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Step of 7 4.073P Refer Figure 4.22 in the textbook for the full wave rectifier circuit. In this full wave rectifier, one diode, either or conducts at any time. During positive half cycle, the diode is forward biased or conducts and the diode D2 reverse biased or do not conduct. During negative cycle, the diode D2 is forward biased or conducts and the diode reverse biased or do not conduct each diode has voltage drop of 0.7 V and in either cycle, one diode conducts The diode D, in the circuit can be replaced with its piece-wise linear model, that the diode is replaced by in series. Neglecting the effect of the equivalent circuit for the right side upper portion of the Center tap is shown Figure + R 10 Figure Step 2 of 7 Apply Voltage Law to the circuit The input to the full-wave rectifier is, The output is obtained with the help of equation (1). The diode conducts during both the half cycles The input/output waveforms together are shown in Figure 2. VD Figure Step In the Figure 2, 0 the angle at which the input signal reaches and the diode starts conducting. The diode conduction terminates at (x-9) and the hence the total conduction angle is Consider the following by observing the waveform: The average value (dc component) of the output is, From the waveform, T=2π The limits of the integration are from to and to Recall equation (1). Here, - in the interval to and also the same in the interval Step Evaluate the integral over the first interval and make twice 2 Now let then and as 0 Therefore, 2V, π (2) Step 5 of 7 (a) The average output voltage is Substitute for in equation (2) calculate the value of 2V, Step of 7 The rms voltage of the input is, 120 Vrms Thus, the peak value the input voltage is, V Write the formula for the turns ratio of the transformer Turns ratio Substitute V for and 16.80 V for Turns ratio 16.80 10.095 Therefore, the transformer turns ratio for each half of the secondary is 10.095:1 Step 7 of (b) The average output voltage is. = 100 V Substitute 100 for in equation (2) calculate the value of 100= Write the formula for the turns ratio of the transformer Turns ratio Substitute V for and 158.179 V for Turns ratio 158.179 1.0728 1 Therefore, the transformer turns ratio for each half of the secondary is .0728