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Unformatted text preview: Problems Section 4.1 4.1 Starting with the current-voltage characteristic for a capacitor C , show that for the case of full-wave rectification and RC filtering v ripple ≈ i Load 2 fC , where i Load is the load current and f is the frequency of the ac input. 4.2 Show that Eq. 4.12 cos φ = 1- v ripple v max applies to both half-wave and full-wave rectification. 4.3 The circuit of Fig. P4.3 features an ideal diode and 0.6-V output ripple. The ac power source ( V s ) produces 18 V rms at 200 Hz. (a) Determine the maximum instantaneous load current (through R ). (b) Determine the time duration of the intervals of forward diode bias. (c) Find the maximum instantaneous diode current. (d) Find the diode peak reverse voltage. v out R 500 C V s + + Ω Figure P4.3 4.4 A particular circuit with RC filtering rectifies a 50-Hz voltage waveform. Two conditions are known: • The capacitor value is 10 mF. • The current to the parallel RC combination has the time dependence shown in Fig. P4.4. (a) Does the circuit feature half-wave or full-wave rectification? (b) Determine the ripple voltage. (c) Find the maximum instantaneous load current. i (A) 10 10 20 t (ms) 0.5 ms Figure P4.4 4.5 Design a capacitively filtered half-wave rectifier circuit to deliver 50 mA to a 400-Ω load resistance with 2-% ripple voltage. Specify the diode ratings. Assume a 60-Hz 115-V (rms) power source. 4.6 Repeat Problem 4.5 with full-wave rectification. 4.7 Design a capacitively filtered half-wave rectifier circuit to deliver 100 mA to a 100-Ω load resistance with 5-% ripple voltage. Specify the diode ratings. Assume a 60-Hz 115-V (rms) power source. 4.8 Repeat Problem 4.7 with full-wave rectification. 4.9 The 4.7-mF (electrolytic) capacitor selected for the RC-filtered power supply of Example 4.1 has a parasitic equivalent series resistance (ESR) of 75 mΩ. Estimate the power dissipated in the capacitor when R L = 200 Ω (minimum load resistance). c 2010 Edward W. Maby All Rights Reserved 4.10 This problem features a diode as a detector . In a simple amplitude modulation (AM) process, a received radio signal has the form v r ( t ) = ˜ v m (1 + m sin ω m t )sin ω c t , where ω c is the “carrier” angular frequency (to which the radio is tuned), ω m is the “modulating” angular frequency of the signal with information content, and constant m is the modulation index (0 ≤ m ≤ 1). In what follows, let ω c and ω m correspond to 10-kHz and 1-kHz frequencies, respectively. In practice, ω c is significantly larger, and ω m is part of a spectrum with particular ˜ v m weightings. (a) Use SPICE to plot v r ( t ) over two ω m periods. Assume that the signal is applied to a 1-kΩ load, and let m = 1....
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- Fall '10
- Fig, Switched-mode power supply, Edward W. Maby