A full-wave diode bridge rectifier is shown in Fig. 1 . The input voltage is vs = 311×sin(100πt) V. The load resistor R is 10 Ω. ( 25 points) Fig. 1. (a) Sketch the waveforms of the output voltage vd and current id, indicate the peak values. (6 points) (b) Calculate the average value of vd and current id. ( 6 points) (c) If the diodes D1−D4 are replaced by thyristors T1−T4, respectively, to form a controllable rectifier. The firing angle of T1 and T2 and the firing angle of T3 and T4 are both π4. Sketch the waveforms of the output voltage vd and current id, indicate the peak values. (6 points) (d) Based on (c), calculate the average value of vd and current id. (7 points)
![A full-wave bridge rectifier circuit is shown in Fig. 2(a) with a "floating" signal generator and grounded load resistor, which is the most common configuration of this rectifier. Its output waveform appears in Fig. 2 b. Note that the output frequency is twice the input frequency, but the time period T and angular period 2π on the horizontal axis refer to the input waveform. Following a similar development to the halfwave rectifier, the dc output voltage from the full-wave bridge rectifier is given by: Vavg = 1π∫θ1 θ2[Vmsin(θ) − 2Vd]dθ Where, the integration is over half the original waveform's period and the 2Vd term is due to the load current flowing through two diodes. The peak output voltage is vo, peak = Vm − 2Vd. The integration limits are found using Eq. 5 with the angles referred to the original input waveform. θ1 = sin−1(2Vd/Vm) and θ2 = π − θ1 However, the full-wave rectifier's conduction angle must be referred to the output waveform's period, which is half that of the input so φ = 2(θ1−θ2). (a) (b) Fig. 2. (a) Full-wave bridge rectifier circuit and (b) output waveform. Perform the following calculations for the full-wave rectifier in Fig. 2. Put your results in Table 1. a. Determine vo,peak, θ1, and θ2 for the rectifier output waveform of Fig. 2 b. b. Calculate the average (dc) value of vo(t) using Eq. 4 . c. Calculate the conduction angle φ.](https://www.doubtrix.com/uploads/editor/6776072514rhzokOtWGl.png)
![Consider the full-wave diode rectifier circuit shown in the figure below. Assuming the input voltage is VAC = 170 sin(120πt) the conduction angle of the diode is 32∘, and the load resistance RL = 500 Ω, and the capacitor CS = 100 μF. We assume that all components are ideal and neglect the voltage drop across the diodes. {For the questions below, please only state the value. No need to include the units in your answers}. (a) Estimate the peak-to-peak ripple voltage in the output voltage VR. [2 marks] (b) The average voltage. [2 marks] (c) The RMS voltage. [2 marks] (d) The form factor. [2 marks] (e) If the ripple voltage across the load resistance RL must not exceed 1 V peak to-peak, calculate the value of smoothing capacitance required. You may assume that the capacitor provides current to the load for each complete cycle of the rectified voltage. [4 marks]](https://www.doubtrix.com/uploads/editor/0294629005gsMjwksRCG.jpg)
