BPlug into

power strip Outlets Rectifier diode Triple-outlet extension cord Twist splices A Plug into power strip Rectifier diode

I First, we square the voltage at every instant in time, so that all the values become positive.

I Second, we average the instantaneous values (the values at each and every possible point in time) for the duration of exactly one wave cycle.

I Finally, we take the square root of the number we get at the end of the second step. Obviously, this process cannot be done literally, because there are infinitely many time points in a wave cycle! But a computer can closely approximate the theoreti- cal RMS value by selecting a gigantic number of evenly spaced time points during the cycle, and performing individual calculations for each point.

When we have a fairly “clean” sine waveof the sort that we find in household util- ity circuits, the RMS voltage is approximately 0.707 times the positive peak voltage, or about 0.354 times the peak-to-peak voltage. Conversely, the positive peak voltage is about 1.414 times the RMS voltage, and the peak-to-peak voltage is about 2.828 times the RMS voltage. For other waveforms such as the one that appears at the out- put end of our rectifier cord, these ratios are different. In this particular device, the RMS output voltage is approximately half as great it would be at the end of an ordi- nary cord.

When a sine-wave source of power is applied to the input of the rectifier cord shown in Fig. AC4-1B, the diode conducts during the half-cycle when the cathode is negative with respect to the anode. During the other half-cycle, the diode behaves as an open circuit. Figure AC4-2 illustrates the situation. At A, we see a graph of the AC input wave. At B, we see a graph of the rectified output wave. The diode, all by itself, forms a half-wave rectifier, which is one of the simplest possible devices for getting DC output from an AC power source.

The DC from a half-wave rectifier isn’t continuous like the DC from a battery. Instead, the rectified voltage and current pulsate as time goes by. In the United States, the pulsation frequency of half-wave-rectified AC is 60 hertz (Hz), equivalent to 60 pulses per second. In some countries it’s 50 Hz. That’s too fast for an ordinary incandescent light bulb to follow along, so the bulb glows continuously as if it’s get- ting DC from a battery.

Measure the Voltages

Set your digital multimeter to display DC (not AC) voltages up to 100 volts (V) or 200 V. Be certain that the meter is set to measure voltage, not current or resistance. One little oversight in this situation can destroy your meter. I know this from experience. Many years ago, I accidentally connected an ohmmeter directly across an active source of utility AC. You can imagine what happened!

Switch off the power strip and unplug it from the wall outlet. While wearing your rubber gloves, insert the meter probes into one of the unused outlets in the

A B Time +200 −100 −200 Instantaneous voltage +100 Time +200 −100 −200 Instantaneous voltage +100 Root- mean- square (RMS) voltage Root- mean- square (RMS) voltage AC waveform Rectified waveform

Figure AC4-2 Half-wave rectification. At A, the AC wave- form as it appears at the power strip. At B, the output waveform as it appears at the cord outlets and across the lamp. Dashed lines indicate root-mean-square (RMS) or effective voltages.

rectifier cord. Make certain that the positive meter lead (red wire) goes to the cath- ode end of the diode as shown in Fig. AC4-3A. Plug the power strip back into the wall outlet, and switch it on. Be sure that the bulb is glowing. The meter should indicate the RMS voltage as a positive value. When I conducted this test, I got a reading of +54.3 V DC.

Switch off the power strip and unplug it from the wall outlet. Transpose the positions of the meter probes in outlet at the end of the rectifier cord. Plug the power strip back in, switch it on again, and note the meter reading. You should get the same absolute DC voltage as before, but with a negative value instead of a positive value. Figure AC4-3B shows the circuit arrangement. I got a reading of−54.3 V DC. B A DC voltmeter 25-W bulb + - Plug into power strip Rectifier diode DC voltmeter 25-W bulb + - Plug into power strip Rectifier diode

Figure AC4-3 _{At A, measurement of the effective DC voltage with the}

meter polarity matching the rectifier output polarity. The meter shows a positive value. At B, measurement of the effective DC voltage with the meter polarity reversed. The meter displays a negative value, but the absolute voltage is the same as before.

Switch off the power strip and unplug it yet again. Set the meter to read AC (not DC) voltages in the range of 200 V or more. Plug the power strip back in, switch it on, and note the number on the display. I got a reading of 121.7 V AC. As long as you make this measurement within a few minutes of the preceding measure- ments, your reading should be a good indication of the AC input voltage that the rectifier cord has received during those tests.

Now Try This!

Measure the voltages at the output of the rectifier cord again. But this time, set your digital meter for AC voltage instead of DC voltage. Again, take extra care to be sure the meter is not set to display current or resistance! Conduct tests with the meter leads connected in both directions. What does your meter say? When I did this test, I got a surprise. The meter display said 0.0 V in one direction and 121.0 V in the other! What happens when you try this test?

A Theory

I’m not sure why my meter behaved as it did under these conditions, because I didn’t actually take the meter apart to see how it’s constructed. But I have a theory. I think that my AC voltmeter is really a DC microammeter connected in series with a diode and a switchable set of large-value resistors. In that case, my meter has its own built-in half-wave rectifier, and it’s calibrated to give a reading of RMS AC voltage by determining the pulsating DC voltage after rectification.

If I’m right, then when the diode in my meter was connected with the same polarity as the rectifier in the cord, the internal microammeter would “see” almost the same situation as it did when I measured the AC voltage directly from the power strip. The only difference would be an extra diode in series, connected in the same direction as the one in the cord. In theory, the extra diode would reduce the reading by a little less than a volt. That’s what I observed.

When the meter polarity was reversed, the diode inside the meter would be con- nected in the opposite direction from the one in the cord. The meter’s diode would cut off one half of the wave cycle while the cord’s diode would cut off the other half. In theory, the two “dueling diodes” would leave the internal microammeter with zero current. That’s exactly what it got.

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