No Slide Title - Autenticação · 2 Introduction Microwave oscillators form an important part of...
Transcript of No Slide Title - Autenticação · 2 Introduction Microwave oscillators form an important part of...
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RF Oscillators
Profª. Maria João Rosário
Instituto de Telecomunicações
Av. Rovisco Pais, 1049-001 Lisboa
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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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Examples
• Oscillator using GaAs technology
Oscillator for 1.5GHz, F20 GEC Marconi
Layout Output Spectrum