Transmission-line resistance compression networks and related techniques

1. A circuit comprising:

first and second loads having substantially the same input impedances under substantially the same operating conditions; and

a transmission-line resistance compression network, including:

an input port;

a first output port coupled to the first load;

a second output port coupled to the second load; and

a transmission-line network coupled to the input port, the first output port, and the second output port, the transmission-line network comprising at least two transmission lines of different lengths;

wherein, for a first operating range, the resistances at input ports of the first and second loads vary over first and second ratios, respectively, the resistance of the input impedance at the input port of the transmission-line resistance compression network varies over a third ratio, and the third ratio is smaller than at least one of the first and second ratios.

2. The circuit of claim 1 , wherein:

the transmission-line resistance compression network is configured to provide substantially balanced splitting of power between the first and second output ports.

3. The circuit of claim 1 , wherein:

the transmission-line resistance compression network is substantially lossless.

4. The circuit of claim 1 , wherein the transmission-line resistance compression network comprises:

a first transmission line having an input and an output, the first transmission line having a length that is a multiple of a quarter wavelength plus a first additional length at a first operating frequency, wherein the output of the first transmission line is coupled to the first output port of the transmission-line resistance compression network; and

a second transmission line having an input and an output, the second transmission line having a length that is a multiple of a quarter wavelength minus the first additional length at the first operating frequency, wherein the output of the second transmission line is coupled to the second output port of the transmission-line resistance compression network;

wherein the input of the first transmission line and the input of the second transmission line are coupled together to form a port.

5. The circuit of claim 1 , wherein:

the first and second loads include rectifier circuits.

6. The circuit of claim 1 , wherein:

the transmission-line resistance compression network is an M-stage network connected to 2 M loads and comprising 2 M transmission-line sections incorporating transmission lines of at least two different lengths, where M is an integer greater than one.

7. The circuit of claim 6 , wherein:

the transmission-line resistance compression network comprises a binary tree of transmission-line sections.

8. A method comprising:

varying a resistance presented to an input port of a first load using a first transmission line segment having a first electrical length at a first frequency, the first load being associated with a first resistance range at the first frequency, the resistance at the input port of the first load varied over a first ratio;

varying a resistance presented to an input port of a second load using a second transmission line segment having a second electrical length at the first frequency, the second load being associated with a second resistance range at the first frequency, the resistance at the input port of the second load varied over a second ratio;

wherein the varying is performed by a transmission-line resistance compression network comprising an input port, a first output port coupled to the first load, a second output port coupled to the second load, and a transmission-line network coupled to the input port, the first output port, and the second output port, the transmission-line network comprising the first transmission line segment and the second transmission line segment, and

providing a resistance range at the input port of the transmission-line resistance compression network that varies over a third ratio, wherein the third ratio is smaller than at least one of the first and second ratios.

9. The method of claim 8 , wherein:

the first and second loads have input impedances that vary in substantially the same manner under similar conditions.

10. The method of claim 8 , wherein:

the first and second transmission line segments each have substantially the same characteristic impedance Z 0 .

11. The method of claim 10 , wherein:

the first transmission line segment has an electrical length of π/2+Nπ+Δθ radians and the second transmission line segment has an electrical length of π/2+Mπ−Δθ radians, where N, Mε[0, 1, 2, . . . ].

12. The method of claim 11 , wherein:

the resistance of the first and second loads at the first frequency vary over a range that 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)|.

13. The method of claim 10 , 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, . . . ].

14. The method of claim 13 , wherein:

the resistance of the first and second loads at the first frequency vary over a range that 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 /|tan(Δθ)|.

15. The method of claim 8 , wherein:

the first and second loads include rectifier circuits.

16. The method of claim 8 , further comprising:

transforming the resistance at the input port of the transmission-line resistance compression network using a third transmission line segment having an electrical length of one quarter wavelength at the first frequency.