Coil Voltage Rectification

Until today, I've setup my two power generation coils in series with a full wave rectifier connecting them to the batteries. Something like the schematic below:

Two Series Coils with a Full Wave Rectifier

This is an OK setup in most situations. It lets us harvest energy from both the positive and negative spikes of voltage in the coils. Additionally, the series coil setup is the only one that makes sense if the coils are not going to be excited by the magnetic field at the same time. So everything should work fine.

The issue is that the full wave rectifier means that the coil voltage is reduced by two diode forward voltage drops before its gets a chance to charge the batteries. These forward voltage drops are anywhere from 0.7-0.3V. I specifically chose my diodes to have a small voltage drop, but when you are only dealing with a 1.3V battery voltage, a voltage drop of about 0.5V is a big deal. So using a half wave rectifier may be a better choice. In this case, you only get to harvest the positive voltage spikes, but you get more out of them, as there is only a single diode drop. This setup would be something like this:

Two Series Coils With a Half Wave Rectifier

So i ran some tests today to compare the two approaches. My prototype board was setup originally to make these specific tests easy, so not too much work was involved. These tests where taken at what would be a decent pace on my bike. Here are the results.

Series Coils With a Full Wave Rectifier

Series Coils With a Half Wave Rectifier

It looks like either choice is OK. Although we are getting less frequent current spikes into the batteries with a half wave rectifier, we are getting much more current per spike (almost 18.5mA peak vs. 12mA peak), for a comparable average charging current (1.5mA vs. 1.45mA). Since the full wave rectifier needs larger voltages, it works better for charging at higher wheel speeds, while the half wave rectifier will charge at lower speeds. Apparently in the middle it doesn't matter. As i'm more likely to go slower on average around town rather than faster, ill change my coil setup to have a half wave rectifier.

An additional issue is the coil resistance. This was touched on in my last  post, but its practical implications where mostly ignored. I'm using very thin wire so i can get the size of my coils down while still using lots of turns. Thinner wire has a larger resistance per meter, and since i'm using so much thin wire, i end up with about 35Ohms of resistance per coil. In a series connection, the coil being excited by the magnets has to drive the resistance of the other coil, as well as the rectifier diodes. This means that as a magnet passes a coil, you end up with the situation seen below.

Equivalent Circuit During Coil Excitation 

Needless to say, this is not ideal. In addition to a voltage drop you have a relatively large resistor in the way. A better solution may be the one below.

Improved Half Wave Coil Setup

Originally i wasn't sure that a half wave vs a full wave was going to make much of a difference and i didn't want to put two full wave rectifiers on the board, so i ignored this setup. But since I'm going to use half wave rectifiers anyway... i thought i might as well give it a shot.

Two Coils With Dual Half Wave Rectifiers

With the same test as before, this setup behaves better. we are up to almost 2.5mA charging current, which is really quite good. Note that to set this up on my board, i inverted one of the coils, which is why it looks like I'm harvesting positive spikes from one coil and negative spikes from the other. This will probably be my final design for the coil rectifiers. I'm glad i took a look at this as the changes made almost doubled my available charging current.

Number of Turns, Revisited.

The number of turns that i estimated on the new coils doesn't seem quite right. which it probably isn't as for the most part its was a complete guess. I thought it may be interesting to put some bounds on this number and do some estimation, so here we go.

The bobbins that I'm using have a window area of about 44mm^2. This is a measure of how much area for copper the coil has. Here, its found by multiplying 4.3mm and 10.2mm. Since the wire i'm using has a diameter of 0.16mm, it has a cross sectional area of 0.02mm^2. This means that at most there could be 2200 turns on this bobbin, probably less. This would be the case if there where no air gaps in between wire, which is impossible as the wire is round. More reasonably, we could look at if the wire a lined up in a grid, each piece sitting on-top of each-other for the maximum airspace. this would give us about 1700 turns. So if i wrapped this perfectly, i would have between 1700 and 2200 turns per coil. Of course i didn't wrap this well, so it's probably much less than this.

When wrapping magnetics, people usually use a scale factor called the "fill factor", or "window utilization factor". This term approximates how much of the window area is actually filled with  copper, vs how much is filled with air due to gaps between turns. This is a percentage, where a fill factor of 0.9 means that 90% of the window area is used by copper, with the remaining 10% filled with air or insulation, etc. The fill factor can vary between about 0.05 for high voltage transformers with lots of isolation between wires, and about 0.5 for a simple hand wound inductor. Using special materials like a foil instead of wire (which rips all the time and is just horrible to work with), or square wire (which is a pain to wrap) can get this number up to about 0.65. For this coil, 0.3 is about the worst reasonable, which gives us 660 turns as a lower bound.

Putting this together, ill use 1700 as an unreasonable upper bound, and 660 as a lower bound. its a decently wide range, but lets me know that i have way more turns than i expected, which makes sense due to the much larger voltages that i was getting.

As a double check, we can measure the resistance of the wires. The inner winding radius is 6.2mm, while the outer is 10.5mm. This gives us an average of 8.35mm, which ill bump up to 9mm because if how things are wound on the bobbin. This leaves us with an average turn length (amount of wire used on each turn) of about 56mm. At room temperature, AWG34 wire has a resistance per meter of about 0.86Ohms. The coils i wound have resistances of 38.1Ohms, and 34.3Ohms, giving approximate number of turns of about 790 and 710 for the two coils. This makes sense, as one gives a slightly higher voltage spike than the other.

So that was fun.