ADL5960ACCZ-R2 datasheet(20/32 Pages) AD

20 / 32 page

Data Sheet

ADL5960

THEORY OF OPERATION

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Rev. A | 20 of 32

Figure 56. Error Model for One-Port S-Parameter Measurements

The flow diagram provides a more detailed description of the

various error contributions that cause the measured reflection coef-

ficient,

ΓM=b0/a0,todifferfromtheactualreflectioncoefficient,

Γ=b1/a1.Thefactor,e11,representsimpedancemismatchof

the VNA port (from 50 Ω). A fraction of b1 is reflected back to the

load. The e01 and e10 factors represent the tracking error. In relation

to the ADL5960, the tracking error comprises insertion loss of the

bridge, the conversion gain from RFIN to IFFx and RFOUT to IFRx,

as well as the mismatch in conversion gain between the channels.

Finally, e00 represents the finite directivity of a practical VNA, a

measure for the ability to separate the forward and reverse traveling

power waves. If the load is a perfect 50 Ω, then b1 = 0 and an ideal

VNA measures b0 = 0. However, in a practical VNA, the directivity

is finite and some signal leaks from the forward path to the reverse

path.

Using Figure 56, the measured reflection coefficient can be ex-

pressed in terms of the error coefficients and the reflection coeffi-

cient of the load as follows:

ΓM=e00+ e01e101−Γe11Γ

(7)

Equation 7 can be rearranged into a linear expression for the error

coefficients as follows:

e00−ΔeΓ+e11ΓM=ΓM

Δe=e00e11−e01e10

(8)

A calibration procedure that measures three different known loads,

that is, collects three combinations of measured and actual reflec-

tion coefficients, can then be used to calculate the error coefficients

as follows:

1−Γ1ΓM1

1−Γ2ΓM2

1−Γ3ΓM3T

e00Δee11

e =

ΓM1ΓM2ΓM3

ΓM

e=T−1ΓM

(9)

After the system is calibrated, the corrected reflection coefficient

can be calculated from the measured coefficient by rearranging

Equation 7:

Γ= ΓM−e00

e11ΓM−Δe

(10)

Although in principle any combination of sufficiently different stand-

ards can be used to calibrate the system, a combination of a short,

an open, and a 50 Ω load are by far the most common choice. Note

that the procedure outlined in Equation 9 needs to be repeated at

every frequency point of interest.

Two-Port Calibration

The calibration procedure for a two-port S-parameter measurement

can be explained using Figure 57. The VNA is modeled by Port 0,

Port 2, and the error model. As a result of the hardware errors in

the system, the measured S-parameters at Port 0 differ from the

actual DUT S-parameters observed at Port 1, and the S-parameters

measured at Port 2 differ from the DUT S-parameters at Port 3. As

long as the error contributions scale linearly with power, the incident

and reflected waves at Port 0 and Port 2 can be related to those at

Port 1 and Port 3 using a block matrix, as follows:

b0a0b2

a2 =

T01T03

T21T23

b1a1b3

(11)

Figure 57. Error Model for Two-Port S-Parameter Measurements

Each of the matrix elements, T in Equation 11, is a 2×2 matrix that

describes the interaction between one VNA port and one DUT port,

resulting in a total of 16 unknown error coefficients. A wide range of

different calibration strategies are reported in literature to determine

either a subset of or all of the error coefficients (matrix elements).

One strategy to simplify the error model assumes that the crosstalk

between the VNA channels is negligible, that is, that contributions

of Port 1 to measurement errors in Port 2, and contributions of Port

3 to measurement errors in Port 0 are very small. This assumption

is plausible in a VNA based on the ADL5960, because each VNA

port is realized by a separate device. Interaction between the VNA

channels can be minimized through careful PCB layout. For this

situation, only the block matrices on the diagonal in Equation 11

have nonzero elements, resulting in the following:

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