Full-wave and bridge rectifiers — Hinglish notes

2.3.2 · Hardware › Diodes & Applications

WHAT is a full-wave rectifier?

WHY two topologies? Dono ka goal same hai (negative half ko upar flip karna). Difference yeh hai ki kaise current route hoti hai taaki current load ke through hamesha same direction mein flow kare.

HOW the center-tapped rectifier works

Ek transformer secondary ka imagine karo jo middle mein top half aur bottom half mein split hai, ek common center point (the tap = 0 V reference) share karte hue.

Positive half-cycle par: top winding positive hoti hai, isliye diode $D_{1}$ conduct karta hai, current $R_{L}$ ke through top→bottom flow karta hai.
Negative half-cycle par: bottom winding positive hoti hai, isliye diode $D_{2}$ conduct karta hai, current $R_{L}$ ke through same direction mein flow karta hai.

Ek waqt mein sirf ek diode conduct karta hai, isliye tumhe ek diode drop ka loss hota hai ( $0.7$ V silicon ke liye).

$V_{o u t, p e ak} = \frac{V _{seco n d a r y, p e ak}}{2} - 0.7 V$

("/2" isliye kyunki secondary ka har aadha hissa total secondary voltage ka sirf aadha carry karta hai.)

HOW the bridge rectifier works

Chaar diodes ek diamond arrangement mein. AC do corners se aata hai; load baaki do corners ke across hota hai.

Positive half-cycle par: diodes $D_{1}$ aur $D_{2}$ (ek diagonal pair) conduct karte hain.
Negative half-cycle par: doosra diagonal pair $D_{3}$ aur $D_{4}$ conduct karta hai.

Dono cases mein current $R_{L}$ ke through same direction mein steer hoti hai.

Har half-cycle mein do diodes series mein conduct karte hain, isliye tumhe do diode drops ka loss hota hai:

$V_{o u t, p e ak} = V_{seco n d a r y, p e ak} - 2 (0.7 V)$

Figure — Full-wave and bridge rectifiers

DERIVATION: Average (DC) value from first principles

Hum rectified waveform ki average height jaanna chahte hain. Full-wave output hai $v (t) = V_{m} ∣ sin ω t ∣$ .

Ek full period $T = \frac{2 π}{ω}$ par average. Kyunki dono humps identical hain, sirf aadhe period $[0, π / ω]$ par average karo:

$V_{d c} = \frac{1}{π / ω} \int_{0}^{π / ω} V_{m} sin (ω t) d t$

$θ = ω t$ , $d θ = ω d t$ let karo:

$V_{d c} = \frac{V _{m}}{π} \int_{0}^{π} sin θ d θ = \frac{V _{m}}{π} [- cos θ]_{0}^{π} = \frac{V _{m}}{π} [- (- 1) - (- 1)]$

$V_{d c} = \frac{2 V _{m}}{π} \approx 0.637 V_{m}$

Yeh step kyun? Integral ek hump ke neeche ka "total area" hai; width se divide karne par average height milti hai — exactly yahi ek DC meter read karta hai.

Compare karo: half-wave mein $V_{d c} = V_{m} / π \approx 0.318 V_{m}$ hota hai. Full-wave exactly double hai — sense banta hai, humne dono humps rakh liye.

DERIVATION: RMS value

$V_{r m s} = \frac{1}{π} \int_{0}^{π} (V_{m} sin θ)^{2} d θ = V_{m} \frac{1}{π} \int_{0}^{π} sin^{2} θ d θ$

$sin^{2} θ = \frac{1}{2} (1 - cos 2 θ)$ use karo:

$\int_{0}^{π} sin^{2} θ d θ = \frac{1}{2} [θ - \frac{s i n 2 θ}{2}]_{0}^{π} = \frac{π}{2}$

$V_{r m s} = \frac{V _{m}}{2} \approx 0.707 V_{m}$

Yeh kyun matter karta hai: rectifying karne se RMS full sine ke comparison mein change nahi hoti, kyunki squaring sign ka difference erase kar deta hai.

DERIVATION: Ripple factor & efficiency

$r$ aise derive kyun karte hain? Koi bhi waveform = DC part + AC (ripple) part. $V_{r m s}^{2} = V_{d c}^{2} + V_{a c, r m s}^{2}$ (yeh orthogonal hain). Rearrange karne par $V_{a c, r m s} = V_{r m s}^{2} - V_{d c}^{2}$ milta hai, phir $V_{d c}$ se divide karo.

Ripple frequency $= 2 f$ (har input cycle mein do humps) — yeh ek key advantage hai: same size ka smoothing capacitor full-wave ripple ko half-wave se kahin better filter karta hai.

Rectification efficiency: $η = \frac{P _{d c}}{P _{a c}} = \frac{( 2 V _{m} / π ) ^{2}}{( V _{m} / 2 ) ^{2}} = \frac{4/ π ^{2}}{1/2} = \frac{8}{π ^{2}} \approx 81.2%$ (half-wave ke 40.6% se double).

Worked Examples

Active Recall

Recall Cover and answer

Full-wave $V_{d c}$ exactly half-wave se double kyun hota hai?
Bridge mein ek saath kitne diodes conduct karte hain? Center-tapped mein?
Kaun si topology mein higher PIV diodes chahiye, aur kitne factor se?
60 Hz supply ke liye ripple frequency kya hogi?
$V_{d c} = 2 V_{m} / π$ do lines mein derive karo.

Recall Explain to a 12-year-old (Feynman)

Ek jhule ki imagine karo jo aage aur peechhe jaata hai. Half-wave rectifier sirf tab push karne deta hai jab jhula aage jaata hai — aadhe pushes waste ho jaate hain. Full-wave rectifier ek smart dost ki tarah hai jo peechhe jaate waqt bhi jhule ko pakadta hai aur us push ko aage ki taraf badal deta hai. Toh jhule ko do baar zyada push milti hai aur woh kaafi smoothly move karta hai. "Bridge" version yeh kaam chaar one-way gates se karta hai taaki jhula hamesha same direction mein jaata rahe, chahe shuru mein kisi bhi direction mein gaya ho.

Flashcards

What is

V_{d c}

of a full-wave rectifier in terms of

V_{m}

V_{d c} = \frac{2 V _{m}}{π} \approx 0.637 V_{m}

What is

V_{r m s}

of a full-wave rectified sine?

\frac{V _{m}}{2} \approx 0.707 V_{m}

Full-wave rectifier ka ripple factor kya hota hai?

r \approx 0.48

Ripple frequency aur input frequency

f

ka kya relation hai?

2 f

(har cycle mein do humps)

Bridge rectifier mein ek saath kitne diodes conduct karte hain?

Do (ek diagonal pair) series mein

Center-tapped rectifier mein ek waqt mein kitne diodes conduct karte hain?

Center-tapped rectifier mein har diode ki PIV kya hoti hai?

\approx 2 V_{m}

Bridge rectifier mein har diode ki PIV kya hoti hai?

\approx V_{m}

Bridge rectifier (Si) ka output peak kya hoga?

V_{m} - 2 (0.7)

Center-tapped rectifier (Si) ka output peak kya hoga?

\frac{V _{sec, p e ak}}{2} - 0.7

Full-wave rectifier ki rectification efficiency kya hoti hai?

8/ π^{2} \approx 81.2%

Bridge center-tap ke comparison mein kam transformer copper kyun use karta hai?

Isko koi center tap nahi chahiye aur yeh har half-cycle mein full secondary use karta hai

Connections

Half-wave rectifiers — 50%-wasteful predecessor
Capacitor filter / smoothing — $2 f$ ripple ko chhote caps ke liye exploit karta hai
Peak Inverse Voltage (PIV) — diode ratings select karta hai
Diode I-V characteristics — $0.7$ V drop ki origin
Transformers — center-tap vs. full secondary
Zener regulator — smoothing ke baad kya aata hai
RMS and average values — integral machinery jo yahan reuse hoti hai