A de-embedding method for multi-port device S-parameter measurement

Abstract

This invention proposes a de-embedding method for S-parameter measurement of multi-port devices, belonging to the field of microwave network parameter measurement. The method eliminates the influence of parasitic pad parameters during two-port S-parameter measurement by treating the pads as equivalent to a parallel admittance network. Furthermore, it can be combined with two-port measurement methods for multi-port device S-parameters, obtaining more accurate S-parameters for multi-port devices while reducing measurement costs. This measurement method is applicable to the de-embedding of on-chip pad parasitic parameters in any two-port on-wafer S-parameter measurement, including the measurement of bonding wire S-parameters.

Description

Technical Field

[0001] This invention belongs to the field of microwave network parameter measurement, specifically a method for removing the influence of pad (PAD) parasitic parameters on the measurement results in two-port S-parameter measurement, thereby obtaining more realistic S-parameters of the device under test. Technical Background

[0002] In RF and microwave circuit design, multiport devices such as bridges and power dividers are widely used. S-parameters are network parameters established by the relationship between incident and reflected signals at each port of a multiport device. By analyzing the S-parameters, parameters such as the isolation of the multiport device can be obtained. For passive devices integrated on a chip, it is inevitable to connect the device under test (DUT) to the measuring instrument through contact between the pads and probes when measuring S-parameters. Since the pads themselves have parasitic parameters, they will inevitably affect the S-parameter measurement results of the DUT. Because the dummy load uses the pads as an auxiliary load for measurement, the influence of parasitic parameters is even more pronounced in the case of S-parameter measurement based on the dummy load. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a de-embedding method for S-parameter measurement of multi-port devices. This method removes the influence of pad parasitic parameters during two-port S-parameter measurement and can be further combined with two-port measurement methods for multi-port device S-parameters, obtaining more accurate S-parameters for multi-port devices while reducing measurement costs. Furthermore, this measurement method is applicable to the de-embedding of on-chip pad parasitic parameters in any two-port on-wafer S-parameter measurement, including the measurement of bonding wire S-parameters.

[0004] The technical solution adopted in this invention is as follows:

[0005] A de-embedding method for S-parameter measurement of multi-port devices includes the following steps:

[0006] S1. Measure the reflection coefficient of the pads of the device under test (DUT) on the chip: First, label all ports of the N-port DUT from 1 to N. The reflection coefficient of the pad corresponding to the port labeled i is denoted as Γ. Li (i = 1, 2, ..., N); When all pads used by the device under test are the same, a vector network analyzer is used to perform single-port measurements on a single pad to obtain the reflection coefficient of the pad. At this time there is When different pads are used for the device under test, a vector network analyzer is used to perform single-port measurements on different pads to obtain the reflection coefficient of the pads corresponding to each port.

[0007] S2. Calculate the S-parameters of the parallel admittance network equivalent to the pads: In two-port measurement, the connection between the pads, the measurement port of the vector network analyzer, and the device under test (DUT) is abstracted as a parallel admittance network. The cascade relationship between the two measurement ports, the two pads, and the DUT is: First Port - First Parallel Admittance Network - DUT - Second Parallel Admittance Network - Second Port. The parallel admittance network is considered as a three-port ideal T-junction, with one port loaded with the equivalent admittance of the pads. In the case of partial loading of the multi-port network, the S-parameters of the remaining unloaded ports are calculated using the following formula:

[0008]

[0009] The S-parameter matrix of an ideal T-type interconnect junction is as follows:

[0010]

[0011] S qq S pp S pq and S qp Let be a submatrix of the S-parameter matrix, then we have:

[0012]

[0013]

[0014] S qq =S T11 =-0.333 (5)

[0015] S qp =[S T12 S T13 [=0.667 0.667] (6)

[0016] Γ L It is the load reflection coefficient, which is Γ in a parallel admittance network. Li (i=1,2,...,N), I is the same as S qq Identity matrices of the same dimension; S qq S pp S pq S qp ,Γ Li Substituting (i = 1, 2, ..., N) and I into formula (1), we obtain the S-parameters of the equivalent two-port parallel admittance network of the pads. When the pads used by the device under test are different, the S-parameters of the equivalent two-port parallel admittance network for each pad are calculated.

[0017] S3. Obtaining raw measurement data using a two-port measurement method for the S-parameters of multi-port devices: Divide the N ports of the device under test (DUT) into two measured ports and (N-2) loaded ports. The auxiliary load of the loaded ports can be a real load or a pad used as a virtual load. Define the measurement ports of the DUT as... Indicates the measurement port of the device under test, x n Let n be the port number of any of the N ports, where n = 1, 2; the loading port is... Indicates the loading port, y m To divide x n The other ports are numbered m = 1, 2, ..., N-2. There are a total of... For each allocation combination, two-port measurements are performed on the measurement ports of each combination. The first port of the vector network analyzer is connected to the port. Second port connection port Obtain the corresponding measurement S-parameter matrix

[0018] S4. Use the ABCD matrix of a parallel admittance network to remove the influence of pad parasitic parameters: First, measure the S-parameter matrix... S-parameter matrix of parallel admittance network Converting to an ABCD matrix, the transformation relationship between the S-parameter matrix of a two-port network and the ABCD matrix is ​​as follows:

[0019]

[0020] Where Z0 is the characteristic impedance of the input and output ports. The measurement S-parameter matrix is ​​obtained based on the cascade relationship. The corresponding ABCD matrix and the measured S-parameter matrix after removing the influence of pad parasitic parameters The relationship between the corresponding ABCD matrices is as follows:

[0021]

[0022] The matrix with subscript C is the S-parameter measurement matrix. The corresponding ABCD matrix, with subscripts P1 and P2 representing the S-parameters of the parallel admittance network. The corresponding ABCD matrix represents the measurement ports. and The two matrices are identical when all parameters of the pads at the two measurement ports are the same. When the pads used at the two measurement ports are different, attention needs to be paid to the correspondence between the pads and the first and second ports. The matrix with subscript P1 corresponds to the pads connected to the first port, and the matrix with subscript P2 corresponds to the pads connected to the second port. The matrix with subscript S is the measurement S-parameter matrix after removing the influence of pad parasitic parameters. The corresponding ABCD matrix. The ABCD matrix corresponding to the measured S-parameter matrix after removing the influence of pad parasitic parameters is obtained by solving equation (8), and then converted into the S-parameter matrix by equation (9).

[0023]

[0024] For each port combination, the measurement S-parameter matrix All of them undergo de-embedding operations.

[0025] S5. Restore the S-parameters of the N-port device under test: intermediate variable matrix A block matrix is ​​given by formula (10):

[0026]

[0027] Among them, Γ T It is a measurement port and The diagonal matrix formed by the corresponding auxiliary load reflection coefficients is used to measure the reflection coefficients of real loads; if virtual loads are used, their reflection coefficients have been measured in S1.

[0028] intermediate variable matrix Submatrix Represented as:

[0029]

[0030] Finally combined The combined measurement and de-embedding results Restore the intermediate variable matrix Reuse Reconstruct the true S-parameters of the device under test. DUT The calculation expression is:

[0031]

[0032] in, The load reflection coefficient matrix is ​​a diagonal matrix composed of the reflection coefficients of all auxiliary loads in the order of their corresponding ports.

[0033] This invention eliminates the influence of pad parasitic parameters on S-parameter measurement results by treating the pads as equivalent to a parallel admittance network, making the multi-port S-parameters obtained by the two-port measurement method closer to the true properties of the device. Attached Figure Description

[0034] Figure 1 This is a loading method for a three-port ideal T-type interconnect junction.

[0035] Figure 2 This is a schematic diagram of the operation of a two-port measurement.

[0036] Figure 3 This is the equivalent admittance network for the pads.

[0037] Figure 4 This refers to the cascading method of the device under test. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0039] This section provides a 5-port device (a monolithic microwave integrated circuit of a passive network) that uses the same standard pads on all ports, using a two-port S-parameter measurement method for multi-port networks based on virtual load as an example.

[0040] S1. First, label the ports of the five-port device as 1 to 5. Use a vector network analyzer to perform single-port measurements on the pads fabricated individually to obtain the reflection coefficient of the pad.

[0041] S2. The equivalent two-port parallel admittance network of the pads can be considered as the case of a three-port ideal T-type interconnect junction being loaded, such as... Figure 1 As shown, the reflection coefficient Substituting into equation (1), the S-parameters S of the equivalent two-port parallel admittance network of the pads are obtained. * .

[0042] S3. Divide the N-port of the device under test into... A combination of two ports to be measured and a port connected to an auxiliary load. The measurement combinations for this five-port device include:

[0043] {j1,j2,k3,k4,k5},{j1,j3,k2,k4,k5},{j1,j4,k2,k3,k5},{j1,j5,k2,k3,k4},{j2,j3,k1,k4,k5}

[0044] {j2,j4,k1,k3,k5},{j2,j5,k1,k3,k4},{j3,j4,k1,k2,k5},{j3,j5,k1,k2,k4},{j4,j5,k1,k2,k3}

[0045] S4. S-parameters obtained for each measurement combination After de-embedding, the S-parameters are converted into the corresponding ABCD matrix using equation (7). The conversion results are as follows:

[0046]

[0047]

[0048] And let the ABCD matrix corresponding to the measured S-parameters after removing the influence of pad parasitic parameters be:

[0049]

[0050] A schematic diagram of two-port measurement is shown below. Figure 2 As shown, the two probes connected to the two-port vector network analyzer are numbered probe 1 and probe 2, respectively. When performing two-port measurements, the influence of the pads is not ignored; the connections of the pads are abstracted into a parallel admittance network, as shown below. Figure 3 As shown. The connection between the on-chip pads and the device under test is equivalent to... Figure 4 The cascade relationship is shown. Solve the equation:

[0051]

[0052] The measured data can be used to obtain S-parameters after embedding the influence of pad parasitic parameters. The corresponding ABCD matrix is ​​then used to obtain the measured S-parameters after removing the influence of pad parasitic parameters through equation (9).

[0053] S5. Calculation The matrix is ​​used here as an example to illustrate the calculation process of the measurement combination {j1,j2,k3,k4,k5}.

[0054] Measure S-parameters after removing the influence of pad parasitic parameters. The calculation yields:

[0055]

[0056]

[0057] The 2×2 submatrix It can be by The specific correspondence is as follows:

[0058]

[0059] After measuring the other 9 measurement combinations, the results were obtained.

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Finally, by combining these 10 sets of results, we obtain...

[0066]

[0067] Since the pads of this 5-port device are of the same type, its reflection coefficient matrix is... for:

[0068]

[0069] Finally, the actual S-parameters S of the 5-port network are obtained through equation (12). DUT .

Claims

1. A de-embedding method for multi-port device S-parameter measurement, characterized in that, Includes the following steps: S1. Measure the reflection coefficient of the pads of the device under test (DUT) on the chip: First, label all ports of the N-port DUT from 1 to N. The reflection coefficient of the pad corresponding to port i is denoted as... When all pads used by the device under test are identical, a vector network analyzer is used to perform single-port measurements on a single pad to obtain the pad's reflection coefficient. At this time there is When the pads used by the device under test are different, a vector network analyzer is used to perform single-port measurements on different pads to obtain the reflection coefficient of the pads corresponding to each port. S2. Calculate the S-parameters of the parallel admittance network equivalent to the pads: In two-port measurement, the connection between the pads and the measurement port of the vector network analyzer, and the device under test, is abstracted as a parallel admittance network. Then, the cascade relationship between the two measurement ports, the two pads, and the device under test is: first port - first parallel admittance network - device under test - second parallel admittance network - second port; the parallel admittance network is regarded as a three-port ideal T-type interconnection, and one port is loaded with the admittance equivalent to the pads; In a multi-port network with partial loading, the S-parameters of the remaining unloaded ports are obtained by equation (1): (1) The S-parameter matrix of a three-port ideal T-type interconnect junction is as follows: (2) , , and For a submatrix in the S-parameter matrix of equation (2), then: (3) (4) (5) (6) in, It is the load reflection coefficient, which is [value] in a parallel admittance network. I represents with Identity matrices of the same dimensions; , , , , Substituting all of I into formula (1), we obtain the S-parameters of the equivalent two-port parallel admittance network of the pads. When the pads used by the device under test are different, the S-parameters of the equivalent two-port parallel admittance network for each type of pad are calculated. S3. Obtain the raw measurement data using the two-port measurement method for the S-parameters of multi-port devices: Divide the N ports of the device under test into two measurement ports and N-2 loading ports. The auxiliary load of the loading ports can be a real load or a pad used as a virtual load. A total of Allocation combinations; Define the measurement port of the device under test as , Indicates the measurement port of the device under test. Let N be the port number of any port among the N ports. The loading port is , Indicates the loading port. To remove The numbers of other ports, ; Two-port measurements were performed on the measurement ports of each allocation combination, and the first port of the vector network analyzer was connected to the port. The second port connects to the port. The corresponding measurement S-parameter matrix is ​​obtained. ; S4. Use the ABCD matrix of a parallel admittance network to remove the influence of pad parasitic parameters: First, measure the S-parameter matrix... S-parameter matrix of parallel admittance network Convert to an ABCD matrix; the following transformation relationship exists between the S-parameter matrix of a two-port network and the ABCD matrix: (7) in, The characteristic impedance of the input / output ports; The measurement S-parameter matrix is ​​obtained based on the cascade relationship. The corresponding ABCD matrix and the measured S-parameter matrix after removing the influence of pad parasitic parameters The relationship between the corresponding ABCD matrices is as follows: (8) Among them, the matrix with subscript C is the measurement S-parameter matrix. The corresponding ABCD matrix, with subscripts as follows: and The matrix is S-parameters of time-parallel admittance network The corresponding ABCD matrix represents the measurement ports. and The pads; when the pads used by the two measurement ports are the same, these two matrices are the same; when the pads used by the two measurement ports are different, attention needs to be paid to the correspondence between the pads and the first and second ports, with subscripts as follows. The matrix corresponds to the pads connected to the first port, with subscripts as follows: The matrix corresponds to the pads connected to the second port; the matrix with subscript S is the measured S-parameter matrix after removing the influence of pad parasitic parameters. The corresponding ABCD matrix; The ABCD matrix corresponding to the measured S-parameter matrix after removing the influence of pad parasitic parameters is obtained by solving equation (8), and then converted into the S-parameter matrix by equation (9). : (9) For each port combination, the measurement S-parameter matrix All undergo de-embedding operations; S5. Restore the S-parameters of the N-port device under test: intermediate variable matrix A block matrix is ​​given by formula (10): (10) in, It is a measurement port and The diagonal matrix formed by the corresponding auxiliary load reflection coefficients is used to measure the reflection coefficients of real loads; if virtual loads are used, their reflection coefficients have been measured in S1. intermediate variable matrix Submatrix Represented as: (11) Finally combined The combined measurement and de-embedding results Restore the intermediate variable matrix reuse Reconstruct the true S-parameters of the device under test The calculation expression is: (12) in, The load reflection coefficient matrix is ​​a diagonal matrix composed of the reflection coefficients of all auxiliary loads in the order of their corresponding ports.

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