Foundations — Link budget — path loss, EIRP, G - T, Eb - N0

3.6.25 · D1 · Physics › Spacecraft Structures & Systems Engineering › Link budget — path loss, EIRP, G - T, Eb - N0

Pehle tum parent note ki ek bhi line nahi padh sakte jab tak tumhe pata na ho ki har chhota symbol picture mein kya matlab rakhta hai. Yeh page unme se har ek ko zero se build karta hai. Upar se neeche padho — har idea agli ke liye ek brick hai.

1. Energy, power, aur unit "watt" ($P$, W)

Ek garden hose ki picture banao. Nozzle par water pressure transmitter power jaisi hai: kitna "push" se tum shuru karte ho. Ek radio transmitter ki power $P_t$ (subscript $t$ ka matlab hai transmit) typically ek spacecraft par kuch watts se tens of watts hoti hai — bahut kam, kyunki space mein electrical power scarce hai.

Yeh topic kyun chahiye isko: link budget mein sab kuch ultimately powers ki comparison hai — jo power tum bhejte ho versus jo arrive karti hai versus noise ki power.

2. Sphere pe spread hona — number $4\pi r^2$

Yeh poore topic ki sabse important picture hai.

$4\pi r^2$ mein har symbol earn karte hain:

• $r$ radius hai — source se distance, metres mein. Figure mein red arrow dekho.
• $\pi$ (pi) $\approx 3.14159$ ek fixed number hai jo circle ki circumference divided by its diameter ke roop mein define hota hai ($\pi =\text{circumference}/\text{diameter}$); yeh har circle ke liye same hai.
• $4\pi r^2$ ek sphere ki surface area hai. Yeh distance ke square ke saath badhti hai: $r$ double karo, aur area chaar guna badi ho jaati hai.

Yeh topic kyun chahiye isko: yeh sphere wahi wajah hai ki signals distance ke saath kamzoor kyun hote hain, aur yeh path loss aur EIRP ki definition dono ka origin hai (dono neeche define kiye hain).

3. Intensity / power density — $I$ ya $S$ (W/m²)

Total power lo aur bubble ki area se divide karo: $S=\frac{P}{4\pi r^2}$

Figure dekho: same chaar "power" ki rays ek chhote square se paas mein guzarti hain, lekin double distance par woh chaar guna bade square mein spread ho jaati hain — har patch ko chauthai mil jaata hai.

Yeh topic kyun chahiye isko: receiving antenna ek bucket hai jo jitni bhi power density uske upar gir rahi hai use pakad leta hai. $S$ baarish hai; antenna thodi si puddle pakadta hai.

4. Antenna gain — $G$ (ek pure ratio, phir dBi)

Real antennas sab directions mein equally radiate nahi karte. Ek dish beam ko focus karti hai, bilkul ek flashlight reflector ki tarah jo bulb ko focus karta hai.

$G=\frac{\text{main beam mein power density}}{\text{power density jo isotropic antenna deta}}$

• $G_t$ = transmit antenna ka gain.
• $G_r$ = receive antenna ka gain.
• Gain of 1 matlab "bilkul bhi focusing nahi" (isotropic). Gain of 300 matlab beam seedha aage 300× zyada intense hai — lekin sides mein kamzoor. Koi bhi antenna power create nahi karta; woh sirf isko redirect karta hai.

Yeh topic kyun chahiye isko: gain budget mein "free help" hai — yeh tumhare precious watts ko Earth ki taraf concentrate karta hai khali space mein waste karne ki jagah.

5. EIRP — power aur gain ko ek number mein combine karna

Ab jo hamare paas power $P_t$ aur gain $G_t$ hai, hum topic ki pehli compound quantity build kar sakte hain.

Dono ingredients multiply karo: $\text{EIRP}=P_t\cdot G_t(\text{watts})$

Yeh topic kyun chahiye isko: EIRP single "kitna zor se hum chillate hain?" number hai budget ke transmitting end par.

6. Decibels — multiplication ko addition mein badle ($10{\log }_{10}$, dB)

Link budget mein numbers tiny ($0.000000000000001$ W received power) se enormous ($10^{27}$ ka path loss factor) tak hote hain. Aise numbers ko haath se multiply karna bahut mushkil hai. Engineers ek trick use karte hain.

Yahan ${\log }_{10}$ (base-10 logarithm) sawaal ka jawaab deta hai "10 ko kisi power par raise karne se yeh number milta hai?" For example ${\log }_{10}(1000)=3$, kyunki $10^3=1000$.

Reference-flavoured decibels (reference $P_{\text{ref}}$ naam mein hi hai):

7. Wavelength aur frequency — $\lambda$, $f$, $c$

Radio signals waves hain. Ek wave ko do numbers describe karte hain.

Yeh ek saath is se locked hain: $c=f\lambda ⟺\lambda =\frac{c}{f}$

Yeh woh symbol hai jo §3 mein promise kiya gaya tha: far-field condition "$r$ ek wave se bahut bada" ab simply $r\gg \lambda$ hai.

Yeh topic kyun chahiye isko: path loss secretly $\lambda$ par depend karta hai — chhoti wavelength matlab receiving antenna "dekhta hai" ek chhota effective area, toh higher frequencies zyada lose karti hain per metre jab tak tum unhe gain se bhi focus na karo.

8. Path loss — $L_p$, range penalty

Ab hum sphere ($4\pi r^2$) ko wavelength ($\lambda$) ke saath combine kar sakte hain topic ke sabse bade loss mein.

$4\pi r/\lambda$ factor kahan se aata hai (WHY, is page par worked):

1. Transmit side: EIRP ka ek source distance $r$ par power density $S=\frac{\text{EIRP}}{4\pi r^2}$ produce karta hai — woh pehla factor $4\pi r^2$ hai (§2–§3 se spreading sphere).
2. Receive side: ek antenna $S$ ka sab nahi pakadta; woh sirf woh power pakadta hai jo uske effective aperture $A_e$ par girti hai (uska catch-area m² mein, §4 mein introduce kiya gaya), toh received power $P_r=S\cdot A_e$. §4 se hamare paas already $A_e=\frac{G_r{\lambda }^2}{4\pi }$ hai — woh doosra factor $4\pi$ hai aur jahan ${\lambda }^2$ enter karta hai.
3. Dono ko saath rakho: $P_r=\frac{\text{EIRP}}{4\pi r^2}\cdot \frac{G_r{\lambda }^2}{4\pi }=\text{EIRP}\cdot G_r\cdot \frac{{\lambda }^2}{(4\pi r{)}^2}$. Antenna gains $G_t,G_r$ strip karo; jo bacha — pure distance-aur-wavelength penalty — woh hai $L_p={\left(\frac{4\pi r}{\lambda }\right)}^2.$

Yeh topic kyun chahiye isko: $L_p$ single "safar kitna cost karta hai" number hai — main cheez jo EIRP aur antenna gains ko overcome karni hoti hai.

9. Noise aur temperature — $T_{\text{sys}}$ (Kelvin), $k$

Transmitter band hone par bhi, ek receiver faint random hiss sunta hai. Yeh noise hai, jo har jagah warm electrons ke jiggling se produce hoti hai — sky mein, ground mein, amplifier mein.

$N_0$ (padhte hain "N-nought") noise power spectral density hai — noise power per hertz, W/Hz mein. Decibels mein $k$ $-228.6$ dBW/K/Hz ban jaata hai (ek constant jo tum har $C/N_0$ line mein added dekhoge, §10 mein define kiya gaya).

$T_{\text{sys}}$ kahan se aata hai iske full story ke liye Noise Temperature and Noise Figure dekho.

Yeh topic kyun chahiye isko: signal tab hi "survive" karta hai jab woh is hiss se zyada loud arrive kare. Noise woh enemy hai jiske against poora budget fight karta hai.

10. Received carrier power aur $C/N_0$

Yeh topic kyun chahiye isko: $C/N_0$ woh jagah hai jahan transmit side (EIRP), safar ($L_p$) aur receive side (gain aur noise) finally ek number mein milte hain.

11. Receiver quality ko ek number mein rakhna — $G/T$

Yeh topic kyun chahiye isko: $G/T$ woh single "figure of merit" hai jo tumhe do ground stations ko ek nazar mein compare karne deta hai, gain aur temperature separately list kiye bina. Yeh seedha $C/N_0$ equation mein fit ho jaata hai: $\frac{C}{N_0}=\text{EIRP}-L_p+\frac{G}{T}-10{\log }_{10}(k)$.

12. Bits, data rate, aur quality — $R_b$, $E_b$, $E_b/N_0$

Digital data bits (0s aur 1s) ki ek stream hai.

Yeh topic kyun chahiye isko: $E_b/N_0$ final verdict hai — woh number jise tum ek threshold se compare karte ho decide karne ke liye ki "link closes" ya "link fails."

Foundations topic ko kaise feed karte hain

Related deeper pages: Free-Space Path Loss Derivation, Fris Transmission Equation, Forward Error Correction, Deep Space Network (DSN).

Equipment checklist

Khud test karo — tum parent note ke liye ready ho jab tum bina dekhey har line ka jawab de sako.