Audio Systems Group, Inc.
More recently, I've been devoting energy to issues
relating to various forms of interference to audio systems from both
power and radio frequency (RF) sources. You'll also find applications
notes for Amateur Radio Operators (Hams).While ASG was in business, I
authored a number of articles and application
notes to explain design concepts, help our clients understand complex
issues, and help users get the most out of their sound systems. They
are listed following the Ham Radio topics.
Links to Other Useful Websites
ON4WW has put together an excellent narrative documenting his work chasing down and eliminating a variety of local noise sources.
Webpages from Ray Rayburn, Rick Chinn, and Bill Whitlock have excellent practical information on the technical side of audo and acoustics. All are members of the Audio Engineering Society Standards Committee, and Rayburn and Whitlock are Fellows of the AES.
Jim Brown's Jazz Page A few years ago, I taught a short class on Listening to Jazz for Pleasure to members of our Life Long Learners chapter here in Santa Cruz. This is a collection of resources I prepared for those attending. It includes listiings of jazz on radio and on the internet, jazz on video, jazz on CD, and hints on how to listen to jazz for pleasure.
This is the Power Point for a tutorial lecture I presented to
several AES conventions on Mixing Live
Jazz (Sub-titled, "It's Not Rock and Roll!" It is
written for sound system
This is the Power Point for a tutorial lecture I presented at the
Stanford Jazz Workshop on Sound And Acoustics For
Jazz Musicians . It is directed toward musicians.
Spectrogram This is the final version of this software, which users of the Elecraft K2 have found useful for alignment of the IF filters. Posted by permsision of the author. Do NOT ask me for help with this software -- I know nothing about it.
Rudy Severns, N6LF, is a contributor to both the ARRL Antenna Book and Handbook; his research is definitive, his topics are very practical, and his writing is both very clear and technically rigorous. Rudy's website is a treasure trove of solid research and applications notes on vertical antennas and their radial/counterpoise systems, especially for 40M and below, Recently he's been concentrating on antennas for the new 630m and 2200m bands. Another recent article debunks the assertion that THHN (insulated house wire) is has more loss than bare copper when used for wire antennas and most radial systems. .
New Additions and Updated Materials
These are FCC Ground Conductivity Maps of the United States. NEW! November 2017
These are slides for my talk at Pacificon about Transmitting Chokes For the 630M Band. NEW! October 2018
This is a new applications note summarizing my work on Chokes and Transformers For Receiving Antennas. NEW! October 2018
These are slides for my talk at Pacificon about the VE3DO Receiving Loop, a compact receiving antenna for 160M and the lower HF bands. NEW! October 2017
This is an applications note I wrote for National Contest Journal this summer on Locating Stubs for Harmonic Suppression. It is in response to an earlier piece on this topic by W2VJN, in which there are some important errors. And here are the Power Point slides for my presentation of this material to NCCC in June `2017. Slide show is NEW! June 2017
This is an applications note I wrote for National Contest Journal called Build Contesting Scores By Killing Receive Noise. Here are the slides for my talk at the 2017 Visalia DX Convention. NEW! May 2017
I put together this slide show to document our three-man, seven-county expedition to Nevada in May, 2016 for the Seventh Area QSO Party. And here are the Power Point slides for W6GJB's great talk at Pacificon in 2016 about how he designed and built that trailer. NEW! October 2016
This is an applications note I wrote for National Contest Journal last fall called How To Achieve Clean, Punchy, Competitive Contest Audio Without Splatter. It includes major contributions from K6XX, who is a design engineer at Elecraft. NEW! May 2016
These are the slides for a Power Point presentation as part of the Pacificon Antenna Forum on an Effective Portable 80M Vertical that old men can rig without hurting themselves. NEW! October 2015
Here is a preliminary in-progress report on my ongoing project to measure the Occupied Spectrum of various ham rigs. This second file includes some of the same data, but focuses on the FTDX5000 before and after implementation of the September 2014 firmware upgrade. For all of these measurements, both of the K3s in use had the original synthesizer board. Note that while these reports use Power Point because it's a good way to view the data, they are not intended for live presentation in their current preliminary form. NEW! March 2015
These are the slides for my 2014 Pacificon talk on Power, Grounding, Bonding, and Audio For Ham Radio. NEW! October 2014
Analysis of Noise Performance of Selected HF Transceivers For nearly a decade, Rob Sherwood, NC0B, has been testing and publishing comparisons of the receive performance of selected transceivers, and receive performance has greatly improved as a result. Transmitter performance has been largely ignored. This document, which compares the data from ARRL lab product reviews, is an attempt to shed the same sort of light on transmitter performance, and encourage manufacturers to do better. NEW! September 2014
A year or so ago, NCJ published my Survey of Bandpass Filters for Contesting . This pdf of that report includes a link to a page with additional pdf files of the raw data for each filter and each band. NEW! September 2014
This new applications note describes low cost USB Audio Interfaces for
use with digital modes, how to know if you need a better interface, and
how to adjust audio levels for best performance and cleanest
transmitting performance. NEW! July 2014
These slides (as a pdf) describe simple way to End Feed a Center-Fed Vertical Dipole using
the coax shield as the lower half of the dipole, and a high impedance
common mode choke as the lower end insulator. NEW! July
This new applications note presents ARRL
Data on Noise Transmitted By Ham Transceivers in
a form that makes it much easier to compare one rig to another.
This is a work in progress, still very preliminary. For additional
background on this, see the slides for K6XX's excellent presentation to
NCCC, one link down. NEW! July 2014
Here are the Power Point slides for K6XX's presentation to the Northern California Contest Club about how to transmit a clean signal on the HF bands. Signal Cleanliness is Godliness NEW! November 2013
Ham Radio Topics
Antennas and Transmission Lines
This is a text version of the the material in "If I Could Put My Vertical On My Roof, Should I" and Antenna Planning for Small HF Station. Antenna Planning NEW! Feb 2016
These are the Power Point slides for the third presentation about vertical and horizontal antennas for the HF bands. Antenna Planning for Small HF Stations (and even larger ones) NEW! May 2014
Here are the Power Point slides for two presentations about vertical antennas at Pacificon in October 2013. If I Could Put My HF Vertical On My Roof, Should I? and 43 Ft Verticals -- What's The Big Deal? NEW! October 2013
These are the Power Point slides for a presentation about 160M antennas at Pacificon in October 2012. Getting On 160M From a Small Lot (and Larger Ones Too). October 2012
These are the Power Point slides for a presentation at Pacificon in October 2012 called Using SimSmith to Design Antenna Matching Networks.
This is Q&A-style tutorial on Coax
and Stubs for use on the HF bands .
Antennas for Limited Space I've spent most of my time in ham radio operating from small city lots. This article shares some ideas that have worked out very well for me. And here are the Power Point slides for a somewhat expanded presentation of these ideas at Pacificon last fall.
Comparing Verticals and Dipoles 9May08 This applications note takes a closer look at the relative performance of wire dipoles and verticals for the 160M, 80M, and 40M ham bands. This piece has largely been replaced by the May 14 piece.
Transmission Lines at Audio Frequencies, and a Bit of History The behavior of cables at audio frequencies is widely misunderstood. This tutorial attempts to shed some light and bring some sanity to the discussion.
These are some practical notes about Hard Line and Hard Line Connectors.
Transmitting Chokes Most
recent update 23Apr10.
This is an expanded Power Point for presentations I've done to several
ham clubs (PVRC, Pacificon, NCCC, NCDXA, REDXA, and Visalia) that
extends my research on ferrites to the design and application of
greatly improved common mode transmitting chokes, also known as
"current baluns." See also RFI, Ferrites, and
Common Mode Chokes For Hams for the tutorial text that goes
with this Power Point, including my "Choke Cookbook."
Hum, Buzz, and RF Interference
RFI, Ferrites, and Common Mode Chokes For Hams Most recent update 5 May 2010. This tutorial is directed specifically to RFI in ham radio applications. It includes an extended discussion of the use of common mode chokes as transmitting baluns, and extensive measured data on ferrite chokes. A chapter on audio and computer interconnections in ham stations shows how to make bulletproof connections between a computer sound card and ham rigs for SSB, RTTY, PSK31, and SO2R contesting without expensive interface boxes, using nothing more than simple cables with the right connectors on each end.
RFI and Ham Radio May 2011 This is a new pdf of the Power Point for a tutorial on RFI I've done for several ham clubs.
Power Supply Bonding And Audio Distortion addresses a construction issue with Astron power supplies that can cause what sounds like RFI. .
This is an applications note on a variety of Power Line RF Filters that I've found at a local electronics surplus house, HSC, also known as Halted. Unfortunately, they are not listed in their internet catalog, so you've got to go to the store to buy them. They're also widely available from industrial electronics suppliers like Allied and Newark.
RF Interference in Audio Systems These are Power Point slides for a tutorial lecture held at the 2008 Fall Convention of the Audio Engineering Society in San Francisco. The presentation describes the fundamental mechanisms by which RF interference occurs, then shows how interference can be avoided by proper system design and how it can be eliminated from existing systems. The next item listed on RFI for Hams covers much of the same material and more, can be studied as a text to go with the Power Point.
Coax Chokes on Low Loss Toroids 5May08 This short research note summarizes and analyzes some recent measurements of chokes wound on Fair-Rite #61 toroids.
Measured Data For HF Ferrite Chokes This data was measured by a ham colleague using well calibrated HP instrumentation, and was published both in my AES Paper (see below) and in various tutorials. Here, all the plots are re-scaled to 1-100 MHz on the frequency axis and 10-1,000 ohms on the reistance/impedance axis to make it easier to compare one material to another and decide how to use these parts on the HF ham bands.
Other Ham Topics
Computer to Radio Interfacing - You Don't Need An Expensive Interface! Most recent update 15 Apr 10. Most hams (including authors of some ARRL publications) believe that transformers, expensive boxes, or even optical isolators are needed to connect computers and other gear to transceivers without hum and buzz. This is sadly (and expensively) wrong, and so are many of the solutions offered. An unshielded transformer or an improper shield connection may CAUSE hum, buzz, and RFI! This Power Point for a presentation to the Northern California Contest Club shows simple and effective solutions, involving no more than a few feet of copper braid and properly wired cables that can connect anything to anything, without transformers, interface boxes, or optical isolators. Audio connections are addressed first, followed by rig control, sending CW, PTT, and RTTY. This material is also covered in tutorial fashion in Chapter 7 (Solving Problems in the Shack) and Appendix 6 (Audio For Ham Radio) of the RFI Tutorial.
Partial Schematic of Ten Tec Titan 425 RF Power Amplifier Most recent update 12 Feb 08 I own three of these vintage amps, and they require frequent maintenance to keep them running. Ten Tec's printed schematics are spread across a dozen sheets, and are difficult to follow. This partial schematic is my attempt to put all of the switching, keying, and control circuitry on a single sheet of paper to make troubleshooting easier. This pdf should print on an 11" x 17" sheet of paper, and can be viewed at any magnification on your computer screen. Note that this schematic does NOT include details of the RF signal chain, but which is much easier to follow in the printed manual. DISCLAIMER: While I've tried to check it carefully, there may be errors in these schematics. Any corrections should be sent to k9yc at arrl dot net.
Keying Logic of Ten Tec Titan 425 RF Power Amplifier Most recent update 12 Feb 08 The keying logic only, formatted for letter sized paper.
Keying Logic of Ten Tec Titan 425 RF Power Amplifier Most recent update 12 Feb 08 Alternate view includes logic sensing of vacuum relay, formatted for letter sized paper.
Power Supply for Ten Tec Titan 425 RF Power Amplifier Most recent update 5 Feb 08 The Power Supply only, formatted for letter sized paper.
RF Switching of Ten Tec Titan 425 RF Power Amplifier Most recent update 8 Feb 08 The RF switching only, formatted for letter sized paper.
Hum, Buzz, and RF Interference -- Written for
Audio Interfacing for Non-Audio Professionals This is the Power Point for part of a tutorial workshop I presented to the 2005 IEEE-EMC Symposium. It includes Bill Whitlock's groundbreaking work on balanced interfaces, and shows why when a cable shield is connected only at one end to prevent shield current, the connection point should always be at the sending end.
Pin 1 Revisited Neil Muncy called our attention to the Pin 1 problem (the improper termination of the shield of audio wiring to the circuit board rather than to the shielding enclosure) in his classic 1994 paper, reprinted in the June 1995 Journal of the AES. When he wrote his paper, most commercially available audio gear had pin 1 problems. It was, indeed, difficult to find equipment without it -- even the most prestigeous consoles had serious pin 1 problems! Over the next decade, the better manufacturers redesigned their products to correct their mistake, but sadly, many have not done so. This is the first installment of a two-part article published in the SynAudCon Newsletter.
Pin 1 Revisited -- Part 2 This is the second installment of a two-part article published in the SynAudCon Newsletter.
Shield-Current-Induced Noise - Part 1 Current flowing on the shield of balanced audio cables will be converted to differential mode voltage on the signal pair by imperfections in cable construction. This is Part One of a series about this matter that I wrote for the SynAudCon Newsletter.
Shield-Current-Induced Noise - Part 2 This is Part Two of a two-part article published in the SynAudCon Newsletter. It also includes recommendations for the termination of audio cables.
Power and Grounding For Audio and Audio/Video Systems -- A White Paper for the Real World This White Paper was commissioned by New Frontier Electronics (the SurgeX people) so they would have something to pass out to contractors and other users of their excellent power products.
Power Systems and Grounding Updated Jun 2012 are the Power Point slides for my Power and Grounding class at InfoComm 2013.
RF Susceptibility of Condenser Microphones Many modern condenser microphones have problems in the presence of strong VHF and UHF transmitters, like FM and TV broadcast stations, 2-way radios, and cell phones. This is an article published in the SynAudCon Newsletter. You can download a much longer and more detailed AES paper that David Josephson and I wrote in 2003 from the AES website.
Understanding How Ferrites Can Prevent and Eliminate RF Interference to Audio Systems This applications note has been significantly revised and expanded since its first posting earlier this year. Even if you've read the earlier version, you should get this one. It has also been turned into an AES Paper for the New York convention in October 2005.
The Effects of Cable on Signal Quality I first studied the loading of output stages of microphones and line level equipment by cable capacitance in 1988. On the basis of that work, I wrote this applications paper for Sound and Video Contractor in 1990.
Termination, Impedance Matching, and the Maximum Power Transfer Theorem in Audio Systems This Tech Topic is the first writing I did for SynAudCon, back in 1982. Back then, folks were slapping 600 ohm resistors on everything that sat still long enough, and this was my contribution to giving the practice a decent burial. Like the special technique that scares away elephants, It appears to have been at least partially successful -- when's the last time you saw a 600 ohm resistor (or an elephant)? There's also some nice tutorial material here on how transformers and passive equalizers work.
When Audio Systems Group, Inc. was active, we carried out an ongoing program of research to advance the state of our art, and publishes the result of that work so that others can learn from it. Most of our research is published in the form of technical papers presented to the Audio Engineering Society. Our research is self-supported, and authors of technical papers are not compensated by the AES.
AES publications can be downloaded from the AES Website. The cost for each convention preprint is $5 for members and $20 for others. (The AES keeps all the money to support its publishing program, a position that the we fully support.) In the past, the library has been available on CDROM (currently 20 CD's in the set). AES publications are now available via online subscription. $115 per year provides full access to the library! The CDROM program is being phased out. The AES now permits authors of convention papers to publish their papers on the internet if they are not published in the Journal of the AES. Click on the links to download them at no cost from the Audio Systems Group, Inc. website.
New Understandings of the Use of Ferrites in the Prevention and Suppression of RF Interference to Audio Systems Building on the work of Muncy, the author has shown that radio-frequency current on cable shields is often cou-pled to audio systems by two mechanisms - "the pin 1 problem" and shield-current-induced noise (SCIN). An improved equivalent circuit for a ferrite choke is developed that addresses both dimensional resonance within ferrites and the self resonance of inductors formed using those materials, then compared with measured data. Field tests show that chokes formed by passing signal cables through ferrite cores can significantly reduce current-coupled interference over the range of 500 kHz to 1,000 MHz. Guidelines are presented for diagnosing the causes of EMI from sources as diverse as AM broadcast transmitters and cell phones. Solutions are presented for use in new prod-ucts and for RFI suppression in field installations. Preprint Number: 6564 Convention: 119 (October 2005) Author: Jim Brown
A Better Approach to Passive Microphone Splitting While there are clear technical advantages to active microphone splitting, operational considerations dictate the use of passive splitting of microphones in most sound reinforcement applications. Modern microphones generally require a load impedance greater than 1,000 ohms, and performance often degrades significantly with heavier loading. Since mix desk input impedances rarely exceed 1,500 ohms, passive splitting utilizing 1:1 turns ratio transformers can seriously degrade microphone performance when driving two or more mix desks. Transformers designed to operate in stepdown mode solve this problem and offer other benefits. This paper reviews current practice, studies stepdown-mode splitting, and reommends that mix desks be designed with higher input impedances and that microphones be designed to work with lower impedance loads. Preprint Number: 6338 Convention: 118 (May 2005) Authors: Jim Brown, Bill Whitlock
Radio Frequency Susceptibility of Capacitor Microphones Neil Muncy has shown that improper termination of shield wiring, commonly called the pin 1 problem, couples noise currents flowing on a cable shield into audio circuitry through common impedance coupling. This paper examines the susceptibility of modern microphones, describes a simple test to find problems, and offers simple solutions. Preprint Number: 5720 Convention: 114 (February 2003) Authors: Jim Brown, David Josephson
Common-Mode to Differential-Mode Conversion in Shielded Twisted-pair Cables (Shield-Current-Induced Noise) Neil Muncy has shown that audio frequency current flowing on the shield of balanced audio wiring will be converted to differential mode voltage by any imbalance in the transfer impedance of cables, and hypothesized that the effect increases linearly with frequency. Whitlock has shown that conversion also occurs with capacitive imbalance. This paper confirms Muncy's hypothesis, and shows that shield current induced noise can be significant in the MHz range. Preprint Number: 5747 Convention: 114 (February 2003) Authors: Jim Brown,; Bill Whitlock
Testing for Radio-Frequency Common Impedance Coupling (the "Pin 1 Problem") in Microphones and Other Audio Equipment The author has shown that a primary cause of VHF and UHF interference to professional condenser microphones is inadequate termination within the microphone of the shield of the microphone's output wiring, a fault commonly known as the pin 1 problem. Tests using only audio frequency test signals generally fail to expose susceptibility to radio frequency (RF) interference. Simple RF tests for pin 1 problems in microphones and other audio equipment are described that correlate well with EMI observed in the field. Preprint Number: 5897 Convention: 115 (September 2003) Author: Jim Brown
A Novel Method of Testing for Susceptibility of Audio Equipment to Interference from Medium and High Frequency Radio Transmitters The author has shown that radio frequency (RF) current flowing on the shield of balanced audio wiring will be converted to a differential signal on the balanced pair by a cable-related mechanism commonly known as Shield-Current-Induced Noise. This paper investigates the susceptibility of audio input and output circuits to differential signals in the 200 kHz - 2 MHz range, with some work extending to 300 MHz. Simple laboratory test methods are described, equipment is tested, and results are presented. Laboratory data are correlated with EMI observed in the field. Preprint Number: 5898 Convention: 115 (September 2003) Author: Jim Brown
Systems for Stereo Sound Reinforcement - Performance Criteria, Design Techniques, and Practical Examples Although stereo systems for large rooms were pioneered in well documented work at Bell Labs in the 1930's, most modern practitioners appear to be ignorant of the most important of that work as applied to modern sound reinforcement. This paper draws on the author's experience over nearly twenty years with both portable and permanent systems using two and three front referenced channels. Design criteria and examples are presented to illustrate both good and bad design practices, and some important pitfalls are noted. Preprint Number: 5666 Convention: 113 (September 2002) Author: Jim Brown
Consumer Video Tape Duplication Techniques: A Tutorial This tutorial paper begins with a survey of the audio parameters of VHS, Beta, and 8 mm videocassette formats, and describes the audio technology necessary for successful operation of a duplication facility. Topics discussed are mastering, duplication, distribution, routing, and signal processing equipment, system design, standards of operation, program interchange, and quality control. Paper Number: 4-010 Conference: The AES 4th International Conference: Stereo Audio Technology for Television and Video (April 1986) Author: Jim Brown
Design Concepts for Mixing Consoles for Multichannel Reinforcement Systems for Music and Theater Over the years, a design concept has evolved for performing arts centers which includes true three-channel sound reinforcement from clusters located left, center, and right at a proscenium arch, with each cluster covering most or all of the audience seating area. Generating a viable three-channel mix for such a system using a currently available mixing console which is a standard product is problematic at best. This paper presents the functional design criteria for a new console which meets the mixing needs of such systems. The work is based on research with clients and other users, as well as the author's experience. A complete functional description of a console is presented, including functional diagrams, along with a thorough discussion of the rationale underlying all operational concepts. Author's Note: The design of mix consoles has progressed significantly since this paper was written, especially in the use and capabilities of VCA grouping functions. As a result, some of the bussing called for in this paper can now be replaced functionally with VCA grouping. Preprint Number: 2849 Convention: 87 (September 1989) Author: Jim Brown
Measurement of the Dynamic Transfer Characteristics of Multiband Signal Processing Systems by Time Delay Spectrometry Multiband broadcast signal processing systems have defied measurement of their dynamic transfer characteristics under the heavy processing ratios commonly in use. The high noise immunity of Time Delay Spectrometry and the averaging capability of a microprocessor based TDS analyzer are combined to investigate the dynamic complex transfer characteristics of several popular processing systems. Measurements will be demonstrated with near inaudibility of the test signal. Preprint Number: 2410 Convention: 81 (October 1986) Author: James W. Brown
Acoustics and Sound System Design
Why Churches Buy Three Sound Systems, and How You Can Buy Only One Most churches are so afraid of buying sound systems that they do it three or four times before they finally end up with one that works well enough to meet their needs! Here's how you can do it right the first time.
Acoustics and Sound Systems in the Contemporary Church The contemporary church is built around communication - verbal, musical, and emotional - as well as worship. The minister communicates with the congregation by preaching, leading prayers, and announcing church activities. Music attempts to communicate ideas and concepts while it simultaneously enhances the worship experience through emotional involvement. The acoustics of the worship space have a profound effect on all of these functions. This article explains these complex issues in plain English for the non-technically inclined.
Sound Reinforcement for Jazz and Other Acoustic Music These are my Power Point slides for a tutorial session held at the 2008 Fall Convention of the Audio Engineering Society in San Francisco. These are my slides -- other members of the panel presented other concepts and other elements of the problem.
The Revitalization of a Community Landmark - The Greensburg Palace Theater The 1200-seat Palace Theater is an anchor of this small town on the western slopes of the Alleghenies just off the Pennsylvania Turnpike east of Pittsburgh. This blow-by-blow description of an historic renovation is a textbook example of how to do it right. We're very proud of everyone involved in this project!
Mixing for Three Channel Sound Reinforcement Two and three channel sound reinforcement is a concept whose time has finally arrived. Two and three channel systems are being successfully used in performance and worship spaces, on Broadway. and in theme parks. A well designed two or three channel system can blow the pants off of a monophonic system which uses significantly more powerful equipment. While this article (published in the March 1998 issue of Sound and Communications) was specifically commissioned to address mixing for these systems, it addresses our design philosophy for these systems as well.
The Acoustics of Sound Systems for Baseball was an invited paper presented to the annual meeting of the Acoustical Society of America in Chicago in June 2001. There is a lot of good information here about how sound behaves outdoors and when traveling long distances. Much of it also applies to sound indoors, especially in larger spaces. And here is a Power Point (97) presentation with a lot more graphs and graphics to go with it.
Loss Data for Digital Audio Cables Balanced twisted pair cables used for both analog and digital audio have significant losses at radio frequencies. This short applications note summarizes manufacturer data for typical products.
Microphone Splitters A tutorial survey of microphone splitters, written for the SynAudCon Newsletter. This piece has been expanded considerably and turned into an AES paper that will be downloadable from the AES website in a few months. (It was presented in May 2005, and it takes several months to get them up on the website.)
Wireless Mics and the Audio Professional This document was first prepared in 1986 for a seminar for the engineering staff at WGN Television. It has since been revised to make it more readable to the less technically inclined, and updated to keep up with new developments both in frequency allocation and technology.
Wireless Mics and Digital Television Our second applications note on wireless microphone technology addresses the impact of Digital Television on the wireless microphone landscape. If you use wireless mics you need to study both of these applications notes.
Which Coax for Wireless Microphone Antennas? This applications note, written for the SynAudCon Newsletter, shows that 75 ohm cable is much less expensive than 50 ohm cable, and works a lot better too!
Spreadsheet for Intermod Prediction This simple Excel spreadsheet illustrates the principles of intermod prediction. It can be used to predict intermod between up to five wireless frequencies and two broadcast carriers. It is also unprotected with all the formulas visible, so you can see how to expand it to consider more channels, or write a far more elegant one. I did this in an hour or so. See "Wireless Mics and the Audio Professional" (above) for a discussion of intermod and how to use the spreadsheet. Click here for the Quattro Pro version.