The
following are excerpts from my book, Wilson’s
Odyssey and the Joy of S.T.E.M. , now for sale at Lulu.com
The
Buzzers
“Well,
one of my responsibilities involved a product that had been in production for
years. It had never been a problem, so I hadn’t bothered even to look at the
design. Suddenly there was a problem and it was mine to fix. It had always been
free of problems, so Production had assembled 600 units before doing any
testing. Then on acceptance testing, every unit they tested failed.
“It was a simple circuit; a wheatstone bridge
drove a sensitive relay, which, in turn, drove a slave relay. The input was one
leg of the bridge and the output was the set of slave relay contacts. When the
input signal was raised to a certain level, the sensitive relay contacts closed
and energized the slave relay. The contacts of the slave relay then lit a lamp.
The circuit was dead simple; small wonder there hadn’t
been a problem.
“But now there was. When the slave relay
closed, it did with such force that it sent a shock through the chassis that
re-opened the sensitive relay. That, of course, re-opened the slave. In time,
the sensitive relay re-closed, causing the slave to re-close and the process
started all over again. This all happened so fast the units became buzzers.
Turns out the slave relay guy had “improved“ it.
“The bosses came up with a number of possible
fixes. Add a vibration isolator to the sensitive relay or the slave or both.
Now we’re talking big development and
testing. And no assurance any of these ideas would work. It looked like we
would need a new design, the 600 units would have to be scrapped. We’d
salvage only the relays. And, of course, our customer would not be happy with
the delay in delivery.
“So I studied the buzzer action, and it
occurred to me that since the slave relay coil was inductive, it might hold
enough current long enough to stay closed until the sensitive relay re-closed,
if there were an alternate path for that current. Then I thought, hey, put a
diode across the slave coil. I got lucky. I put a small, axial-lead diode
across the slave relay coil, and that was all it took to get all 600 units to
work okay. No redesign. No scrapping. No disappointed customer.
Inductance
and Capacitance
“I’ll be working just with power
circuits, and they use only three types of components: inductors, capacitors
and switches. An inductor is like a mass; the same equations apply. David, you
took high school physics. Remember f = ma, force equals mass times
acceleration?” Bob got up and found a pad and pencil. As he talked he began
writing equations. “Look, the equation for inductance is
e = L di/dt
voltage
equals inductance times the rate change in current. Same thing.”
“Why do they use ‘e’ for voltage, why not
‘v?’” asked Linda.
“Picky, picky, picky,” said Bob. “Actually
a good question ‘cause in the old days they called voltage ‘electromotive
force’ or ‘emf’. They did think of voltage as a force.”
“How is ‘a’ like ‘di/dt?’”
asked David.
Bob said “C’mon, acceleration is rate change in velocity, so
f = m dv/dt, but here the ‘v’ is velocity, not voltage. So current is analogous
to velocity.”
“Linda, would you like to watch Ed Sullivan?” Ingrid asked.
“Seems like the time is right,” said
Linda. Bob looked at his wristwatch.
Ingrid said, “No, Bob, Linda’s not
talking clock time.” Ingrid, Linda and David laughed and after a bit, Bob’s
serious demeanor collapsed and he joined in. The ladies left for the sofa to
watch TV.
“So what’s the deal on capacitors?” asked
David.
“For me, a capacitor is like a water
tank. The equation is
v = (1/C) ∫ i dt.
You had integral calculus, right?”
“No.”
“Okay, no problem, we can write it in
arithmetic form where the initial value of time is zero and current is constant.”
He wrote:
v = it/C
“Here ‘v’ is the height of the water in
the tank, which of course would give a force, ‘i’ is flow rate of water so ‘i
t’ is the amount of water gone into the tank and ‘C’ is the cross-sectional
area of the tank.”
“Makes sense,” said David.
“So I just deal with masses and water
tanks,” Bob said. “The E.E. equations are just M.E. equations in disguise.” He
paused. “But get this, if you’re defining something, shouldn’t you use
equations where the left hand side is what you’re defining, like this?” He
wrote:
L = v/(di/dt) C
= i/(dv/dt)
“Here I put ‘C’ in differential
form. So now we can say inductance
is the ratio of voltage across a device to the rate of change of current
through it. And capacitance is the ratio of current through a device to the
rate of change of voltage across it. Look at the symmetry here. Each is the
switcheroo of the other. I’ve never seen those equations in a textbook or
anywhere else; why, I don’t know.”
“Maybe you’re the first to come up with
this.”
“No. Math types probably see this right
away without having to write it out.”
“Nah, they would have written it out.” He
called out, “Hey Ingrid, your husband’s a genius.”
“I know,” she said, “he told me.”
David said, “Bob, one problem: you need a better word than ‘switcheroo.’”
“Okay, but what?”
David said, “How about ‘transposition?’”
“Good, I like it.” Bob affected a
professorial tone: “Inductance and capacitance are voltage-current
transpositions of one another.”
“Sounds good to me,” said David. “Pompous,
but good.”
A Regulated PWM Chopper without Feedback
“Hey,
listen, I got an idea for a regulated output PWM chopper without any feedback.”
Felder smiled. “Regulated without feedback.
This I got to see.”
“Okay, remember how the first PWM control
modules used a zener on the input to the ramp supply?”
“Yeah, and they took a while to figure out
you’re better off without it.”
“Right,” said Wilson, “I pointed that out to
them. A lot of guys must have. So anyway, without the zener, we get line
regulation. You can do the same for load regulation.”
Felder seemed skeptical. “How?”
“Take the ramp feed from the input of the
inductor but, and here’s the key, after its equivalent series resistance.”
Felder looked incredulous for a moment and then
burst out laughing. “And just how do propose to get to that point?”
“Okay to mark up your schematic?”
“In pencil, sure.”
Wilson drew another winding under the inductor,
adding dots to the left side of each and connecting the two right ends
together. He pointed to the open left end of the new winding. “Bingo.”
Folding his arms, Felder rested his elbows on
his desk and leaned forward. He studied what Wilson had drawn. After a while,
he sat back. “ I’ll be darned. I would have sworn it couldn’t be done and it’s
so simple. Did you try this?”
“No, you’re the one working on a PWM. You
should try it.”
The
Cycloconverter
Wilson
gave Freeman the good news. Janssen sat at his own desk across the room. “Let
me get this straight,” said Freeman, “you reduced the energy in the line
inductance by increasing the inductance?”
“Yes.”
He went to the blackboard and began writing:
e = L di/dt
edt = Ldi
“The
reverse recovery time of the SCR, dt, is pretty much fixed. True, it varies
somewhat with reverse current, but as an approximation we can say it’s fixed.
Now since e is fixed, edt is fixed, so Ldi is fixed. If we increase L, di
decreases. So if we, say, double L, di goes in half and di-squared goes to
one-quarter and the energy, one-half Ldi-squared, goes in half.
Increase the L, and you reduce the reverse recovery energy in it.”
Freeman
called Allard in and asked Wilson to repeat his analysis. “Of course!” said
Allard. He laughed with delight. “Beautiful!”
Janssen
frowned. “Why does our customer blow SCRs and we don’t?”
“The
customer has a big machine with low line inductance, and our little lab
machine’s got a much larger line inductance.”
“I
took shots with and without the added inductors,” said Wilson. He handed the
photos to Allard who scanned them and gave them to Freeman. He checked them and
looked at Janssen with raised eyebrows.
Janssen didn’t respond, but said, “You’ve
assumed a fixed reverse recovery time, like it’s all recombination. What if
it’s predominantly swept charge?”
Wilson
went back to the blackboard. “Let’s see. He drew x and y axes labeling them “t”
and “i” and a ramp starting at the origin and terminating with a vertical line.
He tapped the triangular area. “Here’s our stored charge. Now let’s double the inductance.”
He made another ramp with half the slope extending beyond the first vertical
line and ending with another vertical line. “For the same area and half the
slope, the triangle must be longer by a factor of the square root of two and lower
by a factor of the square root of two over two.”
Allard
interrupted, “”Don’t you wish you had multiplied the inductance by four?”
Wilson
laughed. “Right, but let’s press on. So now we get one-half the di-squared and
with double the inductance we get no change in Ldi-squared. Adding inductance
doesn’t help, but doesn’t hurt. So in the real world case, where you’ve got
both recombination and swept charge, adding inductance helps but not as much as
if there were no swept charge.”
“How
do we know you added enough inductance?” Janssen asked. “We” and “you” is
it? Noted.
“I
stiffened our generator with ac caps, so at high frequencies, it was like a
rock, and the added inductors did the job.”
Replacing
a 6-Volt Battery with a 12-Volt Battery
Wilson’s third
SCCA event, his first race, not a driver’s
school, was in Vineland, New Jersey, 30 miles inland from Atlantic City. He took Dave as his pit crew. Bob told Dave about the handling improvements
he had made to the car: tires, shocks and camber. Dave said, “Did you ever
think about going to a 12-volt system? You have to change light bulbs and
headlights, but you can use a 12-volt transistor radio. They don’t
change the starter motor. Why I don’t
know, but they say the car starts better.”
“I thought about it but I decided it wasn’t
a good idea. The starter motor gets less current from the 12-volt battery than
the 6.”
“Less?”
Doesn’t twice the voltage give twice the
current?”
“Not in this case. The starter motor winding
has a resistance that matches the internal resistance of the battery, let’s
say 20 milliohms. Then the total resistance, battery plus motor, is 40
milliohms. That makes the current 150 amps. The 12-volt has twice as many cells
and that alone means twice the resistance. And if the 12-volt battery is the
same size, I mean the same volume, as the 6 volt, the cells must have one-half
the area and that means the resistance is twice as much again, so the total
resistance of the 12 volt battery is 4 times as much or 80 milliohms. So the
total resistance, battery plus motor, is 100 milliohms. Now the current is 12
volts divided by100 milliohms or 120 amps. So going from a 6- volt battery to a
12-volt battery of the same size gives you 20 percent less current in the
starter motor.”
“Sounds to me like you’ve
gone through this before.”
“Yup. It’s a
matter of matching impedance, like with hi-fi speakers. You know how they’re
marked, usually 8 ohms, sometimes 4 or 16 ohms? That’s so
you can match them to the amplifier output impedance.”
“So why do some guys say the engine starts
better with the 12-volt?”
“I don’t
know, maybe they get a hotter spark. Maybe they’ve
got dirty plugs, or wires, or distributor cap, so they need the higher voltage.”
The Three-phase Class B Amplifier
“Well, at first I toyed with the idea
of scrapping the SCR approach and going with a three-phase Class B amplifier.”
“That’s
not very efficient.”
“Actually
it’s not as bad as you might think. A
Class B amplifier has an ideal efficiency of pi over four, 78.6 percent, not so
good. But my analysis of a Class B emitter follower with a three-phase
transformer load says the ideal efficiency is about 86 percent, not so bad.”
“Why
would the efficiency be any better? It’s
still Class B.”
“Aha.
If I’m right, with an emitter follower
output, only two phases conduct at a time. Transformer action makes a third
phase that back-biases the third phase transistors and keeps them from
conducting. It works like the vacuum tube amplifier that Fisher patented in
World War II. “
“What
happened to that Fisher amplifier?”
“Transistors
happened to it. Transistors did
away with all those big output transformers, and you need transformer taps to
make the scheme work.”
“And
with a three-phase load you don’t
need taps?”
“Right.”
“So
why didn’t you use it?”
“I didn’t
know enough about squirrel-cage induction motors, whether or not the coupling
among phases would be tight enough to make the scheme work. Besides, we had
already bought into using SCRs.” He
paused. “If they were looking for low noise, we’d probably have gone Class B.”
“So the motor current would be sinusoidal
and the battery current would have no ripple.”
“Ideally, yes,” said Wilson, “but the
motor is not perfectly linear so you have a choice, make the motor current
sinusoidal and allow a little ripple in the input dc or control it so the input
dc is has no ripple and the motor current has some harmonics. The boat battery
is a lot bigger than the motor so I guess you’d go for ripple-free input dc.”
