4.3.3
Physical layer bits (1s aur 0s) ko signals (voltages / waves) mein convert karta hai — wire pe ya air mein — aur poochta hai: is channel mein bits kitni tezi se push kar sakta hoon?
Do halve master karne hain:
Encoding — kaise kisi bit ko signal ki tarah draw karoon? (NRZ, Manchester)Capacity limits — channel physically kitne bits/sec carry kar sakta hai? (noiseless ke liye Nyquist, noisy ke liye Shannon)
Ek rule jo har data bit ko time ke saath ek voltage pattern pe map karta hai. KYU zaroori hai: receiver sirf voltage vs. time dekhta hai — use bits aur har bit kab shuru hoti hai dono recover karne padte hain (clock synchronization).
==High voltage = 1, low voltage = 0==. Signal bits ke beech mein zero pe return nahi karta — bas poore bit period ke liye level hold karta hai.
Intuition NRZ sasta kyun hai par risky bhi
KYA : Ek symbol per bit, sabse simple. Sabse kam bandwidth use karta hai.KAISE fail hota hai : 00000000 jaisi lambi run sirf ek flat line hoti hai. Receiver ki clock drift ho jaati hai aur woh count bhool jaata hai ki kitne zeros gaye → synchronization loss . Iska ek DC component bhi hota hai (average voltage ≠ 0), jo transformer-coupled lines ke liye bura hai.
Intuition Mid-bit transition genius kyun hai
KYU self-clocking : Kyunki har bit mein ek edge hoti hai, receiver apni clock har bit pe re-sync kar leta hai. "Zeros ke samundar mein kho jaane" ki koi problem nahi.Cost (80/20 key insight) : 2 transitions per bit tak squeeze hoti hain, isliye usi bit rate ke liye NRZ ke double bandwidth ki zaroorat padti hai. Tum bandwidth ko reliable synchronization ke badle mein trade karte ho.Bonus : Koi DC component nahi (har bit high+low mein balanced hai) → AC-coupled media pe kaam karta hai.
Definition Teen quantities jo log confuse karte hain
Bandwidth B B = f hi g h − f l o w Baud rate (symbols/sec): ek second mein kitne signal changes hote hain.Bit rate C bits hote hain.
Agar har symbol log 2 M bit rate = baud × log 2 M
Intuition Zyada levels = zyada bits per symbol kyunAgar ek symbol M M = log 2 M KYU log 2 n 2 n M = 2 n ⇒ n = log 2 M
Intuition Core idea (derive karo)Bandwidth B KYU limit? Bandwidth-B 2 B Nyquist rate hai. Isse tezi push karne par adjacent symbols ek doosre mein smear ho jaate hain (intersymbol interference).
Worked example Worked: phone-grade line, 4 levelsB = 3000 M = 4
log 2 4 C = 2 ( 3000 ) log 2 4 = 6000 × 2 = 12000
Definition Real-world limitReal channels mein noise hota hai. Noise cap lagaata hai ki tum kitne levels M absolute maximum rate deta hai, chahe encoding kitni bhi clever ho.
Worked example Worked: 30 dB telephone lineB = 3000 = 30
Convert kyun karna? Shannon ko linear ratio chahiye: S / N = 1 0 30/10 = 1 0 3 = 1000 C = 3000 log 2 ( 1 + 1000 ) = 3000 log 2 ( 1001 ) ≈ 3000 × 9.97 ≈ 29 , 900
Worked example Dono limits combine karna — M choose karnaEk channel: B = 1 = 63
Shannon: C = 1 0 6 log 2 ( 64 ) = 6 × 1 0 6
Nyquist ko M 2 B log 2 M = 6 × 1 0 6 ⇒ 2 × 1 0 6 log 2 M = 6 × 1 0 6 ⇒ log 2 M = 3 ⇒ M = 8
Yeh kyun matter karta hai: Shannon ceiling batata hai; Nyquist batata hai ki use reach karne ke liye kitne levels chahiye. Achievable rate ke liye dono mein se chhota use karo.
Common mistake dB directly Shannon mein daalnaGalat isliye sahi lagta hai kyunki problem mein "30" number waise hi pada hai. Fix: Shannon linear power ratio use karta hai. Pehle convert karo: S / N = 1 0 30/10 = 1000
Common mistake "Manchester mein zyada bandwidth matlab better hai"Sahi lagta hai kyunki "zyada" acha sunai deta hai. Fix: Manchester ko zyada bandwidth chahiye — yeh ek cost hai. Iska benefit self-clocking aur no DC hai, efficiency nahi.
Common mistake Baud aur bit rate confuse karnaSahi lagta hai kyunki binary NRZ mein dono equal hote hain. Fix: Sirf tab equal hote hain jab M = 2 log 2 2 = 1 M = × log 2 M
Common mistake Noisy real channel pe Nyquist use karnaSahi lagta hai — yeh bada number deta hai! Fix: Nyquist noise ignore karta hai; asli ceiling chhota Shannon value hai. Shannon ko levels badhake beat nahi kar sakte.
Recall Quick self-test (answers chhupa lo)
NRZ lambi zero runs pe sync kyun khota hai? → koi transition nahi hoti → receiver clock drift kar jaata hai.
Manchester har bit pe kya guarantee karta hai? → ek mid-bit transition (self-clocking).
Nyquist formula? → C = 2 B log 2 M
Shannon formula? → C = B log 2 ( 1 + S / N )
Actually kaun si limit use karte hain? → Nyquist aur Shannon mein se chhoti.
Recall Feynman: 12-saal ke bachche ko explain karoSocho tum ek flashlight se secret messages bhej rahe ho. NRZ = "1" ke liye ON rakho, "0" ke liye OFF. Problem: agar tum das "0" bhejo, light bas kaafi der ke liye OFF rehti hai aur tumhara dost nahi bata sakta ki das zeros the ya gyarah — woh count bhool jaata hai. Manchester = tum hamesha har letter ke beech mein blink karte ho, toh tumhare dost ka "tick-tock" step mein rehta hai. Blinking ki cost hai ki flicking dono guna tez karni padti hai (zyada "bandwidth"), par koi count nahi bhoolta. Nyquist kehta hai: ek flashlight sirf itni tez blink kar sakti hai ki blinks blur na ho jaayein. Shannon add karta hai: agar room foggy hai (noise), toh bright-vs-dim levels blur ho jaate hain, toh tum bahut saare brightness levels use nahi kar sakte — yahi true top speed set karta hai.
Mnemonic Do capacity laws yaad karo"Noiseless = Nyquist (dono N se), Noisy = Shannon (S for Signal/noise)."
Formula shape: Nyquist multiply karta hai (2 B log 2 M Shannon andar-one-add karta hai (B log 2 ( 1 + S / N )
Data Link Layer — inhee encoded bits ke upar framing use karta haiModulation (ASK, FSK, PSK, QAM) — M Signal-to-Noise Ratio — Shannon ke andar ka S / N Sampling Theorem — Nyquist mein 2 B Bandwidth vs Bit Rate — baud/level relationship
Line encoding kin dono ke beech map karta hai? Data bits ↔ time-varying voltage/signal patterns
NRZ-L mein 1 aur 0 kya represent karta hai? High voltage = 1, low voltage = 0 (poore bit ke liye level hold hota hai)
NRZ identical bits ki lambi runs mein kyun struggle karta hai? Koi transition nahi hoti, toh receiver clock drift karti hai aur bit-count synchronization kho jaati hai
Manchester kya guarantee karta hai, aur kyun? Har bit pe ek mid-bit transition — isse self-clocking hota hai
NRZ ke comparison mein Manchester ki main cost kya hai? Isko roughly double bandwidth chahiye (ek bit mein 2 transitions tak)
Bit rate vs baud rate ka relation? bit rate = baud × log₂ M, jahan M = number of signal levels
Nyquist capacity formula batao. C = 2B·log₂ M (bits/s), noiseless channel
Nyquist symbol rate 2B kyun hai? Bandwidth-B signal ko 2B samples/sec se fully represent kiya jaata hai (sampling theorem)
Shannon–Hartley formula batao. C = B·log₂(1 + S/N) bits/s noisy channel ke liye
Shannon mein SNR linear (dB nahi) kyun hona chahiye? Formula actual power ratio use karta hai; S/N = 10^(dB/10) se convert karo
30 dB SNR ko linear ratio mein convert karo. 10^(30/10) = 1000
Jab dono apply hon toh kaun si capacity use karte hain? Nyquist aur Shannon mein se chhoti (Shannon noisy channel ka absolute ceiling hai)
Shannon intuition mein noise roughly kitne levels allow karta hai? M ≈ √(1 + S/N)
Channel B=3000Hz, M=4: Nyquist capacity? C = 2·3000·log₂4 = 12000 bits/s
Manchester mid-bit transition
