Calibration Method

To measure the device under test (DUT), cables and high frequency probes are inevitably used to link the DUT to equipment. Besides, the Ground-Signal-Ground (GSG) pad is placed to connect the DUT so that it is possible to make an on-wafer measurement. These interconnections and pads contribute undesired loss and phase delay so they will impact the accuracy of DUT measurement. Consequently, calibration is required to remove these non-ideal effects. THRU-RELECT-LINE (TRL) calibration and multi-line de-embedding method are used to characterize the flip-chip interconnection. The major difference of these two methods is the system

Fig. 2.10. Analysis of detuning effect of the microstrip line under consideration indicates that the line impedance is deviated around 2-Ω.

characteristic impedance for measurement which is frequency dependent in TRL and fixed to 50Ω for multi-line de-embedding method.

(i) TRL Calibration Method [12, 13]

TRL calibration is most often performed when a high level of accuracy is demanded. It does not have calibration standards in the same connector type as the DUT and the standards are easy to manufacture and characterize. Block diagram shown in Fig. 2.11 represents general measurement setup. These non-ideal effects are lumped together in a two-port error box in Fig. 2.11. So a calibration procedure is needed to characterize the error box. The TRL calibration does not rely on known standard loads, but uses three simple connections to characterize the error box

⎥⎦

Fig. 2.11. Block diagram of a general measurement setup.

⎥⎦

Fig. 2.12. Block diagram and signal flow graph for the THRU connection.

completely. These standards are THRU, REFLECT, and LINE.

Fig. 2.12 shows the block diagram and signal flow graph for THRU connection.

Using basic decomposition rules we can get the S-parameters at the measurement plane in terms of S-parameter of the error box, as indicated in (2-2) and (2-3).

2 22 zero-length THRU is more accurate because it has zero loss and no characteristic impedance. The THRU standard is to set the desired reference plane for the measurement.

The reflect connection is shown in Fig. 2.13. The arrangement effectively isolate the two measurement ports, so that R12=R21=0. The signal graph can be easily reduced to show that

Fig. 2.13. Block diagram and signal flow graph for the REFLECT connection.

22

By symmetry we have R22=R11. The Reflect standard can be anything with a high reflection, such as open or short. However, the Reflect standards must have same Γ, reflection coefficient, on both test ports.

Fig. 2.14 shows the Line connection. The signal graph can show that

2 22

By symmetry and reciprocity we have L22=L11 and L21=L12, respectively. The characteristic impedance of line must be of the same impedance as the THRU standard and its length cannot be the same as the THRU standard. The disadvantage of TRL calibration is the limited bandwidth. The LINE standard must be an appropriate electrical length for the frequency range, that is, at each frequency, the phase difference between the THRU and the LINE should be greater than 20 degrees

⎥⎦

Fig. 2.14. Block diagram and signal flow graph for the LINE connection.

and less than 160 degrees. This means in practice that a single LINE standard is only usable over an 8:1 frequency range (Frequency Span/Start Frequency). Therefore, for broad frequency coverage, multiple lines are required.

With equations, (2-2 to 2-6), the S-parameter of the error boxes can be derived, as

well as unknown reflection coefficient, ΓL, and the propagation factor, e^−γL. After the S-parameter of the error box is acquired, the S-parameter is transformed into the transmission matrix so we are able to get the transmission matrix of DUT by (2-7).

⎥⎦

⎢ ⎤

⎣

⎡

' '

' '

D C

B

A = ⁻¹

⎥⎦

⎢ ⎤

⎣

⎡ D C

B

A ⎥

⎦

⎢ ⎤

⎣

⎡

m m

m m

D C

B

A ⁻¹

⎥⎦

⎢ ⎤

⎣

⎡ D C

B

A (2-7)

(ii) Multi-Line De-embedding Method [14]

Any measurement is limited by an inherent flaw due to the test pads and interconnect are required to access the DUT. Multi-line de-embedding method uses two transmission line with different length and its symmetric property to remove the effect of test pad discontinuity.

Consider two transmission line test structure of length

l1 and

l2, where l1<

l2

(Fig. 2.15). If properly designed, the structures will be symmetric about y axis.

Symmetric property means that swapping port 1 and port 2 will not change the resulting S, Z, or Y matrices.

Swap function swaps port 1 and port 2 as indicated in (2-8).

Transmission line can be decomposed into a cascade of 3 two port network, two pads and intrinsic device. Consequently the transmission matrix of test structure

li,

t

Mli, can be represented by the following product:

2

MP represents the intrinsic line segment of structure,

Mli represents the left

-l1. Assuming that the left pad can be modeled as a lumped admittance YL, we have

Fig. 2.15. Multi-line for de-embedding.

This is referred as a lumped pad assumption. The hybrid structure can be expressed in terms of Y parameters, as a parallel combination of intrinsic transmission line and the parasitic lumped pad.

⎥⎦

Because of symmetry of test structure, we can swap the Y parameters of hybrid structure to remove the contribution from test pad so that we can get the intrinsic Y parameters of transmission line with length

l2 Assume the transmission matrix of lossy transmission line can be modeled as

⎥⎦

We can extract the characteristic impedance (Zo) and propagation constant (γ) of the transmission line using

C

ABCD parameters of transmission line can be gained by transforming the

1 2 l

Yl ₋

into its transmission matrix counterpart. From equation (2-12), the YL parameter of

pad is also easily derived, so is its transmission matrix.

After getting the ABCD matrices of transmission line and pads, ABCD of DUT is then acquired by the following equations where _MDUT^Measured is obtained after SOLT calibration.

1 1

1

1 − − −

− × × × ×

= _{CPW PAD DUT}^Measured _{PAD CPW}

DUT M M M M M

M (2-17)