On 1/13/2011 11:05 AM, amdx wrote:
Hi All,
Please look at this in fixed font.
I'm looking for understanding of a series to parallel conversion for
antenna matching.
I'm pretty sure I'm missing something, so point it out to me.
This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.
The tank: L=240uh C=106pf Q = 1000
Tank Z =~1.5 Mohms
Here's my understanding of what I think I'm reading.
I put a matching capacitor in series with the antenna.
Antenna-- -----R-----C--------Match cap-----tank------ground.
and this is supposed to transform the circuit to this.
( Maybe better said, equivalent to this)

l------------l
l l
Antenna--- R C LC---Tank
l l
l------------l
^
Ground

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

So this; Antenna-- -----58R-----270pf--------Match
cap18.5pf-----1.5Mohms------ground.
This converts to;
l-----------------l
l l
Antenna---58R 17pf 1.5M---LC Tank at
l l Resonance
l-----------------l
^
Ground

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.
The purpose of which is to cause minimal loading of the tank by the antenna.
I don't understand how adding a series capacitor makes a parallel
conversion.
What do I misunderstand or do just need to believe the numbers.
Thanks, Mikek


Ah! After studying this for a while, I think I understand what you are
driving at.

Convert series 58R and 17 pF to a parallel equivalent. That is, take the
reciprocal of Z = 58 - 9368j to get Y = 661e-9 + 106.8e-6.

Now, what is the reciprocal of the real part of Y? That's 1/661e-9 or
about 1.5 Meg. So, the real part of the parallel equivalent now looks
like the resistance you are interested in.

Does this help?

Cheers,
John