Distributed Microwave Oscillators: theory and design

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Distributed Microwave Oscillators theory and
design
Alessandro Acampora PhD Student Centre
Tecnologic de Telecomunicacions de Catalunya
(CTTC) Weekly Seminar Series, 10/06/2009
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Outline

• Motivation and Objectives
• Linear and Nonlinear Analysis of an Oscillator
• Numerical techniques for analyzing circuit at µW
  frequencies
• Time Domain
• Frequency Domain
• Parametric Analysis of nonlinear circuits
• Distributed Oscillators and VCO
• Examples
• Design Procedure of a reverse mode DVCO
• Simulation Results
• Implementation and test of a four stage R-DVCO
• Measurements Results
• Conclusions and Future Work

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Motivation Top level perspective

• A plethora of coexisting telco services overcrowd
  the transmission bands (mostly UHF band ,0.3 to
  3 GHz)
• GSM, UMTS standard for mobile telephony
• Wi-Fi or IEEE 802.11(x) for wireless local area
  networks
• WIMAX for Broadband Regional wireless access to
  the Internet
• Wireless information exchange requires ever
  increasing bit rates to support multimedia
  services (translates in need for more bandwidth)
• A flexible receiver architecture would be needed
  to catch signals transmitted at different
  frequencies in a certain range
• Higher data rate services could be more easily
  allocated to higher frequencies

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Device perspective

• Design and implement wide-band tunable receiver
  sub- components
• Oscillators (Voltage Controlled Oscillator)
• Mixers
• The aim will be pursued investigating appealing
  solutions by means of
• Theoretical Analysis
• Simulation, by means of EDA software
• Implementation Test
• Measurements

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SmallSignals (linear) Analysis of a FET Amplifier

• When signals have small magnitude, linear
  approximation holds for the voltages and currents
  of an active device.

Signals cause small variations around a quiescent
point.
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Block Diagram of a Positive Feedback Oscillator

• An oscillator consists of
• an Amplifier (made up of active devices
  transistors)
• a Frequency Selective Network (reactive elements,
  crystal, resonant cavities)
• a Feedback Path, providing regeneration of the
  signal in order to build-up oscillations

Nyquist Criterion for the onset of oscillations
Energy is converted from DC to AC
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Linear Analysis of a Negative Resitance Oscillator

• Partition of the circuit in two parts
• Resonator
• Active part providing negative resistance to
  ensure oscillation start-up and compensate for
  losses

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Determining the oscillation frequency

• The real part of the output admittance is
  negative (delivering power)
• The imaginary part presents positive slope

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Drawbacks of Linear Analysis

• Provides only an estimate of the oscillation
  frequency
• No information about the amplitude (power)
• neither about the harmonic content
• neither about possible spurious oscillations!
• Fact we are neglecting the nonlinear behaviour
  of the FET!
• Linear Analysis result could still be useful as a
  first guess

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Numerical Analysis in Time Domain

• Expression of the fundamental circuit variables
  by means of a system of differential equations

Forward Euler (one step explicit method)
Backward Euler (one step implicit method)
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Numerical Analysis in Frequency Domain Harmonic
Balance

• Time domain simulation could be computationally
  expensive (computation time vs storage
  requirements)
• What is the right time step?
• A network containing distributed elements ( i.e.
  microscrostrip lines) would give rise to
  complicated differential delay equations
• Assuming a periodic behaviour (1- tone
  excitation), taking the Fourier transform at both
  sides

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Harmonic Balance for Autonomous Circuits

• When the circuit to be analyzed is not externally
  forced by input generators, frequency is an
  unknown.
• Convergence to DC steady state solution when
  analyzed with the classical HB.
• Auxiliary generators, mimic the behavior of the
  real ones ? avoid the DC equilibrium point!
  quéré , 1992

The probe is inserted in parallel between an
output node and a reference point (GND).
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Parametric Analysis

• Trace the solution curve versus a critical
  parameter?
• Correspond to a succession of HB problems!
• Difficulties arise when considering multi-valued
  solution curve? a parameter switching algorithm
  is invoked to overcome this difficulty

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Distributed Amplifier Basics

• Distributed Amplifier an old idea to overcome
  the bandwidth-gain limitations Ginzton,1948
• Coupling N stages by means of k-filter sections
  a linear increase in gain is observed, without
  compromising the bandwidth Wong, 1993.

Currents from each output stage are combined in
an additive fashion while parasitic capacitances
are not accumulated
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Forward mode Distributed Oscillator

• Idea add a feedback path and a frequency
  selective network to obtain an oscillator
  Hajimiri, 2001
• The physical length of the path determines the
  operating frequency (as it gets shorter, the
  frequency gets higher)
• Possibility of inserting a varactor diode in
  order to provide limited tuning capabilities

Forward propagating waves are reinserted in the
input line through the feedback loop
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Reverse mode Distributed Voltage Controlled
Oscillator (1)

• Removing drain resistor, it is possible to
  connect drain and gate line together in a
  reverse manner to take advantage of backward
  propagating waves Skvor, 1992
• Effective path length changes when we activate
  one stage at a time, leaving the others switched
  off
• As a consequence, a discrete set of frequencies
  will appear distributed in the pass-band of LC
  filter sections

Higher Frequency correspond to the activation
of the first stage while lower frequency to the
activation of the last one
Transistor T2 is placed crosswise in order to
provide extra gain
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Reverse mode Distributed Voltage Controlled
Oscillator (2)
Impedance of a low pass constant-k filter section
Reverse Gain of the Distributed Amplifier Divina
and Skvor, 1998
The choice of the matching sections is critical
to avoid spurious oscillations!
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Reverse mode Distributed Voltage Controlled
Oscillator (3)

• Tuning capabilities biasing in a complementary
  fashion, two adjacent stages at a time
• A continuous set of frequencies are obtained,
  between two discrete ones Divina and Skvor,
  1995
• Intuitive explanation biasing simultaneously two
  transistor changes the effective path length of
  the feedback signal

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Nonlinear Analysis and Design of a reverse mode
DVCO

• Design Requirements
• Four stages
• Tunable in the range 1 to 3 GHz
• Flat output power (limited fluctuations around 5
  dBm)
• Step-by step approach.
• first schematic included only real transistor
  models, and idealized lumped components and TL
  sections
• linear analysis is performed by checking
  negative resistance zones ? estimate of the
  oscillation frequencies (see next slide)
• Parameters of the LC-sections are chosen
• HB simulation provides the power and harmonic
  content for each discrete frequency

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Simulated Negative Conductance Zones
When each transistor is independently biased we
obtain a zone in which its output admittance
becomes negative. These zones partially overlap
assuring a continuous tuning range!!
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From Schematic to Layout.
The values for LC sections were tuned after
the introduction of layout elements
Vendor model for inductors and capacitors has
been used with appropriate values L3.3 nH and
C1.2 pF assure a (close to) 50 Ohm impedance and
5 GHz for the cut-off frequency of the k constant
filter section
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Nonlinear Analysis and Optimization of a reverse
mode DVCO (2)
Simulations performed by sweeping the frequency,
observing tuning voltages in pairs
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Optimized Output Power

• Heuristic procedure to demonstrate that some
  different biasing scheme (using three stages)
  could lead to a smooth output power
• Tuning performance is nearly the same, while
  output power variations are noticeably reduced

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Measurements Results (1) Tuning
Tuning range 750 MHz to 1.84 GHz
Frequency Gaps are present, the most critical is
between 1.425 and 1.650 GHz
Lab Experience Facing with Hysteresis Phenomena
and Instabilities.
Variation of the bias voltages is highly
symetrical (matching with simulation!!)
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Measurements results (2) Output Power, Current
Consumption
Output power curve and DC current show similar
trends.
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Lesson learned from DVCO implementation

• Accuracy of lumped inductors models was found to
  be critical (shift in the frequency range) and
  vendor -dependent
• Comparison with vendors models and extracted
  parameters (via calibration kit Vector Network
  Analyzer) gave higher value for the measured
  inductances
• Redesign the TL sections in between the first and
  third stage giving them smaller lengths would
  probably reduce the gaps in frequency
• Fine tuning of the lumped elements to reduce
  spurious and unwanted oscillations

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Future Work

• Extend the DVCO tuning range (3 to 10 GHz)
• Study the phase noise in DVCO
• Identify the critical parameters to study
  qualitative change in DVCO behaviour
• Apply the mentioned techniques to study other
  RF/MW sub-components (frequency dividers)

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References

• Wong, 1993 Thomas T.Y. Wong, Fundamentals of
  Distributed Amplification, London, UK Artech
  House 1993. 
• Ginzton,1948 E. L. Ginzton, W. R. Hewlett, J.
  H. Jasberg, and J. D. Noe, Distributed
  Amplification, Proc. IRE, pp. 956-69, August
  1948.
• Kundert, 1990 K.S. Kundert, J.K. White, A.
  Sangiovanni-Vincentelli, Steady-state methods for
  simulating analog and microwave circuits, Kluwer
  Academic Publishers, 1990
• Wu and Hajimiri,2001 H. Wu, A. Hajimiri,
  Silicon-Based Distributed Voltage-Controlled
  Oscillators, IEEE Journal Of Solid-State
  Circuits, VOL. 36, NO. 3, March 2001, pp 493-402
• Skvor, 1992 Z. Skvor, S. Saunders, and C. S.
  Aitchitson, Novel decade electronically tuneable
  microwave oscillator based on the distributed
  amplifier Electron. Lett., vol. 28, no. 17, pp.
  16471648, Aug. 1992. 
• Divina and Skvor, 1995 L. Divina and Z. kvor,
  Experimental verification of a distributed
  amplifier oscillator, in Proc. 25th EuMC 1995
  Conf.. Kent, U.K. Nexus Media Limited, 1995, pp.
  11631167. 
• Divina and Skvor, 1998 L. Divina, Z. Skvor,
  The Distributed Oscillator at 4 GHz, IEEE
  Transactions On Microwave Theory And Techniques,
  VOL. 46, NO. 12, December 1998, pp 2240-2243.

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Thanks for your kind attention!

• Questions?

Alessandro Acampora Ph.D Student , CTTC Centre
Tecnologic de Telecomunicacions de
Catalunya alessandro.acampora_at_cttc.es