Cascade de-embedding methods for rf, mmwave, and photonics transmission lines

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.

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.