# US 2026/0100495 A1 · Cascade de-embedding methods for rf, mmwave, and photonics transmission lines

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2026/0100495 A1
- Document ID: US20260100495A1
- Status: Published application
- Kind: A1
- Application number: 18/981,373
- Filed: 2024-12-13
- Published: 2026-04-09
- Earliest claimed: 2024-10-04
- Assignees: Lorentz Solution, Inc.
- Applicants: Lorentz Solution, Inc.
- Inventors: Jinsong Zhao; Siamak Abdollahi
- Web page: https://patentgrep.com/patent/US20260100495A1

## CPC

- H01P 11/001: {Manufacturing waveguides or transmission lines of the waveguide type}
- H01P: WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE (operating at optical frequencies G02B)

## Abstract

A method of de-embedding includes providing a first transmission line with a first length and a second transmission line with a second length greater than the first length. Each of the first and second transmission lines is terminated by a respective pad at each end thereof. The method further includes obtaining a first matrix representing measured data of the first transmission line, and a second matrix representing measured data of the second transmission line, and constructing a third transmission line having a third length relating to a difference between the second length and the first length and a scaling factor. The method further includes determining a third matrix based on the first matrix, the second matrix, and the scaling factor, and determining a fourth matrix representing intrinsic properties of the first transmission line without parasitic effects of the pads based on the first matrix and the third matrix.

## Claims

### Claim 1

A method of de-embedding transmission lines, the method comprising:
providing a first transmission line formed on a wafer, the first transmission line having a first length L1 and being terminated by a respective pad at each end thereof;
providing a second transmission line formed on the wafer, the second transmission line having a second length L2 and being terminated by a respective pad at each end thereof, the second length L2 being greater than the first length L1;
obtaining a first matrix [TL1_t] representing measured data of the first transmission line including parasitic effects of the pads, and a second matrix [TL2_t] representing measured data of the second transmission line including parasitic effects of the pads;
constructing a third transmission line having a third length L3, the third length L3 relating to a difference between the second length L2 and the first length L1 and a scaling factor s, s being an integer greater than zero;
determining a third matrix [TL3_t] based on the first matrix [TL1_t], the second matrix [TL2_t], and the scaling factor s; and
determining a fourth matrix [TL1] based on the first matrix [TL1_t] and the third matrix [TL3_t], the fourth matrix [TL1] representing intrinsic properties of the first transmission line without the parasitic effects of the pads.

### Claim 2 (depends on 1)

The method of claim 1, further comprising determining a fifth matrix [TL2] based on the second matrix [TL2_t] and the third matrix [TL3_t], the fifth matrix [TL2] representing intrinsic properties of the second transmission line without the parasitic effects of the two pads.

### Claim 3 (depends on 1)

The method of claim 1, wherein the first length is equal to a base length multiplied by n, the second length is equal to the base length multiplied by n+1, where n is an integer greater than or equal to 1.

### Claim 4 (depends on 3)

The method of claim 3, wherein the third length is equal to zero, and the scaling factor s is equal to n.

### Claim 5 (depends on 4)

The method of claim 4, wherein the fourth matrix [TL1] is obtained as follows:
[
T
L
⁢
1
]
=
[
T
L
⁢
3
t
]
-
1
2
×
[
T
L
⁢
1
t
]
×
[
T
L
⁢
3
t
]
-
1
2
.

### Claim 6 (depends on 1)

The method of claim 1, wherein the scaling factor s is an integer relating to a ratio of the first length and the difference between the first length and the second length.

### Claim 7 (depends on 1)

The method of claim 1, wherein L3=s(L1−L2)+L1, and the scaling factor s is a greatest integer less than or equal to
L
1
L
2
-
L
1
.

### Claim 8 (depends on 7)

The method of claim 7, wherein the fourth matrix [TL1] is obtained as follows:
[
T
L
⁢
1
]
=
[
[
T
L
⁢
3
t
]
-
1
2
*
[
T
L
⁢
1
t
]
*
[
T
L
⁢
3
t
]
-
1
2
]
L
⁢
1
L
1
-
L
3
.

### Claim 9 (depends on 1)

The method of claim 1, wherein the first transmission line and the second transmission line are coplanar waveguides formed on the wafer.

### Claim 10 (depends on 1)

The method of claim 1, wherein the first transmission line and the second transmission line operate at millimeter-wave frequencies or sub-terahertz frequencies.

### Claim 11 (depends on 1)

The method of claim 1, wherein each of the first transmission line and the second transmission line includes tapered portions at ends thereof, the first matrix [TL1_t] represents the measured data of the first transmission line including the parasitic effects of the pads and parasitic effects of the tapered portions of the first transmission line, the second matrix [TL2_t] represents the measured data of the second transmission line including the parasitic effects of the pads and parasitic effects of the tapered portions of the second transmission line, and the fourth matrix [TL1] represents intrinsic properties of the first transmission line without the parasitic effects of the pads and the parasitic effects of the tapered portions of the first transmission line.

### Claim 12 (depends on 1)

The method of claim 1, wherein the first transmission line and the second transmission line are multi-port transmission lines.

### Claim 13

A method of de-embedding transmission lines, the method comprising:
providing a first transmission line formed on a wafer, the first transmission line having a first length L1 and being terminated by a respective pad at each end thereof;
providing a second transmission line formed on the wafer, the second transmission line having a second length L2 and being terminated by a respective pad at each end thereof, the second length L2 being greater than the first length L1;
obtaining a first matrix [TL1_t] representing measured data of the first transmission line including parasitic effects of the pads, and a second matrix [TL2_t] representing measured data of the second transmission line including parasitic effects of the pads;
constructing a third transmission line having a third length L3, the third length L3 relating to a difference between the second length L2 and the first length L1 and a scaling factor s, s being an integer greater than zero;
determining a third matrix [TL3_t] based on the first matrix [TL1_t], the second matrix [TL2_t], and the scaling factor s;
determining a fourth matrix [TL1] based on the first matrix [TL1_t], the third matrix [TL3_t], and an empirical de-embedding coefficient cf, the fourth matrix [TL1] representing estimated intrinsic properties of the first transmission line without the parasitic effects of the pads;
performing electromagnetic simulation of a test transmission line to obtain a fifth matrix [TLs], the test transmission line having a length Ls equal to the first length L1 without pads, the fifth matrix [TLs] representing simulated intrinsic properties of the test transmission line;
comparing the fourth matrix [TL1] to the fifth matrix [TLs];
upon determining that deviations between the fourth matrix [TL1] to the fifth matrix [TLs] are greater than a predetermined threshold, adjusting a value of the empirical de-embedding coefficient cf based on the deviations between the fourth matrix [TL1] and the fifth matrix [TLs]; and
performing the determining the fourth matrix [TL1] again until the deviations between the fourth matrix [TL1] and the fifth matrix [TLs] are below a predetermined threshold.

### Claim 14 (depends on 13)

The method of claim 13, wherein L3=s(L1−L2)+L1, and the scaling factor s is a greatest integer less than or equal to
L
1
L
2
-
L
1
.

### Claim 15 (depends on 14)

The method of claim 14, wherein the fourth matrix [TL1] is obtained as follows:
[
T
L
⁢
1
]
=
[
[
T
L
⁢
3
t
]
-
1
2
*
[
T
L
⁢
1
t
]
*
[
T
L
⁢
3
t
]
-
1
2
]
L
⁢
1
L
1
-
L
3
×
c
⁢
f
.

### Claim 16 (depends on 15)

The method of claim 15, wherein the empirical de-embedding coefficient cf has an initial value of 1.

### Claim 17

A non-transitory computer-readable storage medium storing instructions that, when executed by one or more processors, cause a computing device to perform a method of de-embedding transmission lines, the method comprising:
obtaining a first matrix [TL1_t] representing measured data of a first transmission line formed on a wafer, the first transmission line having a first length L1 and being terminated by a respective pad at each end thereof, the measured data of the first transmission line including parasitic effects of the pads,
obtaining a second matrix [TL2_t] representing measured data of a second transmission line formed on the wafer, the second transmission line having a second length L2 and being terminated by a respective pad at each end thereof, the measured data of the second transmission line including parasitic effects of the pads, the second length L2 being greater than the first length L1;
constructing a third transmission line having a third length L3, the third length La relating to a difference between the second length L2 and the first length L1 and a scaling factor s, s being an integer greater than zero;
determining a third matrix [TL3_t] based on the first matrix [TL1_t], the second matrix [TL2_t], and the scaling factor s; and
determining a fourth matrix [TL1] based on the first matrix [TL1_t] and the third matrix [TL3_t], the fourth matrix [TL1] representing intrinsic properties of the first transmission line without the parasitic effects of the pads.

### Claim 18 (depends on 17)

The non-transitory computer-readable storage medium of claim 17, wherein L3=s(L1−L2)+L1, and the scaling factor s is a greatest integer less than or equal to
L
1
L
2
-
L
1
.

### Claim 19 (depends on 18)

The non-transitory computer-readable storage medium of claim 18, wherein the fourth matrix [TL1] is obtained as follows:
[
T
L
⁢
1
]
=
[
[
T
L
⁢
3
t
]
-
1
2
*
[
T
L
⁢
1
t
]
*
[
T
L
⁢
3
t
]
-
1
2
]
L
⁢
1
L
1
-
L
3
.

### Claim 20 (depends on 19)

The non-transitory computer-readable storage medium of claim 19, wherein L3=0, and the fourth matrix [TL1] is obtained as follows:
[
T
L
⁢
1
]
=
[
T
L
⁢
3
t
]
-
1
2
×
[
T
L
⁢
1
t
]
×
[
T
L
⁢
3
t
]
-
1
2
.