# Design and Modeling of RF Circuits

Ηλεκτρονική - Συσκευές

27 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

86 εμφανίσεις

Design and Modeling of RF Circuits

using Design of Experiments

Jai
Narayan

Tripathi

/
Jayanta

Mukherjee

Department of Electrical Engineering

IIT Bombay, Mumbai

400076, INDIA.

VLSI Consortium workshop

29 Oct. 2010

Agenda

Challenges in RF Circuit Design

-

Design Challenges

-

Modeling Challenges

Introduction to DOE

Robust Optimization and ANOVA.

Final Design of Oscillator

Case study 1 : Improving Signal Integrity

-

Statistical Analysis

-

Optimization

-

Results

Case study 2 :
Designing

Low Phase Noise Oscillator

Work in progress

-

Improving Accuracy in Modeling

Future Work

-

Phase Noise Modeling of Ring Oscillator

Objectives

To apply DOE to RF active circuits, to improve and
model their output characteristics.

To develop systematic approach of circuit
design/modeling, using Robust Design approach.

Design Challenges : CMOS Differential
LC Oscillator

Generally used as an Local Oscillator (LO).

Desired frequency can be achieved by setting L
and C.

As the oscillation frequency increases, phase
noise decreases.

How to design at a particular frequency with
minimum phase noise ???

-

as phase noise will be set lower, frequency will

change !!!

Designing Low Phase Noise Oscillator

Designing a CMOS differential LC tank oscillator with minimum phase
noise.

The library used is UMC 180 nm
rf

lib.

The design variables are :

-

Finger number of transistors,

-

Inductor top metal width,

-

Inductor inner diameter,

-

Length of unit square of capacitor, and

-

Width of unit square of capacitor.

Importance of Phase Noise ?

-

QoS

of communication is characterized by Phase Noise.

-

Transceivers have more probability of interference.

-

SNR of a communication system may get affected.

Design Variables (Physical) or Control
Factors for DOE

1) Width of Transistor M1 (Finger no. w1)

2) Width of Transistor M2 (Finger no. w2)

3) Width of Transistor M3 (Finger no. w3)

4) Width of Transistor M4 (Finger no. w4)

5) Width of Transistor M5 (Finger no. w5)

6) Width of finger of Inductor (w6)

7) Width of Capacitor (w7)

8) Diameter of finger of Inductor (d)

9) Length of Capacitor (l)

Quality Engineering

“Quality Engineering” is a branch of engineering
that deals with the yield and the quality of the
production.

DOE techniques are used for Robust
Optimization of an RF Oscillator.

For Orthogonal Experiments, Taguchi Methods
are used to optimize the system.

Design Of Experiments (DOE)

Method to efficiently design a system to maintain
it’s important output parameters within the
robustness limits of the functionality of the system
[5].

1)
Full Factorial Experiments
:

It considers all the possible combinations and
based on the results, optimization is performed. E.g.
in our circuit there will be 2*(3)^7 = 4374
experiments.

2)
Fractional Factorials

:

This method facilitates to perform only certain
combinations out of all the possible combinations.

The set of experiments can be defined either by an
orthogonal array, or by forming a subgroup of the
direct product of
Abelian

groups of orders equal to
the number of levels of each factor [6].

In our case, we are performing 50 certain

These combinations are taken according to
Orthogonal Array (L
50
).

For 9 parameters, the available table is
L50(2^1, 5^11).

Orthogonal Arrays provide best possible
information in least no. of simulations.

Analysis of Variance

It is also called ANOVA.

ANOVA can find out the % contribution of
each factor for the output quality parameter.

Consider a set of n experiments with k design
factors
-

In ANOVA, mean of all the responses is
calculated. Based on the variance of each
response from the mean, the variance
contributed by each factor is calculated.

By ANOVA, % effect of each factor can
also be calculated.

Robust Optimization

Robust optimization means to optimize a design
in such a way that it will certainly work
according to the specifications for which it is
desired to work.

Robust Optimization assures the proper
functioning of the system.

Steps

for Robust Optimization

Taguchi optimization of Active
Circuits

DOE are widely used in electronic
industry for getting better yields [1].

Literature is available for the same, but
most of them talk about passive circuit
optimization or device optimization [2
-
4].

This is an attempt to optimize active
circuits using DOE and Taguchi methods.

Signal Integrity ensures reliable transmission at
higher speeds.

Oscillators are generally used in transceivers,
where we need good SI because the received

The main concern is to improve Eye Diagram.

Case Study 1 : Improving Eye Diagram of

RF Oscillator

Design Parameters and their Levels

1) Width of Transistor M1 (Finger no. w1)

2) Width of Transistor M2 (Finger no. w2)

3) Width of Transistor M3 (Finger no. w3)

4) Width of Transistor M4 (Finger no. w4)

5) Width of Transistor M5 (Finger no. w5)

6) Width of finger of Inductor (w6)

7) Width of Capacitor (w7)

8) Diameter of finger of Inductor (d)

Design Parameter and their values at various Levels

Taguchi Orthogonal Array used for Optimization

Corresponding Results

Sensitivity coefficients vectors calculated
from Ordinary Least Square (OLS) methods

Sensitivity Coefficients for various output parameters

Linear additive models after replacing sensitivity coefficients

Factor Effects on Quality
parameters calculated by ANOVA

Optimization and Final Design

Results and Remarks

Jitter is about 158 psec (130%) reduced.

Eye Height is 1.12 V increased.

In addition of that, SNR is increased by

almost 87%.

Power consumption of optimized design is

16.93 mW compared to 17.67 mW of

standard design.

Case Study 2 : Designing Low Phase Noise 2

GHz Oscillator

The main concern is to reduce phase
noise with minimum deviation in
frequency of oscillation.

Design Parameters and their Levels

1) Width of transistor M1 (Finger no. w1)

2) Width of transistor M2 (Finger no. w2)

3) Width of transistor M3 (Finger no. w3)

4) Width of transistor M4 (Finger no. w4)

5) Width of transistor M5 (Finger no. w5)

6) Width of finger of Inductor (w6)

7) Width of unit square of capacitor (w7)

8) Diameter of finger of inductor (d)

9) Length of unit square of capacitor (l)

Values of Design Parameters at
various Levels

Orthogonal
Array used for
Optimization (part of L
50
)

The same set of experiments was

performed at following temperatures :

1. 15
o
C

2. 25
o
C

3. 35
o
C

4. 45
o
C

5. 55
o
C

Corresponding
Results

ANOVA

This is the case of “smaller the better” for phase
noise.

All the simulation results are converted in to their
logarithmic values (dB).

The overall mean is
-
36.27 dB.

Effect of ‘
w7’

and ‘
l’

on phase noise are 46% and 45%
respectively.

Effect of ‘
d’
on phase noise is 2% but on frequency is
52%.

From the factor effect plot, it is obvious that
w7

and
l

are the most dominating factors for phase noise.

The effect of
d

is a comparatively lesser but
considerable.

The effects of all other factors are very less

From the factor effect plot,
d

is the most dominating
factor for frequency variation.

‘d’

is having 52% effect while
‘w7’
and

‘l’
have 24%
each.

The effects of all other factors are very less

Observations

‘w7’
and

‘l’ ,
both

should be set at level 5, or above
that if allowed.

This will lower the phase noise but the frequency will
be changed as well.

After adjusting both of the above parameters for
minimum phase noise,
‘d’

should be set for minimum
frequency deviation.

Best Settings

After adjusting all the parameters, fine tuning, can be
done and
‘w6’

was also considered to tune frequency
at as near as possible, to the desired frequency.

Thus the best settings are :

w6 : 19 um

w7 : 70 um

d : 126 um

l : 51 um

All other parameters will be at initial values.

Results

Comparison between initial and final designs

Conclusion

There is
3.4 dB
improvement in Phase Noise with
exact frequency (0 % deviation), just by varying the
design variables.

A step by step method is set for designing RF circuit
for achieving a desired output response.

Publications

Jai N.
Tripathi
, J.
Mukherjee
, P. R.
Apte
;
“Designing Asymmetric 2.4
GHz RF Oscillator for Improving Signal Integrity by Design of
Experiments”
, accepted for IEEE Asia Pacific Conference on
Circuits and Systems for Communications, (APCCAS 2010),
Dec 2010, Kuala
lumpur
, Malaysia.

Jai N.
Tripathi
, J.
Mukherjee
, P. R.
Apte
; “
Designing Asymmetric 2.2
GHz RF Oscillator by Design of Experiments using Taguchi Methods
”,
accepted for IEEE European Conference on Circuits and Systems
for Communications , (ECCSC’10), Nov. 23
-

Work in Progress

Increasing accuracy for model fitting.

Increasing the number of levels.

More number of levels can provide better
results.

Using the curve fitting, Polynomials can be
obtained.

Nonlinear optimization with some constraints
can be used later.

Impact of factor ‘L’ on Phase Noise : 5 level response fitted

as a polynomial.

Modeling Challenges for Phase
Noise (Future Work)

Phase Noise Modeling in RF Ring Oscillators.

Leeson’s

Formula as a standard [8].

-

input phase error, loaded quality factor, center frequency and

bandwidth.

There are other formulae in recent literature

-

require
transconductance

of the whole circuit [9].

-

require FFT analysis [10].

-

require device parameters [11].

-

require
rms

jitter and oscillation period [12].

Future Work (
Contd

…)

All of the above mentioned method require
either computer simulations or intense
computing methods.

Work presented here, can be applied to phase
noise modeling for ring oscillators, additive
models can be found for various ring oscillators
of different stages.

Steps to be followed

Steps to be followed (
contd

...)

References

[1] Sammy G. Shina; “Six Sigma for Electronics Design and Manufacturing”; Professional Engineering Series,
McGraw
-
Hill, 2002.

[2] Fauziyah Salehuddin, Ibrahim Ahmad, Fazrena Azlee Hamid and Azami Zaharim; “Application of Taguchi
Method in Optimization of Gate Oxide and Silicide Thickness for 45nm NMOS Device”, International Journal of
Engineering & Technology IJET Vol. 9, No. 10.

[3] Erden Motoglu et al; “Statistical Signal Integrity Analysis and Diagnosis Methodology for High
-
Speed
Systems”; IEEE Transactions on Advanced Packaging, Vol.27, No.4, Nov.2004. Material Science in
Semiconductor Processing, Science Direct, Vol.6, 2003, pp. 107
-
117.

[4] Wei
-
Chung Weng, Fan Yang, Atef Elsherbeni; “Electromagnetics and Antenna Optimization Using Taguchi’s
Method”, Synthesis Lectures on Computational Electromagnetics, Morgan and Claypool Publishers, 2007.

[5] D.R.Cox and N.Reid; “The Theory of the Design of Experiments”; Chapmanb & Hall/CRC, 2000.

[6] A.S. Hedayat, N.J.A. Sloane and John Stufken; “Orthogonal ArraysTheory and Applications; Springer Series in
Statistics.

[7] E.G.A. Gaury, J.P.C. Kleijnen, “Risk Analysis of Robust System Design”, Proceedings of the 1998 Winter
Simulation Conference, pp. 1533
-
1540.

References (
Contd

…)

[8] D. B. Leeson, “A simple model of feedback oscillator noise spectrum", in Proc. IEEE, vol.
54, Feb. 1966, pp.
329

330.

[9] Andrew Buschmeiner and Douglas Frey, “Novel Analysis of Phase Noise in Oscillators", IEEE International
Symposium on Circuits and Systems, 2007. ISCAS 2007.

[10] Oskooei M.S.; Masoumi, N.; Saeidi, R.; “A Novel Model of Phase Noise in Electrical Oscillators", The 17
th
International Conference on Microelectronics, 2005. ICM 2005.

[11] Bosco Leung; “Comparisons of phase noise models of CMOS ring oscillators", 51
st Midwest
Symposium on
Circuits and Systems, 2008. MWSCAS 2008.

[12] Grozing, M.; Berroth, M.; “Derivation of single
-
ended CMOS inverter ring oscillator close in phase noise
from basic circuit and device properties", 2004 IEEE Radio Frequency Integrated Circuits (RFIC) Symposium,
2004. Digest of Papers.

Any Questions ????????

Thank You !!!