power electronics daniel hart

1. Chapter 3
Half-Wave rectifier
The Basics of Analysis

2. 3.2 RESISTIVE LOAD

3. 3.2 SINGLE-PHASE HALF-WAVE RECTIFIERS (R Load)
Average voltage across the resistor and current:
RMS voltage and Current :
Average Power absorb by the resistor:

4. 3.3
RESISTIVE-INDUCTIVE
LOAD

5. 3.3 SINGLE-PHASE HALF-WAVE RECTIFIERS (RL Load)
Applying KVL on the circuit to find the equation of current:
Solving the first order differential equation we get:
It is convenient to write current equation as function of t:
To find the β (angle at which current is zero) put i(β) = 0 in above equation:
The equation above needs MATLAB program to solve.

6. 3.8 HALF-WAVE RECTIFIER WITH A CAPACITOR
FILTER (Creating a DC Voltage from an AC Source)

7. 3.8 HALF-WAVE RECTIFIER WITH A CAPACITOR
FILTER (Creating a DC Voltage from an AC Source)
Output voltage across the capacitor or resistor is given by:
Solving for θ (angle at which diode turns OFF and capacitor start to provide voltage to resistor)
:
Solving for α (angle at which diode turns ON again and capacitor start to charge) :
The equation above needs MATLAB program to solve.

8. 3.8 HALF-WAVE RECTIFIER WITH A CAPACITOR
FILTER (Creating a DC Voltage from an AC Source)
Source or Diode current is given by:
Peak diode current occurs when the diode turns on at t=α
The peak-to-peak ripple for the circuit is expressed as

9. 3.8 HALF-WAVE RECTIFIER WITH A CAPACITOR
FILTER (Creating a DC Voltage from an AC Source)
Average output voltage can be measured using equation above but it can be calculated
easily by assuming linear curve in charging and discharging.
Average diode current or average supply current.
Since the voltage across diode is periodic therefore
average capacitor current is zero therefore:

10. 3.9 THE CONTROLLED HALF-WAVE RECTIFIER

11. 3.9 THE CONTROLLED HALF-WAVE RECTIFIER With Resistive Load
Average (DC) output voltage across the resistor can be expressed as:
RMS output voltage across the resistor can be expressed as:

12. 3.9 THE CONTROLLED HALF-WAVE RECTIFIER With RL Load

13. 3.9 THE CONTROLLED HALF-WAVE RECTIFIER With RL Load
RMS output voltage across the resistor can be expressed as:
The extinction angle is defined as the angle at which the current returns to zero, as in
the case of the uncontrolled rectifier. When t = β.
The equation above needs MATLAB program to solve.
Average (DC) output voltage across the load and average current can be expressed as:
RMS load current can be expressed as: