Transmission-line resistance compression networks and related techniques
A resistance compression network to shape an input impedance at a port for transferring energy to multiple loads at a first frequency includes first and second transmission line segments having outputs for coupling to first and second loads and having different electrical lengths at a first frequency and a compression port coupled to inputs of both the first and the second transmission line segments. Over a set of operating conditions of interest, an equivalent resistance looking into the compression port at the frequency varies over a first resistance range as equivalent resistances of the first and second loads vary over a second resistance range and a range ratio associated with the first resistance range is less than a range ratio associated with the second resistance range and the range ratio of a subject range is a ratio of a largest resistance value in the subject range to a smallest resistance value in the subject range.
1. A resistance compression network to shape an input impedance at a port for transferring energy to multiple loads at a first frequency, the resistance compression network comprising:
a first transmission line segment having a first electrical length at the first frequency, the first transmission line segment having an output for coupling to a first load;
a second transmission line segment having a second electrical length at the first frequency, the second electrical length being different from the first electrical length, the second transmission line segment having an output for coupling to a second load; and
a compression port coupled to inputs of both the first and the second transmission line segments;
wherein, over a set of operating conditions of interest, an equivalent resistance looking into the compression port at the first frequency varies over a first resistance range as equivalent resistances of the first and second loads vary over a second resistance range, wherein a range ratio associated with the first resistance range is less than a range ratio associated with the second resistance range, wherein the range ratio of a subject range is a ratio of a largest resistance value in the subject range to a smallest resistance value in the subject range.
2. The resistance compression network of claim 1 , wherein:
the first and second loads have input impedances that vary in substantially the same manner under similar conditions.
3. The resistance compression network of claim 1 , wherein:
the first and second loads have input impedances that are approximately resistive at the first frequency.
4. The resistance compression network of claim 1 , wherein:
the first and second transmission line segments each have substantially the same characteristic impedance Z 0 .
5. The resistance compression network of claim 4 , wherein:
the first transmission line segment has an electrical length of π/2+Nπ+Δθradians and the second transmission line segment has an electrical length of π/2+Mπ−Δθradians, where N, Mε[0, 1, 2, . . .].
6. The resistance compression network of claim 5 , wherein:
the resistance range of the first and second loads at the first frequency has a lower bound R L,min , an upper bound R L,max , and a center value R L,center that is the geometric mean of R L,min and R L,max ; and
the characteristic impedance Z 0 of the first and second transmission line segments is approximately:
Z 0 =R L,center /|cot(Δθ) |.
7. The resistance compression network of claim 4 , wherein:
the first transmission line segment has an electrical length of π+Nπ+Δθ radians and the second transmission line segment has an electrical length of π+Mπ−Δθ radians, where N, Mε[0, 1, 2, . . . ].
8. The resistance compression network of claim 7 , wherein:
the resistance range of the first and second loads at the first frequency has a lower bound R L,min ,an upper bound R Lmax ,and a center value R L,center that is the geometric mean of R L,min and R L,max ; and
the characteristic impedance Z 0 of the first and second transmission line segments is approximately:
Z 0 =R L,CENTER /|tan(Δθ)|.
9. The resistance compression network of claim 1 , wherein:
the first and second transmission line segments have different characteristic impedances.
10. The resistance compression network of claim 1 , wherein:
the resistance compression network is configured to provide substantially the same power to the first and second loads if the first and second loads have substantially the same impedance.
11. The resistance compression network of claim 1 , wherein:
the resistance compression network is configured for use with loads that include rectifier circuits.
12. The resistance compression network of claim 1 , further comprising:
a quarter-wave transformer coupled to the compression port to transform the impedance looking into the compression port.
13. The resistance compression network of claim 1 , wherein:
the compression port is a first compression port; and
the resistance compression network further comprises:
a third transmission line segment having a third electrical length at the first frequency, the third transmission line segment having an output for coupling to a third load;
a fourth transmission line segment having a fourth electrical length at the first frequency, the fourth electrical length being different from the third electrical length, the fourth transmission line segment having an output for coupling to a fourth load; and
a second compression port coupled to inputs of the third and fourth transmission line segments;
wherein, over the set of operating conditions of interest, an equivalent resistance looking into the second compression port at the first frequency varies over a third resistance range as equivalent resistances of the third and fourth loads vary over a fourth resistance range, wherein a range ratio associated with the third resistance range is less than a range ratio associated with the fourth resistance range.
14. The resistance compression network of claim 13 , further comprising:
a fifth transmission line segment having a fifth electrical length at the first frequency, the fifth transmission line segment having an output coupled to the first compression port;
a sixth transmission line segment having a sixth electrical length at the first frequency, the sixth electrical length being different from the fifth electrical length, the sixth transmission line segment having an output coupled to the second compression port; and
a third compression port coupled to inputs of the fifth and sixth transmission line segments;
wherein, over the set of operating conditions of interest, an equivalent resistance looking into the third compression port at the first frequency varies over a fifth resistance range as equivalent resistances at the first and second compression ports vary over the first and third resistance ranges, respectively, wherein a range ratio associated with the fifth resistance range is less than range ratios associated with the first and third resistance ranges.
15. The resistance compression network of claim 14 , further comprising:
a quarter wave transformer coupled to the third compression port.
16. The resistance compression network of claim 13 , wherein:
the resistance compression network is configured for use with loads having input impedances that vary in substantially the same manner under similar conditions.
17. The resistance compression network of claim 13 , wherein:
the third electrical length is substantially equal to the first electrical length; and
the fourth electrical length is substantially equal to the second electrical length.
18. The resistance compression network of claim 14 , wherein:
the fifth electrical length is substantially equal to the first electrical length;
the sixth electrical length is substantially equal to the second electrical length;
the characteristic impedances of the first, second, third, and fourth transmission line segments are substantially the same; and
the characteristic impedances of the fifth and sixth transmission line segments are substantially the same as each other, but different from the characteristic impedances of the first, second, third, and fourth transmission line segments.