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Can someone please give me an intuitive explanation of open stubs?

enter image description here

I have the length-based mathematical derivation and explanation from my textbook, but I am looking for an intuitive one.

For example, for an open stub (circuit 2), I think of it as an open ended transmission line through which the wave travels and gets reflected due to the open end, hence travelling double the distance. The reflected wave (from the open stub) will come back, get evenly distributed to both sides (term 3 and term 4), hence adding to the total reflection and transmission. Hence, S33 should be greater than S11 (which it is as shown below) at every frequency.

But:

  1. The above behaviour will be exhibited irrespective of the length of the stubs (I guess). I mean,even if its length is less than a quarter wave, it will still reflect but it's behaviour is capacitive. How is that justified? Similarly, will it behave like an inductor when its length is more than a quarter wavelength?

  2. Why, in circuit 2, does it behave like an open circuit (as visible from Smith chart)? And for shunt stub hasn't changed at all (the point is at the centre of the chart)? (Again, maybe it can be explained mathematically, but intuitively?)

reflection Coefficient of above circuits

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  • \$\begingroup\$ one question at a time please. \$\endgroup\$ Jan 31 at 22:26
  • \$\begingroup\$ @JasenСлаваУкраїні Thanks for responding. It's a question on intuitive explanation of of stubs. A general explanation on stubs without specifics would have gotten my question marked as "too general to answer" which is why I have put up several specifics. \$\endgroup\$ Jan 31 at 22:50
  • \$\begingroup\$ 1 yeah it's general what aspect of how a shorted stub works are you interested in? what it does to signals? how it works from a txline viewpoint, from an em-wave viewpoint, from a lumped model viewpoint? from a frequency domain viewoint? time domain? 2 and 3 have so many punctuation and grammar errors that I'm having trouble guessing what they are intended mean. maybe the Smith chart and S paramters make it clear but that's not a language I'm fluent in. \$\endgroup\$ Jan 31 at 23:24
  • \$\begingroup\$ @JasenСлаваУкраїні, Perhaps an explanation from Tx line and em wave viewpoint ? I have tried to explain the working(don't know if it is correct) of open stub in the question.Perhaps a similar explanation from tx line point of view? Thanks \$\endgroup\$ Jan 31 at 23:35
  • \$\begingroup\$ @JasenСлаваУкраїні, Pardon my grammer and spelling mistakes.I have edited the question. \$\endgroup\$ Jan 31 at 23:52

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This answer unfortunately is a non-answer, and you will probably find it unsatisfying, but I am going to share it in hopes it will help. During my schooling and first few years working in industry, I too struggled to find intuitive explanations for electromagnetic phenomena like transmission line and stub behavior. I think this it is natural for us to try and understand things by relating them to other things we already know.

I often hear people describing voltage and electric current by relating them to things like gravity and water flow in pipes. This helps to an extent, but the analogy eventually breaks down, and the person trying to understand often gets hung up on the details where the analogy doesn't apply. At the end of the day, our intuition can only take us so far in understanding a new concept, and I would even say it can hinder our grasp of the topic by distracting us from the actual physics. The reality is, there is no intuition behind why a wave responds the way it does to a stub or how it responds. The question of how or why is simply answered by the mathematical equations governing the subject. Laplace's equation applies to gravity, and Maxwell's equations apply to electromagnetics. There may be similarities, but we're doing ourselves a favor by keeping them distinct.

Relating to one of your questions, sometimes people try to gain intuition based on assumptions that are not applied correctly such as "if the length of the transmission line (or stub) is less than a quarter wavelength, I can ignore it" This may be the case depending on your tolerance for error, but the math will tell you that to some degree, that stub will affect your circuit no matter how small it is. It's up to you to determine, based on the math, whether you can tolerate the error introduced by simplifying your analysis to ignore it.

Now intuition certainly has its place in physics and engineering. However, I would argue that intuition answers the question "what" instead of "how" or "why" and comes from experience rooted in the math.

For example, when I look at a circuit design where there is a resistor in between two ICs, my intuition tells me the resistor is going to smooth the signal edges because it forms a low-pass filter with the receiver pin capacitance. That intuition tells me what is going to happen, and comes from experience and my basic understanding in the math behind filtering. Likewise, if I see the same circuit with a via instead of a resistor, my intuition tells me that via will create an open stub and can create reflections. The exact nature of those reflections depends on several factors including the via size, the board thickness, where it is along the trace, and the frequency of the signal and its harmonics. That's when I sit down and do some calculations or simulations to find the best place for that via or to find out if I need to get rid of it altogether.

Early on in your career, you will not have intuition about all the problems you encounter, and that is ok. As you are learning, focus on understanding the math / physics relating to fundamental equations and concepts. Once you gain experience in labs or in your job, the intuition will come naturally.

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For the shorted stub, consider a transmision line fed with opposite signals from impedance matched sources at each end.

what is the signal amplitude at the mid-point?

what signal do the sources see?

How does changing the length of the line change what is received?

What if the line is slightly lossy?

How much current would flow through a short placed at the midpoint? (no current in the short, all current is in the line conductors)

what would the sources see if instead of driving the line they were driving stubs half as long?
this is same as above but split in half. this time the current crosses between the conductors causing an inverted signal to return - in the double ended model these currents cancelled

Basically a shorted stub looks like a symmetrical inverted source twice as far away.

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