CSE251 Diode Applications – Rectifier Circuits

2 Block diagram of a DC power supply. One of the most important applications of diodes is in the design of rectifier circuits. Rectifier circuits can be classified in two groups: 1. Half-wave (HW) rectifier 2. Full-wave (FW) rectifier

3 Half-Wave (HW) Rectifier  The HW rectifier circuit utilizes alternate half-cycles of the input sinusoid. Actual Implementation Half Wave (HW) Rectifier Circuits

4 Analysis of HW Rectifier: Ideal Diode Model Half Wave (HW) Rectifier Circuits

5 Analysis of HW Rectifier: Ideal Diode Model DC or Average Output Voltage Half Wave (HW) Rectifier Circuits

6 Analysis of HW Rectifier: Ideal Diode Model RMS (Root Mean Square) Voltage Half Wave (HW) Rectifier Circuits

7 Analysis of HW Rectifier: Ideal Diode Model Peak Inverse Voltage (PIV) i D = 0 0 V v D = v S During the negative half-cycle, the diode is reverse biased. As the current through the circuit is zero, there is no voltage drop across R. Therefore, all the supply voltage will appear across the diode. The maximum voltage that appears across the diode while reverse biased is the peak voltage, V P, and is known as the peak inverse voltage (PIV). The diode must be able to withstand this voltage without breaking down. +V P -V P Half Wave (HW) Rectifier Circuits

8 Analysis of HW Rectifier: Constant Voltage Drop Model Constant voltage drop model assumes a constant voltage drop across the diode while it is forward biased. Exercise: Find V dc and V rms of the output voltage of a HW rectifier circuit assuming constant voltage drop model. Half Wave (HW) Rectifier Circuits

10 Half-Wave (HW) Rectifier with a Filter Capacitor  Although the rectification stage makes the sine wave voltage to be positive, the rectifier’s result is not as “flat” a DC value as we would like to have from a reliable voltage source.  The capacitor is included to help smooth out the ripples that result in the output from the rectification stage.  Recall that the voltage across a capacitor cannot change instantaneously, but rather it requires a certain amount of time before it is fully charged.  Large capacitance values help suppress the quickly changing voltage from the rectifier and result in a flatter DC value being supplied to the load. Typical power supply designs use relatively large capacitor values (greater than 1000 μF). Half Wave (HW) Rectifier Circuits

11 Half-Wave (HW) Rectifier with a Filter Capacitor Half Wave (HW) Rectifier Circuits

12 Half-Wave (HW) Rectifier with a Filter Capacitor Half Wave (HW) Rectifier Circuits Voltage  During the positive half-cycle, capacitor is charged to the peak supply voltage Vm.  As the supply voltage starts decreasing from its peak value, the diode turns off. Since n-side is at higher voltage than the p- side due to capacitor voltage.  The capacitor discharges through the load resistor with the RC time constant.  As the capacitor voltage goes below the rising supply voltage, the diode turns ON, supply voltage supplies load current and at the same time charges the capacitor to the peak supply voltage V m.  The diode remains ON for the time  T.  The variation in the output voltage V r is called the Ripple voltage.

13 HW Rectifier with a Filter Capacitor: Ripple Voltage  As the voltage across a capacitor decreases exponentially,  As a small value of V r is desired for most power supplies, -(T-  T)/RC should be small (<< 1). As for e -x = 1 – x, for x << 1, Half Wave (HW) Rectifier Circuits Voltage

14  So the ripple voltage is,  Large values of C will keep V r small. So one must select, RC >> T. Half Wave (HW) Rectifier Circuits Voltage Average Load Current, I L  Average load voltage is, V dc ≈ V m – V r /2.  Average load current, I L = V m /R. Ripple Factor HW Rectifier with a Filter Capacitor: Ripple Voltage

15 Full-Wave (FW) Rectifier  The FW rectifier circuit utilizes both halves of the input sinusoid. Full Wave (FW) Rectifier Circuits

16  For the positive half of the AC cycle: Full Wave (FW) Rectifier Circuits  For the negative half of the AC cycle:

17  Input and output wave shapes of a FW rectifier circuit assuming constant voltage drop model: Full Wave (FW) Rectifier Circuits Ideal Diode Model:

18 FW Rectifier Circuits with Filter Capacitor

19 Frequencies of HW and FW rectified voltages derived from 60 Hz sine wave. FW Rectifier Circuits with Filter Capacitor

20 Comparison of ripple voltages for HW and FW rectified voltages with the same filter capacitor and load and derived from the same sinusoidal input voltage. FW Rectifier Circuits with Filter Capacitor

21 Average Load Voltage, Ripple Voltage and the Ripple Factor Average load voltage: V dc ≈ V p – V r /2. Ripple Voltage: V r ≈ V p /fRC HW Rectifier V r ≈ V p /2fRC FW Rectifier Ripple Factor: r ≈ V r(rms) /V DC f is the frequency of the unrectified AC input voltage. Output voltage wave shape of a rectifier circuit with the filter capacitor showing the peak (V p ), average (V DC ) and the peak-to-peak ripple (V r(pp) ) voltages at the load.