[HBR] HBR2K -- Chapter 14 -- Large Signal Performance, Part 4
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Sun, 13 Apr 2003 22:01:58 -0400
Mike asked:
> How are you measuring IP3 (the 3rd order intercept point)? To the best of
> my knowledge it is not a measurable quantity, but is extrapolated from
> other measurements? Right now I am still having trouble with your numbers,
> which of course does not make them wrong, it is just that I would like to
> understand.
I knew someone would ask, eventually. And given the number of
mistakes on the way to doing it right, I'm happy to have someone
check the method. But I'll try to tell a complete story for those who
are interested but (unlike Mike) not familar with this area.
In brief, 'IP3', the intermodulation third order intercept, is the one-
figure way to compare the strong signal handling ability of one
receiver to another -- or to itself, while under development -- without
knowing the strength of the signals used to make the measurement.
You can think of it as the strength (power level) of two equal input
signals at a specified spacing that would be required to produce a
distortion product equal in strength to the signals themselves.
However this can't actually be measured because the receiver under
test will overload and go into gain compression well before the point
is reached. Instead we test at lower levels and extrapolate to
determine the IP3 number.
The 'intercept' is because if you plot the strength of the input signals
the slope of the input signal is 1 and the slope of the distortion
product is 3; the power level at which they cross is the intercept.
And that is how it is measured -- by locating the two lines and doing
the math (for straight lines it's not that complicated!) to determine
where they would cross if extended. Even the measurement isn't
that hard -- since the slope and origin of one line is known and the
slope of the other is also known, we need only determine how far
apart the lines are along any horizontal line to locate the second line.
In practice I doubt anyone draws the lines. You just plug your
numbers into a simple formula based on the geometry and you have
IP3.
The '3' and 'third order' is for the distortion product we measure. Of
course two input signals combine in an infinite number of ways.
However the third order combination is the worst for most practical
receivers and all the others get better or worse along with it, so it is
conventionally taken as the measure of receiver goodness in a strong
signal environment.
1st order is the signals themselves. They're not distortion products.
2nd order is any combination of two of them -- 2xA, 2xB, A+B and A-
B. If 'A' is at 3560 kcs and 'B' is 3580 kcs, then the second order
products caused by mixing of these signals are at 7120, 7140, 7160
and 20 kcs. These, however, are so far removed from the input
signal frequencies that any decent receiver front end should dispose
of them.
Things get a lot more interesting when we combine three to get the
3rd order products. These are 2xA+B, 2xB+A, 3xA, 3xB, 2xA-B,
and 2xB-A. The first four are 10,700 kcs and 10,720, 10,680, and
10,740 (again, not likely to be a problem) and 3540 and 3600.
Whoops. The last two are only 20 kcs each way from the input
signals. This is problem we might face trying to hear a weak one
with strong stations 20 and 40 kcs away on the same side. At
some strength of those two stations their 3rd order distortion product
in our receiver will blot out the station we want to hear. However for
a good receiver, they have to be much stronger than for a poor one.
Now the situation of strong signals located exactly 20 and 40 kcs
from a desired weak signal might seem so rare as to be unimportant.
But ... what about the possibility of exactly 21 and 42 kcs? 18.4
and 36.8 kcs? 27.333 and 54.666 kcs +/- half our filter bandwidth?
We really have to be concerned about the sum of all those
possibilities. The occurance of at least some of these combinations
is essentially certain on a crowded band -- say 40 meters in the
evening, during a DX contest. A 'strong' receiver has a big payoff in
that situation.
The real situation is way too complicated to use for testing so by
convention we measure receiver strength with exactly two signals at
a stated spacing. Common spacings are 2 kcs (tests the receiver
end to end, including audio stages), 20 kcs, (tests everything up to
the sharp filter), and 100 or 200 kcs which mostly tests the RF
stages. The most common single test uses 20 kcs because it's
(usually) the stuff ahead of your filters that's gonna get you -- as in
HBR2K, which is currently trashing the input signal in the 2nd mixer.
Those who want to see numbers on darn near every receiver you can
think of in the last few decades, can visit:
http://sherweng.com/table.html
Now for doing the tests -- this will be somewhat simplified. The
setup is two 'good' signal generators -- reasonably stable, and *with a
pure output.* (I use a pair of URM-25D's) They're connected
together through a 'hybrid combiner' -- basically a device that will add
two signals together (a) without distorting them, and (b) without
letting either signal generator 'see' the signal from the other. The
combiner is needed because nearly all signal generators are non-
linear with respect to a signal put in at the output. And if your signal
sources have any kind of distortion, how the heck can you measure
distortion in a receiver?
The output of the combiner goes to a step attenuator -- typically you
can attenuate the input signal in 1-db steps from 0 to 100 db or so.
1. Disable one generator. Tune the receiver (peak preselector if
any) to the other, disable the AGC, and determine the weakest
signal that can be heard over the receiver's internal noise. I use the
signal strength that will cause the audio output voltage to triple -- i.e.,
signal+noise/noise = about 10 db.
This signal strength is the 'noise floor.' You take the signal from the
generator, deduct 6 db for the loss of the combiner, and deduct the
setting on the attenuator. Measurements are stated relative to 1 mw
(at 50 ohms, 1 mw would be about 230,000 uV). Adequately
sensitive receivers range maybe -110 dbm to -140 dbm. ('dbm' = 'db
below 1 milliwatt). For HBR2K, measuring at the filter driver, this
number might be -107 dbm; call this 'NF'.
Re-enable the AGC and determine the signal strength required for a
convenient fairly low S-meter reading. 'Fairly low' is because some
receivers will automatically turn on an attenuator at readings of S9
and above, which would invalidate the measurements. This will be a
much stronger signal than above -- on HBR2K maybe -79 dbm. Call
this number 'S,' for single signal.
Now tune the signal generator away by 20 kcs. Turn on the second
generator and tune it 40 kcs away. These settings have to be
accurate enough that the distortion product will be in the receiver's
passband, preferably exactly at the same frequency you used for the
first two measurements; a frequency counter is the most convenient
way. Adjust the generators for equal signal strength. Without
readjusting the receiver, crank the attenuation down until the
distortion product is at the same chosen level on the S-meter. This
will require a very much higher signal level -- maybe -16 dbm in my
current testing; call this 'T', for two-tone.
The three measurements are used in the following two calculations:
IP3 = (3xT - S)/2
Using the example figures: (3x(-16)-(-79))/2 = +15.5 dbm
IFDR = 2/3 x (IP3-NF)
2/3 x (15.5-(-107) = ~ 82 db
IFDR says how far up you can go from the noise floor with interfering
signals before you just start to experience interference.
The clearest discussion I've found of two-tone testing and related
issues is at:
http://www.aoruk.com/comments.htm
My few-years-old *Handbook* attempts an explanation and even
attempts to explain the math by reference to the geometry.
Perhaps someone has a later handbook that does so successfully.
Guess that's it. Thanks, Mike. Back to the receiver!
Walt Hutchens
KJ4KV