Full-Wave Rectifier with Filter Capacitor

Calculate ripple voltage and charging voltage at bridge rectifier

Bridge Rectifier with Smoothing

With Filter Capacitor (Smoothing Capacitor)

Calculation of ripple voltage and voltage drop under load. The filter capacitor smooths the pulsating DC voltage.

Input Voltage Type
V
V
2 × 0.7V for silicon bridge
µF
Ω
Ω
Transformer winding resistance
Hz
Results
Input Values
Input URMS:
Input UPeak:
Output Values
No-Load Voltage:
Voltage Under Load:
Load Current:
Critical Values
Ripple Voltage (VPP):
Diode Reverse Voltage:
Voltage Range
Maximum Voltage:
Minimum Voltage:

Voltage Diagram with Ripple Voltage

Voltage Analysis

The right column shows the minimum output voltage (blue) and the ripple voltage (red stacked). The total height corresponds to the maximum voltage.

Filter Capacitor Principle
  • Capacitor charges to peak voltage
  • Discharge through load resistance between pulses
  • Ripple voltage due to charge/discharge cycles
  • Larger capacitor = lower ripple voltage
Bridge rectifier with capacitor

Circuit diagram: Bridge rectifier with filter capacitor

Typical Values
Small Power Supplies (up to 1A): C: 1000-4700µF Ri: 2-10Ω
Medium Power Supplies (1-5A): C: 4700-22000µF Ri: 0.5-5Ω
Large Power Supplies (>5A): C: 22000µF+ Ri: 0.1-2Ω
Capacitor Dimensioning
Rules of thumb:
• 1000µF per 1A load current (minimum)
• 2000-5000µF per 1A for low ripple voltage
• At 5V: Minimum 4700µF per 1A
• At 12V: 2200µF per 1A sufficient
• At 24V+: 1000µF per 1A acceptable
Practical Limits
Acceptable ripple voltage: <10% of output voltage
Low voltages (<12V): Problematic
High currents (>5A): Prefer switching regulators
Precision applications: Linear post-regulator needed
Capacitor lifetime: Consider ripple current

Theory of Rectification with Filter Capacitor

Operating Principle

The filter capacitor (smoothing capacitor) smooths the pulsating DC voltage of the rectifier. It charges to the maximum voltage during peak times and discharges through the load resistance until the next charging pulse arrives.

Charging and Discharging Process
  • Charging time: Very short (only around the peak value of the sine voltage)
  • Discharging time: Between charging pulses (at 50Hz mains: ~10ms)
  • Charging current: Very high, as only short charging time available
  • Discharging current: Constant, determined by load resistance
Mathematical Relationships
No-load voltage:
\[U_{No-load} = \sqrt{2} \cdot U_{RMS} - U_D\]
Ripple voltage:
\[U_{Ripple} = \frac{I_L}{2 \cdot C \cdot f}\]
Load voltage:
\[U_{Load} = U_{No-load} \left(1 - \sqrt{\frac{R_i}{2 \cdot R_L}}\right)\]
Reverse voltage:
\[U_{Reverse} = \sqrt{2} \cdot U_{RMS}\]
Design Criteria
Parameter Uncritical Acceptable Critical
Ripple Factor < 5% 5-15% > 15%
Capacitor per Ampere > 5000µF/A 2000-5000µF/A < 2000µF/A
Internal Resistance < RL/20 RL/20 to RL/10 > RL/10
Transformer Utilization 90-95% 80-90% < 80%
Advantages
  • Simple construction
  • Low cost
  • High reliability
  • No switching frequency interference
  • Good overload capability
Disadvantages
  • High ripple voltage
  • Poor load regulation
  • Large, heavy capacitors
  • High peak current through diodes
  • Transformer over-dimensioning needed
Applications
  • Simple Power Supplies: For non-critical applications
  • Pre-stabilization: For linear regulators
  • Battery Chargers: With downstream regulation
  • Motor Drives: DC motor supply
  • Audio: With additional filtering
Voltage Waveforms and Component Selection
Full-wave without capacitor

Without capacitor: Pulsating DC voltage

Full-wave with capacitor

With capacitor: Smoothed voltage with ripple component

Capacitor Selection
Capacitance: 1000-5000µF per ampere load current
Voltage rating: Minimum 1.5× peak voltage
Ripple current: Sufficient for charging current peaks
Lifetime: Prefer low-ESR types
Temperature: 105°C types for better lifetime
Diode Selection
Reverse voltage: Minimum 2× input peak voltage
Current: 2-3× average current (due to peaks)
Schottky diodes: For low voltages (<12V)
Fast diodes: For reduced reverse recovery
Cooling: Use heat sinks for high currents
Symbol Directory
UNo-loadNo-load voltage (without load) [V]
ULoadOutput voltage under load [V]
URippleRipple voltage (peak-to-peak) [V]
UReverseMaximum diode reverse voltage [V]
CLFilter capacitor (smoothing capacitor) [µF]
RiInternal resistance of source [Ω]
RLLoad resistance [Ω]
fMains frequency [Hz]


Other electronics functions

LED resistor  •  Zener diode resistor (variable)  •  Zener diode resistor (fix)  •  Half-Wave rectification  •  Half-Wave rectification with capacitor  •  Full-Wave rectification  •  Full-Wave rectification with capacitor  •