Understanding RF Transmission Lines: From Circuit Theory to EM Field Theory

[david845]

I really hope i can get some answers to the questions that have been plaguing me for some time. I'm more conceptual, and math does not satisfy my curiosity so I was hoping the experts here could fill in some blanks:

In making a jump from learning DC/low frequency AC to RF, i studied transmission lines and the finite speed of light. From my understanding, even connecting a single wire to the hot terminal of a battery would produce a transient current until the battery "sees" the open circuit and returns to open circuit conditions where no current flows. As this happens at almost the speed of light we cannot notice the transient conditions. The incident voltage wave from connecting an alternating voltage source to the TL only travels slightly slower than speed of light (c) through the medium. To me, this means that if the physical length of the TL is much shorter than the wavelength of the signal of a corresponding frequency (like 60HZ AC power lines), then simple circuit theory applies because 1/2 wave cycle could never complete itself and reverse direction before the wavefront reaches the load. (Am i correct so far?)

Consequently, a TL that is physically long compared to the wavelength breaks down circuit theory. I do understand that in a TL terminated in an open circuit that the wave will reflect at the open circuit and will superpose with subsequent oncoming waves and produce a standing wave. Is the standing wave important in order for the antenna to radiate? It seems with the ends open circuited there has to be reflection, but every book i read says if the load is terminated with a matched impedence then there is no reflection and all the energy is lost to radiation...how is this possible? If a dipole antenna is merely a continuation of the TL (2 conductors separated and left open circuited) how can there not be any reflection and all the power is transduced into radiation? Why do we need to view the TL as a series of lumped elements (R,L,C - though i understand self Inductance and mutual capacitance how does it affect the voltage/current in the TL?). Is a resonant antenna 1 where the 1/2 wave cycle reverses as it JUST reaches the open circuit?

I appreciate ANY help in answering as many questions as you can. I've seen a lot of people with the exact same question - but I also have never seen an answer that satisfied any of them.

 

[nsaspook]

It's hard to know where to start with your questions without a lot of background on what you currently understand.

I've found this site to be very good about understanding the intuitive aspects of antennas and transmission line interaction.

http://www.antenna-theory.com/

The subject of Antennas is best understood intuitively; this is in stark contrast to the methods in University, where complex math pervades every page. I do not think this approach effectively teaches antenna theory. In these pages you will not find rigorous mathematical analysis which only apply in the simplest of antenna cases (and are ultimately artificial for the real world); I will try to state facts and a minimum of math except where necessary.

 

[marcusl]

1. Yes, an electrically short line can be modeled by circuit theory. BTW, be careful about assuming that all 60 Hz power lines are electrically short. High voltage lines carrying current across the country can span an appreciable fraction of a wavelength.
2. A dipole antenna is not a transmission line in the classical sense. A TL confines fields to a small region (principally between the wires) so as to minimize power loss through radiation. When a parallel transmission line's wires are opened up at right angles, fields are efficiently coupled to free space (that's what defines an antenna--it radiates). As a result, you no longer have an open circuit. Antennas have a definite impedance, the real part of which--called "radiation resistance"--represents power coupled to space and radiated away. You'll find that the radiation resistance of a half-wave dipole is 73 ohms--not even close to an open circuit. For efficient coupling, the transmission line is mated to the antenna through an impedance matching device, to prevent reflections at the antenna terminals.
3. Viewing a TL in terms of lumped elements (LRC) is convenient because engineers are generally comfortable with these building blocks. Keep in mind that this model is a discrete approximation to a continuous physical system that, furthermore, is most useful at low frequencies. TL's are more properly described by differential equations (look up Telegrapher's Equations, e.g.).
4. A resonant antenna does not operate into an open circuit. It couples energy into free space, which has a characteristic impedance of ~377 ohms.

 

[Baluncore]

The radiating element of a resonant antenna should be “tuned” to the signal frequency. The TL should be coupled to the radiating element by a network that matches the impedance.

Analysing or designing antennas is a two step process. Firstly, an art; visualisation of the structure and of the way RF currents will flow, resonate, and radiate. Secondly, a science; an association of the appropriate mathematical relationships to provide the numbers.

RF engineering appears as a black art to the beginner, then as understanding of the concepts builds, the mathematical footings are developed, and experience is gained, it gradually becomes a science. The best RF engineers are borne that way, they have an excellent 3D imagination coupled with a skill in applied mathematics and numerical modelling tools.

 

[david845]

I appreciate the generic answers, but I am looking for something a bit more intuitive. Math is a language, like English, and I'm asking someone to answer my questions in English since its my first language and calculus is a distant second. Any experienced engineers who have transitioned from circuit theory to TL theory who can help ease the transition? Unfortunately, most are content memorizing words without truly understanding them as evidenced here.

 

[marcusl]

??
The subject matter you asked about is complex, and involves significant subtlety. The responders to your post went out of their way to describe things as intuitively as possible, using English and avoiding math at your own request. Insulting us, our abilities and our knowledge base is uncalled for.

 

[nsaspook]

I appreciate the generic answers, but I am looking for something a bit more intuitive. Math is a language, like English, and I'm asking someone to answer my questions in English since its my first language and calculus is a distant second. Any experienced engineers who have transitioned from circuit theory to TL theory who can help ease the transition? Unfortunately, most are content memorizing words without truly understanding them as evidenced here.

'There is no spoon' Intuition on a abstract subject like EM energy is developed by years of hard work and sometimes burned fingers. Baluncore is correct, you have must have at least a basic mathematical footing on EM field theory before you can understand it in any intuitive way as the wiring is just a way to focus and direct the flow of energy from point to point. To visualize something dynamic your brain needs to be able to predict the future and we normally do that by matching past memory patterns of thought from experience. Without that experience we have no patterns so it's really necessary to generate that 'database' first. Take your time, it will begin to become clearer.