## Ftwe Voltage

Figure 4

Figure 5

Connect the primary wires up so that positive and negative are switched from what they were at first (Figure 6). The current in the primary goes the other direction now, and therefore so does magnetic field. You could say the magnetic field decreased from zero to some negative value. Again a changing magnetic field induces a current in the secondary, and the bulb glows.

Figure 6

It was the changes in the DC voltage that induced current in the primary. But ac (alternating current) is always changing. For example America's 120 vac sloshes from +165 volts to -165 volts sixty times a second. An ac voltage applied to the primary, creates an ac voltage on the secondary. For a perfect transformer, the voltage of the primary divided by the voltage of the secondary is equal to the number of turns in the primary divided by the number of turns in the secondary.

Vp/Vs = Np/Ns where V and N refer to voltage and number of turns, and the subscripts p and s refer to the primary and secondary coils. If you fed the transformer (Figure 3) 15 volts ac, you'd see 3 volts ac on the secondary, since

(150 turns/ 30 turns) = 5 = (15 volts ac/ 3 volts ac).

A transformer like this, with less secondary turns than primary turns (Ns < Np) is called a step-down transformer. What would happen if you exchanged the primary and the secondary? You would get a step-up transformer. If you plug 15 volts ac into the side with 30 coils, you'd see 15 volts ac x (150 / 30) = 75 volts ac.

And that's all there is to it. The transformers in inverters, and in wall cubes (the things that you plug in the wall to power small 9 Volt or 6 Volt appliances), and big utility transformers you see on power poles — all of them work pretty much the same way.

### DC to DC Converters

Doing the transforming thing for DC is more difficult. The problem is that you can only get energy out of magnetic fields if they're changing. And you can't make changing magnetic fields with DC. You could take DC, and chop it up into ac, and then run it through a transformer to change its voltage, and rectify it back to

DC. Indeed, this is sometimes done. But in addition to something that chops electricity, this approach requires a transformer (two coils of wire), and a full wave rectifier (four diodes), and filtering capacitors. A "switching" DC to DC converter is an elegant, efficient solution. It requires, in addition to a "chopper", only one coil of wire (an inductor), and a single diode, and (usually) a couple of capacitors for filtering. They come in three flavors: Buck, Boost, and Inverting.

### The Kluge Firefighting Buck Converter.

Dr. Kluge and his duck friends are on fire duty, putting out boat fires. The fireboat they've constructed has a tank of water on a high platform. This is great for making a high pressure spray of water, but it only lasts for a short time — until the tank runs out. Is there a way they can use the water in the tank to pump some ocean water so they can get more water (but at a lower pressure) for fighting fires?

The Dr. Kluge solution: use a turbine attached to a flywheel, a check valve, and a valve that can be quickly opened and closed by a dedicated duck. When the duck's valve is open wide, water from the tank flows out through the hose, spinning up the turbine and the flywheel as it goes. Then the duck closes the valve. The flywheel keeps the turbine spinning, now strongly sucking water up from the check valve to the ocean. When the turbine slows down, the duck opens his valve again to speed it up. Now the water coming out the hose for the fire is the water from the tank plus the pumped water from the ocean.

### Buck Converters

Buck converters change DC electricity from a higher voltage to a lower voltage. They're the most common DC to DC converter in the renewable energy world. Linear Current Boosters and other pump controllers are buck converters. They work a lot like Dr. Kluge's fire boat. A coil of wire (an inductor) plays the role of the flywheel and turbine. A diode is the check valve to the ocean, and the "duck valve" is an oscillator and a power transistor — usually a FET. (For more on components, see the Basic Electricity articles in HP#32, #34, #35).

Let's start with the circuit off: no currents flowing and no magnetic fields. When the transistor is turned on, current starts to flow from the higher voltage supply, through the inductor, to the load. The increasing current stores up energy as a magnetic field in the inductor. When the transistor turns off, the energy stored in the inductor works to keep pulling current — but from where? Up from the diode from ground! Eventually the energy stored in the inductor is expended pumping this current up through the diode. Then the transistor turns on again, bringing current from the higher voltage source, charging up the inductor.

Figure 7: Dr. Kluge's fireboat does with water what a buck converter does with electricity.

Is this rigorous enough for you? I can explain it without talking about "energy" if you want. When the transistor turns on, increasing current in the inductor builds an increasing magnetic field which, in turn, induces a voltage opposing the increasing current. When the transistor is turned off, the current through the inductor is no longer increasing — it's decreasing, and the magnetic field begins to decrease. The inductor's decreasing magnetic field drops the voltage at point X to -0.6 Volts, and current flows up through the diode, through the inductor, and out to the load. (If the diode weren't there, the voltage at X would drop well below -0.6 Volts.) The collapsing magnetic field provides the voltage "rise" across the inductor to pump current to the load. Finally, the transistor turns on again, repeating the cycle. Capacitors on both sides of the DC converter absorb voltage ripples caused by this somewhat jerky process. See the Home Brew in this issue for a simple buck regulator you can build to efficiently provide up to 3 Amps at 12 Volts DC from any 14 to 40 Volt source.

### Boost Converter

Rearrange the transistor, inductor, and diode, and you get a boost converter: low voltage/high current in — high voltage/low current out. Have you ever looked at how a hydraulic ram pump works, using a lot of water falling a short distance to pump a small amount of water higher? (See HP#28, page 11 for a diagram) A boost converter is the ram pump's closest electrical cousin. The transistor to ground entices increasing current to flow through the inductor. Then the transistor is switched off, and the current (driven by the inductor's collapsing magnetic field) has no place to go except out the diode to the higher voltage load.

Figure 9: Boost converter.

Figure 8: Buck converter

Figure 9: Boost converter.

Inverting Buck/Boost Converter

There's one last rearrangement of the inductor, transistor, and diode, making an inverting converter. Put in some positive DC voltage and you get out a negative DC voltage. When the transistor is turned on, an increasing current flows through the inductor to ground, building up the inductor's magnetic field. When the transistor is turned off, the inductor's collapsing magnetic field sucks current through the diode, dropping the voltage of the load below ground.

Inverting converters are versatile: the magnitude of the output voltage can be greater or less than the input voltage depending on the frequency and duty cycle of the oscillator. But they require greater currents through the transistor than do the buck or boost circuits above. This means bigger, more expensive transistors.

Figure 10: Inverting converter.

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Author, Experimenter, and Artist: Chris Greacen, Rt 1 Box 2335B, Lopez Island, WA 98261. Thanks to Anne Brandon, Beaverton, OR, for the idea of the plumbing inductor.

BRASCH LABS camera-ready 3.65 inches wide by 4.8 inches high

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