how to measure antenna impedance ?
 

All,

I am trying to measure antenna impedance. For this I intend to us a directional
coupler to isolate reflected signal. After using the coupler for a while I
believe that it introduces a phase shift, that shift seems to be related to
frequency. This creates a bit of a catch 22. Antenna resonance is defined as the
frequency where there is no reflected complex component. If the tool to measure
this is also frequency dependent how can this be accomplished? Is this even the
best method?

Do bi-directional couplers automatically compensate for frequency shift?

Thanks - Dan kb0qil

how to measure antenna impedance ?
 

Hi Dan

Normally you would calibrate your test gear against a known resistive
load first. If you coupler creates a phase shift that can be compensated
for either in the test equipment or by varying the feedline length.
(ouch!) All the network analysers I have used allow you to calibrate
50r, open or short.

You can further test you setup by measuring known lengths of coax
"stubs" that would present a reactive load.

I imagine a directional coupler would introduce a phase shift as it has
an electrical length that must be allowed for.

I saw a real impressive antenna impedence measuring device that used
coaxial cable as the tuned reference elements. It was of course
frequency dependent. It was made for 2M but I guess the design would be
easy to replicate for other frequencies given. It has about 10% usable
bandwidth. I was going to make one for HF with BNC terminated coax
lengths for each band, but never did!

Go to http://www.vhfdx.oz-hams.org/and Measurements

or

http://www.vhfdx.oz-hams.org/docs/ZMeterVK2ZAB.pdf

Apologies for not answering your exact questions.


Cheers Bob W5/VK2YQA


dansawyeror wrote:


All,

I am trying to measure antenna impedance. For this I intend to us a
directional coupler to isolate reflected signal. After using the coupler
for a while I believe that it introduces a phase shift, that shift seems
to be related to frequency. This creates a bit of a catch 22. Antenna
resonance is defined as the frequency where there is no reflected
complex component. If the tool to measure this is also frequency
dependent how can this be accomplished? Is this even the best method?

Do bi-directional couplers automatically compensate for frequency shift?

Thanks - Dan kb0qil

how to measure antenna impedance ?
 

I am trying to measure antenna impedance. For this I intend to us a
directional coupler to isolate reflected signal. After using the coupler
for a while I believe that it introduces a phase shift, that shift seems
to be related to frequency. This creates a bit of a catch 22. Antenna
resonance is defined as the frequency where there is no reflected complex
component. If the tool to measure this is also frequency dependent how can
this be accomplished? Is this even the best method?

Do bi-directional couplers automatically compensate for frequency shift?

Thanks - Dan kb0qil

What you are measuring with a directional coupler is the complex reflection
coeficiant. If the measurement is for low frequencies (i.e. 30 MHz), and
the load is at the input of the directional coupler, then you will probably
obtain a realistic figure for complex "Gamma". Ideally you need a short
circuit, open circuit, and 50 ohm load to determine if the system is
calibrated.

Short circuit Gamma = 1 180
Open circuit Gamma = 1 0
50 Ohm Gamma = 0

If the load is at the end of a length of coaxial cable you have to
comphensate for the phase shift error at every measurement frequency.

Since you are dealing with complex numbers it is tedious to determine the
actual load impedance. The following app. note should help:

http://www.maxim-ic.com/appnotes.cfm/appnote_number/742

HP's app. note at http://www.sss-mag.com/pdf/hpan95-1.pdf is also very
helpful.

Regards,

Frank

how to measure antenna impedance ?
 

Network analyzers incorporate a concept called a "reference plane". This
is a theoretical point at which the measurement is actually made. It's
desirable to have this point be at the DUT connector. (In precision
and/or extremely high frequency measurements, the point within the
connector becomes important, and even a sex-change adapter can't be
tolerated between calibration and measurement.) Software in the network
analyzer is told where the reference plane is to be by means of a rather
involved calibration procedure, then the network's software corrects for
the phase shift and impedance magnitude transformation of the cable
between the reference plane and the analyzer itself. It effectively
makes the reference plane the point being measured, rather than the
analyzer input terminal.

When you make manual measurements, you have to do the correction
yourself. So what you need to know is the impedance and length of the
line between your point of measurement and the DUT. This can be
determined in the same way as it's done for some network analyzer
calibrations -- by measuring the impedance with the DUT replaced with a
short circuit, an open circuit, and a known load impedance, then solving
the resulting set of simultaneous equations. Once you know the impedance
and length of the cable between where your measurement is correct and
the DUT, you can calculate the actual DUT impedance from your measured
value. I do this routinely at HF, when I measure antenna impedance at
the input end of a transmission line. Accuracy is best when the
impedance being measured isn't far from the Z0 of the transmission line,
and the transmission line is short. The longer the line and the greater
the difference between line Z0 and DUT impedance, the greater the
sensitivity to measurement error in both the measured DUT impedance and
the line Z0 and length. A surprisingly small amount of line loss can
also skew the measurements quite badly if Z0 and DUT impedance are quite
different. If you need accurate results, you should do an error analysis
to see how far off your calculated result can be, given the estimated
accuracy of your measurement and calibration.

As I mentioned in my earlier posting, most people overestimate their
ability to make accurate RF measurements. It's not at all trivial. Be
sure to check your results frequently by measuring known load impedances
close to the values being measured. How do you find the values of those
"known" load impedances? Well, welcome to the world of metrology!

Roy Lewallen, W7EL

how to measure antenna impedance ?
 

On Sat, 03 Dec 2005 21:13:36 -0800, Roy Lewallen
wrote:

As I mentioned in my earlier posting, most people overestimate their
ability to make accurate RF measurements. It's not at all trivial. Be
sure to check your results frequently by measuring known load impedances
close to the values being measured. How do you find the values of those
"known" load impedances? Well, welcome to the world of metrology!

Roy, I've seen your postings hereabouts over the years and you've
always struck me as one of the most knowledgeable posters on this,
*the* most technically-challenging of all hobbies.
I've recently bought a VNA and am going about the laborious process of
setting it up with precisely-cut interconnects to the T/R bridge. Next
thing I need to know is...
Say I have a mica capacitor (for example) that I want to check for its
SRF. How should I mount this component so as to minimize stray L&C
from anything other than the component itself? IOW, what 'platform'
(for want of a better word) do I need to construct to permit accurate
measurements of this cap's RF characteristics in isolation?
Thanks,
Paul
--

"What is now proved was once only imagin'd" - William Blake

how to measure antenna impedance ?
 

On Sat, 03 Dec 2005 17:33:18 -0800, dansawyeror
wrote:

All,

I am trying to measure antenna impedance. For this I intend to us a directional
coupler to isolate reflected signal. After using the coupler for a while I
believe that it introduces a phase shift, that shift seems to be related to
frequency. This creates a bit of a catch 22. Antenna resonance is defined as the
frequency where there is no reflected complex component. If the tool to measure
this is also frequency dependent how can this be accomplished? Is this even the
best method?

This depends a lot on what instrument you are connecting to this
coupler. If it's nothing more than a power sensor, then you are
making scalar measurements and phase is meaningless.

You would calibrate by placing a short on the measurement (antenna)
port and getting a 100% reflection reference (rho=1). You would
determine the magnitude of the reflection coefficient by ratioing this
to the measured value.

If you have a magnitude and phase sensitive instrument (vector
analyzer) then, as others have answered, you calibrate with additional
reference standards. In any event, the phase shift through the
coupler is compensated for by the calibration process.


Do bi-directional couplers automatically compensate for frequency shift?


No. The provide for a simultaneous sample of the forward and
reflected signals.

how to measure antenna impedance ?
 

Wes,

Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected signals
changed by the same about?

Thanks - Dan kb0qil


Wes Stewart wrote:
On Sat, 03 Dec 2005 17:33:18 -0800, dansawyeror
wrote:


All,

I am trying to measure antenna impedance. For this I intend to us a directional
coupler to isolate reflected signal. After using the coupler for a while I
believe that it introduces a phase shift, that shift seems to be related to
frequency. This creates a bit of a catch 22. Antenna resonance is defined as the
frequency where there is no reflected complex component. If the tool to measure
this is also frequency dependent how can this be accomplished? Is this even the
best method?


This depends a lot on what instrument you are connecting to this
coupler. If it's nothing more than a power sensor, then you are
making scalar measurements and phase is meaningless.

You would calibrate by placing a short on the measurement (antenna)
port and getting a 100% reflection reference (rho=1). You would
determine the magnitude of the reflection coefficient by ratioing this
to the measured value.

If you have a magnitude and phase sensitive instrument (vector
analyzer) then, as others have answered, you calibrate with additional
reference standards. In any event, the phase shift through the
coupler is compensated for by the calibration process.


Do bi-directional couplers automatically compensate for frequency shift?



No. The provide for a simultaneous sample of the forward and
reflected signals.

how to measure antenna impedance ?
 

Wes,

Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected signals
changed by the same about?

Thanks - Dan kb0qil


Wes Stewart wrote:
On Sat, 03 Dec 2005 17:33:18 -0800, dansawyeror
wrote:


All,

I am trying to measure antenna impedance. For this I intend to us a directional
coupler to isolate reflected signal. After using the coupler for a while I
believe that it introduces a phase shift, that shift seems to be related to
frequency. This creates a bit of a catch 22. Antenna resonance is defined as the
frequency where there is no reflected complex component. If the tool to measure
this is also frequency dependent how can this be accomplished? Is this even the
best method?


This depends a lot on what instrument you are connecting to this
coupler. If it's nothing more than a power sensor, then you are
making scalar measurements and phase is meaningless.

You would calibrate by placing a short on the measurement (antenna)
port and getting a 100% reflection reference (rho=1). You would
determine the magnitude of the reflection coefficient by ratioing this
to the measured value.

If you have a magnitude and phase sensitive instrument (vector
analyzer) then, as others have answered, you calibrate with additional
reference standards. In any event, the phase shift through the
coupler is compensated for by the calibration process.


Do bi-directional couplers automatically compensate for frequency shift?



No. The provide for a simultaneous sample of the forward and
reflected signals.

how to measure antenna impedance ?
 

Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected
signals changed by the same about?

Thanks - Dan kb0qil

The phases seen at each coupled port should be identical to the phase of the
forward and reflected signals. This is easily verifiable, and frequency
independant, as follows:

No load -- forward and reverse amplitudes equal, and in phase;
Short circuit at output -- forward and reverse amplitudes equal, and 180
degrees phase difference;
50 ohm load -- reverse than forward by = specified coupler directivity,
and phase difference can 0 theta +/ 180.

This is only true if the frequencies are low enough such that the standards
do not require quantification by the use of "Standard definitions" -- see
www.vnahelp.com.


Regards,

Frank

how to measure antenna impedance ?
 

On Sun, 04 Dec 2005 15:25:51 +0100, Paul Burridge
k wrote:

Say I have a mica capacitor (for example) that I want to check for its
SRF. How should I mount this component so as to minimize stray L&C
from anything other than the component itself? IOW, what 'platform'
(for want of a better word) do I need to construct to permit accurate
measurements of this cap's RF characteristics in isolation?

Hi Paul,

Accuracy and precision is no good unless you can duplicate the test
rig to the eventual environment of use. That said, precision
capacitors and inductors are three leaded devices. The third lead
goes to the shield around them. Obviously for either, a shield
changes what would have been the nominal value for the component.
However, that change also swamps all the variables that could disturb
the accuracy. In other words, the shield enforces a fixed environment
that reduces all other stray influences to a minimum.

In so doing, I've been able to measure standard capacitors and
inductors out to 9 places. Without those third lead configurations,
the same components would easily lose 3, 4, or 5 of those digits.

So one way to mount a mica cap would be over and close to a ground
plane that extends beyond its foot print by a significant distance.
This proximity would swamp the effects of other components nearby
causing a shift in the resonance (if and when they were added, or
removed). Building a cage around the capacitor would reduce these
effects even further. Of course, all such measures would shift the
native resonance, but you are never going to achieve that frequency
anyway.

You can, of course, elect to go the other way with a minimal ground
proximity. In that case you would use microstrip techniques to build
the test rig, making the strip with equal to the width of the
component (presumably being surface mount). However, SRF becomes
rather meaningless except as a general indicator. This is because
changing the board material from alumina to epoxy; or changing from a
series to shunt application can shift this frequency by 20% to 40%.

Another issue is with the leads themselves. ESR for caps can easily
tally up to a tenth of an Ohm and you have to select your caps on this
basis as much as for their inductance. In this regard, you measure
the D of the cap (dissipation factor) not Q (although each is the
inverse of the other, there are D instruments specifically for this).
This tenth Ohm is NOT necessarily in the wire lead (a common
misconception) but rather in all the parallel (or worse, series of the
wrapped cap) plate connections. For surface mount caps, you may want
to mount them 90° (up on edge rather than flat on face) to the board
to double the first PRF resonance and reduce the insertion losses
there and above.

The short answer to your question is how stable, and how accurate do
you want to reproduce the measurement to your application?

73's
Richard Clark, KB7QHC

how to measure antenna impedance ?
 

dansawyeror wrote:
Do the measuring ports of a bi-directional coupler accurately represent
or preserve the relative phases of the signal?

Let's look at a typical SWR meter sampling circuit. The current is
sampled by a one turn primary on a ferrite toroid. The voltage is
sampled by a tap on the line close to the point at which the toroid
is mounted. At HF frequencies, a wavelength is so long compared to
that configuration that physical sample point errors are usually
considered to be negligible. That obviously changes at UHF+.

No coupler 100% preserves the relative phases. The question is:
What is the accuracy? For any configuration, a worst-case accuracy
can be specified. At 4 MHz, it's not a problem. At 4 GHz, it's a
big problem. At visible light frequencies, most don't even try.
--
73, Cecil http://www.qsl.net/w5dxp

how to measure antenna impedance ?
 

Frank,

The bi-directional coupler is a machined block about 1 x 3 x 5. The inside is a
straight through line, the pickups are simply terminated one loop lines. It is a
UHF coupler that works reasonably down to 2 meters. When I configure this to
look at the forward and reflected 'open' circuit case they are not in phase.
Reflected lags forward by about 40 degrees. (I checked the connection delay and
this is not a cable issue.) This is frequency independent. Shorting the output
reverses this relationship. The outputs are terminated in 50 Ohms so I conclude
it is a 50 Ohm device. When I terminate the device in 50 Ohms the forward and
reflected outputs are out of phase by about 140 degrees.

What is the significance a non frequency dependent phase shift between forward
and reflected? This shift is frequency independent.

Thanks - Dan kb0qil


Frank wrote:
Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected
signals changed by the same about?

Thanks - Dan kb0qil


The phases seen at each coupled port should be identical to the phase of the
forward and reflected signals. This is easily verifiable, and frequency
independant, as follows:

No load -- forward and reverse amplitudes equal, and in phase;
Short circuit at output -- forward and reverse amplitudes equal, and 180
degrees phase difference;
50 ohm load -- reverse than forward by = specified coupler directivity,
and phase difference can 0 theta +/ 180.

This is only true if the frequencies are low enough such that the standards
do not require quantification by the use of "Standard definitions" -- see
www.vnahelp.com.


Regards,

Frank

how to measure antenna impedance ?
 

Paul Burridge wrote:
On Sat, 03 Dec 2005 21:13:36 -0800, Roy Lewallen
wrote:


As I mentioned in my earlier posting, most people overestimate their
ability to make accurate RF measurements. It's not at all trivial. Be
sure to check your results frequently by measuring known load impedances
close to the values being measured. How do you find the values of those
"known" load impedances? Well, welcome to the world of metrology!


Roy, I've seen your postings hereabouts over the years and you've
always struck me as one of the most knowledgeable posters on this,
*the* most technically-challenging of all hobbies.

Thanks for your vote of confidence. But on the topic of network analyzer
measurements, I gladly defer to Wes Stewart, Tom Bruhns, and other
posters who have spent much more time making real-life measurements with
them than I have. I've used them from time to time, and for some really
challenging measurements, but not by any means as much as those folks have.

I've recently bought a VNA and am going about the laborious process of
setting it up with precisely-cut interconnects to the T/R bridge. Next
thing I need to know is...
Say I have a mica capacitor (for example) that I want to check for its
SRF. How should I mount this component so as to minimize stray L&C
from anything other than the component itself? IOW, what 'platform'
(for want of a better word) do I need to construct to permit accurate
measurements of this cap's RF characteristics in isolation?

In general, you minimize stray inductance by keeping leads short, and
capacitance by keeping conductors apart. The ideal setup is a coaxial
environment right up to the DUT, but even that is subject to coupling
around the DUT, both from one terminal to the other and from each
terminal to ground. If possible, the best plan is to calibrate out the
strays. That's a science and art in itself, and I'll have to yield to
people with more experience than mine for practical information about
how best to do this.

The effect of the strays depends heavily on what you're measuring. For
example, if you're measuring a low impedance, you can get by with more
shunt C than if you're measuring a high impedance. If you're measuring a
high impedance, you can tolerate more series inductance than when
measuring a low impedance. So when you inevitably find that you have to
make tradeoffs in designing a fixture, the trades you make will depend
on what you expect to measure.

Roy Lewallen, W7EL

how to measure antenna impedance ?
 

Dan,

your original posting says the shift you are getting is frequency dependent.
Your last posting says it is not. Which one I read wrong?

Thks
Ivan

"dansawyeror" wrote in message
...
Frank,

The bi-directional coupler is a machined block about 1 x 3 x 5. The inside
is a
straight through line, the pickups are simply terminated one loop lines.
It is a
UHF coupler that works reasonably down to 2 meters. When I configure this
to
look at the forward and reflected 'open' circuit case they are not in
phase.
Reflected lags forward by about 40 degrees. (I checked the connection
delay and
this is not a cable issue.) This is frequency independent. Shorting the
output
reverses this relationship. The outputs are terminated in 50 Ohms so I
conclude
it is a 50 Ohm device. When I terminate the device in 50 Ohms the forward
and
reflected outputs are out of phase by about 140 degrees.

What is the significance a non frequency dependent phase shift between
forward
and reflected? This shift is frequency independent.

Thanks - Dan kb0qil


Frank wrote:
Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent
or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected
signals changed by the same about?

Thanks - Dan kb0qil


The phases seen at each coupled port should be identical to the phase of
the
forward and reflected signals. This is easily verifiable, and frequency
independant, as follows:

No load -- forward and reverse amplitudes equal, and in phase;
Short circuit at output -- forward and reverse amplitudes equal, and 180
degrees phase difference;
50 ohm load -- reverse than forward by = specified coupler
directivity,
and phase difference can 0 theta +/ 180.

This is only true if the frequencies are low enough such that the
standards
do not require quantification by the use of "Standard definitions" --
see
www.vnahelp.com.


Regards,

Frank

how to measure antenna impedance ?
 

The posts refer to two different couplers, the first posting is in reference to
a Mini-circuits ZFDC-1-3. The last posting is in reference to a bi-directional
coupler as described. At this point the objective is to 'learn' as much as
possible about the operation of couplers.


Ivan Makarov wrote:
Dan,

your original posting says the shift you are getting is frequency dependent.
Your last posting says it is not. Which one I read wrong?

Thks
Ivan

"dansawyeror" wrote in message
...

Frank,

The bi-directional coupler is a machined block about 1 x 3 x 5. The inside

is a

straight through line, the pickups are simply terminated one loop lines.

It is a

UHF coupler that works reasonably down to 2 meters. When I configure this

to

look at the forward and reflected 'open' circuit case they are not in

phase.

Reflected lags forward by about 40 degrees. (I checked the connection

delay and

this is not a cable issue.) This is frequency independent. Shorting the

output

reverses this relationship. The outputs are terminated in 50 Ohms so I

conclude

it is a 50 Ohm device. When I terminate the device in 50 Ohms the forward

and

reflected outputs are out of phase by about 140 degrees.

What is the significance a non frequency dependent phase shift between

forward

and reflected? This shift is frequency independent.

Thanks - Dan kb0qil


Frank wrote:

Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent

or

preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected
signals changed by the same about?

Thanks - Dan kb0qil


The phases seen at each coupled port should be identical to the phase of

the

forward and reflected signals. This is easily verifiable, and frequency
independant, as follows:

No load -- forward and reverse amplitudes equal, and in phase;
Short circuit at output -- forward and reverse amplitudes equal, and 180
degrees phase difference;
50 ohm load -- reverse than forward by = specified coupler

directivity,

and phase difference can 0 theta +/ 180.

This is only true if the frequencies are low enough such that the

standards

do not require quantification by the use of "Standard definitions" --

see

www.vnahelp.com.


Regards,

Frank

how to measure antenna impedance ?
 

On Sun, 04 Dec 2005 07:57:55 -0800, dansawyeror
wrote:

Wes,

Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected signals
changed by the same about?

Thanks - Dan kb0qil

I'm not sure I understand the question(s) but in the case of a vector
reflectometer using a dual directional coupler maybe this will help.

Here is a dual directional coupler.


Reverse Forward
| |
| |
|----------R R ---------|
X X
Input --A-----------------------B--C Load


Let's say that at frequency, F, the coupling factor (X) is -10 dB with
no phase shift between point B and the forward port and between point
A and the reverse port to keep it simple.

So a wave propagating in the forward direction (Input -- Load)
induces a signal at the forward port that is 10 dB below the input at
0 degrees phase with respect to point B. A wave propagating in the
opposite direction has the same relationship at the reverse port; 10
dB down and 0 degrees phase with respect to point A.

A to Reverse and B to Forward -might- track reasonably well in both
magnitude and phase, but in this case, it's immaterial.

Because B-A and C-B 0 there will be a frequency dependent phase
difference between A, B and C.

When we calibrate using a short on the load port here's what happens.

The signal at the forward port becomes the reference, i.e., unity
amplitude and 0 degrees phase.

The short creates a 100% reflection and -180 degree phase shift. This
signal propagates back down the main line to the source, which is
assumed to be a perfect match, so there is no re-reflection. A -10 dB
sample (by definition: unity) is coupled to the reverse port, with a
phase shift, theta(F), determined by the electrical length of the line
C - B - A.

Unless we are lucky enough to be Lotto winners, the signal at the
reflected port -will not- be 1 @ ang-180 deg. So our calibration
routine must do whatever math is necessary to make the ratio B/A = 1 @
ang-180. This fudge factor is then applied to all subsequent
measurements to "correct" the data.

Now to address (I think) your question. If we change frequencies,
theta(F) changes and the fudge factor no longer corrects for it.
While the coupling factors might track, it is of little consolation
because the calibration is good only at the frequency where it was
performed. Automatic network analyzers perform calibration at each
test frequency, or at least enough points to interpolate between.

how to measure antenna impedance ?
 

Wes,

Thanks. If I read the gist of your reply the physical dimensions are the root
cause of the phase difference between the forward and reflected signals. Is this
true?

Thanks again - this is very helpful. Dan - kb0qil

Wes Stewart wrote:
On Sun, 04 Dec 2005 07:57:55 -0800, dansawyeror
wrote:


Wes,

Your answer to the question about bidirectional couplers was they do not
compensate for phase shift. Let me ask it again:

Do the measuring ports of a bi-directional coupler accurately represent or
preserve the relative phases of the signal?

To put it another way is the phase shift of the driving and reflected signals
changed by the same about?

Thanks - Dan kb0qil


I'm not sure I understand the question(s) but in the case of a vector
reflectometer using a dual directional coupler maybe this will help.

Here is a dual directional coupler.


Reverse Forward
| |
| |
|----------R R ---------|
X X
Input --A-----------------------B--C Load


Let's say that at frequency, F, the coupling factor (X) is -10 dB with
no phase shift between point B and the forward port and between point
A and the reverse port to keep it simple.

So a wave propagating in the forward direction (Input -- Load)
induces a signal at the forward port that is 10 dB below the input at
0 degrees phase with respect to point B. A wave propagating in the
opposite direction has the same relationship at the reverse port; 10
dB down and 0 degrees phase with respect to point A.

A to Reverse and B to Forward -might- track reasonably well in both
magnitude and phase, but in this case, it's immaterial.

Because B-A and C-B 0 there will be a frequency dependent phase
difference between A, B and C.

When we calibrate using a short on the load port here's what happens.

The signal at the forward port becomes the reference, i.e., unity
amplitude and 0 degrees phase.

The short creates a 100% reflection and -180 degree phase shift. This
signal propagates back down the main line to the source, which is
assumed to be a perfect match, so there is no re-reflection. A -10 dB
sample (by definition: unity) is coupled to the reverse port, with a
phase shift, theta(F), determined by the electrical length of the line
C - B - A.

Unless we are lucky enough to be Lotto winners, the signal at the
reflected port -will not- be 1 @ ang-180 deg. So our calibration
routine must do whatever math is necessary to make the ratio B/A = 1 @
ang-180. This fudge factor is then applied to all subsequent
measurements to "correct" the data.

Now to address (I think) your question. If we change frequencies,
theta(F) changes and the fudge factor no longer corrects for it.
While the coupling factors might track, it is of little consolation
because the calibration is good only at the frequency where it was
performed. Automatic network analyzers perform calibration at each
test frequency, or at least enough points to interpolate between.