Updated June 26,
here to go to our main measurement page
here to go to our page on characteristic impedance
here to go to our Smith chart page
here to go to our time domain reflectometry page
Click here to go to our page on quarterwave transformers
This page will tie together some different attempts of measuring characteristic impedance (Z0). About the only thing they have in common is they all use electrical measurements of transmission lines, as opposed to electromagnetic or closed-form simulations. Only one solution (so far) is capable of measuring Z0 over frequency such that dispersion can be observed.
Can you measure Z0 with an ohm-meter?
Measuring Z0 using reflection coefficient
Measuring Z0 on a Smith chart
The Microwaves101 way to measure Z0
Measuring Z0 using ABCD parameters
Measuring Z0 with time domain reflectometry (separate page)
Can you measure Z0 with an ohm-meter?
New for April 2012! Here is some text from the "E-how" web site, that shows how to test a 50 or 75 ohm cable. There is a lot of misinformation on the world wide web, you have to be careful. They sure have a lot of sponsored links though!
1. Set your multimeter to an ohms scale around 100 ohms. A higher scale works, but avoid moving into a scale close to 1k ohms or higher. Coaxial cable is typically rated to operate at 50 or 75 ohms so the scale should be at or greater than these ratings.
2. Disconnect both ends of the cable from their connections.
3. Test the length of the cable by placing a multimeter probe on each end of the cable, touching the center wire emerging from the coaxial connector.
4. Read the multimeter display. A reading around the 50 ohm or 75 ohm rating of the cable indicates that the cable is working properly across its length. A reading of infinite resistance indicates a break somewhere along the the inside of the cable. A reading of zero indicates a potential short between the inner cable and its shield.
There is no better way to say this, than "what an idiot!" The bad advice continues, we won't provide any more of it.
What is this thing called characteristic
impedance, also known as "Z-zero"? Let's start with a
common misconception. If you have a 50-ohm coax cable (or microstrip
line or any other 50 ohm transmission line) that isn't connected
to anything on either end, and connect an ohmmeter across it, you
might expecting to read 50 ohms if you were new to microwave engineering.
But you'll measure an open circuit (unless something is loading
the opposite end which means you didn't follow our simple instructions...)
nowhere near fifty ohms. What's going on?
But wait, Jens from Denmark wants
you to know that the above statement is not 100% technically correct:
On the new page for characteristic
impedance, you start out by claiming that you cannot measure anything
if you connect an ordinary ohmmeter to a 50 ohm cable or microstrip.
This is simply because the line is too short for the meter to
get the reading. The meter may take about 1 second to get a stable
reading. If you take a loss free transmission of say c x 1.5 (about
4.5 x exp(8) meters!) you will get a reading that lasts about
3 seconds. You may have some practical problems with this experiment
though. The line will wind the equator about 11.25 times. And
getting it lossless will also be difficult.
Thanks, and let us know when
you have that cable in place so we can perform the measurement!
And now an opposing viewpoint
We're inclined to agree with
Raphael on this, but we look forward to further discussion! And
here comes some more discussion from Mark, who agrees with Jens...
I believe Jens is somehow
wrongly deriving is conclusion from the wave propagation phenomena.
As I see it, assuming you could make the experiment, you would
never see (let's say) 50 Ohm on your meter because traditional
multimeters derive resistance from measured voltage and current
to display the result of V / I and you would never have any current
flowing between the two conductors.
The definition of resistance
is "the opposition to the flow of electric current"
whereas the definition of impedance is "The opposition to
an alternating current". Meaning that a 50 Ohm "resistance"
behaves the same (offer the same opposition to current) in both
direct or alternating current. A 50 Ohm "impedance"
on the other hand does not necessarily behave the same in direct
or alternating current.
It's not because an impedance
has only a real part that's it's necessarily a "resistance"
... it might just still be an "impedance".
Z = R + jX
Z = R
Although a DC measurement
will indeed show no current passing through an unterminated coaxial
cable, in a short term view (think in nanoseconds) this is incorrect.
When you touch your meter leads to the cable, those leads are
at a different electrical potential when compared to the electrical
potential between the center conductor and the shield. In order
to equalize the potential between the test leads and the cable,
current MUST flow. After all, you need charge to have an electrical
potential and you need a current to create that charge. During
the time where the initial energy applied to the cable is still
propagating away from the meter, the meter will indeed read 50
ohms. The problem is, as Jens pointed out, you would either need
a very fast multimeter or a very long cable to actually see 50
ohms on a display.
To look at it another way,
a lossless cable can be approximated as an infinite series of
"L" shaped series inductor, shunt capacitor pairs. When
you think in terms of series inductors and shunt capacitors, you
can easily imagine getting a different reading until all the L's
and C's have stabilized at their steady state values.
To state that the meter
would always read an open, requires information to travel faster
than the speed of light. After all, how can the meter find out
if a cable is terminated until it "queries" it with
electrons? For the first 100 us, a 100 us long cable is going
to look the same to a meter regardless of any open, short, or
loaded conditions on the other end. To do otherwise would require
information to travel faster than the wave propagating along the
I have trouble with the message
that a meter would take a "look" at the impedance in the
first nanosecond and give a meaningful result. The operator would
wait a few seconds for the measurement, and he would see an open,
then eat another bite of his donut. But you have all given us food
for thought! - Unknown Editor
Measuring Z0 from reflection coefficient
This came from Doug. Thanks! We have also seen it written up in the Microwave Office tutorial.
If you measure an unknown cable with unknown Z0, just take the measured S-parameters and renormalize them to whatever value gives you the greatest return loss (i.e., S11< -20 dB or so). It won't depend on the length (however, it needs to have some measurable length, say greater than lambda/8). The normalised impedance that gives the lowest value is the Z0 of the unknown transmission line. For example, ideally, a 75 Ohm transmission line normalised to 75 Ohms will give infinite return loss.
If you display this on a Smith chart, the correct Z0 is the one that gives you the tightest ball in the center. We'll add a picture one of these days. But be aware, it is not possible to see the small effects of dispersion in transmission lines in this method.
Measuring Z0 on a Smith chart
If you plot S11 on a Smith chart,
for a line length of unknown impedance, it traces a circle, with
one point on the circle's circumference at the center of the chart.
The diameter of the circle is mathematically related to the line's
impedance. If the line were a quarter
wave, if you plotted it in frequency up to the quarterwave point
it transcribes a half circle. It is easy to figure out the relationship
of the line impedance for this case.
Below is a 25 ohm line "measured"
between two fifty ohm terminations:
When we plot the reflection
coefficient on the Smith chart, you can see the circle that develops
to the left of the 50 ohm point. When the line reaches a half wavelength,
the circle is complete, then it merely traces over itself as you
go further up in frequency. The marker shows an impedance of 0.25 normalized to Z0, or 12.5 ohms (0.25 x 50 ohms).
At marker m1 the line forms
a classic quarterwave transformer, at this frequency the network
appears like a real 12.5 ohm load:
where ZT is the impedance of
the line (acting as a quarterwave transformer), Zin is the impedance
looking in to it, and Z0 is the system impedance which terminated
both ends of the line.
The impedance of the line is
thus related to the diameter of the circle its reflection coefficient
traces over frequency. Just don't make the mistake that the center of the circle represents the transformer's impedance, it does NOT. You have to use the equation shown above to solve for ZT.
By the way, the reflection coefficient magnitude when you are on the real axis to the left of Z0 is:
Which in this case is 0.6 (or -4.43 dB if you prefer decibels.
If your reflection coefficient was to the right of Z0 (and on the real axis) the reflection coefficient would be:
If you mix these up, the only error will be that the quantity will be a negative number.
The Microwaves101 way to measure Z0
Below we will discuss an idea we had for measuring characteristic
impedance of a transmission line, based on a question that came
our way. It is probably not much more than a mathematical exercise,
but you never know when it might be useful. If someone gave you
a coax cable and didn't know if it was 75 or 50 ohms, this trick
might do the job. Its really a calculation of Z0 based on
a direct measurement of reflection coefficient. And it is fully capable of measuring dispersion, or that property of microstrip and other not-completely-TEM transmission lines where Z0 changes with frequency (at least in theory!) Here's the premise:
You don't need a full half-wave
line to trace out the circle to find its diameter... to determine the diameter of a circle
all you need is three points. The circumscribed circle of the triangle
they form is easy to calculate, you can look
up the formula on Wikipedia. Now you can measure the characteristic
impedance of a line from three frequency points of S11 magnitude
We made an Excel sheet that makes the "diameter" calculation
from each set of three successive frequency points. Then it converts
to impedance versus frequency. The Excel file is called Impedance
Calculator 101.xls, look for it
There are possible errors that need to be minimized for this technique
to produce an accurate assessment of Z0. If there are parasitics
in the measurement (connectors on the ends of a cable of unknown
impedance for example) then the calculation could be off. The S-parameters
need to be fully deembedded for best results. You will see from
the plot that the calculated impedance varies over frequency. Perhaps
the lowest error occurs at the lowest frequency, if someone else
wants to speculate on this we'd like to hear
There are two solutions to the
math. We didn't figure out how to make the spreadsheet smart enough
to choose the correct one, but it is easy to pick the right one.
If the circle is to the left of center, Z<Z0. To the right, Z>Z0.
We were given reflection coefficient
from an electromagnetic simulation of a transmission line. Below
it is plotted (by the spreadsheet) from zero to 10 GHz. The circle
is to the right side of the origin, so the transmission line must
be greater than 50 ohms. Sorry, we were too lazy to plot the data
on an actual Smith chart!
Now here's what the spreadsheet
comes up with for Z0: the characteristic impedance of the line is
somewhere between 69 and 75 ohms. A 69 ohm transformer would make the load look like a 95.2 ohm load, or a reflection coefficient of 0.311, which is right about where that circle crosses the X-axis.
Why does the impedance vary over frequency? It probably doesn't... this is "measurement error" due to parasitics in the electro-magnetic simulation.
Measuring Z0 from ABCD parameters
Some of you may have noticed that Z0 is front-and-center in two of the ABCD parameter equations. Something we'll exploit later!
Got a cleaner simulation? Send it our way and we'll try to analyze it!