filters

filters

1. What a Filter Is (in Power Supply: Rectifier Filter)

Filter = circuit that smooths pulsating DC from rectifier into near-constant DC by removing AC ripple, using reactive elements ($C, L$) that store energy.

Placed after rectifier, before load/regulator.

2. Types (exam list)

Filter	Circuit	How It Works	Ripple & Use
Capacitor filter (C)	$C$ in parallel with $R_L$ (most common, shunt)	Charges to $V_m$ during diode conduction (low impedance), discharges slowly through $R_L$ when diode blocks (time constant $τ=R_L C$ ≫ $T$) ⇒ voltage holds near $V_m$ with small sawtooth ripple	Simple, cheap, ripple

(half-wave $f$, full-wave $2f$); voltage rises to $V_m$ (higher than without) |
| Inductor filter (L) | $L$ in series with $R_L$ (choke) | Opposes $di/dt$ ($v_L=L di/dt$), smooths current ⇒ current more constant, voltage across $L$ drops AC | Less used alone (bulky, $R$ loss), but good for heavy load where $R_L$ small |
| LC (L-section / choke-input) | $L$ series, then $C$ shunt | $L$ blocks AC, $C$ shunts residual → better ripple | Better regulation, used for high current |
| π (CLC) filter | $C$ - $L$ - $C$ or $C$ - $R$ - $C$ | Two $C$ with $L/R$ between ⇒ double filtering | Very low ripple, for sensitive loads, but with $R$ has drop |

3. Ripple Calculation (capacitor filter — most asked)

• Half-wave:

,

• Full-wave:

(since $f$ doubles, half ripple for same $C$)

Form factor: larger $C$ or smaller $I_{dc}$ ($R_L$ large) ⇒ smaller ripple but higher cost, inrush current at turn-on.

4. Worked Examples

(a) Half-wave with C=1000µF, I_dc=100mA, f=50Hz: V_r≈0.1/(50·1e-3)=2V, V_dc≈17-1=16V (if Vm=17) ✓

(b) Full-wave same: V_r≈0.1/(100·1e-3)=1V ⇒ smoother.

(c) Need ripple <1V for full-wave at 1A, C=1000µF: V_r=1/(100·1e-3)=10V? Actually need larger C: C= I/(2f V_r)=1/(100·1)=10,000µF.

(d) Why capacitor filter bad for variable load? V_dc drops with load (since discharge faster) ⇒ poor regulation; LC better.

(e) L filter: X_L=2πfL for ripple frequency (100Hz) ⇒ large L needed (henries) for significant blocking, bulky.

5. Exam Points

• Define filter as smoothing after rectifier — 3 marks, frequent.
• List C, L, LC, π types with circuit — 5-7 marks, very frequent (often ask to compare C vs L).
• Derive capacitor ripple $V_r=I/(fC)$ (half) and $I/(2fC)$ (full) — 5 marks, very frequent.
• Mention $τ=R_L C ≫ T$ for small ripple — 3-5 marks, frequent.