[HBR] HBR2K -- Chapter 14 -- Large Signal Performance, Part 4

[email protected] [email protected]
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