[Amps] antennas that are 1:1 vswr all over the band

[David Kirkby]

Dennis12Amplify at aol.com wrote:

> In a message dated 12/23/04 2:28:57 PM Central Standard Time, 
> david.kirkby at onetel.net writes:
>
>     You have a L in series with an R. You have a C in series with an
>     R. You
>     then put the series RC and series LC in parallel with each other.
>
>     Now make R=sqrt(L/C) and find the resonate frequency.
>
>     f=????
>
>  
>  I'll give it a try!

Good.

>  
>  
> F=1/(2pi*sqrt(L*C))    The standard resonance equation still applies....

No, that is not true. That equation is valid only for the series LC  or 
series LRC circuit. 

But it is *not* valid for a parallel circuit that has some resistance in 
one or both arms. It is a useful approximation if there is low 
resistance and exact if there is none, but can not be used in this case.

>  
>  But.....
>  
> At resonance XL=R and Xc=R (by your design requirement above).
> Providing equal leading and lagging branch circuit currents and 
> opposite phase shifts;
> and and overall Q=0.25
>  
>  With a Q of .25 you will have a very hard time seeing or measuring 
> any 'resonance' effect.

Again, you can't make an assumption. You are using formula that are 
approximations -  as such the Q is not 0.25, but will be lower.  
However, you are getting warm. You have realised the phase shifts on one 
arm lag and the other lead. Could they be made to cancel each other out?

Lets take some values, so people can plug it into their computers. 
Anyone with a computer modeling program should be able to give us a plot 
of VSWR vs frequency.

Let's arbitrarily choose L=2500H and  C=1F.  We must make R=sqrt(L/C), 
since I stated that in the original circuit I proposed. This come out at 
50 Ohms - how convenient !!  (If you want to test this on a board and 
don't have any 2500H inductors in your spares box, then instead use 
L=50nH, C=20pF, so again R=50 Ohms.)


Now 6 questions.

1) What impedance does this present at DC?

(The inductor will be effectively a short circuit and the capacitor 
effectively an open circuit, so this is easy to work out in your head 
without a calculator.)

2) What is the VSWR in a 50 Ohm system at DC? This follows from (1) of 
course. If you don't like the idea of a VSWR at DC, do it at 
0.0000000000000000000000000000000001 Hz instead. The answer will be 
****exactly**** the same.

3) What impedance does this present at an infinitely high frequency? 
(You can see the capacitor will be like a short circuit, and the 
inductor an open circuit), so again you can do this easily without too 
much thought.

4) What is the VSWR  in a 50 Ohm system at an infinity high frequency?  
This follows from (3) of course.

5) What is the impedance at 1.6 MHz, 50 MHz, 144 MHz or any other 
frequency you choose to pick?

This is more difficult to work out in your head, so you either have to 
analyse it fully if you know enough AC theory, or stick it into a 
computer program such as Spice and let it sort it out.

6) What is the VSWR at 1.6 MHz, 50 MHz or 144 MHz or any other frequency 
you choose to pick? This follows from (5) of course.

If you get the answers right to 2, 4, and 6, you will see how my circuit 
is relevant to the title of this post - it is also a Christmas quiz, 
although I am sorry there are no prizes.


G8WRB.