A method of calibrating an automatic multiprobe measurement line

Abstract

A new method is proposed for determining the relative transfer coefficients of the sensors in a standing-wave analyzer based on a multiprobe measurement line, which is used with loads whose parameters are known only subject to some error. The method is based on the exact solution of the long-line equations obtained by the maximum-likelihood method.Standing-wave analyzers based on multiprobe measurement lines are widely used to automate measurements on UHF circuit parameters [1--4]. The measurements involve analyzing the field distribution within the line, which is dependent on the load parameters (amplitude and phase of the reflection coefficient) and on the amplitude of the wave in the line. Then three probes are sufficient to give a system of nonlinear equations in terms of the unknowns. Additional probes are often used to extend the working frequency range [1][2][3].The UHF system in the line gives rise to a standing wave whose parameters are related to those of the generator and load. The following conditions are assumed:1) the line is free from loss; 2) the probes lie at exactly known distances from the load; 3) the probe reflection coefficients are negligibly small, i~e., the probes do not disrupt the field pattern; and 4) the detectors in the probes have ideal square-law characteristics.To provide low probe reflection coefficients, the outputs must work into attenuators that heavily attenuate the coupling between the probes and the field within the line (less than 30 dB). This is responsible for the low signal-noise ratio at the detector output, which represents serious interference for precision measurements. However, the signals at the detector inputs are weak (some microvolts), and the requirement of square-law characteristics is met. With these assumptions, the model for the line is represented by the system [3, 5] uj =ajU2[l+p 2 +2cos(tp-4/r, dj/)Q]+~j, j=I,N, (1) in which uj is the voltage amplitude at the output from probe j; ctj is the transfer coefficient for probe j; U 2 is the square of the amplitude of the standing wave; 9 and tp are the modulus and phase of the load's reflection coefficient; dj is the distance from the load connection to probe j; ~, is the wavelength in the line; ~/is the error in measuring the voltage at probe j; and N is the number of probes. The additive errors ~j are due primarily to the shot noise in the detectors and the thermal noise in the amplifiers in the data collection board, so they may be considered as independent normally distributed quantities having zero mathematical expectation and unknown variance ~2.The accuracy of such an analyzer is determined primarily by the errors: the noise in the detectors and amplifiers, errors in estimating the probe transfer coefficients (calibration errors), and error in determining the wavelength in the line. As a rule, the main source of error is the error in calibrating the probe relative transfer coefficients.Calibration Method Analysis. The relative transfer coefficients are usually found by calibrating the line with a...

A Multi-Probe Microwave Reflectometer Using an Improved Calibration Algorithm

“…The principal advantage of the arrangement is its simplicity, since three fixed detector probes placed along the transmission line can replace typical alternative arrangements of directional couplers and bridges. A variety of different methods for determining the calibration constants of the system have been reported [1][2][3][4][5][6]. The researchers so far have made various assumptions in determining the calibration constants, such as neglecting line losses, dispersion in the line, loading effects of the probes and inexact positioning of the detection probes.…”

“…Considering V+e i = Vq, and a phase error term e for 0 each probe, equation (1) will become: V=V F I+F e;e S e(VaiE i ;i = tZ23 (2) Where (t -2,/k) corresponds to the detection probe location from the load with some unknown phase error.…”