×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

lpda design

lpda design

(OP)
In the design of a log periodic one of the key steps is identifying the avarage characteristic impedance of a dipole. For a typical application see http://www.conformity.com/0005emc.html. The expression for this is given as 120*ln[(L/D) - 2.25)], where L is the length of the dipole and D the diameter. Does anyone know the origins of this expression, and how it was derived? The only time I have ever seen it is with reference to LPDA design.

Any help would be appreciated.

RE: lpda design

ref. www.salsburg.com/Log-Periodic.pdf (?)

Obviously the units of length and diameter don't matter since they're cancelled out. The "120" is probably the same 120 as the exact value of the Zo of free space (120*Pi = 377 ohms).  The "2.25" looks like it might be a 'conglomeration' of several other constants.

The formula is obviously incomplete (simplified) because it doesn't include the spacing between the ends of the dipole elements at the feedpoint.  Imagine if the dipole elements were of very large diamter and brought very close together - they could form an easily adjustable (spacing) capacitor across the feedpoint.  Obviously you could then make the element lengths slightly longer or shorter and have some ability to tune your antenna to different feedpoint impedances.

RE: lpda design

(OP)
Thanks much for the comments. The salsburg.com ref is the Peter Rhodes, K4EWG, write up on the log periodic from the ARRL Ant. HB of 1974. I suspect that much of it was based on the work of Carrel and Isbell, listed in the bibliography.

I think the expression is most like the one for the reactance of a dipole: j120*ln(L/D)-1]/tan(pi*L/lambda).

Simplified though the expression may be, it seems to work. For example, if I model lpda designs using numbers from the nomogram for Ro,SWR, tau given in the Rhodes reference you mention, it works for Ro values between 60 and 90 ohms.

The reason for the original question is that I was wondering if I could rely on it for making a pcb based lpda.
My feeling is that the dipole impedance term would have to be modified by a velocity factor that was a mix of air and pcb dialectric. However, given that the impedance of a dipole in an array is found by solving a complex matrix consisting of self and mutual impedances, I guess I'm just amazed the expression works at all.

Maybe if I could figure out exactly what the original expression was intended to represent, I could substitute the correct value into the expression in the Rhodes reference for phase line impedance. Since the latter expression is a function of tau, sigma, Ro and dipole impedance, I'm guessing I could use it for pcb designs if I could get the dipole term right - so it would help if I knew where it came form or how it was derived. I have some early Carrel and Isbell papers on order. Maybe I'll find an answer in one of them.

RE: lpda design

Check out "Antenna Enginerring Handbook" by Henry Jasik first edtion chapter 18, section 3 (pages 18-10 thru 18-32)for some insight.
Note: See page 14-3 in the second edtion version of the same book :"Antenna Enginerring Handbook" by Richard Johnson & Henry Jasik.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Resources

Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a partâ€™s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!