BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 are plots which illustrates a dominant RF signal's angle, a smaller signal's RF angle and a composite angle obtained by adding the two RF signals over a period;
FIG. 2 is a composite plot which illustrates a composite power for the two RF signals of FIG. 1 over a period;
FIG. 3 is a period-averaged composite angle plot which illustrates an average of the composite angle for the two RF signals of FIG. 1 over a period; and
FIGS. 4-7 illustrate a pair of examples of two RF signals' signals added together and the resultant composite signal.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
Referring first to FIGS. 1, 2 and 3, FIG. 1 shows an angle plot for two RF signals over time which includes a composite angle obtained by adding two RF signals together. The plot identified by the reference numeral 20 is the composite angle for the two RF signals. The plot identified by the reference numeral 22 is the dominant RF signal's angle. The plot identified by the reference numeral 24 is the smaller RF signal's angle. FIG. 2 illustrates a composite power plot, identified by the reference numeral 26, for the RF signals over time.
FIG. 3 illustrates a period-averaged composite angle plot, identified by the reference 28, for the composite angle of the two RF signals over time. The period-averaged composite angle 28 of FIG. 3 is the dominant signal's angle over the time period of approximately one second and has a value of −0.15 degrees. It should be noted that the average of the period-averaged composite angle 28 of FIG. 3 is the same as the dominant signal's angle 22 of FIG. 2.
In addition to the average over the frequency difference period providing the dominant signal's angle (for signals with at least a 5% difference in power return), the angle during peaks in power return provides an angle voltage centroid between the two RF signals. For the example illustrated in FIGS. 1-3, the angle at peak power, identified by the reference 30 in FIG. 1 is −0.034 (FIG. 1) for a 1.9751 volt RF signal at −0.1511 degrees and a 0.9605 volt RF signal at 0.2027 degrees.
The centroid is determined using the following expression:
where:
- A1 is the dominant RF signal's voltage and Angle1 is the dominant RF signal's angle (calculated via period averaging of composite); and
- A2 is the smaller RF signal's voltage and Angle2 is the smaller RF signal's angle.
The centroid is calculated using the expression as follows:
This calculation confirms that the angle at the power peak is equal to the centroid.
The voltage magnitude of the two RF signals is calculated by noting the power at the peak of plot 24 (FIG. 2) and the power at the minimum of plot 24. The following expression are used to determine peak power and minimum power:
Power_Peak=(A1+A2)̂2 (2)
Power_Min=(A1+A2)̂2 (3)
The dominant RF signal's voltage A1 is calculated using the following expression:
A=1/2×(sqrt(Power_Peak)+sqrt(Power_Min)) (4)
The smaller RF signal's voltage A2 is calculated using the following expression:
A2=1/2×(sqrt(Power_Peak)−sqrt(Power_Min)) (5)
For the plot illustrated in FIG. 2, the peak power is 9.36 dB and the minimum power is 0.078 dB. Converting from dB power to linear power results in the following:
Power_Peak=10̂(9.36/10)=8.63
Power-Min=10̂(0.078/10)=1.02
The dominant RF signal's voltage A1 is then calculated as follows:
A1=1/2×(sqrt(8.63)+sqrt(1.02))=1.97
The smaller RF signal's voltage A2 is then calculated as follows:
A2=1/2×(sqrt(8.63)−sqrt(1.02))=0.96
It should be note that the values of A1 and A2 calculated using expressions 4 and 5 are identical to the values used to determine the Angle_Centroid in expression (1).
The Angle_Centroid is also defined by the following expression:
Angle_Centroid=Angle_at_Power_Peak (6)
and Angle1 is also defined by the following expression:
Angle1=Angle_Averaged_Over_Period (7)
The average of Angle1 is calculated between nulls 32 (FIG. 1).
With the angle centroid Angle_Centroid being provided by the angle at which the power peaks, the dominant signal angle Angle being provided by the average composite angle over a frequency difference period, and the two signals' voltage A1 and A2 from the peak and minimum power values, the smaller signal's values can be calculated using the following expression:
Angle 2=[(A1+A2)×Angle_Centroid−A1×Angle1]/A2 (8)
Thus, both RF signals' angles can be calculated simultaneously, even though one RF signal may be dominated by the other RF signal.
Referring to FIGS. 4-7, FIGS. 4 and 5 illustrate a first example of two RF signals' signals added together. In FIG. 4, plot 40 is the dominant RF signal's angle, plot 42 is the smaller signals' angle and plot 44 is the composite angle. FIG. 5 represents the calculated angle with plot 46 representing the calculated angle for the dominant RF signal and plot 48 representing the calculated angle for the smaller RF signal.
Similarly, FIGS. 6 and 7 illustrate a second example of two RF signals' signals added together. In FIG. 4, plot 50 is the dominant RF signals' angle, plot 52 is the smaller signals' angle and plot 54 is the composite angle. FIG. 5 represents the calculated angle with plot 56 representing the calculated angle for the dominant RF signal and plot 58 representing the calculated angle for the smaller RF signal.
Various power differences were used with the calculated angles of FIG. 5 having a 0.7 dB power difference, and the calculated angles of FIG. 7 having a 20 dB power difference.
From the foregoing, it may readily be seen that the present invention comprises a new, unique and exceedingly useful and effective method for solving for two RF signals' angular position which constitutes a considerable improvement over the known prior art. Many modifications and variations of the present inventions are possible in light of the above teachings. It is therefore to be understood that within the scope of the amended the invention may be practiced otherwise than as specifically described.
Patent Application
20080030397
