Millman's Theorem; Worth a second look....

I have found that half the challenge and 100% of the fun of electronics is being able to accurately predict what is happening in one's circuit. Fortunately, there are many powerful circuit analysis techniques available for use in predicting what is occuring in one's circuit. Most of these techniques are introduced and explained in the AAC ebook at www.allaboutcircuits.com.

One of the available techniques consistently fails to garner much consideration. That technique is Millman's Theorem. It has been my observation that the application of Millman's Theorem in the analysis of electronic circuits is extremely rare. I have often wondered why this is.

When it comes to analyzing a given circuit, I suspect there are at least two factors influencing one's choice of technique. A strong factor would be the emphasis placed on a given technique taught in electrical engineering courses. Naturally, any complete circuits course will introduce a student to all of the techniques that are available. It is also only natural for an instructor to favor one technique over the others based on his or her personal preference. A second factor is based on the student's personal preference. Once all of the techniques have been studied, a student will select the technique with which he or she feels most comfortable. The odd thing is that when I examine textbooks of today, I find that few if any make even a passing acknowledgement of Millman's Theorem.

Another factor shaping today's trends in circuit analysis is the ready availability of powerful circuit analysis software. These software based tools will no doubt become the analysis method of choice in the future. For the present, myself and others of my generation still derive a great deal of satisfaction and even pleasure from working through even a simple circuit using the techniques that have served us so well over the years.

As an Electrical Engineer with 35+ years of experience, I have analyzed hundreds of complex analog circuits. During the early years of my career I worked through, what were for me, tough circuit analysis problems. In many of the cases, I found the practical application of KVL and KCL to my day to day circuit analysis tasks was more than a little tedious.

After several years in the field, I began to long for a world with fewer equations and even fewer unknowns. Then one day, while wondering if there was an easier way to tackle circuit analysis, I pulled out one of my course text books and leafed through it. I ran across a section that was not more than half a page in length. The section was an introduction to what was called at the time "short-circuit" analysis. Several decades later, I would learn that this "short-circuit" analysis had become known as "Millman's Theorem". The title of the book I was leafing through was "Pulse, Digital, and Switching Waveforms", authored by Millman and Taub. You will recognize that one of the authors of my textbook was Jacob Millman, the individual for whom Millman's Theorem was named.

Intrigued, I read the section in my textbook several times and remembered that this particular section was not one that the instructor had spent a lot of time on. After several readings, I slowly began to see that there was something to this technique far beyond the simple illustrative example provided in the textbook. I gradually started using the technique as a substitute for the KVL and KCL techniques to which I was accustomed and found that it was much easier and quicker to get to the answer than had been the case with the "tried and true" KVL and KCL method.

The one thing that I believe tends to make Millman's Theorem look so limited in its application is the deceptively mundane examples used to introduce the concept. These example are often so simple that most electrical engineers look at them and scoff. The message conveyed by these simple examples is that Millman's Theorem is limited to circuits that have only a simple topology. I have found that nothing could be further from the truth.

Since my epiphany some 30 years ago, I have used Millman's Theorem as my circuit analysis technique of choice. I have found it to be more often than not, well up to the task of solving some of the most complicated circuits I have encountered. I hasten to add that Thevenin's Method is an important adjunct to Millman's Theorem. It is by using the power of Thevenin's Method to rearrange multi-loop circuits that the full power of Millman's Theorem can be applied.

I hope that those who take the time to read this blog entry will take a second look at Millman's Theorem. I believe those that do will discover as did I that it is a circuit analysis technique that has much to offer.

More Millman's Theorem info to come.....

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