Electronic Design

What's All This Finite-Gain Stuff, Anyhow? (Part I)

I have been asked, "Why is it so hard to measure temperature?" I point out that 100 years ago, any attempts to make precision voltage measurements weren't done by a DVM or voltage meter, but by a big voltage divider (potentiometer) and a voltage null meter. Even as recently as 30 years ago, this was done for the best precision.

Likewise, for most of the last 100 years, precision temperature measurements were made by comparing an unknown temperature to that on a "temperature divider." The ends of the "temperature divider" were held at known, precisely calibrated temperatures, and the temperature along the big temperature divider was proven to be a linear function of the position.

I came home last night and opened up all of my junk mail. (Last year, I received 746 mail-order catalogs, weighing 242 pounds, plus thousands of advertisements, and thousands of requests for charitable giving. It's too bad I don't have a wood stove to burn them in and keep my house warm. But I do recycle all of that paper.)

I was throwing out a lot of useless paper when I noticed some phrases enclosed with the PG&E bill. (I'm sure you know how Pacific Gas & Electric, also known as "Pigs, Greed & Extortion," is notorious for all of its problems.) The little fly-sheet advised us, "Be sure to set your thermostat no higher than 64° in the winter, but set your air conditioner's thermostat to 78° in the summer." That sounds like good frugal advice, but it doesn't sound like we're going to get very comfortable until energy prices come down a lot.

But I got a rule-bender, good for the summer. Let's put my computer table near the window where my air conditioner is running. I can arrange some ducts or drapes to send the cool air right to my legs. I'll put some drapery over the table, down to the floor, to keep the cool air around my legs. Then I will arrange things so that the air wafting out from under the table will flow past my arms and head. Even when I set the room's thermostat at 80°F, the room might run around 79°, but I can be cool and comfortable at 68°F or 66°F, or as I prefer.

What I have done is to locate myself at a good place in the servo loop, in the thermal divider, part way between the source of cool air and the thermostat. It's not cheap to cool the whole room to 66°F, but I can make sure that I'm in the region where the temperature really is as cool as I like.

If I really have to cool off the whole room so that everybody is comfortable, then this scheme doesn't help much. But at least I can make sure that only the room where I'm located will be cooled. Letting the rest of the house stay hot may be acceptable, and more comfortable—and save a lot of money!

Hey, when I was a kid, most people heated just two or three rooms of their houses. Bedrooms and other rooms were mostly left unheated in cool weather. Nobody assumed a right to affordable energy to keep every room toasty warm in winter—or cool in summer. Maybe we're headed back there.

Here in San Francisco, we get natural air conditioning on many days, so I have never bought an air conditioner. But the summertime weather does run cool. The claim that "The coldest winter I ever spent was a summer in San Francisco," is a great line, and partly true.

Okay—now that summer's cool weather is here, I will put my computer table right in front of the hot-air duct. I'll drape some fabric all over the table-top, down to the floor, to hold the heat. I can set the thermostat at 63°F, but because I'm closer to the heat source, I can be comfy and warm even when the rest of the room is chilly. I can stay much warmer than the thermostat setting because I'm putting myself at the right place in the "thermal divider."

In fact, if natural gas prices continue to go up, I might just buy an air conditioner. Of course, I will only want to run it as an air conditioner, one or two days in a summer, or more likely, in the fall, when we get most of our warm weather. But during the winter and the rest of the year, I will mount it backwards in a window. I'll need a special mounting so the controls and front panel won't get wet, but that's not hard. I'll just let it run as needed, pumping cool air outside, and pumping heat into the house.

If I apply 1 kW to any resistive space heater, I can't get more than 1 kW of heat into my house. If I generate 1 BTU/second, I only generate 1055 W. If I burn one "therm" of gas in an efficient furnace, I may get better than 90% of those 100,000 BTUs to warm my house. But if I run 1 kW-hour of electric power into my backwards air conditioner, I can get 3 or 4 kW-hours of heat pumped into my house. If the inside air and outside air are only 5°F to 15°F apart, I might even get more than a gain of five—to be determined. If the outside temperature is more than 30°F or 40°F below the house's temp, the gain still may be better than two! This gain might vary a lot, depending on the model or type of the air conditioner. Still, when the cost of energy gets ridiculous, spending $200 for a good air conditioner could be a good investment. More shortly—in two weeks.

All for now. / Comments invited!
RAP / Robert A. Pease / Engineer
[email protected]—or:

Mail Stop D2597A
National Semiconductor
P.O. Box 58090
Santa Clara, CA 95052-8090

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