An Introduction to the The Fifth Pillar for Amateur Radio
William E. Sabin, WØIYH
At the Dayton Hamvention in May 2008, ARRL President Joel Harrison, W5ZN, announced the formation of a Fifth Pillar for amateur radio, combined with the in-existence Four Pillars (Public Service, Advocacy, Education and Membership). The purpose of the new Pillar is to encourage and enhance math, science and engineering appreciation and skills. Individuals who are interested in and involved with, at various levels, the rapidly expanding modern-age technology developments in electronic hardware and software are the intended audience. This applies in particular for us as it pertains to the art and science of Amateur radio communications, not only at the “black box” and “operating” levels, all of which are very important, but equally important at the math, science, analysis and design levels.
This concept was encouraged by Dave Sumner, K1ZZ, in the August 2008 QST Editorial. QEX and other ARRL Technical staff members are very active in advancing the Fifth Pillar ideas. The new ARRL website wedothat-radio.org is dedicated to this effort. Traditional (“legacy”) methods are also respected, as they should be.
Many national governments, including the USA, are deeply concerned with inadequate awareness and education by the general public in the fields of math and science. Many nations are ahead in this respect. The Fifth Pillar effort is dedicated to adding to the improvements in deficiencies of this kind. This brief and simple example article is also dedicated to this effort.
A Modern Discrete-Method for Signal Analysis and Design
The modern personal home computer, in conjunction with an elegant and sophisticated mathematics calculation program, Mathcad Version 14.0 [Ref. 1], is employed in this brief article at an introductory level that is very user-friendly. This program is used to calculate, process and graph-plot a variety of signal-processing and very many other kinds of math problems. The so-called symbolic math methods {see the Mathcad User Guide, Chapter 13} are also used in modern math computing. This software is an outstanding tutorial tool for the advancement of the engineer’s and student’s math skills, which is considered to be an important goal in today’s advanced technology environment.
The signals and their analyses can be in the time domain or the frequency domain, and they can be linear in nature or non-linear. Signals, before and after processing, can be switched back and forth easily between time domain and frequency domain. A complete Mathcad 14.0 program, with perpetual usage, is attached to the new book Discrete-Signal Analysis and Design [Ref. 2]. This is a special and very generous Mathcad promotional offer by the PTC company. The User Guide that is on the compact disk can be placed on the Desktop as an icon.
Example: A three-tone distortion simulation. [Ref 3.]
A typical discrete-signal processing example will help to illustrate just a few of the basic ideas of Mathcad usage in the practical world of electronic design. This and similar examples can also be further explored with circuit simulation programs such as Multisim (student edition) by National Instruments (http://www.ni.com/academic/multisimse.htm) using accurate models of I.C.’s, transistors, diodes, tubes and many kinds of passive components. In addition to the three desired tones, a large undesired “out-of-band” signal that contributes to distortion products will be examined.
Time domain information can be converted to spectrum results. After modifying the frequency spectrum, for example by introducing a filter or a signal interference or random noise (additive or multiplicative), the modified time domain results can then be obtained. We can also begin with various spectrum shapes that achieve certain desired time-domain results.
Certain communications waveforms use methods similar to this example, and laboratory test equipment (http://www.ni.com/analysis/) is used to perform discrete-time and discrete-frequency tests automatically. Pseudorandom data error rates can be evaluated.
Analysis of the Example.
- Illustration A & B
Part (A) shows the time-domain input Vsig(n) and part (B) the time-domain output Vout(n) of an amplifying device that is perfectly linear. The device delivers only output signals that are proportional to those at the input, i.e.,Vout(n) = Vsig(n)1.0 times a voltage gain constant Gv. The signals in Part (A) are at frequencies 4, 7 and 9. Another much smaller input at frequency 29 will be considered a little later. Observe also the DC bias Vdc on the device. This is called the “operating point.”
Part (C) is the two-sided (positive-frequency and negative frequency) phasor spectrum of the output as calculated by the Discrete Fourier Transform (DFT) of the time-domain output (part B) of the device. Part (D) shows the same actual positive-frequency signals as the input. We get these positive-frequency signals by combining the positive-frequency phasors and the negative-frequency phasors. Chapter 2 of the Sabin book explains how this is done. Also, Chapter 1 discusses phasors vs signals.
Part (E) introduces a nonlinearity, the exponent 1.5, which is often used in text books [see Sabin ch. 2], in the transfer function of the device. This creates distortion products in the form of new frequencies at the output Vout(n) that are not present in the input Vsig(n). In the signal spectrum Vout(k) of part (F) many, but not all, of the nonlinear output products are identified. For example, the term at (k) = 3 is due to the term at (k) = 4 interacting with the term at (k) = 7. The 1.5 exponent also increases the voltage gain, in this particular example, to Gv1.5. Gv can also be a more complicated time-varying function of (n) such as [Gv(n)]1.5.
Another consequence of the nonlinearity is that the spectrum phasors, therefore also the signals, are “complex” and may possibly display items that have a real (Re) part, an imaginary (± j Im) part, a magnitude ( | | ) and phase angle (Θ) with respect to some “reference” phase such as zero. The graphs of parts (F) and (G) would identify these. Mathcad can be instructed to calculate and plot all of these results.
In part (G) the interfering “out-of-band” signal at (k) = 29 is greatly increased in amplitude so that distortion terms are emphasized. The ability of a strong out-of-band interferer to corrupt a desired signal spectrum is illustrated. In particular, the spurious product at (k) = 6 stands out. In addition to this large distortion term, there are many smaller distortion products that can degrade the desired weaker signals. Also 4, 7 and 9 are degraded slightly. This is very serious interference that can be difficult and expensive to repair, especially in wideband high-level systems where filtering of strong interfering signals is expensive. A tunable notch filter is sometimes possible for constant interferers, but costly high dynamic range equipment is often indicated. We see this effect in practical environments, for example in HF/VHF/UHF radio. We now see it also mathematically.
Beyond this simplified introduction, a much more complete study would be well-justified. For a closer look at the various related technologies for this and many other topics, visit the new ARRL website www.wedothat-radio.org.
Ref 1.
Mathcad, version 14.0, PTC company, Needham, MA.(http://ptc.com/products/mathcad/) The Mathcad program is very mature and has a history of fourteen versions in more than 25 years.
Ref 2.
Discrete-Signal Analysis and Design, by William E. Sabin, published in January 2008 by www.wiley.com Interscience Division, available from the ARRL Bookstore, item #0140 at http://www.arrl.org/catalog/, search: Sabin.
Ref 3.
Sabin, W0IYH. QEX, Nov/Dec 2008 “A Modern Discrete-Method for Signal Analysis and Design” pp 36-38.
Bill Sabin, W0IYH
About the author:
Bill Sabin received the call Sign W9YFA in 1941 in Covington, KY at age 15. This changed to W4YFA in 1946, and to W0IYH in Iowa (Collins Radio Company) in 1964. He holds BSEE and MSEE degrees from the U of Iowa. He retired from the Rockwell Collins Company in Cedar Rapids IA in 1990. He is co-editor of and contributor to, with E.O. Schoenike, three books on Single-Sideband and HF Radio. He is the author of more than 40 technical articles and portions of the ARRL Handbook (1995 to 2009 editions). In 1983 he received the annual ARRL Technical Excellence Award. He is a member of ARRL, Life Senior Member of IEEE, and member of the ARRL DXCC Honor Roll.
Bill Sabin W0IYH, w.sabin@mchsi.com
