Shut up and calculate wave guides

[Ahmad Kishki]

i have been using Pozar's microwave engineering so far in my electromagnetics courses, and i have become increasingly frustrated with its "shut up and calculate" approach. I am fed up. Wave guides are explained very poorly, with me wasting so much time to try to reason each step. The book isn't for undergraduates as its says in the preface, but our uni nevertheless follows it.

So, can i get recommendations for books about waveguides that don't follow such an attitude of "shut up and calculate"?

I am well versed in (undergraduate) electrodynamics having done a two semester course for it - but i am not well acquainted with transmission line theory. I am an undergraduate communications engineer.

Thank you

 

[jasonRF]

Could you give an example of what is frustrating? My copy of Pozar isn't with me right now, but I have always found it to be reasonable for most topics.

In any case, many engineering electromagnetics books cover this material. I would recommend looking at the following in your university library:

• Electromagnetic waves, by Inan and Inan (very well written in general)
• Electromagnetic waves and radiating systems, by Jordan and Balmain (tends to have a lot of words in-between equations to explain what is going on)
• Fields and waves in communication electronics, by Ramo, Whinnery and Van Duzer (very good for transmission lines and waveguides, in my opinion. One of the few books I have essentially worn out because I have used it so much)
• Field and wave electromagnetics, by Cheng (worth a look)
• Foundations for microwave engineering, by Collin (some like it better than Pozar, but I find Pozar to be more clear for most topics)

More importantly, look at other books that are shelved nearby these (especially ones with "engineering electromagnetics" in the title). You will likely find one that works for you, and since we all learn differently what works for you may not work for me!

A nice, free online book is at:

http://www.ece.rutgers.edu/~orfanidi/ewa/

jason

 

[Ahmad Kishki]

I am just frustrated at how pozar leaves many steps without explaining them. The thing that frustrated me the most was how we have a scalar potential field in TEM modes, i didnt feel that if the transverse component of the curl of e equals zero should imply a transverse scalar potential. Pozar doesn't even take the time to explain it, or how is it mathematically the way it is.

The free book looks very interesting, thank you for your well written answer :)

 

[jasonRF]

Collin (at least the first edition that I have) is very strong on the field theory analysis. For the particular issue you state, it is easiest (for me) to understand if I let z be the propagation direction and break up the electric field into $\mathbf{E} = \mathbf{E}_{xy} + \mathbf{E}_z$, with $\mathbf{E}_{xy} = E_x \hat{\mathbf{x}} + E_y \hat{\mathbf{y}}$ and $\mathbf{E}_z = E_z \hat{\mathbf{z}}$, and likewize for $\mathbf{H}$. Then Faradays law breaks up into two equations
$$\nabla \times \mathbf{E}_{xy} = -j \omega \mu \mathbf{H}_z$$
and
$$\nabla \times \mathbf{E}_z = -j \omega \mu \mathbf{H}_{xy}$$

For TEM waves, $\mathbf{H}_z = 0$, so the first equation is simply
$$\nabla \times \mathbf{E}_{xy} = 0.$$
This means that the line integral of $\mathbf{E}_{xy}$ around a contour confined to the xy plane will be zero. In other words,
$$\mathbf{E}_{xy} = - \nabla_{xy} \phi.$$
for some scalar potential, and I have defined $\nabla_{xy} = \hat{\mathbf{x}} \frac{\partial}{\partial x} + \hat{\mathbf{y}} \frac{\partial}{\partial y}$.

jason

 

[jasonRF]

Forgot to mention that the scalar potential is a function of x and y only. I also dropped a few steps:

The z dependence for TEM waves is assumed to be $\exp(- j \beta z)$. Thus all of hte field components are functions of x and y only, multiplied by the exponential factor for the z dependence. Then
$$\nabla \times \mathbf{E} = (\nabla_{xy} - j \beta \hat{\mathbf{z}}) \times (\mathbf{E}_{xy} + \mathbf{E_z}) = -j \omega \mu (\mathbf{H}_{xy} + \mathbf{H}_z)$$
or
$$\nabla_{xy} \times \mathbf{E}_{xy} - j \beta \hat{\mathbf{z}} \times \mathbf{E}_{xy} + \nabla_{xy} \times \mathbf{E}_z- j \beta \hat{\mathbf{z}} \times \mathbf{E}_z= -j \omega \mu (\mathbf{H}_{xy} + \mathbf{H}_z)$$
Then we use $\hat{\mathbf{z}} \times \mathbf{E}_z =0$, $\nabla_{xy} \times \mathbf{E}_z = \nabla_{xy} \times E_z \hat{\mathbf{z}} = -\hat{\mathbf{z}} \times \nabla_{xy}E_z$, and the fact that $\nabla_{xy} \times \mathbf{E}_{xy}$ only has z components to get the two Faraday's law equations in my previous post, which should be written:
$$\nabla_{xy} \times \mathbf{E}_{xy} = -j \omega \mathbf{H}_z$$
and
$$\nabla_{xy} \times \mathbf{E}_{z} - j \beta \hat{\mathbf{z}} \times \mathbf{E}_{xy} = -\hat{\mathbf{z}} \times \nabla_{xy} E_z - j \beta \hat{\mathbf{z}} \times \mathbf{E}_{xy} = -j \omega \mathbf{H}_{xy}$$
Note that this last equation was incorrect in my first post. sorry!
jason

 

[Meir Achuz]

Chapter 12 of this book <https://www.amazon.com/dp/0805387331/?tag=pfamazon01-20 derives the fields for waveguides and cavities.

 

[Ahmad Kishki]

Collin (at least the first edition that I have) is very strong on the field theory analysis. For the particular issue you state, it is easiest (for me) to understand if I let z be the propagation direction and break up the electric field into $\mathbf{E} = \mathbf{E}_{xy} + \mathbf{E}_z$, with $\mathbf{E}_{xy} = E_x \hat{\mathbf{x}} + E_y \hat{\mathbf{y}}$ and $\mathbf{E}_z = E_z \hat{\mathbf{z}}$, and likewize for $\mathbf{H}$. Then Faradays law breaks up into two equations
$$\nabla \times \mathbf{E}_{xy} = -j \omega \mu \mathbf{H}_z$$
and
$$\nabla \times \mathbf{E}_z = -j \omega \mu \mathbf{H}_{xy}$$

For TEM waves, $\mathbf{H}_z = 0$, so the first equation is simply
$$\nabla \times \mathbf{E}_{xy} = 0.$$
This means that the line integral of $\mathbf{E}_{xy}$ around a contour confined to the xy plane will be zero. In other words,
$$\mathbf{E}_{xy} = - \nabla_{xy} \phi.$$
for some scalar potential, and I have defined $\nabla_{xy} = \hat{\mathbf{x}} \frac{\partial}{\partial x} + \hat{\mathbf{y}} \frac{\partial}{\partial y}$.

jason

Thank you for the very well written solution. :) wish you all the success in life :)