1. Recall Lecture 8 Full Wave Rectifier Rectifier Parameters
Center tapped
Bridge
Rectifier Parameters
PIV
Duty Cycle

2. Example: Half Wave Rectifier
Given a half wave rectifier with input primary voltage, Vp = 80 sin t and the transformer turns ratio, N1/N2 = 6. If the diode is ideal diode, (V = 0V), determine the value of the peak inverse voltage.
Get the input of the secondary voltage:
80 / 6 = V
PIV for half-wave = Peak value of the input voltage = V
𝑉 𝑃 𝑉 𝑆 = 𝑁 1 𝑁 2

3. Example: Full Wave Rectifiers
Calculate the transformer turns ratio and the PIV voltages for each type of the full wave rectifier
center-tapped
bridge
Assume the input voltage of the transformer is 220 V (rms), 50 Hz from AC main line source. The desired peak output voltage is 9 volt; also assume diodes cut-in voltage = 0.6 V.

4. Solution: For the center-tapped transformer circuit the peak voltage of the transformer secondary is required
The peak output voltage = 9V
Output voltage, vo = vs - V
Hence, vs = = 9.6V  this is peak value! Must change to rms value
Peak value = Vrms x 2
So, vs (rms) = 9.6 / 2 = 6.79 V
The turns ratio of the primary to each secondary winding is
The PIV of each diode: 2vs (peak) - V = 2(9.6) = = 18.6 V

5. Solution: For the bridge transformer circuit the peak voltage of the transformer secondary is required
The peak output voltage = 9V
Output voltage, vo= vs - 2V
Hence, vs = = 10.2 V
Peak value = Vrms x 2
So, vs (rms) = 10.2 / 2 = 7.21 V
The turns ratio of the primary to each secondary winding is
The PIV of each diode: vs (peak) - V = = 9.6 V
 this is peak value! Must change to rms value

7. Filters
A capacitor is added in parallel with the load resistor of a half-wave rectifier to form a simple filter circuit. At first there is no charge across the capacitor
During the 1st quarter positive cycle, diode is forward biased, and C charges up.
VC = VO = VS - V.
As VS falls back towards zero, and into the negative cycle, the capacitor discharges through the resistor R. The diode is reversed biased ( turned off)
If the RC time constant is large, the voltage across the capacitor discharges exponentially.

8. Filters
During the next positive cycle of the input voltage, there is a point at which the input voltage is greater than the capacitor voltage, diode turns back on.
The diode remains on until the input reaches its peak value and the capacitor voltage is completely recharged.

9. Capacitor discharges through R since diode becomes offVp Vm
Quarter cycle; capacitor charges up
Capacitor discharges through R since diode becomes off
Input voltage is greater than the capacitor voltage; recharge before discharging again
VC = Vme – t / RC
NOTE: Vm is the peak value of the capacitor voltage = VP - V
Since the capacitor filters out a large portion of the sinusoidal signal, it is called a filter capacitor.

10. Figure: Half-wave rectifier with smoothing capacitor.
Ripple Voltage, and Diode Current
Vr = ripple voltage
Vr = VM – VMe -T’/RC
where T’ = time of the capacitor to discharge to its lowest value Tp T’
Vr = VM ( 1 – e -T’/RC )
Expand the exponential in series,
Vr = ( VMT’) / RC
Figure: Half-wave rectifier with smoothing capacitor.

11. Hence for half wave rectifier
If the ripple is very small, we can approximate T’ = Tp which is the period of the input signal
Hence for half wave rectifier
Vr = ( VMTp) / RC
For full wave rectifier
Vr = ( VM 0.5Tp) / RC

12. Example Consider a full wave center-tapped rectifier
Example Consider a full wave center-tapped rectifier. The capacitor is connected in parallel to a resistor, R = 2.5 k. The input voltage has a peak value of 120 V with a frequency of 60 Hz. The output voltage cannot be lower than 100 V. Assume the diode turn-on voltage, V = 0.7 V. Calculate the value of the capacitor.
VM = 120 – 0.7 = V
Vr = – 100 = 19.3 V
19.3 = / (2*60*2500*C)
C = 20.6 F

13. Example Consider a full wave bridge rectifier. The capacitor C = 20
Example Consider a full wave bridge rectifier. The capacitor C = 20.3 F is connected in parallel to a resistor, R = 10 k. The input voltage, vs = 50 sin (2(60)t). Assume the diode turn-on voltage, V = 0.7 V. Calculate the value of the ripple voltage.
Frequency = 60 Hz
VM = 50 – 1.4 = 48.6 V
Vr = 48.6 / (2*60*10x103*20.3x10-6)
Vr = 2 V

14. MULTIPLE DIODE CIRCUITS

15. Example 1
Cut-in voltage of each diode in the circuit shown in Figure is 0.65 V. If the input voltage VI = 5 V, determine the value of R1 when the value of ID2 = 2ID1. Also find the values of Vo, ID1 and ID2 .Assume that all diodes are forward-biased.

16. Example 2
The figure shows a multiple diode circuit. If each diode cut-in voltage is Vγ= 0.7 V, determine ID1, ID2 and VO for R2 = 1.1 k.