Electricity: measuring and testing – Impedance – admittance or other quantities representative of... – Distributive type parameters
Reexamination Certificate
2001-03-09
2003-10-07
Le, N. (Department: 2858)
Electricity: measuring and testing
Impedance, admittance or other quantities representative of...
Distributive type parameters
C324S633000, C324S639000, C324S640000, C324S642000, C324S643000, C324S647000, C333S034000, C333S246000, C333S263000
Reexamination Certificate
active
06630833
ABSTRACT:
BACKGROUND: THE “LOAD-PULL” EFFECT
It is well known to electrical engineers generally (and particularly to microwave engineers) that the frequency of an RF oscillator can be “pulled” (i.e. shifted from the frequency of oscillation which would be seen if the oscillator were coupled to an ideal impedance-matched pure resistance), if the oscillator sees an impedance which is different from the ideal matched impedance. Thus, a varying load impedance may cause the oscillator frequency to shift.
1
1
Any electrical oscillator can be “pulled” to some extent—that is, its frequency can be shifted—by changing the net impedance seen by the oscillator. However, in many systems which use oscillators, pulling of a resonant circuit's frequency is undesirable. An oscillator which is too easily pulled may be overly susceptible to irrelevant external circumstances, such as changes in parasitic capacitance due to human proximity or temperature change. Normal techniques to avoid oscillator pulling include using isolation/buffering circuits between the oscillator and the variable load, and/or using a high-Q tuned circuit to stabilize the oscillator.
The present application sets forth various innovative methods and systems which take advantage of this effect. In one class of embodiments, an unbuffered
2
RF oscillator is loaded by an electromagnetic propagation structure which is electromagnetically coupled, by proximity, to a material for which real time monitoring is desired. The net complex impedance
3
seen by the oscillator will vary as the
2
An unbuffered oscillator is a oscillator without buffer amplifiers or attenuators. Amplifiers boost the output power and provide isolation from the load impedance changes. Attenuators decrease the amplitude while providing an isolation of two times the attenuation. In the load pulled oscillator configuration the oscillator feedback path that supplies the phase shift needed for oscillation is separated from the load.
3
A “complex” number is one which can be written as A+Bi, where A is the number's “real” part, B is the number's “imaginary” part, and i
2
=−1. These numbers are added according to the rule
(
A+Bi
)+(
C+Di
)=(
A+C
)+(
B+D
)
i,
and are multiplied according to the rule
(
A+Bi
)(
C+Di
)=(
AC−BD
)+(
AD+BC
)
i.
Complex numbers are used in representing many electrical parameters. For example, impedance can be represented as a complex number whose real part is the resistance, and whose imaginary part is equal to the reactance (inductance or capacitance).
Similarly, permittivity can be represented as a complex number whose imaginary part represents resistive loss, and whose real part represents reactive loading, by the medium, of the propagating electromagnetic wave. characteristics of the material in the electromagnetic propagation structure varies. As this complex impedance changes, the oscillator frequency will vary. Thus, the frequency variation (which can easily be measured) can reflect changes in density (due to bonding changes, addition of additional molecular chains, etc.), ionic content, dielectric constant, or microwave loss characteristics of the medium under study. These changes will “pull” the resonant frequency of the oscillator system. Changes in the medium's magnetic permeability will also tend to cause a frequency change, since the propagation of the RF energy is an electromagnetic process which is coupled to both electric fields and magnetic fields within the transmission line.
Background: Properties of a Dielectric in a Transmission Line
To help explain the use of the load-pull effect in the disclosed innovations, the electromagnetics of a dielectric-loaded transmission line will first be reviewed. If a transmission line is (electrically) loaded with a dielectric material, changes in the composition of the dielectric material may cause electrical changes in the properties of the line. In particular, the impedance of the line, and the phase velocity of wave propagation in the line, may change.
This can be most readily illustrated by first considering propagation of a plane wave in free space. The propagation of a time-harmonic plane wave (of frequency f) in a uniform material will satisfy the reduced wave equation
(∇
2
+k
2
)
E
=(∇
2
+k
2
)
H
=0,
where
E is the electric field (vector),
H is the magnetic field (vector), and
∇
2
represents the sum of second partial derivatives along the three spatial axes.
This equation can be solved to define the electric field vector E, at any point r and time t, as
E
(
r,t
)=
E
0
exp[
i
(
k·r−&ohgr;t
)],
where
k is a wave propagation vector which points in the direction of propagation and has a magnitude equal to the wave number k, and
&ohgr;=Angular Frequency=2&pgr;f.
In a vacuum, the wave number k has a value “k
0
” which is
k
0
=&ohgr;/c
=&ohgr;(&mgr;
0
&egr;
0
)
½
,
where
&mgr;
0
=Magnetic Permeability of vacuum (4&pgr;×10
−7
Henrys per meter),
&egr;
0
=Electric Permittivity of vacuum ((1/36&pgr;)×10
−9
Farads per meter), and
c=Speed of light=(&mgr;
0
&egr;
0
)
−½
=2.998×10
8
meters/second.
However, in a dielectric material, the wave number k is not equal to k
0
; instead
k=&ohgr;/(c(&mgr;
r
&egr;
r
)
½
)
=&ohgr;(&mgr;
0
&mgr;
r
&egr;
0
&egr;
r
)
½
,
where
&mgr;
r
=Relative Permeability of the material (normalized to the permeability &mgr;
0
of a vacuum), and
&egr;
r
=Relative Permittivity of the material (normalized to the permittivity &egr;
0
of a vacuum).
Thus, if the relative permeability &mgr;
r
and/or the relative permittivity &egr;
r
vary, the wave number k and the wave propagation vector k will also vary, and this variation will typically affect the load pulled oscillator frequency.
4
4
The full analysis of wave propagation in a cavity or at a boundary is much more complex, but in any case wave propagation will depend on the wave number, and the foregoing equations show how the wave number k can vary as the medium changes. See generally, e.g., R. Elliott,
Electromagnetics
(1966); J. Jackson,
Classical Electrodynamics
(2d ed. 1975); G. Tyras,
Radiation and Propagation of Electromagnetic Waves
(1969); R. Mittra & S. Lee,
Analytical Techniques in the Theory of Guided Waves
(1971); L. Lewin,
Theory of Waveguides
(1975); all of which are hereby incorporated by reference.
Frequency Hopping in a Load-Pulled Oscillator
In a typical free-running oscillator, the oscillator frequency is defined by a resonant feedback circuit (the “tank” circuit), and can also be pulled slightly by a reactive load,
5
as noted above. Thus, such an oscillator can be broadly tuned by including a varactor in the tank circuit.
6
5
The degree by which the reactive load can change the oscillator's frequency will depend on the coupling coefficient between the load and the tank circuit. Thus, an increased coupling coefficient means that the oscillator frequency will be more sensitive to changes in the load element. However, the coupling coefficient should not be increased to the point where spectral breakup (multiple frequency operation) occurs, since this would render the desired measurement of the oscillator signal impossible.
6
This is one type of voltage-controlled oscillator (VCO).
As the oscillator's frequency is thus shifted, the phase difference between the energy incident on and reflected from the load element (which is preferably a shorted transmission line segment) will change. This phase difference will be equal to an exact multiple of 180° at any frequency where the electrical length of the transmission line segment is an exact multiple of &lgr;/4.
As the oscillator frequency passes through such a frequency (i.e. one where the transmission line segment's electrical length is equal to a multiple of &lgr;/4), the load's net impedance will ch
Groover III Robert O.
Hamdan Wasseem H.
Le N.
Phase Dynamics Inc.
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