Mike Gruchalla mgruch@gmail.com

Technical Wizard, Expert on Almost Everything, Consultant to Congress
-- will also do yard work --

My Writings and a Few Other Interesting Things
Accelerating Universe

The Accelerating Universe
Evidence now suggests that the mass at the outer reaches of the universe is accelerating away. This was not expected, or even postulated. To explain these new findings, concepts such as dark energy, dark matter, quintecence, and even rethinking the cosmological constant have been proposed. These are arcane concepts, and there is considerable controversy as to how, or even if, these apply. But, consider that the acceleration of the universe is simply due to the gravity of the universe itself pulling and accelerating the mass at the outer edges of the universe forward in spacetime. This work explores my thesis to explain the acceleration of the universe.

Meeting US Energy Demends
Meeting US Energy Demands
Until late 1950, the United States was energy self-sufficient. Can we achieve this again?
In this work, I look at the basic magnitude of US-energy use including the various energy sources that we presently rely on. I also explore some of the proposed approaches to meeting our national energy needs, such as solar and wind, showing how ineffectual these are. But, I don't propose any solutions to this problem. If I could solve this problem, I would already be making hotel reservations in Stockholm!

Driving-Point-Impedance Analysis
Driving-Point Impedance Analysis
Although this piece is not my work, I believe this analysis approach is something that every electronic engineer must know and understand, and I am therefore including it here. The structured approach to analog circuit analysis termed “Driving-Point-Impedance Technique” was pioneered by Dr. Ruben Kelly at the University of New Mexico in Albuquerque. This is a Sandia National Laboratories report (SC-M-71 0896) by Mr. Howard Thomas penned in 1971. Although this is a rather historical work, it is still directly applicable to any contemporary analog design tasks.

Sandia National Laboratories Report SC-M-71 0896, 1971

Defining the Decibel
The Decibel - Just what is this parameter?
The decibel, dB, is a very common parameter, but just how is it actually defined, and how is it properly used? This parameter is often misused because its origins and meaning have been forgotten. If you ever hear someone ask: “Is that dB power or dB voltage … ,” that individual does not know the proper use of the dB. In this work I dig up a bit of history of the dB and show how it is properly applied, and then provide a few examples of its use and misuse.

Ham Radio, Vol. 18, No. 2, February, 1985, pp. 51-55

Quality Factor Q
The parameter quality factor, or “Q,” is a very common parameter and often utilized to specify the quality of various circuit elements such as capacitors, inductors, resonators, etc. But, just what is Q, how is it defined, and how is it computed? In this work I derive the quality factor from its fundamental definition and show how this is applied in various applications.

Accelerating Universe
Dynamic Range
Dynamic range is typically an important parameter in data-acquisition systems. However, its meaning is often confusing. Users of the systems need the dynamic range specified in terms that are actually usable for data-acquisition. But manufacturers often define dynamic range in a manner that provides the largest value, but that is not particularly useful in actual data collection. In this work, I examine the dynamic-range parameter specifically showing how it is used usefully and what to be on the lookout for in manufacturers' specifications.

CVR Analysis
The Current-Viewing Resistor - CVR
The Current-Viewing Resistor, commonly termed a “CVR,” is a very simple sensor – simply a low-value resistor in series in the conduction path of a current to be measured. However, its simplicity is deceiving. Very often the data collected using a CVR is more a function of the circuit configuration than the actual CVR response. In this paper, I review the CVR implementation with specific attention to the sources of error and how these are introduced.

Gravimeter Noise Analysis
Thermodynamic Noise Limits of the Gravimeter
An interesting instrument is the simple spring-mass gravimeter. At its simplest level, a gravimeter is nothing more than a spring supporting a proof mass coupled to a damping element to provide a critically-damped or over damped system. Gravity simply displaces the mass against the spring constant, and this displacement provides a measure of the gravitational force. Although a very simple sensor, these instruments are quite sensitive. For example, it is quite straightforward to detect the change in gravity between one stair tread and the next on a stairway. But, as with all physical measurements, thermodynamic noise limits the sensitivity of the sensing mechanism. This is true not only for electronic sensors, but also mechanical sensors such as the gravimeter. I develop the thermodynamic noise-limited sensitivity of the simple spring-mass gravimeter in t his paper.

An edited version of this work was published in Geophysics, November-December, Vol. 64, No. 6, 1999, pp. 1708-1719.

Image Scanning
Image Scanning - How Much Resolution is Enough?
The resolution of image scanners and digital imaging in general is increasing almost geometrically. At what point does the digital resolution exceed the resolution needed? How much image resolution is enough? The answer to this of course is quite subjective, and is directly dependent on the application. In this work I examine classical “wet” photographic systems and derive a rough but reasonably defensible estimate of the digital resolution necessary to record effectively all the information in a photographic image.

Communications Quarterly, Vol. 9, No. 3, 1999, pp. 9-24.

Optimizing Amplifier Gain-Bandwidth Product
Optimizing Gain-Bandwidth Product of Cascaded Amplifiers
When two or more amplifiers having a well-behaved gain-bandwidth product such as operational amplifiers are cascaded, perhaps to provide additional gain, the combined bandwidth is typically diminished. For example, if two amplifiers having a gain of 16 and a first-order bandwidth of 1MHz (gain-bandwidth product of 16MHz) are cascaded, the midband gain will be 256, but the bandwidth will be about 500kHz. However, if 4 such amplifiers programmed for a gain of 4 and a bandwidth of 4MHz (gain-bandwidth product of 16MHz) are cascaded, the midband gain will again be 256, but the bandwidth will be about 3MHz. In this work I derive the optimum gain of the for cascaded amplifiers to provide the maximum gain-bandwidth product. Oddly enough, the optimum voltage gain for a modest number of stages is the square root of e, or about 1.65V/V, or about 4.3dB.

Communications Quarterly, Vol. 1, No. 4, 1991, pp. 68-72 Vol. 9, No. 3, 1999, pp. 9-24.

Optimizing Amplifier Noise Performance
Optimizing Amplifier Noise Performance
It is often thought that to optimize the noise performance of an amplifier, it is necessary to match the amplifier input impedance to the load impedance. This seems logical since this is the condition of maximum power transfer of the source signal to the amplifier input. And it is totally incorrect. To achieve optimum noise performance, the source resistance must be matched to the amplifier equivalent input noise voltage and current sources. Oddly, the actual amplifier input impedance is not a factor in this noise-matching process. In this paper I analyze the noise-matching process and develop the relationship between the source impedance and amplifier parameters.

© Copyright 1999-2017, Michael E. Gruchalla, All Rights Reserved