Hi Group,

I have a pi-network, or at least I believe it is a pi-network in my
antenna tuner. It has two caps to ground and one in series inductor.

If I tune my SWR for 1:1 and go back and measure each value of the
capacitors and inductor, is there a equation or computer program I can
use these measured values to obtain my complex impedance at the input
of the coax cable?

de KJ4UO

Arn't you going around your hindparts to get to your elbow?

Connect an MFJ259B or similar and measure at the coax.

Once these valuses are measured at the frequency of interest, you can
determine from the tuners specs if you will be able to achieve a match. If
you can already achieve a match isn't determining the value simply a neat
mental exercise?

wrote in message
ups.com...
Hi Group,

I have a pi-network, or at least I believe it is a pi-network in my
antenna tuner. It has two caps to ground and one in series inductor.

If I tune my SWR for 1:1 and go back and measure each value of the
capacitors and inductor, is there a equation or computer program I can
use these measured values to obtain my complex impedance at the input
of the coax cable?

de KJ4UO

On 31 Jul 2005 21:01:19 -0700, "
wrote:

Hi Group,

I have a pi-network, or at least I believe it is a pi-network in my
antenna tuner. It has two caps to ground and one in series inductor.

If I tune my SWR for 1:1 and go back and measure each value of the
capacitors and inductor, is there a equation or computer program I can
use these measured values to obtain my complex impedance at the input
of the coax cable?

You ought to be able to do it from first principles, the computation
is not that difficult.

Some of the issues include your estimate of the value of the
capacitors, the value of inductance, and the Q of the inductor. You
could try to form a value for those by substitution of some known
capacitors and "matching up" a known load, working back to estimate C,
L, then use those values to solve the unknown case. The accumulated
error might render the answer of little value.

One program that springs to mind that solves a pi network is in the
Hamcalc suite, but IIRC, it treats all components as ideal (ie
lossless). Reg Edwards has another that you could play with, and IIRC,
it does allow you to specify unloaded Q of the inductor.

Have a play, you have nothing to lose and everything to learn!

Owen
--

On 31 Jul 2005 21:01:19 -0700, "
wrote:
I have a pi-network, or at least I believe it is a pi-network in my
antenna tuner. It has two caps to ground and one in series inductor.

If I tune my SWR for 1:1 and go back and measure each value of the
capacitors and inductor, is there a equation or computer program I can
use these measured values to obtain my complex impedance at the input
of the coax cable?

Hi OM,

Good time to learn the Smith Chart. The components in that network
are simply arcs moving the presented Z to the transformed Z (50Ohms).
Unfortunately this is easier said than done - or understood. Like all
skills, time and practice are necessary.

As for understanding, the Smith Chart will bring that quicker than any
software - which simply dumps an answer in your lap, the quality or
actual utility of which is as much a mystery as the problem you wanted
to solve. There are a multitude of network settings that will satisfy
the matching and software or equations will do little more than say
"yup, that setting does exactly as you observed." Not very filling,
but when you do the same thing on the Chart, you can see where you are
going before you get there. This means you also have the choice of
choosing the best path (shortest). It would be a rare piece of code
that could do that - from a mountain of formulas.

73's
Richard Clark, KB7QHC

On 31 Jul 2005 21:01:19 -0700, "
wrote:

Hi Group,

I have a pi-network, or at least I believe it is a pi-network in my
antenna tuner. It has two caps to ground and one in series inductor.

If I tune my SWR for 1:1 and go back and measure each value of the
capacitors and inductor, is there a equation or computer program I can
use these measured values to obtain my complex impedance at the input
of the coax cable?

de KJ4UO


I would caution you in regard to measuring the values of the C's and
the L of your pi network. If you actually have an RF bridge or other
test equipment suitable for accurately making such measurements, you
are indeed lucky. Even with such equipment, you should realize that
you will have to disconnect certain components from one another in the
tuner in order to actually make the measurements on each of the three
components. You are also probably going to have to remove some of
those components entirely in order to make the measurements with
reasonably short leads. For anything below 10 MHz, the lead length
will not be a significant factor.

Assuming that you are successful in making the measurements with good
accuracy, the necessary calculations require a good knowledge of
complex numbers and complex arithmetic - much of which is adequately
explained in the Amateur Radio Handbook.

My suggestion at that point would be to simply post your results,
including the frequency of measurement, to this forum and request that
one of us make the calculations for you. I'm sure many, including
myself, would be glad to do that for you. It's the quickest way, by
far.


Bob, W9DMK, Dahlgren, VA
Replace "nobody" with my callsign for e-mail
w9dmkatcrosslinkdotnet
http://www.qsl.net/w9dmk
http://zaffora/f2o.org/W9DMK/W9dmk.html

If he has an RF bridge, couldn't he simply terminate the tuner's input
with 50 ohms resistive and measure the impedance at the tuner's output?
Well, the conjugate, anyway. I'm trying to imagine the benefit of doing
it that way, rather than simply measuring the impedance at the
transmission line directly.

Chuck,
NT3G

W9DMK (Robert Lay) wrote:
On 31 Jul 2005 21:01:19 -0700, "
wrote:


Hi Group,

I have a pi-network, or at least I believe it is a pi-network in my
antenna tuner. It has two caps to ground and one in series inductor.

If I tune my SWR for 1:1 and go back and measure each value of the
capacitors and inductor, is there a equation or computer program I can
use these measured values to obtain my complex impedance at the input
of the coax cable?

de KJ4UO



I would caution you in regard to measuring the values of the C's and
the L of your pi network. If you actually have an RF bridge or other
test equipment suitable for accurately making such measurements, you
are indeed lucky. Even with such equipment, you should realize that
you will have to disconnect certain components from one another in the
tuner in order to actually make the measurements on each of the three
components. You are also probably going to have to remove some of
those components entirely in order to make the measurements with
reasonably short leads. For anything below 10 MHz, the lead length
will not be a significant factor.

Assuming that you are successful in making the measurements with good
accuracy, the necessary calculations require a good knowledge of
complex numbers and complex arithmetic - much of which is adequately
explained in the Amateur Radio Handbook.

My suggestion at that point would be to simply post your results,
including the frequency of measurement, to this forum and request that
one of us make the calculations for you. I'm sure many, including
myself, would be glad to do that for you. It's the quickest way, by
far.


Bob, W9DMK, Dahlgren, VA
Replace "nobody" with my callsign for e-mail
w9dmkatcrosslinkdotnet
http://www.qsl.net/w9dmk
http://zaffora/f2o.org/W9DMK/W9dmk.html

I have an MFJ-269 which I can measure the input to the coax and get a
direct impedance measurement.

Then I would put the tuner in line with the MFJ-269 as the source and
adjust the tuner until I see 50 + j0 on the MFJ.

I would follow by measuring the pi-network components also using the
MFJ as it will measure values at the desired RF frequency.

I would keep the signal frequency low so that stray inductance and
capacitance do not affect the measurement.

What I would like to do is see by using the values I obtain, calculate
the cable load and compare with MFJ direct measurement.

I will review the handbook to see if there is a standard equation
knowing the values and assume that the Q of the inductor is greater
than 10.




All in the fun of the hobby.


de KJ4UO

That's a worthwhile educational exercise.

You might find a single equation, but it gets a bit messy. However, it's
easily done in a few steps, if you're comfortable with complex
arithmetic. I use an HP48GX calculator for this sort of thing, since it
readily and directly handles complex numbers.

Call the capacitor on the input side of the network C1 and the on the
output side C2, and the inductor L. First calculate the reactance of
each of them at the frequency of interest, Xc1, Xl, and Xc2. You'll find
formulas for those in the Handbook. Note that Xc1 and Xc2 will be
negative and Xl will be positive.

First calculate the parallel combination of the load impedance (Zl) and
Xc2. That will be the impedance seen looking toward the load from the
output side of the inductor: Za = Zl || Xc2 = (Rl + jXl) || (jXc2),
where Xc2 is negative. The combined impedance of two impedances Z1 and
Z2 in parallel are 1 / ((1/Z1) + (1/Z2)) = (Z1 * Z2) / (Z1 + Z2).

Now add Xl to your result to find the Z looking into the input side of
the inductor: Zb = Za + jXl. (If the inductor has appreciable loss, use
Zl = Rl + jXl instead of just jXl.) Finally, calculate the parallel
combination of that impedance and the impedance of the input capacitor
to find the impedance looking into the network: Zin = Zb || jXc1,
remembering that Xc1 will be negative.

You can of course combine all this into one equation, but it gets pretty
big. I prefer to do it in steps, one of the reasons being that I
understand exactly what I'm doing at each step rather than just dumping
numbers into an equation and hoping that what comes out is right. A
Smith Chart gives you an even better feel for what's going on, and this
would be a good opportunity to get acquainted with that valuable tool.
You might solve the problem both arithmetically and by using the Smith
Chart and compare results.

If you aren't comfortable with complex arithmetic, the equations get
considerably more complicated since you'll have to deal with the
resistance and reactance separately. If that's the case, I second the
advice already given that you either solve it using a Smith Chart or
consider just letting one of the other folks on this group do the
calculation for you.

Roy Lewallen, W7EL

wrote:
I have an MFJ-269 which I can measure the input to the coax and get a
direct impedance measurement.

Then I would put the tuner in line with the MFJ-269 as the source and
adjust the tuner until I see 50 + j0 on the MFJ.

I would follow by measuring the pi-network components also using the
MFJ as it will measure values at the desired RF frequency.

I would keep the signal frequency low so that stray inductance and
capacitance do not affect the measurement.

What I would like to do is see by using the values I obtain, calculate
the cable load and compare with MFJ direct measurement.

I will review the handbook to see if there is a standard equation
knowing the values and assume that the Q of the inductor is greater
than 10.




All in the fun of the hobby.


de KJ4UO

On Mon, 01 Aug 2005 12:21:59 GMT, chuck wrote:

If he has an RF bridge, couldn't he simply terminate the tuner's input
with 50 ohms resistive and measure the impedance at the tuner's output?
Well, the conjugate, anyway. I'm trying to imagine the benefit of doing
it that way, rather than simply measuring the impedance at the
transmission line directly.

Chuck,
NT3G

I will break my own rule of not responding to responders and answer
your question - otherwise you would assume that I was ignoring you.

If I might answer a question with a question - why do you think that a
tuner would give up its settings so easily? It's a an interesting
speculation. First, let me clarify what I mean by a Tuner's input
terminal and its output terminal. Considering that a tuner handles
transmitted power in one direction only, we should refer to its
"input" side as the port that connects to the transmitter and its
"output" port as the one connecting to the antenna or feedline.

That agrees with what I interpret your post as suggesting. Therefore,
a 50 ohm termination at the "input" side "should" produce a measured
impedance at the "output" port that is, as you say, the complex
conjugate of the impedance seen looking into the transmission line. I
haven't done a rigorous analysis of that configuration, but it
certainly seems reasonable and correct. It would, indeed be an optimum
way of inferring the impedance that the original poster is trying to
measure.

I see nothing wrong with your suggestion and would recommend it.

I also see no reason to do any of that as it would be just as easy to
measure the transmission line input impedance directly - as you said.

It's amazing how much good stuff comes out of the woodwork when people
are interested in their hobby and interested in learning.

Thanks,

Bob, W9DMK, Dahlgren, VA
Replace "nobody" with my callsign for e-mail
w9dmkatcrosslinkdotnet
http://www.qsl.net/w9dmk
http://zaffora/f2o.org/W9DMK/W9dmk.html

If the tuner can cope, there's not much interest in what the input
impedance of the transmission line is.

What IS of interest is what impedance terminates the remote end of the
transmission line. Usually this is the antenna. And usually this is
impractical to measure directly.

From the input impedance of the transmission line, Program ZL_ZIN
computes the input impedance of the antenna (or whatever may be at the
other end ). It is also necessary to know the length of the line and
its Zo.

Download in a few seconds program ZL_ZIN from website below and run
immediately,
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........