VLSI Consortium workshop
29 Oct. 2010
Design and Modeling of RF Circuits
using Design of Experiments
Jai Narayan Tripathi / Jayanta Mukherjee
Department of Electrical Engineering
IIT Bombay, Mumbai
400076, INDIA.
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.
Oscillator Circuit implemented in ADS
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
combinations i.e. experiments, instead of
about 1.9 million experiments.

These combinations are taken according to
Orthogonal Array (L50).

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.
• Additive Model for factor effects
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.

Case Study 1 : Improving Eye Diagram of
RF Oscillator

Signal Integrity ensures reliable transmission at
higher speeds.

Oscillators are generally used in transceivers,
where we need good SI because the received
signal is already distorted.

The main concern is to improve Eye Diagram.
Oscillator Circuit implemented in ADS
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 L50)
The same set of experiments was
performed at following temperatures :
1.
 2.
 3.
 4.
 5.

15oC
25oC
35oC
45oC
55oC
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. 23-25, Belgrade, Serbia.
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 17th
International Conference on Microelectronics, 2005. ICM 2005.
•
[11] Bosco Leung; “Comparisons of phase noise models of CMOS ring oscillators", 51st 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 !!!