This document discusses improving the third order intercept point (IIP3) of an RF circuit design using source degeneration technique. It begins with introductions to linearity, intermodulation, and IIP3. It then describes a simulation conducted in ADS of a low noise amplifier circuit using cascaded N-type MOSFET transistors. The simulation showed an IIP3 of -3dB without source degeneration. By adding a 1.5nH inductor to the source, the IIP3 improved by 5dB to 2dB, demonstrating the IIP3 improvement possible with source degeneration. The document concludes by reiterating the use of source degeneration to linearize a system and increase its IIP3.

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IIP3 improvement
using Source
Degeneration
Technique
RFIC design Course
Ahsan Ghoncheh
RFIC, Fall 2016
Professor Reza Moazzam
UCSD Extension

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Acknowledgment
Special thanks to Prof. Reza Moazzam for his RFIC Course at USCD Extension and
to Ata Sarrafinazhad for his guidance on the Advance System Design
simulation.

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TABLE OF CONTENTS
ACKNOWLEDGMENTS .................................................................................................. 2
TABLE OF CONTENTS.................................................................................................... 3
LIST OF TABLES .............................................................................................................. 4
1. Introduction................................................................................................................... 5
1.1 Linearity...................................................................................................................... 5
1.2 Intermodulation............................................................................................................. 8
1.3 Third order Intercept Point............................................................................................ 9
2 Third-order intercept point improvement ..................................................................... 10
2.1 Source Degenaration...................................................................................................11
2.2 Our ADS Simulatoin for Source Degeneration............................................................11
Conclusion ........................................................................................................................ 16
References........................................................................................................................... 3

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TABLE OF Figures
Fig 1 Real resistor Linearity ......................................................................................... 6
Fig 2 Output voltage behavior vs Temperature........................................................ 6
Fig 3 Supply Current behavior vs Temperature....................................................... 7
Fig 4 IMD,HD ,IIP2 and IIP3 caused by two frequencies.................................... 8
Fig 5 IIP3 ......................................................................................................................... 10
Fig 6 Source degeneration .................................................................................................11
Fig 7a Our ADS Settings................................................................................................... 12
Fig 7b LNA MOSFET Circuit without using Source Degeneration................................. 13
Fig 8 IIP3 simulation without using source degeneration................................... 14
Fig 9 LNA MOSFET Circuit using Source Degeneration ................................................ 15
Fig 10 IIP3 simulation using source degeneration............................................................ 16

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1. Introduction
In this article we are going to talk briefly about linearity and what intermodulation
and mainly IIP3 (Third order intercept point) is. Why Third order Intercept point is
important in linearity by simulating a design for calculating the IIP3 through
Advanced Design System (ADS), This design would be a N Type MOSFET Cascade
LNA and in the end and using source degeneration technique we would show the
IIP3 improvement.
1.1 Linearity
The basic formula for any engineer is V = R × I and as we know it is not
accurate100%. In an ideal world it is exact but the because when our V and I are
larger than what our device can handle or other conditions like high and low
temperature, humidity, and pressure compensates and therefore we won’t have
the ideal ohm law. We want the resistor, R, to be as linear as possible and remain
so over wide ranges of signals and conditions. In reality, characteristics of devices
due to limitations of the devices affects. IC components require linearity monitor
and studies therefore linearity studies should also be done in developing
components such as switches, amplifiers, VCOs, mixers, and LNAs. Avoiding or
weak study and optimization on such studies result in instabilities, failure to meet
specs, and interferences which might even result in malfunctions or destroying the
device or entire system. [1]

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Fig1. Real resistor Linearity is corrupted when I and V passes physical limitation.[1]
In the above figure you can find the behavior of a simple resistor for when it reaches
over its limits in Fig1. We have also provided examples on output voltage vs
temperature behavior in Fig2 as well as temperature behavior vs supply current in
Fig3.
Fig2.Output voltage behavior vs Temperature increase [2]

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Fig3.Supply Current behavior vs Temperature increase [3]
When bringing up a RF component such as front end cellular modules including
but not limited to Switches LNA, mixers, filters an PA we have a large signal
dynamic therefore they can produce harmonics, interferences, and saturation
which are effects of nonlinearities. Different parameter standards are usually
used in order to characterize the non-linarites of input vs outputs which some a
brief list would be 1dB compression point (CP-1dB),Compression dynamic range
(CDR),Spurious-free dynamic range (SFDR),Desensitization dynamic range (DDR)
and Intercept points (IPn)
In this article we exclusively study on the intercept points, IP3) to show
nonlinearity affecting useful signals.

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1.2 Intermodulation
Before discussing on what IP3 is we should first briefly talk about Intermodulation.
When more than two frequencies have amplitude modulation because of
nonlinearities in a system, Intermodulation or Intermodulation Distortion would
happen which is abbreviated as IM and IMD. When Intermodulation happens, each
of the two frequencies form additional signals at harmonic frequencies called
harmonic distortion as well as a series of multiplication of sums and subtractions
of the main two frequencies. The two frequencies and intermodulation distortions
caused by them up to the third order are shown in figure 4.
Figure 4. Two fundamental signals and IMD,HD ,IIP2 and IIP3 caused by them[4]

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1.3 Third-order intercept point
In an ideal linear system if we have xt  as input, we would be having yt  as output
using the below linear equation. α1 is gain of the system.[5]
yt   1 xt 
But due to non-linearity limitations of our system the actual output signal we would
get from the given input would be as below according to Taylor series expansion.
If we only have one signal coming in the system it would result in distortions such
as harmonics which can be removed using Low pass or Band Pass filters.
yt   1 xt 2 x2
t 3 x3
t 
Now let’s assume we have two frequencies as we mentioned in the 1.2 section, the
Intermodulation topic. Lets define our input is the two fundamental signals as
below:
xt  A1 cos1t  A2 cos2t
When bringing in the equation above in our output equation we would have the
below result:
yt  1 A1 cos1t  A2 cos2t2 A1 A2 cos1  2 t 2 A1 A2 cos1 2 t
3 3
A2
A 3 3
A2
A
 1 2
cos21 1 2 t  1 2
cos2  2 t
4 4
3 A2
A 3 A2
A
3 3 2 1 cos2  t  2 1 cos2  t
For analyzing the previous equation below are the importing considerations:
 The first order ω1 and ω2 terms are our desired output terms.
 ω1±ω2 terms are the second-order intermodulation products ,IM2.
 2ω1±ω2 and 2ω2±ω1 terms are third-order intermodulation products,IM3.
Second-order intermodulation can usually be eliminated using different techniques
but the challenge is meeting third order intermodulation specs. The desired output
terms increases with the input amplitude, but according to the equation given
above the IM3 output is growing with A3
. When the First order Amplitude output
meets with A3
is where IIP3 orthird-order intersection point and the output is the
output-referred IP3, or OIP3defined as shown in Fig. 5.We define IIP3 formula as
4 4

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below:
IIP3 
4 1
3 3
Fig. 5 Desired Output, Third Order and Second order products.[7]
2 Third-order intercept point improvement
There are various techniques on reducing the IIP3 such as Negative Feedback,
Derivative superposition, Post correction, Biasing in strong inversion, using wide
device and thick oxide, Source degeneration and much more techniques which are
useful in optimization and improving the third order intercept point during our
simulation and design . In this article we would be working on the source
degeneration technique.

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2.1 Source Degenaration
We can degenerate an output signal which will lead to lowering and linearizing the
stage’s gain curve [hasht] by using the resistance Rs to the source terminal of a
common-source stage. [8]
Fig6. An NMOS transistor with source degeneration is equivalent to a single
transistor with a smaller transconductance and larger output impedance.[8]
According to the equation mentioned above the limit of Gm with respect to Rs is is
1/Rs, meaning that larger source resistances will make the gain a weaker function
of gm and more linear. The source degeneration is used as a feedback and by tuning
it we can make the system more linearized.
2.2 Our ADS Simulatoin for Source Degeneration
After defining the concepts of IIP3 now we will work on the simulation did through
Advanced Designed Systems (ADS) software. We have designed a Low Noise
Amplifier as shown in Fig.6 which is created by cascading two N-Type MOSFET
Transistors. It is good to mention the MOSFET3 is used for biasing the supply.

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7a)

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7b)
Fig7. a) is a screenshot of the settings we have defined for our cascade MOSFET
design of LNA and b) shows the actual circuit.

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Note that we have not defined any source impedance in our design and have
connected the our source in MOSFET1 to Ground.
Our Third-order intercept point using the simulation in ADS would be according to
Fig.9 which when tracing our two point it would be reaching at -3dB.
Fig8. IIP3 simulation without using source degeneration
Now if we use the same simulation we have used before and only add a 1.5nH
inductor in our source Resistor we would be improving our third order intercept
point for 5dB. Please note the reason we have used inductor instead of resistor is

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resistor would cause noise. Therefore inductor would be a better choice for our IIP3
optimization. You can see our ADS Design in Fig10.
Fig 9) Adding 1.5 nH to source of our N Type Cascaded MOSFET1

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By adding an inductor and looking at our Third-order intercept point using the
simulation in ADS seen in fig. 11we would see our IIP3 has improved from -3dB to
2dB which is a 5dB improvement.
Fig 10. IIP3 simulation using source degeneration
Conclusion
In this article we started by an introduction to Linearity and Intermodulation and
concentrated on what IIP3 is. Afterward we named different techniques on
reducing the IIP3 and concentrated and introduced source degeneration, which
we can make the system more linear using it and practically designed a N-Type
MOSFET LNA in order to measure its IIP3 and and used source degeneration to
see the improvement of IIP3 in our simulation using the discussed technique by
5dB.

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References
[1] Behzad Razavi, RF Microelectronics, 2nd
edition: Prentice Hall 2011.
[2] “http://www.edn.com/design/test-and-measurement/4376465/The-IP3-
specification-demystified”
[3] “http://analog326.rssing.com/chan-13870196/all_p1.html”
[4] “http://e2e.ti.com/cfs-file/__key/communityserver-blogs-components-
weblogfiles/00-00-00-03-25/4466.Figure2.JPG”
[5] “http://www.cliftonlaboratories.com/norton_amplifier.htm”
[6] Behzad Razavi, Design of Analog CMOS Integrated Circuits: McGraw-Hill,
2001.
[7] ”Wikipedia,http://en.wikipedia.org/wiki/Third_order_intercept_
point”
[8] http://www.radio-electronics.com/info/rf-technology-
design/receiver-overload/intercept-point-third-order.php”
[9] Ali Sheikholeslami ‘Source Degeneration’ IEEE SOLID-STATE
CIRCUITS MAGAZINE, Summer 2014