Van's Blog: An Unexpected Circuit

Introduction

I am going to write a short paper. It's going to be a fun paper because like you, I don't know how it is going to turn out. That should make it interesting for both of us. Today's topic is a little weird - it arose in a rather offhanded way. I wanted to write about it because it was like stumbling on buried treasure. I am going to write in the first person because it is easier for me to express myself that way.

The stupefying beauty of this is that if I don't succeed, it is incredibly possible that you may. If I happen to succeed, we both get a useful tool.

Background

The problem is this. I need 50 Volts of Direct Current in a lightweight and portable package. 50 VDC, not 6, 9, 12 or 24. It is okay if I have to use an outlet or extension cord but I need 50 VDC. One more thing - I need 600 Watts of it. Because power is voltage times current there will be 12 Amperes flowing through a wire somewhere. Oh and one last thing - I need this 50VDC with 600 Watts of power constantly available on the shortest of notice, say 1/20,000^th of a second and also in a sustained manner.

Please don't hang up when you read the following statement. Stay with me, it will be worth your while.

An electronic circuit is a mathematical proof.

A circuit is a proof. It is a proof in an ideal sense with idealized components. It is a proof in a real sense with real-world components. If a circuit works, then the system that it represents is true. Many mathematical and mechanical systems have equivalent circuits. We will revisit this powerful idea.

Possible Ingredients

Lead-Acid

50 VDC is a weird number to want. I could use four 12 Volt lead-acid batteries, settling out of court for 48 Volts, knowing full well Lead-acid batteries are not 12 Volts they are 12.63 Volts. I would settle for 50.52 VDC. Lead-acid batteries have two problems though, lead and acid. The first problem, Lead, is toxic, and more seriously, it is heavy. I don't like heavy things. I don't like lugging them around. The second problem, Acid, is also toxic, and more seriously, it burns stuff. I don't like burns and that yucky corrosion that forms on car batteries. So let's just drop lead-acid.

Lithium

I could use thirteen 3.7 Volt lithium-ion polymer batteries, settling for 48.1 Volts. Lithium batteries have two problems, cost and explosion. I don't like things that are too expensive for widespread distribution. Also they explode if they aren't charged carefully. I can handle a small battery exploding. That might even be fun. A battery with nearly a horsepower is not small and neither is its explosion. So strike lithium.

Step Down Transformer

I could use a 120 VAC step-down transformer to transform household current to the lower AC value and then rectify and filter that into 50 VDC.

Two problems emerge. Even ordinary 120 VAC step-down transformers are expensive and they are heavy. I already mentioned my dismay with lugging expensive stuff around. The astute reader will note that this is a lie. I mentioned my dismay with lugging heavy things around and my dismay with things that cost too much, but I did not mention my dismay with lugging expensive stuff around. In that subtle distinction, there is meaning. You might think I don't like lugging expensive stuff around because of theft, and that would be true, but that was not the point. The point was, I never said that, but if one wasn't careful, one might assume I said it, and leave the encounter thinking something was said that wasn't. The structure of this argument is similar to a circuit we will discuss in a moment.

Now since I have ruled out batteries or transformers I need what is called a switching power supply. Switching power supplies are cheap and abundant, but they have a problem that intimately affects their use. They create NOISE. Electrical noise. Electrical noise bothers me more than weight or cost.

MOSFET Modulation: Smooth, Quick, Efficient

What I would like to do is somehow sample 120 VAC in a smooth, quick, and efficient way. Then I can rectify it into 50 VDC and filter it according to standard practice. So now, we have an apparently simpler problem than 600 Watts of 50 VDC. I just need 600 Watts of 50 VAC. Ignore that because of efficiency more than 600 Watts is needed. Ignore that because of voltage regulation, a more than 50 VAC is needed. Settle for 600 Watts of 50 VAC. If it is made from 120 VAC smoothly, quickly and efficiently the rest is cake.

What if instead of brutal switching, which creates far-reaching wideband racket, we gently turn something on and turn something off in a smooth and efficient way?

This circuit does that… partially. The control gate of an N-Channel MOSFET is fed with a version
of the same signal we are trying to clamp to 50 VAC. I say, "clamp" because when the voltage goes over 50 VAC we don't want any part of it. We especially don't want to accept this higher voltage and in turn dissipate the excess energy as noise or heat.

We can exactly tailor how much of the positive going side of the 120 VAC makes it to the voltage probe by adjusting the values of R1 and R2. If they are equal, we get 50 VAC on the positive going side of the wave:

So just like that we are halfway done. The signal is about 50 VAC on the top. In the figure above, both the 120 VAC signal and the output signal are drawn.

We would like to do the same thing on the bottom, so let's start simple and build a circuit that just does the opposite of the first one. Maybe then, we can combine them to get what we want. A circuit might do the "opposite" is one that uses a P-Channel MOSFET, the "opposite" of an N-Channel MOSFET:

After trying some different configurations we run it and get what we want –the negative side of the 50 VAC is present:

Now perhaps we can combine the two that will clamp both sides of the waveform to 50 VAC.

Running the simulation, we obtain:

We have achieved our objective. A real circuit might have some additional parts for protection, but this shows that the configuration is valid.

What I did not show you was the search process that a reasonable person might have employed to come up with this configuration.

If you look closely at the schematics, you will notice that MOSFETS are not commutative.
With the gate in the middle, they can be put in forwards or backwards.

This gives rise to four possible circuits, since there are two MOSFETS in use, and only one circuit topology will produce ("prove") the correct waveform.

In addition, the MOSFETS need not live on the positive supply, they could also be placed on the bottom of the load, but because of symmetry, this would still prove the correct waveform:

So now, we have eight possible circuits of which two are equivalent and correct and six are incorrect.

Additionally we can swing one MOSFET around to be on top of the load and one on the bottom:

Which produces the following output:

Swinging the P MOSFET around instead of the N MOSFET produces a similar incorrect outcome. That makes 2 of 10 possible configurations correct.

We can increase that by 4 more configurations by pivoting each MOSFET in the swung around configurations, which also produce incorrect outcomes.

If I have counted correctly, 2 out of 14 configurations are correct. But now we are not doing circuit design. We are searching over a space of possible connection topologies for a topology that proves (produces) the waveform we sought. Each of the topologies proves something, but only two proved what we set out to prove.

Conclusion

We have succeeded! It was discovered that we can produce (prove) the desired waveform and discovered two topologies that were satisfactory. The circuits we have produced are equivalent to other systems that have similar algebraic or mechanical characteristics. These equivalent circuits and their topologies not only model the equivalent algebraic and mechanical forms, they model the search process we might employ to discover useful circuits along with its combinatorial growth.

Easter Egg

I mentioned above that "protective circuitry" was needed to take this synthetic design into a practical unit. It turns out that the MOSFET gates need their voltage clamped to around +/- 10 volts. So the working design looks like this. Twelve parts drawn from 5 types, not counting power cord, fuse and load. An ounce of material you can hide in your hand. Two MOSFETS and power diodes in the top section, all in T-220 cases on a heat sink to handle 12 amps. The “Logic” section on bottom, runs on 6 milliamps that turns on the MOSFETS in 7 microseconds. 576 Watts. $9.15 worth of parts, the front-end of a $600` power supply. Those savvy in the trade will notice that this is a smoother version of an H-Bridge circuit used to control motors, so they don't jerk as much when doing, "the robot".