Variable 360° Vector-Sum Phase Shifter With Coarse and Fine Vector Scaling

A CMOS vector-sum phase shifter covering the full 360° range is presented in this paper. Broadband operational transconductance amplifiers with variable transconductance provide coarse scaling of the quadrature vector amplitudes. Fine scaling of the amplitudes is accomplished using a passive resistive network. Expressions are derived to predict the maximum bit resolution of the phase shifter from the scaling factor of the coarse and fine vector-scaling stages. The phase shifter was designed and fabricated using the standard 130-nm CMOS process and was tested on-wafer over the frequency range of 4.9–5.9 GHz. The phase shifter delivers root mean square (rms) phase and amplitude errors of 1.25° and 0.7 dB, respectively, at the midband frequency of 5.4 GHz. The input and output return losses are both below 17 dB over the band, and the insertion loss is better than 4 dB over the band. The circuit uses an area of 0.303 mm2 excluding bonding pads and draws 28 mW from a 1.2 V supply.

Numerical Modelling of Eddy Current Probes for CANDU® Fuel Channel Inspection

Multi-frequency Eddy Current (EC) inspection with a transmit-receive probe (two horizontally offset coils) is used to monitor the Pressure Tube (PT) to Calandria Tube (CT) gap of CANDU® fuel channels. Accurate gap measurements are crucial to ensure fitness of service; however, variations in probe liftoff, PT electrical resistivity, and PT wall thickness can generate systematic measurement errors. Validated mathematical models of the EC probe are very useful for data interpretation, and may improve the gap measurement under inspection conditions where these parameters vary. As a first step, exact solutions for the electromagnetic response of a transmit-receive coil pair situated above two parallel plates separated by an air gap were developed. This model was validated against experimental data with flat-plate samples. Finite element method models revealed that this geometrical approximation could not accurately match experimental data with real tubes, so analytical solutions for the probe in a double-walled pipe (the CANDU® fuel channel geometry) were generated using the Second-Order Vector Potential (SOVP) formalism. All electromagnetic coupling coefficients arising from the probe, and the layered conductors were determined and substituted into Kirchhoff’s circuit equations for the calculation of the pickup coil signal. The flat-plate model was used as a basis for an Inverse Algorithm (IA) to simultaneously extract the relevant experimental parameters from EC data. The IA was validated over a large range of second layer plate resistivities (1.7 to 174 µΩ∙cm), plate wall thickness (~1 to 4.9 mm), probe liftoff (~2 mm to 8 mm), and plate-to plate gap (~0 mm to 13 mm). The IA achieved a relative error of less than 6% for the extracted FP resistivity and an accuracy of ±0.1 mm for the LO measurement. The IA was able to achieve a plate gap measurement with an accuracy of less than ±0.7 mm error over a ~2.4 mm to 7.5 mm probe liftoff and ±0.3 mm at nominal liftoff (2.42±0.05 mm), providing confidence in the general validity of the algorithm. This demonstrates the potential of using an analytical model to extract variable parameters that may affect the gap measurement accuracy.