# OIP3 and P1dB 9.6dB Relationship - RF Cafe Forums

The original RF Cafe Forums were shut down in late 2012 due to maintenance issues. Original posts:

stef
Post subject: OIP3 and P1dB 9.6dB relationship Posted: Mon Nov 26, 2007 4:55 am

Lieutenant

Joined: Mon Nov 26, 2007 4:42 am
Posts: 4
Location: France
here goes:
i have been playing with this relationship for a bit, and i thought everything was clear. however, as it is usually the case, it is not all that clear.

assuming a exponential law device, operating at 3V, correctly biased class A and loaded to provide a P1dB of say, 20dBm, i can expect a OIP3 of 29.6dBm.
so far so good.

on top of this, i can extrapolate IM3s at 0dBm to be 0-29.6*2 = -60dBc. (i might have left a 3dB factor out, but nevermind, it's not the point)

what would now happen if i changed my transistor to a devices limited to 3.5V in breakdown voltage ? if i measured the IM3s at 0dBm, nothing indicates to the devices that the RF swing is limited at 3.5V (it wont go that far at 0dBm). so as far as the small signal operating point is concerned, we are in the same conditions as in the first case. so i could extrapolate my OIP3 to 29.6dBm again...

However, my P1dB has dropped to around 10dBm (due to the drop in breakdown)... so how does this 9.6dB ratio works again ? in the second case, it sounds more like OIP3 = P1dB + 19.6dB.

so obviously there is a condition i am missing. what is it ?
what is it in the second case that will bring my IM3s right up ?

thank you for your lights !

Top

jaslovkel
Post subject: Posted: Mon Nov 26, 2007 11:49 am

Captain

Joined: Tue Jun 26, 2007 10:27 am
Posts: 11
Location: Dallas, TX
Hi stef,

When it comes to distortion, the theory behind the results and the normal relationships is considering many approximations. The theoretical results are totally independent of the breakdown voltage of the transistor itself. Instead, a few assumptions had to be made about the device operation. Some of the typical assumptions are: the input/output signals will not be too large, the device stays in the desired region of operation throughout the entire swing of the signal, you are operating with a considerable back-off from the theoretical 1dB compression.

If you work out the math yourself, you see that the results are only valid in a certain range. This is because the series expansion used to calculate the distortion metrics is only valid for particular input/output values. One of the conditions of the series expansion is that there is no signal clipping. If your input or output swing is clipped (hitting one of the rails), then the device is no longer working as it should and it will not have the normal relationships that we like to use. Also, if the swing is too large, the device itself may move out of the desired region of operation or be operating in a transition region causing undesired results.

Basically, the 9.6dB rule is valid as long as the higher order non-linearity terms can be neglected. This implies the input signal and the output signal are not too large and are far from the theoretical 1-dB compression point. If the signal begins to be too large, the well-known relationships do not hold true anymore and higher order nonlinearity analysis must be performed to get a more accurate result.

Hope this helps.

-J

Top

stef
Post subject: Posted: Mon Nov 26, 2007 12:19 pm

Lieutenant

Joined: Mon Nov 26, 2007 4:42 am
Posts: 4
Location: France
yes,
i sort of get a better idea of the problem.
thanks !

Top

jaslovkel
Post subject: Posted: Mon Nov 26, 2007 5:14 pm

Captain

Joined: Tue Jun 26, 2007 10:27 am
Posts: 11
Location: Dallas, TX
This is in addition to my previous post.

More explanation to why the P1dB is so much lower than the previous case is also due to the linear gain of the amplifier. If it is connected in a common emitter configuration, the input and output signals will be 180 degrees out of phase. Therefore, the collector-base junction diode will have two 180 degree out of phase signals across the anode and cathode. The output signal will be the input signal times the gain with the 180 degree phase shift. Therefore, if the gain is high enough, the input signal is high enough, and there is not much headroom left to keep the device operating in the active region, then the collector base diode will become forward biased and you will compress your signal much quicker than desired. The IM3 products will be effected by this also, but this compression will cause the developed equations to not properly predict what you want.

-J

Top

IR
Post subject: Posted: Tue Nov 27, 2007 4:50 pm

Joined: Mon Jun 27, 2005 2:02 pm
Posts: 373
Location: Germany
Hi Stef,

2 things for you to know/consider:

1. According to IEEE small signal conditions are obtained as long as the IMR (Inter-modulation Ratio) which is the difference between the first and third order products (IM3) is >20dB. P1-P3>20dB.

2. The so called ''rule of thumb'' of 9.6dB is not accurate. The difference between P1dB and OIP3 can be much larger than this number! This difference is much dependant on the transistor's technology. You can take a look at some MMIC amplifiers data sheet and see that the difference can reaco also to 20dB.

Top

stef
Post subject: Posted: Wed Nov 28, 2007 4:20 am

Lieutenant

Joined: Mon Nov 26, 2007 4:42 am
Posts: 4
Location: France
Thanks IR,
but i am afraid the 9.6dB is not just a rule of thumb. it comes from a mathematical derivation based on the third order polynomial response of amplifiers (at small output power).
on the other hand, i agree that it can be much higher. I devellopped internally matched FETs in GaAs with a ratio of over 17dB between P1dB and P1dB. (but this was a compromise between max efficiency and linearity).
it's not much the case of getting higher IP3, but rather lowering P1dB.

The problem here is slightly different, i think i am getting to the bottom of it though.

Top

asaf
Post subject: Posted: Wed Mar 26, 2008 5:23 am

Lieutenant

Joined: Thu Oct 11, 2007 7:58 pm
Posts: 3
Hi ,

The 9.6dB is the differnce coming out from IIP3 to I1dBcp.
So, Isn't the differnce between OIP3 and I1dBcp should be 8.6dB?

Thanks.

Top

asaf
Post subject: Posted: Wed Mar 26, 2008 5:25 am

Lieutenant

Joined: Thu Oct 11, 2007 7:58 pm
Posts: 3
sorry ,

the last line should say:
So, Isn't the differnce between OIP3 and O1dBcp should be 8.6dB?

Top

yendori
Post subject: Posted: Wed Apr 02, 2008 10:21 am

General

Joined: Thu Sep 25, 2003 1:19 am
Posts: 50
Location: texarcana
While the scientists calculate the difference in P1dB and IP3 I have designed many amplifiers and seen a great deal of variation in difference, 5-15dB at least.

Scientist are always a few variables short of reality.

Yendori

Top

Tony Kurlovich
Post subject: Posted: Fri May 16, 2008 5:47 pm

Captain

Joined: Thu Oct 19, 2006 6:02 pm
Posts: 7
Analog perspective:
The most common distortion contributor cited, is the transconductance changing with input signal voltage (ignoring loading effects). In simple undegenerated bipolar and most FET devices, will have a habit of yielding 20log(3) or 9.54db. Degeneration will stretch this a little but at the expense of gain. This is a good rule for small signal or current mode outputs.

Where the breakdown comes in to play is it forces down the supply voltage used and/or induces breakdown. Output signal voltage can push the device into deep saturation. This effect is usually masked by the transconductance effect until you hit saturation. Many devices that have P1db to IP3 of 12 to 20db are likely of this type. Raising the supply voltage should have a weak effect on the transconductance but a stronger effect in the saturation effect. This is seen a lot in medium and high power amplifiers where excess power supply voltage can cut into efficiency. A cascode configuration can be good for some surprises too.

If you are improving IM3 for what appears to be no good reason, check it at other levels to see if the calculated IP3 has shifted and check IM5. This happens with Class B and AB amplifiers where IP3 is an inappropriate measure unless an input power is specified.

Posted  11/12/2012

RF Cafe Software

Wireless System Designer

RF & EE Symbols Word
RF Stencils for Visio
Calculator Workbook
RF Workbench
Smith Chartâ„¢ for Visio
Smith Chartâ„¢ for Excel

1996 - 2022
Webmaster:
Kirt Blattenberger,
BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:
AirplanesAndRockets.com

Try Using SEARCH
to Find What You Need.
There are 1,000s of Pages Indexed on RF Cafe !