Oscillator DesignGuide Reference

This document provides reference information on the use of the Oscillator DesignGuide.

Oscillator DesignGuide Structure

The Oscillator DesignGuide is integrated into Agilent EEsof's Advanced Design System environment, working as a smart library and interactive handbook for the creation of useful designs. It allows you to quickly design oscillators, interactively characterize their components, and receive in-depth insight into their operation. It is easily modifiable to user-defined configurations. The first release of this DesignGuide focuses on RF printed circuit boards and microwave oscillations.

In addition to the requirements of the ADS software, the Oscillator DesignGuide requires approximately 30 MBytes of additional storage space.

The Oscillator DesignGuide contains templates that can be used in the ADS software environment. It consists of generic colpitts, clapp, modified colpitts, modified clapp, and hartley oscillator design examples, and a library of components and component characterization tools.
To assist both expert and novice oscillator developers in creating designs of various complexity, each example design is divided into three groups:

• Quick and simple push-button nonlinear oscillator measurements
• Easy-to-use design tools for small- and large-signal designs
• Customized library of components and component characterization tools

To access these groups, select DesignGuide > Oscillator DesignGuide from the ADS Schematic window, then select the appropriate examples and tools.

Push-Button Nonlinear Measurements

The push-button nonlinear measurements are recommended as a starting point for both expert and novice users creating large-signal designs. For the expert, these measurements provide an overview of tool capabilities. For the novice user, they provide a working oscillator together with simulations of its typical characteristics of nonlinear designs. The full set of available large-signal measurements in the Generic Oscillator example are described in the following table. Subsets of these measurements appear in other examples. Refer to the section Additional Examples

Descriptions of Push-Button Measurements

Linear and Nonlinear Design Tools

The linear and nonlinear design tools are intended to facilitate you in designing an oscillator from scratch and in gaining insight into an existing oscillator. The full selection of tools is contained in the Generic Oscillator example. Other examples use only those tools that are useful in their particular case.

Descriptions of Design Tools

Components and Component Characterization Tools

The items in the Components and Component Characterization libraries contain a small custom library of resonators and devices, which can help in either modifying an existing oscillator or assembling a new one. They include device DC and S-parameter characteristics, as well as resonator and filter S-parameter and impedance/admittance characteristics.

The following tables provide schematic filenames and brief descriptions for each component and brief descriptions for each component characterization tool.

Active Device Components

Subcircuit Components

Oscillator Core Circuits

The following image shows the cClappCore.dsn oscillator core schematic symbol.

Bipolar Clapp Oscillator Schematic Symbol

The cClappCore.dsn oscillator operates from 0.5 to 15GHz using the existing component values in the Clapp oscillator sub-circuit. Resonator tank components Ct and Lt are automatically calculated with approximations referenced to 1GHz and displayed on some display pages. The Ground or Series Resonator port is either connected directly to ground or connected to ground through a series resonator. The Variable Capacitance Tuning Port is used for VCO design by coupling a varactor diode across the tank capacitor Ct. Coupling is accomplished by capacitor Ccpl. Larger values of Ccpl yield tighter coupling and wider tuning range for a given amount of tuning capacitance variation. The OscPort1 and OscPort2 ports are either connected directly together or connected through a series resonator. You can connect the OscPort test probe between these two ports for harmonic balance oscillator simulations. The Output Port is used for oscillator signal output. The variable Ctune sets the oscillator at the desired oscillation frequency when the capacitance across the Variable Capacitance Tuning Port is equal to the Ctune set value. The following image shows an example of the Clapp Oscillator subcircuit.

Bipolar Clapp Oscillator Subcircuit

Increase capacitors C1 and C2 for lower frequency oscillator circuits. Adjust resonator frequency offset (currently 390E6) to recenter oscillator frequency.

Bipolar Hartley Oscillator Schematic Symbol

The preceding image shows the cHartleyCore.dsn oscillator core schematic symbol. This oscillator operates from 1 to 1000MHz using the existing component values in the Hartley oscillator sub-circuit. The resonator tank component Ct is scaled from 500MHz with an approximation and displayed on some display pages. You can connect the Ground or Series Resonator to the port directly to ground, or it can be connected to ground through a series resonator. The Variable Capacitance Tuning Port is used for VCO design by coupling a varactor diode across the tank capacitor Ct. Coupling is accomplished by capacitor Ccpl. Larger values of Ccpl yield tighter coupling and wider tuning range for a given amount of tuning capacitance variation. The OscPort1 and OscPort2 ports are either connected directly together or connected through a series resonator. For harmonic balance oscillator simulations, connect the OscPort test probe between these two ports. The Output Port is used for oscillator signal output. The variable Ctune sets the oscillator at the desired oscillation frequency when the capacitance across the Variable Capacitance Tuning Port is equal to the Ctune set value. The following image shows the Hartley Oscillator subcircuit.

Bipolar Hartley Oscillator Subcircuit

Increase inductors L1 and L2 for lower frequency oscillator circuits. Adjust resonator capacitor Ct reference value (currently 21.3pF) to recenter oscillator frequency.

Bipolar Modified Clapp Oscillator Schematic Symbol

The preceding image shows the cModifiedClappCore.dsn oscillator core schematic symbol. The cModifiedClappCore.dsn oscillator operates from 0.7 to 7.2GHz using the existing component values in the Modified Clapp oscillator sub-circuit. Resonator tank components Ct and Lt are automatically calculated with approximations referenced to 1GHz and displayed on some display pages. The Ground or Series Resonator port can be connected directly to ground or connected to ground through a series resonator. The Variable Capacitance Tuning Port is used for VCO design by coupling a varactor diode across the tank capacitor Ct. Coupling is accomplished by capacitor Ccpl. Larger values of Ccpl yield tighter coupling and wider tuning range for a given amount of tuning capacitance variation. The OscPort1 and OscPort2 ports are either connected directly together or connected through a series resonator. You can connect the OscPort test probe between these two ports for harmonic balance oscillator simulations. The Output Port is used for oscillator signal output. Variable Ctune sets the oscillator at the desired oscillation frequency when the capacitance across the Variable Capacitance Tuning Port is equal to the Ctune set value. The following image shows the Modified Clapp Oscillator subcircuit.

Bipolar Modified Clapp Oscillator Subcircuit

Increase capacitors C1 and C2 for lower frequency oscillator circuits. Adjust resonator frequency offset (currently 290E6) to recenter oscillator frequency.

Bipolar Modified Colpitts Oscillator Schematic Symbol

The preceding image shows the cModifiedColpittsCore.dsn oscillator core schematic symbol. This oscillator operates from 0.8 to 6.5GHz using the existing component values in the Modified Colpitts oscillator sub-circuit. Resonator tank inductor Lt is automatically calculated with an approximation and displayed on some display pages. The Ground or Series Resonator port can be connected directly to ground or connected to ground through a series resonator. The Variable Capacitance Tuning Port is used for VCO design by coupling a varactor diode across the tank inductor Lt. Coupling is accomplished by capacitor Ccpl. Larger values of Ccpl yield tighter coupling and wider tuning range for a given amount of tuning capacitance variation. The OscPort1 and OscPort2 ports are either connected directly together or connected through a series resonator. Connect the OscPort test probe between these two ports for harmonic balance oscillator simulations. The Output Port is used for oscillator signal output. The variable Ctune sets the oscillator at the desired oscillation frequency when the capacitance across the Variable Capacitance Tuning Port is equal to the Ctune set value. The following image shows the Modified Colpitts Oscillator subcircuit.

Bipolar Modified Colpitts Oscillator Subcircuit

Increase scaled 10nH inductance reference value for lower frequency oscillator circuits. Tank inductance Lt is scaled from 1GHz using an approximation. Increasing C1 and C2 capacitors yields a lower frequency oscillator as well.

Available Component Characterization Tools

Generic Oscillator Example

The oscillator circuit for the Generic Oscillator example is set up as follows:

• Resonator
• Oscillator active part (OscCore)
• Lload, which can include buffering amplifier and matching circuits

The tools consists of three parts, as explained in the Oscillator Design Guide Structure section.
For simplicity, we show the buffering amplifier in two designs only and don't include the matching circuits. The generic resonator is presented here by a series resonant circuit shunted by a capacitance, which can model either a tuning capacitance, or the effect of packaging.

The OsCore is the Colpitts structure, which was introduced soon after the invention of triode (called audion at the time). It is still widely used. It uses a capacitive RF transformer to provide feedback. The transformer capacitors together with the inductor determine the oscillation frequency f = 1/sqrt(L × C1 × C2/(C1+C2)).

The Load models impedance, as seen by the OsCore component. Typically, this is the input impedance of the buffering amplifier(s) (including matching circuits) and the actual load.

Oscillator Simulation

The oscillator designs included in this DesignGuide provide easy access to observing the nonlinear behavior of an oscillator. The circuit design for the generic example is shown in the Structure of Oscillator Circuit section It includes fixed load, a clearly visible active circuit, and the tunable resonator separated by the OscPort component.

Structure of Oscillator Circuit

Single-Frequency Oscillations

The results of single-frequency oscillations in the following image show output and resonator voltages. They also provide oscillations frequency, power harmonic content, the corresponding time-domain waveform, and the values of DC power and RF output power.

Results of Single-Frequency Oscillations

Dynamics of Single-Frequency Oscillations

The graph in the following image shows waveforms of Collector-Emitter voltage and the collector current of the OsCore BJT superimposed on BJT's DC characteristics.

Dynamics of Single-Frequency Oscillation

Single-Frequency Oscillations with Noise

The graph in the following image shows single-frequency results with the noise characteristics of Vout and Vres. It also lists the components that affect the noise the most. You can specify the range after which small contributors to noise will be neglected. In this example, the range is set to 15 dB.

Single-Frequency Oscillations with Noise

Frequency Pulling

The following image shows results after the original circuit is modified for frequency pull. Changes include the varying load and a simple buffer amplifier, which was added to make pulling values realistic. The load is specified in terms of VSWR. You can determine the best variation. The graph shows that frequency variation for varying phase of the load. VSWR is fixed, with its value shown above the plot. By moving the marker on the VSWR selection plot, you can obtain the results for other VSWR values. The corresponding load characteristic and the corresponding value of Vout fundamental are shown in the lower plots. The equation with pulling value will be added.

Results with Circuit Modified for Frequency Pulling

Frequency Pushing

The following image shows results after the frequency pull circuit is modified for frequency push, with fixed load (vswr=1, phi =0) and varying bias on oscillator's transistor Vcc. The display presents frequency variation with Vcc.

For Vcc=8V, the circuit does not oscillate, which results in the error message. Nevertheless, the sweep is performed, showing oscillations for higher bias. Two markers on the plot allow us to zoom in at the frequency plot. The plot to the right is determined by markers position. The corresponding value of Vout fundamental is shown in the lower plot.

Results with Circuit Modified for Frequency Pushing

Tuned Oscillations

The following image shows the resonator voltage and its harmonics. It provides the tuning characteristics of sweeps vs. capacitance vs. frequency.

Resonator Voltage and Harmonics

Linear Design Tools

The designs used for linear applications provide tools to investigate oscillations conditions. They belong to two groups, as follows:

• Necessary oscillation conditions
• Check for Nyquist stability criterion, using the linearized version of the OscPort component, called OscTest.

Load-to-Resonator Mapping

Load-to-resonator mapping is represented by the design MapLoad.dsn and the graph MapLoad.dds. The design consists of the oscillator circuit without the resonator. The buffer and load are replaced by varying load. The load values correspond to main traces on a Smith chart (shown in the loadmap.dds display). You can specify the number of samples per trace and the radius of the small circle. On the resonator side, the circuit is terminated by an S-parameter port. S-parameter analysis is performed over frequency band determined that you specify so that the mapping can be analyzed at various frequencies.

The purpose of the analysis is to observe how the different values of the load will be detected by the resonator. The values that map outside the unit circle are of particular interest. These are the values that will provide negative resistance facing the resonator, so that the necessary oscillations conditions will be satisfied.

The graph MapLoad.dds, as shown in the following image, represents load values and their image in the resonator plane. Color-coded markers facilitate orientation. The marker on the bottom plot selects frequency at which the mapping is performed.

Load Values and Their Image in Resonator Plane

Resonator-to-Load Mapping

Resonator-to-load mapping is represented by the design MapInput.dsn and the graph MapInput.dds, as shown in the following image. The design is dual to load-to-resonator mapping, and it determines the image of the resonator at the buffer amplifier input. Consequently, it is useful in designing of the amplifier matching circuit. A special case restricted to a unit circle input gave rise to the method of stability circles (see Reference 1 in the Bibliography ).

Resonator-to-Load Mapping

Stability Via Nyquist Plots

The design Nyquist Stab shows the use of the OscTest component. The results shown for different choices of the OscTest characteristic impedance Zo illustrate the importance of the Nyquist plot. Zo is swept from 1.5ohm to 21.5 ohm in 10 steps. The plots clearly show that it is the encirclement of 1+j0 that matters (as we know from the Nyquist theorem) and not the value of S11 at the crossing of the real axis. The justification of this statement is illustrated by two simple designs (NyqStab, NyqStabA) described in the next section.

Resonator-to-Load Mapping

Theory of Stability vs. Nyquist Plots

There is a widespread belief [3,7,9,10,11,12,13,14,15] that the stability of oscillators can be determined by a particular criterion. When the phase of the transfer function is zero and the magnitude (at the same frequency) is larger than one, the system is unstable. The circuit shown in the criterion is usually presented as two equations:
arg(Sn) = -arg(Sr), | Sn Sr | > 1
Consider a simplest possible linearized oscillator, as shown in the following image. The circuit has the resonator's resistance rr=1/G = 100.0 ohm and the active (linearized) resistance ra = 1/g'(Vo) = -5.0 ohm and is obviously unstable.

Stability Via Nyquist Plots

The Nyquist plots and equation were checked for different values of the characteristic impedance Zo. The system stability depends on the position of poles of the transfer function Sr(s)Sn(s). If the function possesses poles in the right half plane, the system is unstable. It follows from the Nyquist criterion that the presence of poles in the right-half plane and the system instability can be determined by the encirclements of point 1+j0 by the osctest generated contour S11 = Sr(jw)Sn(jw).

The Nyquist plots obtained for Zo = 2.0, 82.0, 162.0 ohm are shown in the following image.

Nyquist Plot for Simple Linearized Oscillator

The three values of Zo are chosen so that we get respectively:
Zo < |ra| < rr, |ra| < Zo < rr
and
|ra| < rr < Zo
The circuit is obviously unstable. Consequently, the Nyquist loop, shown in the plots on the left in the following image, encircles the point 1+j0 for every value of Zo. However, if we turn to the magnitude-phase plots (shown to the right), then the circuit instability will be hard to deduce. Finally the intuitive condition (1)( SnSr >1 for arg(SnSr)= 0) obviously fails for Zo = 82.0 and Zo=162.0 ohm.

The SrSn contours clearly show that it is the encirclement of 1+j0 that matters (as we know from Nyquist theorem) and not the value of SnSr at the crossing of the real axis.

The Nyquist criterion is most useful when the open loop system is stable. In that case, the stability of the feedback system is determined by the closing of the feedback loop. The following image shows a variation of our original circuit.

Nyquist Plot for Simple Circuit

In the circuit shown, the resistances were interchanged, resulting in an active resonator, for which adding the 100 ohms in parallel (i.e. loop closing) does not change its instability. Obviously, in this system, the Nyquist loop does not encircle the 1+j0 . This is because the open loop transfer function Yn Zr = (s/rrC)/(s² +s/raC + 1/LC) has two poles in the right half plane and loop closing does not add any new poles.

Therefore the position of the OscTest probe (which automatically computes SrSn in the simulator) should be carefully chosen. It should be placed between the resonator and the active circuit so that the open-loop system is stable.

The plots of S11 for Zo = 2.0,82.0,162.0 need to be considered.For Zo = 82.0, 162.0 the Nyquist loop does not encircle 1+j0, as expected. However, for Zo=2.0 it does, which seems contrary to the fact that the resonator circuit is active. The explanation for this is that the open loop S-parameter transfer function:
Sr(s) = (Zr-Zo)/(Zr + Zo)= - (s2 + s((1/ra)-(1/Zo))/C+1/LC)/(s2 + s((1/ra)+(1/Zo))/C+1/LC)
has all poles in the left hand plane for Zo<|ra|. Only closing the loop makes the system unstable.

Using Nonlinear Design Tools

Large-Signal S-Parameter Design

In the steady-state, because of intrinsically nonlinear behavior of oscillators, signals are no longer sinusoidal. Consequently, the concepts of impedance and S-parameters are not obvious. However, in high-Q circuits, in which signals are represented by their fundamental components, there is a natural way to define the large-signal impedance, or large-signal S-parameters. In this section, we define the large signal S-parameters and demonstrate that the equations
arg(Sn) = - arg(Sr)
| Sn Sr | = 1
determine amplitude and phase of oscillations.

The steady state periodic oscillations can be represented by their Fourier series:
v(t) = Σ |vn| cos(nωt + jn) i(t)= Σ |in| cos(nωt + ψ n)

For a high-Q resonator the higher harmonics are negligibly small and voltage and current can be approximated by:
v(t) ≈ |V| cos(ωt + j)
i(t) ≈ |I| cos(ωt + ψ )
where
V = |V| exp(jj), and I = |I| exp(jψ)
denote the fundamental components of voltage and current.

Thus the signals are represented by their complex amplitudes V and I, for which we define the large-signal incident and reflected waves:
a = (V + Zo × I)/(2 √ Zo), b = (V - Zo × I )/(2 √ Zo)

On the resonator side, we have a = Sr b , with b = b(a) on the active circuit side. These two relationships provide us with the steady-state equations a = Sr b(a). After defining the large signal S-parameter: Sn = b(a)/a the steady state equation can be represented as a = Sr Sn a, which leads to: 1 = Sr Sn, which is equivalent to the equations.

Solving Harmonic Balance Convergence Problems

Harmonic balance simulation in Advanced Design System is an excellent way to analyze many oscillators in the frequency domain. Occasionally, you might have an oscillator that converges in a time-domain simulation, but the harmonic balance oscillator algorithm is unable to find the solution. There are two techniques in ADS for solving those oscillators:

• Analyzing the large-signal loop gain in harmonic balance to find the point of oscillation and using that as an initial guess for the full harmonic balance oscillator analysis
• Using a transient analysis to produce an initial guess for harmonic balance oscillator analysis.

In the DesignGuide > Oscillator menu, select Solving Harmonic Balance Conversion Problems for several useful design examples.

For more information on these techniques, refer to Simulation Techniques for Recalcitrant Oscillators.

Oscillator Core Examples

Oscillator Cores (cClappCore, cHartleyCore, cModifiedClappCore, and cModifiedColpittsCore) are compatible with simulation and measurement setups outlined by the Generic Oscillator Example. These core oscillator circuits are configured for low resistance loads. (50ohm is used for these four oscillator cores, although other load values are possible.) The design and display filenames for these examples follow a naming convention that indicates oscillator type and simulation setup as follows:

• OscillatorTypeSimulationType.dsn
• OscillatorTypeSimulationType.dds

where:
OscillatorType indicates one of the following topologies: Clapp, Hartley, Modified Clapp, or Modified Colpitts.
SimulationType provides one of the following simulation set-ups or measurements: FixedFreqOsc, FreqPull, FreqPush, FreqTune, LSSpar, MapInput, MapOutput, NyqStab, or Phase Noise.

For example, the simulation that determines oscillator frequency of a Clapp oscillator has the design filename ClappFixedFreqOsc.dsn and a data display filename ClappFixedFreqOsc.dds. This simulation predicts oscillation frequency, output power, and calculates tank components Lt and Ct. The accompanying data display presents these results.

The cClappCore circuit is used to illustrate available simulation setups offered in the design guide.

Oscillator Core Circuit Simulation Connections

The preceding image shows the Clapp oscillator harmonic balance simulation ClappFixedFreqOsc.dsn that determines oscillation frequency, output power and tank component values at 1GHz. The OscPort probe is shown connected between the active device and tank resonator. Resonator tank components Lt and Ct are computed and shown on the companion data display page.

Oscillator Core Series Resonator Connection Alternatives

Oscillator core circuits (cClappCore, cHartleyCore, cModifiedClappCore, and cModifiedColpittsCore) are compatible with series resonators in two ways.

Series Resonator Connection Between Tank and Active Circuit

The first possibility shown in the preceding image connects the series resonator between the tank circuit and active device. If resonator losses are low, the series resonator can also be connected between the bipolar base terminal and ground as shown in the following image.

Series Resonator Connection Transistor Base and Ground

Additional Examples

Following are examples in addition to the primary example, as described in Generic Oscillator Example.

The design and display filenames for these examples follow the generic oscillator naming convention with 3-letter prefixes attached to the generic names, as follows:

• xxxgenericoscillator name.dsn
• xxxgenericoscillator name.dds

where xxx stands for one of: saw, vco, xto, or yto.
For example, VCO Large Signal S-Parameters have the filenames vcoLSSpar.dsn and vcoLSSpar.dds.

Crystal Oscillator (XTO)

These oscillators are notable for their high frequency stability and low cost. Typical structure is that of a Colpitts oscillator with quartz crystal resonator introduced into feedback path. Mechanical vibrations of the crystal stabilize the oscillations frequency. Vibration frequency is sensitive to temperature. Therefore, temperature compensation circuits are often used to improve frequency stability. Crystal resonators are typically used in the range up to 100 MHz (to a few hundreds of MHz if resonating on overtones).

SAW Resonator Oscillator (SAW)

Principle of operation is similar to that of crystal oscillator with the quartz resonator replaced by a Surface Acoustic Wave oscillator. SAW resonators are used in frequency range up to 2 GHz.

Voltage Controlled Oscillator (VCO)

In any of the preceding structures, frequency tuning can be provided by adding a varactor diode to the resonator. The varactor diode serves as a voltage controlled capacitor. It has very fast tuning speed (GHz/nsec) and low Q. Consequently, the varactor can be used with LC elements to provide wide tuning (with poor frequency stability) or with a crystal, SAW or DRO resonator for narrow tuning with better frequency stability.

At microwave frequencies, the device capacitances become significant, resulting in a different (often simpler) circuit. The operation principles, remain the same.

YIG Tuned Oscillator (YTO)

For a very wide band (that can reach decade) tuning with high frequency stability and for frequency range of 1 GHz to 50 GHz. YIG (Yttrium-Iron-Garnett) resonators are used. The YIG sphere behaves like a resonator with 1000-to-8000 unloaded Q resulting in very good frequency stability. The resonator are tunable over wide bandwidth with excellent linearity (~0.05%). For fine tuning (for phase-lock), or frequency modulation an FM coil can be added.

Bibliography

1. G.R.Basawapatna, R.B.Stancliff, "A Unified Approach to the Design of Wide-Band Microwave Solid State Oscillators," IEEE Trans. MTT-27, May 1979, pp 379-385.
2. Fundamentals of Quartz Oscillators" HP Application Note 2002.
3. R. T. Jackson, "Criteria for the Onset of Oscillations in Microwave Circuits," IEEE Trans. MTT-40, Mar 1992, pp 566-568, "Comments on ``Criteria...,'' IEEE Trans. MTT-40, Sept 1992, pp1850-1851.
4. A. P. S. Khanna, "Oscillators" in Chapter 9 of "Microwave Solid State Circuit Design" by I. Bahl P. Bhartia, J.Wiley 1988.
5. Khanna and Obregon - "Microwave Oscillator Analysis" - IEEE Trans.vol. MTT-29, June 1981, pp 606-607.
6. M.Odyniec, "Nonlinear Synchronized LC Oscillators, Theory and Simulation," IEEE Transactions, MTT-41, May 1993, pp 774-780.
7. M.Odyniec, "Benchmarks for Nonlinear Simulation," APMC'94, Tokyo, Japan, Dec. 6-9 1994.
8. M.Odyniec, "Stability Criteria via S-parameters," EUMC'95, Bologna, Italy, Sept. 4-8, 1995.
9. V.Rizzoli, F. Mastri, and D, Maroti, "General noise analysis," IEEE Trans. MTT-37, Vol.1, No. 1, January 1989.
10. C. Schiebold, "Getting Back to the Basics of Oscillator Design," Microwave Journal, May 1998.
11. J.C. Slater, "Microwave Electronics," Van Nostrand, Princeton, 1950.
12. "S-parameter Design," HP Application Note 159 .
13. A. Sweet, "MIC and MMIC Amplifier and Oscillator Circuit Design," Artech House, Boston 1990.
14. D. Warren et al., "Large and Small Signal Oscillator Analysis," Microwave Journal, May 1989.
15. J.J. D'Azzo, C. H. Houpis, "Feedback Control Systems," McGraw-Hill New York 1960.
16. J. W. Boyles, "The Oscillator as a Reflection Amplifier..." Microwave Journal, June 1986.
17. J.L.J. Martin and F.J.O.Gonzalez, "Accurate Linear Oscillator Analysis and Design," Microwave Journal, June 1996.
18. Z. Nativ and Y. Shur, "Push-Push VCO Design with CAD Tools. "
19. Microwave Journal, February 1989.
20. M. Odyniec, "Stability Criteria via S-parameters "European Microwave Conference, Bologna, Italy, September 1995.
21. A. Przedpelski, "Simple, Low Cost UHF VTOs "RF Design," May 1993.
22. N. Ratier et al. "Automatic Formal Derivation of the Oscillation Condition", IEEE Int. Frequency Control Symp. 1997.
23. T. Razban et al.,"A Compact Oscillator..." Microwave Journal, February 1994.
24. S. Savaria and P. Champagne, "Linear Simulators..." Microwave Journal, May 1995.

Selected Papers

1. Basawapatna and Stancliff - "A Unified Approach to the Design of Wideband Microwave Solid State Oscillators" - IEEE trans. vol MTT-27, May 1979, pp 379-385.
2. Khanna and Obregon - "Microwave Oscillator Analysis" - IEEE Trans. vol. MTT-29, June 1981, pp 606-607.
3. M.Odyniec, "Nonlinear Synchronized LC Oscillators, Theory and Simulation," IEEE Transactions, MTT-41, May 1993, pp 774-780.
4. M.Odyniec, "Benchmarks for Nonlinear Simulation," APMC'94, Tokyo, Japan, Dec. 6-9 1994.
5. M.Odyniec, "Stability Criteria via S-parameters," EUMC'95, Bologna, Italy, Sept. 4-8, 1995.