What Is a Filter Capacitor?

A filter capacitor is used after a rectifier to reduce the voltage ripple produced when AC is converted into DC.

AC
 │
 ▼
┌─────────────┐
│  Rectifier  │
└──────┬──────┘
       │
       +───────┬────── DC
               │
              ─── C
              ───
               │
              GND

The capacitor charges near the peak voltage of the rectified waveform and then supplies current to the load while the rectifier voltage falls below the capacitor voltage.

Filter Capacitor Formula

For a full-wave rectifier, the approximate required capacitance is:

C = I / (f × Vr)

where:

• C = capacitance in farads
• I = load current in amperes
• f = ripple frequency in hertz
• Vr = allowed ripple voltage in volts

For a full-wave rectifier connected to a 50 Hz supply, the ripple frequency is approximately 100 Hz.

fripple = 2 × fmains

For a half-wave rectifier:

fripple = fmains

Filter Capacitor Calculator

Example — 2 A Power Supply

Suppose a full-wave bridge rectifier supplies a load requiring 2 A. The allowable ripple voltage is 2 V and the mains frequency is 50 Hz.

I = 2 A

Vr = 2 V

fmains = 50 Hz

fripple = 2 × 50

fripple = 100 Hz

The required capacitance is:

C = I / (f × Vr)

C = 2 / (100 × 2)

C = 0.01 F

Therefore:

C = 10,000 µF

A practical design would then select an appropriate standard capacitor value while also checking voltage rating, ripple-current rating, temperature and tolerance.

Full-Wave vs Half-Wave Rectification

A full-wave rectifier produces ripple at twice the mains frequency. Therefore, for the same load current and allowed ripple voltage, a full-wave rectifier requires approximately half the capacitance of a half-wave rectifier.

Ripple Voltage

The approximate peak-to-peak ripple voltage of a capacitor-input rectifier is:

Vr = I / (f × C)

This means:

• Higher load current increases ripple.
• Larger capacitance decreases ripple.
• Higher ripple frequency decreases ripple.

Ripple Voltage Calculator

Example — 10,000 µF at 2 A

For a 2 A load using a 10,000 µF capacitor and a 50 Hz full-wave rectifier:

C = 10,000 µF
  = 0.01 F

fripple = 100 Hz

The approximate ripple voltage is:

Vr = I / (f × C)

Vr = 2 / (100 × 0.01)

Vr = 2 V

Therefore, the approximate ripple is 2 V peak-to-peak.

Multiple Filter Capacitors in Parallel

Large filter capacitors are commonly connected in parallel when a larger total capacitance is required.

Ctotal = C1 + C2 + C3 + ...

For example:

4 × 10,000 µF

Ctotal = 40,000 µF

The voltage rating of every capacitor must be appropriate for the supply voltage.

Filter Capacitor Bank Calculator

Capacitor Voltage Rating

The capacitor voltage rating must be higher than the maximum voltage that can appear across the capacitor.

For a transformer secondary followed by a bridge rectifier, the capacitor can charge to approximately the peak of the AC waveform, minus the rectifier voltage drop.

Vpeak ≈ Vrms × 1.414

For example, a 35 VAC transformer secondary has an approximate peak voltage of:

Vpeak = 35 × 1.414

Vpeak ≈ 49.5 V

The actual DC voltage will depend on load, transformer regulation, rectifier losses and ripple.

Filter Capacitor Voltage Calculator

Choosing the Voltage Rating

The calculated peak voltage should not be treated as the capacitor's recommended operating voltage. A suitable safety margin should be provided.

For example, if the unloaded DC voltage can approach approximately 50 V, selecting a capacitor rated for only 50 V leaves essentially no margin for supply variation or transient conditions.

A higher voltage-rated capacitor may therefore be appropriate, depending on the design.

Ripple Current Rating

The filter capacitor must also be capable of handling the ripple current produced by the rectifier and load.

A capacitor can have adequate capacitance and voltage rating while still being unsuitable if its ripple-current rating is too low.

This is especially important in:

• Power amplifiers
• Switch-mode power supplies
• High-current linear power supplies
• Motor power supplies
• Industrial power supplies

Why Larger Is Not Always Better

Increasing filter capacitance reduces ripple, but a very large capacitor also increases the current drawn by the rectifier when the capacitor is initially charged.

This is known as inrush current.

Power ON
   ↓
Capacitor initially discharged
   ↓
Large charging current
   ↓
Rectifier / transformer stress

For large capacitor banks, the rectifier, transformer, wiring, fuse and switching components should all be selected to handle the resulting inrush current.

Filter Capacitors in Audio Amplifiers

Large electrolytic capacitors are commonly used in the power supplies of class-AB audio amplifiers.

For example, a high-current amplifier may use several large capacitors connected in parallel on each supply rail.

+V ────┬── 10,000 µF ── GND
       ├── 10,000 µF ── GND
       ├── 10,000 µF ── GND
       └── 10,000 µF ── GND

The total capacitance is:

Ctotal = 40,000 µF

The actual design must also consider ripple current, ESR, capacitor voltage rating, transformer regulation and amplifier peak current.

DC Output Voltage and Ripple

A capacitor-input rectifier does not produce perfectly constant DC. The capacitor charges near the peaks of the rectified waveform and then discharges into the load between peaks.

       Peak
        /\
       /  \       /\
──────/    \─────/  \─────
      ← Vr →

The voltage difference between the capacitor's maximum and minimum voltage is approximately the ripple voltage.

Effect of Load Current

For a fixed capacitor and ripple frequency, increasing load current increases ripple voltage.

I ↑
↓
Vr ↑

This is why a power supply designed for a high-current load usually requires significantly more filter capacitance than a low-current supply.

Effect of Capacitance

For a fixed load current and ripple frequency:

C ↑
↓
Vr ↓

Doubling the capacitance approximately halves the ripple voltage, assuming the other conditions remain unchanged.

50 Hz and 60 Hz Supplies

For a full-wave bridge:

50 Hz mains → approximately 100 Hz ripple

60 Hz mains → approximately 120 Hz ripple

The higher ripple frequency of a 60 Hz supply allows slightly lower capacitance for the same load current and ripple voltage.

Common Mistakes

• Using mains frequency instead of ripple frequency for a full-wave rectifier.
• Forgetting that full-wave rectification doubles the ripple frequency.
• Ignoring capacitor voltage rating.
• Ignoring ripple-current rating.
• Using an excessively small capacitor and accepting excessive ripple.
• Using an extremely large capacitor without considering inrush current.
• Ignoring transformer regulation and unloaded DC voltage.
• Ignoring rectifier voltage drop.
• Reversing the polarity of an electrolytic capacitor.

Key Points

• Filter capacitors reduce the ripple produced by rectifiers.
• For a full-wave rectifier, ripple frequency is approximately twice the mains frequency.
• The basic formula is C = I / (f × Vr).
• Higher load current requires more capacitance.
• Higher ripple frequency requires less capacitance for the same ripple.
• Higher capacitance produces lower ripple.
• Voltage rating must account for the rectified peak voltage and safety margin.
• Ripple-current rating is important in high-current power supplies.
• Large capacitor banks can produce significant inrush current.