Dave, as I said on the previous page, “Using diodes instead of resistors in a DC circuit does not save power. The power dissipated by the diode is exactly the same as that dissipated by the resistor that produces the same voltage drop.”
In an AC circuit, a half-wave rectifier can be used to reduce the RMS voltage by about 30 percent. In this case, the diode does run cooler because it simply shuts off the current half the time rather than trying to carry the current and create a voltage drop, which is the situation we’re dealing with here.
JO, I integrated the waveforms analytically. I derived two expressions:
halfavg = -k / 2 + (sqr(2 - k*k) + k * asin(k / sqr(2))) / pi
The first one gives the average voltage, relative to the RMS voltage of the original sinewave, for each half wave, as a function of k, the ratio of the total diode drop to the original RMS voltage. Differencing two halfavg values, one for each polarity, gives the overall DC output. When k is the same for each half wave, that difference is obviously zero–no DC. But with two different values of k, corresponding to different numbers of diodes, a non-zero DC component emerges.
halfms = ((1 + kk) * (pi / 2 - asin(k / sqr(2))) - 1.5 * k * sqr(2 - kk)) / pi
The second one gives the average of the square, relative to the square of the RMS voltage of the original sinewave, for each half wave, as a function of the same k. Adding two halfms values, one for each polarity, gives the square of the overall RMS output. The square-root of that sum, multiplied by the original RMS voltage, is the RMS result.
For the DC rectifier drop, I used the first equation, adding the two terms instead of differencing, to account for the rectification, and using 2 extra diodes in each direction.