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# What is the connection between IP3 and 1dB comp. point5

## What is the connection between IP3 and 1dB comp. point

(OP)
Hello everyone,

Help needed:
What is the connection between IP3 and 1dB compression point in RF Amplifiers ? as I understood, when I deal with Amp. with high IP3 (for example: +30dBm) there is a problem to measure it with spectrum analyzer...

And I don't know what's the answer ?

I assume that for seeing the IP3 spurious, I need to inject very high power signal which might compress the Amp.
but I can't figure other way for measure the IP3 power without injecting very high signal and compressing the Amp. ??!!

Thank you for the Help !!!

### RE: What is the connection between IP3 and 1dB comp. point

I think you will find that you do not directly measure IP3. IP3 is an extrapolated point which is probably not achievable in practice due to limiting and/or destruction of the device. The use of IP3 is to calculate distortion at low signal levels, not high signal levels.

There is no link between IP3 and 1dB compression as far as I know.

### RE: What is the connection between IP3 and 1dB comp. point

3

If you measure IIP3 with 2 tones and then measure Input P1dB with 1 tone you will find that IIP3 is 9.63 dB higher than P1dB.  This also goes for OIP3 and output P1dB.

You can do the analysis if you like... it's a couple of pages though.  Apply Vin(t)=A.Cos(w1.t) to a non-linear device with Vo(t) =  a1.Vin(t) + a2.Vin(t)^2 + a3.Vin(t)^3 .  Collect all terms at the fundamental frequency and divide it by the expected linear gain (a1.A) and set this equal to 0.89125 to determine the value of A for the P1dB point (assume a3 is negative valued to achieve gain compression).  Next, apply Vin(t)=A.Cos(w1.t) + A.Cos(w2.t) to and collect all terms at the 2w2-w1 and divide all that by a1.A and set that equal to 1 for the IP3 point.  Determine the value of A for the IP3 point.  Now, take the ratio of A,P1dB and A,IIP3 and you'll get 9.63dB

Good Luck,
John

### RE: What is the connection between IP3 and 1dB comp. point

(OP)
Thank you guys for the detailed answers - I really appreciate it,

logbook:
You absolutely right, IP3 is a theoretical point indeed.

What I meant was, if you have an Amp. with IP3 value of +30dBm. you should expect for a problem with measuring it (of course - in the linear part - small signals)

John (bearing01):
Please give me a link for such analysis, it very hard to understand what you meant...
However, it's not make sense because if always the IP3 is 9.63dB above the 1dB Comp. Point, whats the point measuring it (the IP3)?! - did I missed something ?

I know there is a rule of thumb about this but you can open any data sheet of any Microwave Amp. and see alot of various combinations of IP3 / 1dBCP.
In the university we learned that for a proof you might neet a lot of papers and pencils but for refuting, you just need one little example and I have a lot !
( For example: mini-circuits LZR-2400LN has IP3=+45dBm and 1dBCP=24dBm )

I had a work interview and this is what he asked me:
Whats the connection between IP3 and 1dBCP, and I didn't know the answer - I told him that for as far that I know, there is no connection...
And after a several seconds of silence he asked me about the range of IP3 in Amp that I worked with, and I told him 10-15dBm ~, and he said, thats the reason...
and since its a cellular company which work with very demanding output Amp, with very high IP3, I assumed that I should expect for connection between those two parameters in this IP3 range...

But I don't have a thinking direction and its very interesting me...

What you think ?

### RE: What is the connection between IP3 and 1dB comp. point

2
9.63 dB huh?  Couldn't you try to be more precise?  In reality, the difference between IP3 and P1db is all over the place, depending on how sharply the compression point is achieved.

### RE: What is the connection between IP3 and 1dB comp. point

(OP)
biff44 - what you mean by "how sharply the compression point is achieved" ?

### RE: What is the connection between IP3 and 1dB comp. point

Well...take a look at WJ'w AM1 chip: OIP3=39 dBm, P1db=18 dBm.  Thats a 21 dB difference.  I have seen devices with only a 5 dB difference.  The device physics have a big role.

It also matters, for 2 tone IP3 testing, what the combined power in both tones is.  You get a different OIP3 prediction at different test powers.

Also, it matters a lot, especially if the two tones are close together in frequency, how big the DC bypass caps are and the power supply impedance.

### RE: What is the connection between IP3 and 1dB comp. point

As far as getting thru a job interview question, I would recommend something like this:

P1db is related to how much maximum output power a device can put out.

OIP3 is a measure of the amount of unwanted spurious signals generated by a device that is operating near its compression point.  Communications networks are sensitive to these unwanted spurious signals, as they can jam an adjacent communications channel, or distort a modulation scheme.

OIP3 is measured by having a device output two sine waves, and reading the unwanted spurious tones generated.  The two sine waves superimpose.  At some instances in time, the two superimpose as a maximum envelope--at which time they are being the most distorted (clipped envelope) by the devices limited P1db capacity.

So, the lower the P1db, the more the evelope of superimposed tones is distorted, and the worse the OIP3 will be.

If you want to get fancy, you can also tell him that there is significant AM to PM conversion near the P1dB point, so phase modulation can be distorted as well.

### RE: What is the connection between IP3 and 1dB comp. point

The IP3 (referred to input or output) is just a figure of merit for the linearity of the amplifier.  Amplifiers need to be linear so they can pass the undesired large adjacent signals (the jammers) while still amplifying the small desired signal (the channel of interest).  The higher the IP3 then the less gain compression the amplifier will suffer... and less distortion from mixing of the jammer with the desired signal will fall next to the desired signal at baseband (and this 3rd order distortion can't be filtered). Receiver designers are more concerned with input IP3 because this gives them an idea how large a jammer (at the antenna) the amplifier can handle.  If you're designing a Power Amplifier then you're more concerned with output IP3.

In the real world (in practice) when you design receivers the spec's are typically more specific than IIP3 or P1dB.  If you have a good system's engineer then he will taylor the block specifications to more specific specifications like "the 3rd order distortion rejection with out of band jammer at X dBm = IMR3 spec or IP3 with specific tone power".  The IP3 considering in band jammer is also spec'ed by determining the maximum acceptable signal swing hitting the baseband ADC (ie 250mV) and then back calculating the required input power hitting the input of the receiver to generate 250mV at the baseband output (considering mixer/filter/LNA gains)ie: Z dBm.  Then you apply two test tones to the input of your receiver each with (Z-6) dBm and you should get 250mV max peak swing out of the baseband.  Now, with the applied Z-6 dBm tones the 3rd order distortion products should not be higher than the noise floor of the receiver to avoid 3rd order distortion... thus giving you your in band IP3 specificaiton  .The P1dB spec is not used to the extent which it is taught in school.  I have only seen it used in one place.  That is, making sure the amplifier gain does not compress by more than 1dB when the worst case (maximum power) jammer enters the receiver with the desired signal.  The gain compression suffered by the desired low power signal is measured and when the gain of the desired signal is reduced 1dB then this is the gain compression breaking point.

The answer to your interview question was 9.6dB as stated above.  If any of you disagree then it's because you don't know the answer.  It's standard textbook theory that you will learn in any graduate RFIC circuit design course.  I don't know of a web page that shows this derivation but 9.6dB to 10dB difference between P1dB and IP3 is the widely accepted figure of merit.  Any RF designer knows (or should know) this.  I'm not sure about the data sheets you're looking at or how it was measured.  The relation between IP3 and P1dB being 9.6dB is assuming you are measuring the IP3 with low power tones, meaning that if you increase the tone power by 1dB then the 3rd order products (IM3) will rise by 3dB.  As you turn up your test tone power and they approach the 1dB compression point the device is no longer small signal non-linear and (IM3:desired) is no long 3:1 and this will cause the 9.6dB rule of thumb to not apply because your test tones are too hot and they're driving the device large signal non-linear.

To test the Input IP3 of your device you drive it with 2 tones w1 and w2.  The output will have 3rd order distortion products 2w1+w2 and 2w2-w1 which is your IM3.  Take either one of these tones and find the IMR3 which is your output tone power minus the adjacent IM3 power.  Now, your IIP3 is the power of one of your input test tones (at the signal generator) plus 0.5*IMR3.  If you're performing this test in the lab with the signal generator and spectrum analyzer you have to:
1. make sure there is no distortion generated by the signal generator.  Typically you will have 2 signal generators (1 test tone per sig. gen.) and both tones are combined in a 2:1 power combiner that has only 3dB power isolation.  Therefore, the test tones from opposite machines can enter the other machine and create 3rd order distortion in the signal generator itself.  Make sure you use attenuators on the signal generator's SMA outputs (like 10dB pads) to ensure an extra 10dB isolation on each machine.
2. When you choose the test tone power level you don't want it too hot... because if it is then your distortion won't be 3:1 for IM3-vs-test tone slope.  If it is, then you're not measuring small signal IP3.  Make sure that if you increase the test tone 1dB then the 3rd order distortion increases by 3dB.
3. You can follow up your IP3 measurement by doing a P1dB measurement.  Apply 1 tone at a XdBm and then at (X+10)dBm.  See if the gain dropped by 1dB.  If it didn't then increase X by 1dB and re-check the gain (at X+i+10)dBm.  When your gain is down by 1dB then the X+i is your input P1dB point. Check to see if it is 10dB below your measured IP3!

One caevat is when you have high frequency distortion.  The 9.6dB rule of thumb generally applies for frequency independent circuits (ie: no caps/inductors or frequency response).  In a system with frequency response the a1 + a2^2 + a3^3 + .... analysis typically gets more complicated because you have to account for phase and frequency effects... requiring you to use volterra analysis.  However, the 3:1 relationship between 3rd order distortion and test tone still applies unless your test tones are widely spaced to place your IM3 distortion far away to suffer different frequency response than the test tone.

AM to PM conversion effects on IP3 are typically only considered in power amplifier designs where you are basically more concerned with Adjacent Channel Power Ratio (ACPR), which can be related to IP3.  If you measure the IP3 of your PA with small test tones then AM-to-PM conversion isn't as much an issue.  However, small signal IP3 in a PA isn't very useful information because you care about large signal 3rd order and adjacent channel distortion... not small signal IP3.  THerefore, the 9.6dB rule of thumb isn't really applicable because in a PA your spec and required linearity is derived from large signal distortion, not small signal distortion which is 3:1.

### RE: What is the connection between IP3 and 1dB comp. point

I found this URL that contains a document that details the above derivation of IIP3 -vs- P1dB as I described.  You will find in this document the 9.6dB rule of thumb on pp8.

http://www.designers-guide.com/Analysis/intercept-point.pdf

### RE: What is the connection between IP3 and 1dB comp. point

(OP)
!!! Wow !!!

I read your answer and your attached article several times, and you succeeded to convince me for all the Amplifiers which could be described with this mathematical expression,

But, there is always - but - what about all the others ?!

What's the problem with all the Amplifiers which have diffrent than 10dB difference between the P1dB and the IP3 ?
It's not make sense that all those companies don't know how to calculate IP3, right ? - it's on their data-sheets ?!

I will add two question that were risen during my research:

* Is there an importance for the distance between the fundamental injection and the IP3 product ? ( assume that we stay in the in-band range - still flat... - I'm asking it because I saw a data sheet of an amplifier with more that 20 dB difference between IP3 an the P1dB, they put a little asterisk beside the IP3 data and below is written: "1 MHz spacing" - is it important ?

* what is special with the cellular feed-forward amplifiers kind - what is the explanation in this case ? ( citation: "Some of the new feedforward cellular amplifiers have TOI specification greater than 30 dB above the 1 dB compression point...")

Thanks a lot...

### RE: What is the connection between IP3 and 1dB comp. point

"1 MHz spacing":  if you have two tones at 1 KHz spacing, you would need 1000 times the amount of DC bypass capacitance on the power supply as you would with two tones at 1 MHz.  Also, with that whoping big capacitance, you would need very low series resistance in the capacitors.  Not easy to do.

"Feedforward amp":  In a feedforward amp, you take an amp that is generating, say, -20 dBc third order intermod products.  You deliberately generate your own set of -20 dBc intermod products, and you at your products to the unwanted ones at the output of the amp.  If your products are at the same amplitude, phase, and group delay as the unwanted products, they will cancel.  So all bets are off-- this is not a simple amplifying device, but a complex nulling subsystem.

### RE: What is the connection between IP3 and 1dB comp. point

I believe biff44 has the answer to your question regarding larger than 10dB gap between P1dB and IP3.  When you study PA's you should cover one section on either signal pre-distortion for linearization or cover a topic on feed back distortion.

We all know that adding feedback (or degeneration) to an amplifier will simultaneously increase P1dB and because it's now more linear the IP3 will also go up.  The same sort of thing happens if you add some attenuation between your input and the actual input of the amplifier... the signal gets attenuated so the signal generator can be turned up even more before going non-linear.  In such a case the 10dB rule of thumb stands.  In a circuit like this the output of the amp has the fundamental, 2nd harmonic, 3rd harmonic... and so on.  Now, with feedback that output signal is fed back into the input to basically subtract with the input signal.  However, the signal we're feeding back has 2nd harmonic in it.  This 2nd harmonic (2w2) of the 2nd tone will enter the non-linear amplifier and mix with the fundamental (w1) to generate 2w2-w1 and 2w2+w1 which is 3rd order distortion.  This distortion at the output will be 10dB away from the P1dB.  How to break the 10dB relationship?

Take a simple NPN BJT transistor amplifier that has an emitter degeneration inductor.  The collector current entering that inductor has fundamental, 2nd harmonic, 3rd harmonic... etc.  The 2nd harmonic goes through the inductor and generates some voltage at 2w2 on the emitter, goes through the base-emitter capacitance and ends up on the base.  If we put a series LC circuit on the base (shunt to ground) then any 2w2 that appears on the base (amp input) will get attenuated and not enter the amplifier input to generate the expected additional 3rd order distortion.  This will make the IP3 higher.  Now, the 2w2 LC trap on the base looks like a capacitor to the fundamental w1 frequency coming in... and lets just say we make that capacitance as part of the intput matching circuit.  The amplifier's P1dB is the same regardless of the existance of the LC trap on the base but the 3rd order distortion in the output will be less with the LC trap than without.  This circuit should not have the 10dB relationship between P1dB and IP3.

Having said all that...  I still believe the interviewer was looking for the 9.6dB answer.  Methods to improve IP3 performance beyond the 9.6dB mark will depend on the distortion linearization technique employed... and the performance you achieve will also depend on component and part-to-part variation as well as performance over temperature.

### RE: What is the connection between IP3 and 1dB comp. point

(OP)
Finally, now I can go to sleep peacefully...
The answer for the interviewer was not such a big deal - to understand this point was the most important for me...

I must say that it was a honor to be part of such a fertile discussion - tho, I just asked the questions...

! Keep help each other !

Alot of thanks for everyone who took a part in this...
Sincerely,
Guy

### RE: What is the connection between IP3 and 1dB comp. point

Hi guys, I'm a new graduate telecom engineer and i'm studying elec eng atm, we just leant the p1db and IP3 stuff in the lecture recently, the discussion above was
very helpful for me to understand about the 1db comp pt and the IP3.

### RE: What is the connection between IP3 and 1dB comp. point

There were some attempt in the pass to use 1dB compression to calculates ip3. As far I know, non of them work for real life device - specially amplifiers. Rohde & Schwarz as well Agilent try , as I remember the reading were all of the place.

The idea was to use power sweep to get the gain compression and use geometric series to calculate ip3. That work perfectly on the paper and in simulation programs ,however in real life there are fare more obstacle that prevent to make proper measurement.
One thing that I so, was the problem with the initial calibration (simple thru calibration - not full 2 port).
The reason for simple thru cal is that it is not simple to perform full 2 port cal with let say 50dB safety attenuator on your receiver port.
That can create significant error in measurement.

The resolution of the sweep was a problem too (let say 201 points, this may not be sufficient data specially if you miss the particular compression point that you expected).
Speed of the measurement was also an issue (201 points need like 200ms to 1s or more to find one ip3 point) that not much faster then standard ip3 setup (2 generators and spectrum analyzer under computer control).

Measurement of ip3 up to let say 50-55dBm on standard ip3 setup should not be a problem. What I mean by standard is 2 generator, buffer amplifiers, two 10db attenuators and resistive combiner/splitter and spectrum analyzer.
Most modern spectrum analyzer give you at list 100dBc for IM3 so if you set your output power from your AMP to 0dBm u can get IP3 max 50dBm... or may be 40dbm - your unit should be like 20dBc below the measured setup performance to limit the error.

The ip3 measurement in general should be perform in linear mode of the DUT (that usually mean that you should set your output power from DUT at list 10dB below measured 1dB compression)

Spacing the 2 tons might be important when phase noise of the signal is significant or very high IP3 (65dBm and up for passive devices usually) should be measured.
High power IP3 required much more sophisticated setup (band pass filters to separate individual frequency components...).

The 9.6dB that sup oust to be some theoretical difference between P1dB and IP3 do not have much to do to real world.  Usually the IP3 is more then 9.6dB when compare to P1dB.

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