I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek

On 1/23/2011 11:10 AM, amdx wrote:
I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek


I cheated. I used a Smith chart.

It is 170 - j530.

Cheers,
John

On Jan 23, 11:10*am, "amdx" wrote:
I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
*I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
*I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
*Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
*I need the R and the C of the antenna.http://i395.photobucket.com/albums/p...naat500Khz.jpg

* * *Thank you, Mikek

The Smith Chart says about 178+j521.

Gary N4AST

On 1/23/2011 11:10 AM, amdx wrote:
I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek

Work backwards. You have a 55 ohm resistor in series with a 310 ohm
reactance. Get the equivalent parallel combination of that (the complex
reciprocal). Take the reciprocal of the capacitor (just invert the Xc
and change the sign). Add the two complex numbers. Take the reciprocal
of the answer. This is the impedance the antenna sees looking into the
network. The antenna is the complex conjugate of that (just swap the
sign of the imaginary part).

Does this help?

John

Dear Mikek (no call sign):

Assuming that the inductor is 3 +j310 because it must have some loss and
calling the capacitor -j717, my trusty calculator estimates the antenna
looks like 159 -j526. The real part seems high - probably due to ground
losses.

However, the idea that even such a simple an antenna can be modeled as an R
and C over the AM broadcast frequency range seems unlikely.

An instrument such as the AIM4170C would provide Z with greater confidence
and do so at each frequency of interest. However, in the broadcast band it
is not clear that such a set of impedances can be used for something useful.
What is the actual goal?

Regards, Mac

"amdx" wrote in message ...

I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek


J. C. Mc Laughlin
Michigan U.S.A.
Home:

"John - KD5YI" wrote in message
...
On 1/23/2011 11:10 AM, amdx wrote:
I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the
band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek

Work backwards. You have a 55 ohm resistor in series with a 310 ohm
reactance. Get the equivalent parallel combination of that (the complex
reciprocal). Take the reciprocal of the capacitor (just invert the Xc and
change the sign). Add the two complex numbers. Take the reciprocal of the
answer. This is the impedance the antenna sees looking into the network.
The antenna is the complex conjugate of that (just swap the sign of the
imaginary part).

Does this help?

John

I don't know, I not there yet.

55 + i310
complex reciprocal
55 - i310 / 55^2 + 310^2
reduce
55 - i310 / 3025 + 96100
reduce further
55 - i310 / 99125
Take the reciprocal of the capacitor (just invert the Xc and change the
sign).
Xc = -i717 so 1/i717 ???
Add the two complex numbers.
(55 - i310 / 99125) + (1/i717)
Any mistakes yet?
Going further doesn't get me the answer you have.
Mikek

"J. C. Mc Laughlin" wrote in message
...
Dear Mikek (no call sign):

Assuming that the inductor is 3 +j310 because it must have some loss and
calling the capacitor -j717, my trusty calculator estimates the antenna
looks like 159 -j526. The real part seems high - probably due to ground
losses.

From what I have read it seems very high, could I have 130 ohms of ground
loss?
I don't think so.

I'll be looking into the ground, I think it is just a 6 foot rod, I put it
in years ago.
I'll add FWIW, I connected the AC ground from a receptacle and it made zero
change.

However, the idea that even such a simple an antenna can be modeled as an
R and C over the AM broadcast frequency range seems unlikely.

Ya, that's not the plan, I'll check it every 100 khz and make a graph, with
R and C.


An instrument such as the AIM4170C would provide Z with greater confidence
and do so at each frequency of interest. However, in the broadcast band
it is not clear that such a set of impedances can be used for something
useful. What is the actual goal?

I put the antenna up for multiple use, but to start, I want to use it with a
crystal radio,
the measurements may help me figure out the series cap (range) needed to
make an
R match to the tank circuit over the band.
And it's a project that forces me learn some math.
Thanks, Mikek





Regards, Mac

"amdx" wrote in message ...

I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the
band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek


J. C. Mc Laughlin
Michigan U.S.A.
Home:

On 1/23/2011 7:58 PM, amdx wrote:
"John - wrote in message
...
On 1/23/2011 11:10 AM, amdx wrote:
I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the
band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek

Work backwards. You have a 55 ohm resistor in series with a 310 ohm
reactance. Get the equivalent parallel combination of that (the complex
reciprocal). Take the reciprocal of the capacitor (just invert the Xc and
change the sign). Add the two complex numbers. Take the reciprocal of the
answer. This is the impedance the antenna sees looking into the network.
The antenna is the complex conjugate of that (just swap the sign of the
imaginary part).

Does this help?

John

I don't know, I not there yet.

55 + i310
complex reciprocal
55 - i310 / 55^2 + 310^2
reduce
55 - i310 / 3025 + 96100
reduce further
55 - i310 / 99125
Take the reciprocal of the capacitor (just invert the Xc and change the
sign).
Xc = -i717 so 1/i717 ???

??? = +.001395

Add the two complex numbers.
(55 - i310 / 99125) + (1/i717)
Any mistakes yet?

Well, no, but you should simplify here.

Going further doesn't get me the answer you have.

I can't tell why because you didn't show your work.

Mikek



Convert the series impedance 55 + j310 to its parallel equivalent
admittance (1/(55+j310) as follows:

1/(55+j310) = (55-j310)/(55+j310)(55-j310)

In other words, multiply the numerator AND denominator of 1/(55+j310) by
the conjugate (55-j310) of the denominator.

This gives (55-j310)/(3025+96100) or (55-j310)/99125 which is an
admittance of 554.85e-6-j3.127e-3.

The capacitor's parallel equivalent admittance is 1/(0-j717). So, when
numerator and denominator are multiplied by the conjugate we get

0+j717)/(0+514.089e3) or j717/514.089e3 which is 0+1.395e-3.

Now the sum of (554.85e-6 - j3.127) and (0 + 1.945e-6) is

554.855e-6 - j1.733e-3

This the parallel equivalent (the admittance) of your components and
what the antenna is seeing.

Following in the steps of my second and third sentences above, the
equivalent series impedance of your network looking back toward the
resistor is the reciprocal of that, or

167.63 + j523.5

This is the impedance the antenna sees. The antenna's equivalent
impedance is the conjugate of that. That is, the antenna looks like an
impedance of 167.63 - j523.5 according to your data.

A calculator that handles complex numbers is invaluable. I have one on
my computer's desktop. I also have an electronic Smith chart which is
usually faster. If you need a link, let me know.

This whole thing may look a bit complicated to you if you are not
familiar with complex numbers. Look up how to do X, /, +, - using
complex numbers and get familiar. It will help.

Cheers,
John

Dear Mikek: Thank you for your response. Knowing goals is important.

A great deal could be learned by using an antenna modeling computer program
such as EZNEC.

Note that my estimate of the antenna's Z is calculated with one assumption
(some loss in the series inductor) and that its calculations equate 55 + j0
to the impedance of the inductor, capacitor and antenna. Some of the
calculations I have seen seem to assume that one has applied 55 ohms and
then look backwards from the antenna.

Place my estimate of 159 -j526 in parallel with -j717 and then add (the
series) 3 + j310. You should fine the result to be
55.053 -j 0.0711 which is close to 55.

Maximizing the sensitivity of a semiconductor diode detector is probably
done empirically because of the difficulty of finding an appropriate model
for the non-linear detector. Expect that the apparent answer will be
amplitude dependent.

Do report you findings. Regards, Mac

"amdx" wrote in message ...


"J. C. Mc Laughlin" wrote in message
...
Dear Mikek (no call sign):

Assuming that the inductor is 3 +j310 because it must have some loss and
calling the capacitor -j717, my trusty calculator estimates the antenna
looks like 159 -j526. The real part seems high - probably due to ground
losses.

From what I have read it seems very high, could I have 130 ohms of ground
loss?
I don't think so.

I'll be looking into the ground, I think it is just a 6 foot rod, I put it
in years ago.
I'll add FWIW, I connected the AC ground from a receptacle and it made zero
change.

However, the idea that even such a simple an antenna can be modeled as an
R and C over the AM broadcast frequency range seems unlikely.

Ya, that's not the plan, I'll check it every 100 khz and make a graph, with
R and C.


An instrument such as the AIM4170C would provide Z with greater confidence
and do so at each frequency of interest. However, in the broadcast band
it is not clear that such a set of impedances can be used for something
useful. What is the actual goal?

I put the antenna up for multiple use, but to start, I want to use it with a
crystal radio,
the measurements may help me figure out the series cap (range) needed to
make an
R match to the tank circuit over the band.
And it's a project that forces me learn some math.
Thanks, Mikek





Regards, Mac

"amdx" wrote in message ...

I put up a long wire antenna, it is an inverted C.
The antenna is resonant at 3.55 Mhz.
I want to characterize it an the AM broadcast band.
I have made a measurement at 500 Khz and I had to install a parallel
capacitor
to get my variable inductor to bring phase to zero.
I don't know how to do the math to find the impedance of the antenna
with the L and C in the circuit.
Can someone look at my drawing and give me the math so I can figure out
the impedance. Then I can get the numbers at other frequencies for the
band
and calculate those impedances.
See drawing here. I want to calculate the Unknown Impedance.
I need the R and the C of the antenna.
http://i395.photobucket.com/albums/p...naat500Khz.jpg

Thank you, Mikek


J. C. Mc Laughlin
Michigan U.S.A.
Home:

"J. C. Mc Laughlin" wrote in message
.. .
Dear Mikek: Thank you for your response. Knowing goals is important.

A great deal could be learned by using an antenna modeling computer
program such as EZNEC.

Note that my estimate of the antenna's Z is calculated with one assumption
(some loss in the series inductor) and that its calculations equate 55 +
j0 to the impedance of the inductor, capacitor and antenna. Some of the
calculations I have seen seem to assume that one has applied 55 ohms and
then look backwards from the antenna.

Place my estimate of 159 -j526 in parallel with -j717 and then add (the
series) 3 + j310. You should fine the result to be
55.053 -j 0.0711 which is close to 55.

Maximizing the sensitivity of a semiconductor diode detector is probably
done empirically because of the difficulty of finding an appropriate model
for the non-linear detector. Expect that the apparent answer will be
amplitude dependent.

Do report you findings. Regards, Mac


"J. C. Mc Laughlin"

Hi J. C.
If your interested in the diode characterists Ben Tongue has done a lot of
crystal radio work.
http://www.bentongue.com/xtalset/xtalset.html
Articles 6, 7, 8, 9 , 10, 15A, 16, 17A, 27 and 28 are all about detector
diodes and there characteristics.
Thanks, Mikek