmission Line Theory

• Transmission Line Equations (Derivation from distributed R, L, G, C):

  ∂V/∂x = - (R + jωL) I , ∂I/∂x = - (G + jωC) V

  Solve → Wave equations: ∂²V/∂x² = γ² V, ∂²I/∂x² = γ² I

• Primary Constants: R (Ω/m), L (H/m), G (S/m), C (F/m).

• Secondary Constants:

  • Propagation Constant: γ = α + jβ = √{(R + jωL)(G + jωC)}

  • Characteristic Impedance: Z₀ = √{(R + jωL)/(G + jωC)}

  • Phase Constant: β = ω√{LC} (for low loss, R << ωL, G << ωC).

  • Phase Velocity: v_p = ω/β = 1/√{LC}.

  • Wavelength: λ = 2π/β = v_p / f.

• Voltage & Current at any point x (from load z=L):

  V(x) = V⁺ e^{-γx} + V⁻ e^{γx}

  I(x) = (V⁺/Z₀) e^{-γx} - (V⁻/Z₀) e^{γx}

  V(x) = V⁺ (e^{-γx} + Γ e^{γx})

  I(x) = (V⁺/Z₀) (e^{-γx} - Γ e^{γx})

  where Γ = (Z_L - Z₀)/(Z_L + Z₀) (load reflection coefficient).

• Special Cases:

  • Quarter-Wave Line (l = λ/4, βl = π/2): Z_in = Z₀² / Z_L. Impedance inverter.

  • Half-Wave Line (l = λ/2, βl = π): Z_in = Z_L. Impedance repeater.

  • Short-Circuited (Z_L=0): Z_in = j Z₀ tan(βl).

  • Open-Circuited (Z_L=∞): Z_in = -j Z₀ cot(βl).

• Reflection Coefficient (Γ): Ratio of reflected to incident voltage wave. |Γ| ≤ 1 for passive load.

• VSWR (Voltage Standing Wave Ratio): S = (1+|Γ|)/(1-|Γ|). S ≥ 1.

• Reflection Loss (RL): RL(dB) = -20 log₁₀|Γ|.

• Insertion Loss (IL): Power delivered to load with line vs. with line replaced by Z₀ directly. IL = 10 log₁₀(1-|Γ|²) for matched source.

• Distortions:

  • Frequency Distortion: α not constant with ω → different freq components attenuated differently.

  • Phase Distortion: β not linear with ω → different freq components delayed differently.

  • Distortionless Line Condition: α constant, β ∝ ω. Requires R/G = L/C and low loss (R << ωL, G << ωC).

5. Smith Chart Applications

• Impedance Matching: Normalize Z_L to z_L = Z_L/Z₀. Plot on Smith chart. Move towards generator using constant VSWR circles (adding transmission line) or stub matching (adding shunt/series reactance).

• Admittance Conversion: Rotate 180° (point through center) or add 1/z.

• Reflection Coefficient: Directly read Γ from chart (radius/angle).

• VSWR: Read from outermost scale.

• Stub Matching: Find point where Y = 1 ± jB (shunt stub) or Z = R ± jX (series stub). Distance to generator gives stub location, susceptance/reactance gives stub length.

6. Impedance Matching

• Single Stub Matching:

  • Shunt Stub: Normalize Z_L → z_L. Move towards generator to point where Re(z) = 1 (on g=1 circle). Read distance d. At that point, read y = 1 + jb. Stub length l_stub from y=∞ (short) or y=0 (open) to jb.

  • Series Stub: Move to Im(z)=0 circle. Read d. Read z = r ± jx. Stub length to cancel jx.

  • Disadvantage: Stub location depends on Z_L. Not fixed.

• Double Stub Matching:

  • Two stubs at fixed distances d₁, d₂ (usually λ/8 or λ/4 apart).

  • First stub adjusts conductance to 1, second stub adjusts susceptance to 0.

  • Advantages: Stub positions fixed (fabrication easier), wider bandwidth than single stub (two degrees of freedom).

7. Attenuators

• Symmetrical Attenuators: Z_in = Z_out = Z₀.

  • T-Type: R₁ = Z₀ (K-1)/(K+1), R₂ = 2Z₀ K/(K²-1), where K = voltage attenuation ratio (V₁/V₂).

  • π-Type: R₁ = Z₀ (K+1)/(K-1), R₂ = Z₀ (K²-1)/(2K).

• Asymmetrical Attenuators: Z_in ≠ Z_out. Used for impedance transformation. Design based on required Z_in, Z_out, and attenuation.

8. Special Transmission Lines

• Microstrip Line:

  • Structure: Conducting strip on dielectric substrate over ground plane.

  • Effective Dielectric Constant: ε_eff = (ε_r + 1)/2 + (ε_r - 1)/2 * 1/√(1+12d/W) (for W/d ≥ 1). ε_eff < ε_r.

  • Characteristics: Quasi-TEM mode. Z₀ depends on W/d, ε_r. Used in PCBs, microwave ICs.

  • DiagramSEARCH: "microstrip line cross section diagram"

• High-Frequency Lines:

  • Skin Effect: R ∝ √f. Current concentrates on surface.

  • Dielectric Losses: G ∝ f tanδ.

  • Radiation Losses: Significant for open structures (e.g., microstrip).

9. Equalizers

• Full Series Equalizer: Series LC network inserted in line to compensate for frequency distortion.

  • Design: L = R₀/ω_c, C = 1/(R₀ ω_c) for low-pass equalizer. Attenuates high frequencies to flatten overall response. ω_c chosen based on distortion profile.

Final Note: This summary strictly follows the APPROVED OUTLINE and covers all HIGH-FREQUENCY PAST PAPER TOPICS for UNIT 5. Focus on derivations (TL equations, T/π conversion), formulas (Erlang B, PG, Z_in, γ), definitions (coherence bandwidth, fading types), and diagrams (19-cell cluster, GSM architecture, Smith chart applications). Practice numerical problems on FDMA channel count, CDMA BER, TL constants, and image impedance.