Voltages at Full-Wave Rectifier

Calculator for calculating RMS and average voltage at bridge rectifier

Full-Wave Rectifier Calculator

Bridge Rectification

Calculation without filter capacitor. Both half-waves are utilized, resulting in lower ripple and better transformer utilization.

V
Input voltage as RMS or peak value
V
2 × 0.7V for silicon bridge
Results
Input Values
Input URMS:
Input UPeak:
Output Values
After Diodes U2:
Output Uavg:
Output URMS:
Rectifier Types
Bridge Rectifier: 4 Diodes UD = 1.4V Best Efficiency
Center-Tap Rectifier: 2 Diodes UD = 0.7V Transformer with center tap

Voltage Diagram

Voltage Comparison

Comparison of different voltage values at the full-wave rectifier. The average voltage is the DC component.

Operating Principle
  • Both half-waves are rectified
  • Better transformer utilization than half-wave rectifier
  • Lower ripple in output voltage
  • Higher output power possible
Bridge rectifier

Circuit diagram: Bridge rectifier (4 diodes)

Practical Calculation Examples

Example 1: Mains Transformer 230V

Given: Mains voltage 230V (RMS value), Bridge rectifier

Step-by-Step Calculation
1. Input peak voltage: \[U_{1s} = U_{1RMS} \times \sqrt{2} = 230V \times 1.414 = 325.2V\]
2. Peak voltage after diodes: \[U_{2s} = U_{1s} - U_D = 325.2V - 1.4V = 323.8V\]
3. Average voltage (DC component): \[U_{avg} = \frac{2 \times U_{2s}}{\pi} = \frac{2 \times 323.8V}{3.14159} = 206.2V\]
4. RMS value of output voltage: \[U_{RMS,out} = \frac{U_{2s}}{\sqrt{2}} = \frac{323.8V}{1.414} = 229.0V\]
Result: Uavg = 206.2V, URMS = 229.0V
Application: Basis for DC power supplies after filtering
Example 2: 24V Transformer

Given: 24V secondary voltage (RMS value), Bridge rectifier

Low-Voltage Rectification
1. Input peak voltage: \[U_{1s} = 24V \times \sqrt{2} = 24V \times 1.414 = 33.9V\]
2. Peak voltage after diodes: \[U_{2s} = 33.9V - 1.4V = 32.5V\]
3. Average voltage: \[U_{avg} = \frac{2 \times 32.5V}{\pi} = \frac{65V}{3.14159} = 20.7V\]
4. RMS value: \[U_{RMS,out} = \frac{32.5V}{\sqrt{2}} = \frac{32.5V}{1.414} = 23.0V\]
5. Loss due to diodes: \[\text{Loss} = \frac{1.4V}{33.9V} \times 100\% = 4.1\%\]
Result: Uavg = 20.7V, Loss = 4.1%
Note: At low voltages, diode loss becomes significant
Example 3: Comparison Bridge vs. Center-Tap Rectifier

Given: 15V secondary voltage, comparison of both rectifier types

Detailed Comparison
Bridge Rectifier (4 diodes)
Input peak voltage: \[U_{1s} = 15V \times \sqrt{2} = 21.2V\]
After diodes (2 × 0.7V): \[U_{2s} = 21.2V - 1.4V = 19.8V\]
Average voltage: \[U_{avg} = \frac{2 \times 19.8V}{\pi} = 12.6V\]
Loss: \[\frac{1.4V}{21.2V} = 6.6\%\]
Center-Tap Rectifier (2 diodes)
Required voltage per half: \[U_{Half} = 15V \text{ (per side)}\]
After diode (1 × 0.7V): \[U_{2s} = 21.2V - 0.7V = 20.5V\]
Average voltage: \[U_{avg} = \frac{2 \times 20.5V}{\pi} = 13.0V\]
Loss: \[\frac{0.7V}{21.2V} = 3.3\%\]
Comparison: Center-tap rectifier has lower losses (3.3% vs 6.6%)
But: Bridge rectifier doesn't require center tap on transformer
Efficiency Considerations
High voltage (230V): Diode loss ~1-2%
Medium voltage (24V): Diode loss ~4-6%
Low voltage (5V): Diode loss ~15-25%
Use Schottky diodes for low voltages
Practical Applications
DC Power Supplies: After filtering and regulation
Battery Chargers: Simple circuits
Motor Controls: Brushless DC motors
Measuring Instruments: RMS value display

Theory of Full-Wave Rectifier

Operating Principle

The full-wave rectifier uses both half-waves of the AC voltage for rectification. This leads to better transformer utilization and lower ripple in the output voltage compared to the half-wave rectifier.

Bridge Rectifier vs. Center-Tap Rectifier
Property Bridge Rectifier Center-Tap Rectifier
Number of Diodes 4 2
Voltage Drop 2 × UD = 1.4V 1 × UD = 0.7V
Transformer Simple secondary winding Center tap required
Efficiency Lower (higher losses) Higher (lower losses)
Application Standard for DC power supplies High-frequency power supplies
Mathematical Relationships
Peak value after diodes:
\[U_{2s} = U_{1s} - U_D\]
Average value (DC component):
\[U_{avg} = \frac{2 \cdot U_{2s}}{\pi}\]
RMS value output:
\[U_{RMS,out} = \frac{U_{2s}}{\sqrt{2}}\]
Form factor:
\[F = \frac{U_{RMS}}{U_{avg}} = \frac{\pi}{2\sqrt{2}} = 1.11\]
Ripple and Spectrum
  • Fundamental ripple frequency: 2 × mains frequency (100Hz at 50Hz mains)
  • Ripple: Significantly lower than half-wave rectifier
  • Spectrum: Harmonics at 100Hz, 200Hz, 300Hz, ...
  • Filter effort: Lower effort required for smoothing
Advantages
  • Better transformer utilization
  • Lower ripple
  • Higher output power possible
  • Lower ripple frequency (100Hz)
  • Proven, robust technology
Disadvantages
  • Higher diode losses (4 vs 2 diodes)
  • More components required
  • Higher reverse voltage per diode
  • More complex circuit
Application Areas
  • DC Power Supplies: Linear and switching
  • Battery Chargers: Simple design
  • Motor Drives: DC motor supply
  • Measuring Instruments: Analog instruments
  • Audio: Amplifier power supplies
Voltage Waveforms
Half-wave voltage waveform

Half-wave rectifier: Only positive half-waves

Full-wave voltage waveform

Full-wave rectifier: Both half-waves utilized

Symbol Directory
U1,RMSInput voltage (RMS value) [V]
U1sInput voltage (peak value) [V]
U2sOutput voltage (peak value after diodes) [V]
UavgAverage value of output voltage (DC component) [V]
URMS,outRMS value of output voltage [V]
UDDiode forward voltage [V]
FForm factor (URMS/Uavg) [-]


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  •