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RF Oscillators

Profª. Maria João Rosário

Instituto de Telecomunicações

Av. Rovisco Pais, 1049-001 Lisboa

mrosario@lx.it.pt

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Introduction

Microwave oscillators form an important part of all

microwave systems such as those used in radar,

communication links, navigation and electronic

warfare.

With the fast improvement of technology there has

been an increasing need for better performance of

oscillators.

The emphasis has been on low noise, small size, low

cost, high efficiency, high temperature stability and

reliability

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Introduction

• Oscillator:

A microwave oscillator is a circuit that converts DC

power to RF power

• Design:

A solid state oscillator uses an active device such

as a diode or transistor, together with a passive

circuit.

• Non linear behaviour:

Is necessary to stabilize sinusoidal steady state RF

output signal.

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Introduction

Steady state:

Begins when the output signal is periodic.

Transient Response:

Time between t=0 until steady sate is achieved. In order

to obtain growing oscillations the circuit must present

poles on the right side of the complex plan at t=0.

TR PR

Vout

t -20

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Oscillators Characterization

• Frequency of oscillation f0

Frequency of the fundamental at the output signal.

• Output Power

Available power at the output at frequency f0.

• Efficiency

Ratio between output power and the power delivered by

power supply.

• Harmonic Distortion

Due to the existence of harmonics at the output signal.

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Oscillators Characterization

• Spurious Response

Output signals at frequencies that are not related with

oscillator frequency.

• Amplitude Noise

Random variation on the output signal amplitude.

• Phase Noise

Random variation on the output signal frequency.

• Pulling

Variation of f0 due to variations of load impedance.

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Oscillators Characterization

• Pushing

Variation of f0 due to bias voltage variations.

• Long term stability

Variation of f0 due to aging processes and, or heating.

Usually is referred on long periods in time such as hours,

days, weeks, month, years and is measured in parts per

million.

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Oscillators Classification

oscillators

sinusoidal

relaxation

RC LC cristal RC Emitter

coupled I cte

Output sinusoidal Output triangular or square

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Oscillation Concepts

Oscillators are a class of circuits with 1 terminal or port, which

produce a periodic electrical output upon power up.

Most of us would have encountered oscillator circuits while

studying for our basic electronics classes.

Oscillators can be classified into two types: (A) Relaxation and (B)

Harmonic oscillators.

Relaxation oscillators (also called astable multivibrator), is a class

of circuits with two unstable states. The circuit switches back-and-

forth between these states. The output is generally square waves.

Harmonic oscillators are capable of producing near sinusoidal

output, and is based on positive feedback approach.

Here we will focus on Harmonic Oscillators for RF systems.

Harmonic oscillators are used as this class of circuits are capable

of producing stable sinusoidal waveform with low phase noise.

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Oscillation Concepts

Consider the classical feedback system with non-inverting amplifier,

Assuming the feedback network and amplifier do not load each other,

we can write the closed-loop transfer function as:

We see that we could get non-zero output at So, with Si = 0, provided

1-A(s)F(s) = 0. Thus the system oscillates!

Feedback network

F(s)

A(s)

Positive

Feedback

Si(s) + So(s)

High impedance

Non inverting amplifier

E(s)

T(S)=A(s)F(s)

)s(Si)s(F)s(A

)s(A)s(So

1+

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Oscillation Concepts

The condition for sustained oscillation, and for oscillation to startup

from positive feedback perspective can be summarized as:

Take note that the oscillator is a non-linear circuit, initially upon

power up, the condition of will prevail. As the magnitudes of

voltages and currents in the circuit increase, the amplifier in the

oscillator begins to saturate, reducing the gain, until the loop

gain A(s)F(s) becomes one.

A steady-state condition is reached when A(s)F(s) = 1.

For sustained oscillation 1-A(s)F(s)=0 Barkhausen criterion

For oscillation to startup |A(s)F(s)|>1 arg(A(s)F(s))=0

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Oscillation Concepts

Positive feedback system can also be achieved with inverting amplifier

Feedback network

F(s)

-A(s)

inversion

Si(s) + So(s)

Inverting amplifier

E(s)

T(S)=A(s)F(s)

)s(Si)s(F)s(A

)s(A)s(So

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• To prevent multiple simultaneous oscillation, the Barkhausen

criterion should only be fulfilled at one frequency

• Usually the amplifier A is wideband, and it is the function of the

feedback network F(s) to select the oscillation frequency, thus

F(s) is a high Q passive network.

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Introduction – RF Oscillator

• In RF oscillator (foscillator>300MHz), feedback method to induce

oscillation can also be employed. However, it is difficult to

distinguish between the amplifier and the feedback path, owing

the coupling between components and conductive structures on

the printed circuit board (PCB).

• An alternative perspective is to use the 1-port approach.

• We can view an oscillator as an amplifier that produces an

output when there is no input.

• Thus it is an unstable amplifier that becomes an oscillator!

• The concept of stability analysis of small signal amplifiers using

stability circles can be applied to RF oscillator design.

• Here instead of choosing load or source in the stable region of

the Smith Chart, we purposely choose load or source impedance

in the unstable region. This will result in either |ρe|>1 or |ρs|>1.

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Introduction – RF Oscillator

• For instance by choosing the load impedance at the unstable

region, we could ensure that |ρI|>1. We then choose the source

impedance properly so that |ρIρG|>1 and oscillation will start up.

• Once oscillation starts, an oscillation voltage will appear at both

the input and output of a 2-port network. So it doesn´t matter

whether we enforce |ρIρG|>1 or |ρSρL|>1, enforcing either one will

cause oscillation to occur.

• The key to fixed frequency oscillator design is ensuring that the

criteria |ρIρG|>1 only happens at one frequency, so that no

simultaneous oscillations occur at other frequencies.

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Non linear

device

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It is always possible to represent

an oscillator on the following way

Classic Theory

• Analysis as negative resistance

Block A: part of the circuit with non linear behaviour. Its behaviour

depends on the value of V (or I), but is weakly dependent on frequency.

Block B: part of the circuit with linear behaviour strongly dependent on

frequency.

Axis aa’: axis that divides the two blocks. Is an invariant of the oscillator. Is

chosen in a way that all the active elements are in block A.

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• Start-up conditions in impedance

If I sinusoidal

Classical Theory

-ZA(I,) =

ZB(ω)

Point P: graphic solution

Free oscillations I0 [ZA(I,) + ZB()]=0

0 = [ZA(I,) + ZB()].I V = -ZA(I,).I

V = +ZB().I

Condition of

oscillation

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YA(V,ω)

• Start-up conditions in admittance

If V sinusoidal

Classical Theory

-YA(V,) = YB(ω) Point P: graphic solution

Free oscillations V0 [YA(V,) + YB()]=0

0 = [YA(V,) + YB()].V I = -YA(I,).V

I = +YB().V

Condition of

oscillation

I

YB(ω) V

Re

Im

0

-YA(V)

YB(ω)

P

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• Start-up conditions in terms of reflection coefficient

Classical Theory

|ρNL| . |ρC| =1

arg(ρNL) + arg(ρC) = 0

[SNL(V)] = [bNL]/[aNL]

[SC(ω)] = [bC]/[aC]

Condition of

oscillation

SNL(V)

aNL aC

SC(ω) bNL bC

Free oscillations

[ac] = [SA(V)] . [ SC()] . [aC]

Describing the nonlinear circuit by SNL and the passive circuit by SC

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• Oscillation start-up requirements - voltages and currents

To oscillate block A must deliver power

V1A=V1B I1A=-I1B

V2A=V2B I2A=-I2B

Oscillation start-up

requirements

Classic Theory

A

B

I1A I2A

I1B I2B

V1A

V1B

V2A

V2B

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• Frequency Stability

Classic Theory

The oscillations are considered stable if any perturbation in

the RF voltage or current of the circuit at any instant decays

itself, bringing the oscillator back to its point of equilibrium

• The oscillation condition can present more then one solution

• Each solution can correspond to a stable or unstable point

Figure of merit for stability

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• Stability as negative resistance

Classic Theory

Impedances Admitances

Point P is stable if the angle ψ is between 0 and π

ψ ψ

0

Im

Re

YB(ω) -YA(V)

P

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• Phase Noise

Classic Theory

Output spectrum

Phase noise is the frequency domain representation of rapid

short-term random fluctuations in the phase of a waveform

caused by time domain instabilities. The fluctuations manifest

themselves as sidebands which appear as a noise spectrum

spreading out either side of the signal.

Phase noise is typically expressed in units of dBc/Hz

(c=carrier) representing the noise power relative to the carrier

contained in a bandwidth, centered at a certain offset from the

carrier, PN/P0/B.

f0 Δf B f

sidebands P0

PN

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Dielectric Resonators

Dielectric resonators are used

in several fields of applications

such as filters and oscillators

The whole frequency range

(0.8-50GHz) is covered through

6 selected materials with

dielectric constants ranging

from 24 to 78 and providing Q-

factor from 100000 to 40000

).L

a(

a)GHz(f

r453

340

0,5 < a/L < 2

a – radius (mm)

L – length (mm)

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Dielectric Resonators Oscillators

10GHz DRO

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Examples

Colpitz Oscillator

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Examples

• Oscillator using GaAs technology

Oscillator for 1.5GHz, F20 GEC Marconi

Layout Output Spectrum

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Examples

• Oscillator using BiCMOS technology

Oscillator for 2.4GHz, BiCMOS 0.8μm AMS

Layout Output Spectrum