David E. Bockelman

Combined differential and common-mode scattering parameters: theory and simulation

A theory for combined differential and common-mode normalized power waves is developed in terms of even and odd mode impedances and propagation constants for a microwave coupled line system. These are related to even and odd-mode terminal currents and voltages. Generalized s-parameters of a two-port are developed for waves propagating in several coupled modes. The two-port s-parameters form a 4-by-4 matrix containing differential-mode, common-mode, and cross-mode s-parameters. A special case of the theory allows the use of uncoupled transmission lines to measure the coupled-mode waves. Simulations verify the concept of these mixed-mode s-parameters, and demonstrate conversion from mode to mode for asymmetric microwave structures. >

Pure-mode network analyzer for on-wafer measurements of mixed-mode S-parameters of differential circuits

A practical measurement system is introduced for measurement of combined differential and common-mode (mixed-mode) scattering parameters, and its operation is discussed. A pure-mode system measures network parameters of a differential circuit in the fundamental modes of operation, and has improved accuracy over a traditional network analyzer for the measurement of such circuits. The system is suitable for on-wafer measurements of differential circuits. The transformation between standard S-parameters and mixed-mode S-parameters is developed. Example microwave differential structures are measured with the pure-mode vector-network analyzer (PMVNA), and the corrected data is presented. These structures are simulated, and the simulated mixed-mode S-parameters correlate well with the measured data.

Accuracy estimation of mixed-mode scattering parameter measurements

The pure-mode vector network analyzer (PMVNA) provides direct measurement of differential circuits. Residual error models are derived for the PMVNA and a traditional four-port vector network analyzer (FPVNA). The residual error models are used to calculate the maximum and root-mean-square uncertainties in measurements of mixed-mode scattering parameters of a typical differential amplifier. The uncertainties produced by the PMVNA are compared to the transformed mixed-mode S-parameters of the FPVNA. The PMVNA is shown to have lower uncertainty when measuring differential devices.

Combined differential and common-mode analysis of power splitters and combiners

Power splitter/combiner phase and magnitude imbalance is analyzed in terms of simultaneous orthogonal modes of propagation. These simultaneous modes are defined as differential and common-mode. A new measure of splitter imbalance is suggested in the common-mode rejection ratio (CMRR). Measured response of a 180/spl deg/ hybrid splitter is represented in terms of the differential and common-mode responses, and the CMRR is calculated. Combiner imbalance is also analyzed in terms of differential and common-mode responses, and response metrics are suggested. Analytical expressions for CMRR of several common splitters is given as functions of phase and magnitude imbalance. >

Calibration and verification of the pure-mode vector network analyzer

In this paper, the calibration of a pure-mode vector network analyzer (PMVNA) is presented in detail. The analyzer is intended for the measurement of mixed-mode scattering parameters (s-parameters) of differential circuits, but is also suitable for measurement of general microwave networks with up to four ports. The theory of calibration of the analyzer is developed in terms of a general n-port analyzer, including the correction of port-to-port crosstalk. The type of the standards used in calibration is examined, and the minimum number of standards are summarized for various levels of crosstalk correction. A new standard for all multiport network analyzer calibrations is introduced. A calibration is performed from 0.25 to 25.25 GHz based on standards with coaxial connectors, and verification standards are measured. The measured data is compared with National Institute of Standards and Technology (NIST) traceable measurements, and errors are found to be generally less than /spl plusmn/1 dB in transmission. In many cases, the error is less than the uncertainty of the NIST traceable measurements.

Direct measurement of crosstalk between integrated differential circuits

Silicon integrated-circuit test structures have been fabricated that allow direct measurement of crosstalk between differential transmission lines and between single-ended transmission lines in the presence of metal ground plane. The differential test structures are characterized with mixed-mode scattering parameters (common mode, differential mode, and mode conversion), as measured with the pure-mode vector network analyzer. Comparisons with simulation show good agreement for differential-mode crosstalk, and the dependence of crosstalk on transmission-line separation is presented. Difficulties in simulating crosstalk fur even simple structures illustrate the utility of direct measurement of crosstalk.