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OIP3 and P1dB 9.6dB relationship - RF Cafe Forums
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Post subject: OIP3 and P1dB 9.6dB relationship Posted: Mon
Nov 26, 2007 4:55 am
Joined: Mon Nov 26,
2007 4:42 am
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)
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
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
thank you for your lights !
Post subject: Posted: Mon Nov 26, 2007 11:49 am
Joined: Tue Jun 26, 2007 10:27 am
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
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.
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.
Post subject: Posted: Mon
Nov 26, 2007 12:19 pm
Joined: Mon Nov
26, 2007 4:42 am
of get a better idea of the problem.
Post subject: Posted: Mon Nov 26, 2007 5:14 pm
Joined: Tue Jun 26, 2007 10:27 am
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.
Post subject: Posted: Tue Nov 27, 2007 4:50 pm
Joined: Mon Jun 27, 2005 2:02 pm
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.
subject: Posted: Wed Nov 28, 2007 4:20 am
Joined: Mon Nov 26, 2007 4:42 am
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).
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.
Posted: Wed Mar 26, 2008 5:23 am
Thu Oct 11, 2007 7:58 pm
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?
Post subject: Posted: Wed Mar 26, 2008 5:25 am
Joined: Thu Oct 11, 2007 7:58 pm
the last line should say:
So, Isn't the differnce
between OIP3 and O1dBcp should be 8.6dB?
Post subject: Posted: Wed Apr 02, 2008 10:21 am
Joined: Thu Sep 25, 2003 1:19 am
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.
Post subject: Posted: Fri May 16, 2008 5:47 pm
Joined: Thu Oct 19, 2006 6:02 pm
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
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
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.