A study of the causes of inaccuracy in broadband RF transmission
bridges, and a demonstration of the methods that can be used
to correct them.
Main document (version 1.01, 10th Feb. 2014)
Work files (spreadsheets can be opened using Apache OpenOffice)
testbrg61-12_1.ods - Prototype test bridge data analysis.
capcal_p500.ods - 500 pF reference capacitor calibration curve.
capcal_8-48.ods - 40 pF reference capacitor calibration curve.
testbrg61-12_2.ods - Optimised test bridge with 500 pF reference capacitor.
testbrg61-12_3.ods - Optimised test bridge with 40 pF reference capacitor.
testbrg61-12_4.ods - Generator side shield earth, 500 pF ref.cap.
testbrg61-12_5.ods - Generator side shield earth, 40 pF ref.cap.
mismatch_sim.ods - Effect of through-line mismatch on in-phase response.
testbrg61-12_6.ods - Apparent sec. capacitance with 75.5 Ω ref. load
testbrg61-12_7.ods - Apparent sec. capacitance with 50 Ω ref. load
testbrg61-12_8.ods - No Faraday shield. Uncompensated. 50 Ω ref. load.
testbrg61-12_9.ods - No Faraday shield. Uncompensated. 75.5 Ω ref. load.
testbrg61-1210.ods - No Faraday shield. Load port capacitance neutralisation.
testbrg61-1211.ods - No Faraday shield. Herzog neutralisation.
testbrg61-1212.ods - Load port capacitance neutralisation.
testbrg61-1213.ods - Quadrature current neut. via Faraday shield.
testbrg61-1214.ods - Herzog neutralisation.
testbrg61-1215.ods - Load-side voltage sampling
testbrg61-13_1.ods - No Faraday shield. Phase shift neutralisation.
testbrg61-13_2.ods - Quad. current neut. to unloaded aux. winding.
testbrg61-13_3.ods - Quad. current neut. to loaded aux. winding. Fixed load.
testbrg61-13_4.ods - Quad. current neut. to loaded aux. winding. Var. load.
testbrg61-13_5.ods - Phase shift neutralisation.
testbrg61-14_1.ods - No Faraday shield. Quad voltage neut. 40 pF ref. cap.
testbrg61-14_2.ods - Quad voltage neut. 40 pF ref. cap.
testbrg61-14_3.ods - Quad voltage neut. 3 pF - 30 pF trimmer.
A self-evaluating precision reference bridge. D W Knight - Follow-up article
US Pat. No. 2808566 - Douma's bridge .
AC electrical theory, by DWK (source of the phasor theorems used here).
Scientific Data Analysis, by DWK (linear regression procedures and statistical methods).
Amplitude response of conventional and maxflat current transformers, DWK.
+ spreadsheets Maxflat_test1.ods , & Maxflat_test2.ods .
Current transformer efficiency factor (DWK) + spreadshet Itr_effy.ods .
Hatfield LE-300A/1 TRAB (Laboratory bridge used for the L and C measurements).
US Pat. No. 4739515 - Herzog's compensation method.
US Pat. No. 2134589 - Stanek's Faraday shielded current transformer.
An impedance monitoring bridge can be characterised by choosing two independent (or nearly independent) circuit parameters related to the magnitude and phase of the load impedance at balance. By adjusting the selected parameters to balance the bridge exactly with a reference load attached, the deviations of the parameters from their target values can be used to compute the bridge error at a given frequency. In a bridge that uses a capacitive potential divider for voltage sampling (Douma's bridge), suitable parameters are the lower voltage-sampling network capacitance and the LF-compensation resistance. The balance point can be located with great precision by using a communications receiver as the detector. Shielding and the use of common-mode chokes in the earth-loop between the signal generator and receiver prevents errors due to spurious signal injection. The optimised system can make relative phase measurements with an RMS uncertainty of about ±0.0075 degrees.
The effect of the series inductance of the lower voltage sampling capacitor is clearly determined by the data. Compensation for this parasitic reactance can be obtained by inserting a small adjustable inductance in series with the upper voltage-sampling arm. Magnitude flatness of around ±0.03% over 5 octaves is possible by this method.
The parallel-equivalent secondary-inductance of the current transformer is a strongly conserved model parameter. The measurement of parallel secondary capacitance is however skewed by through-line mismatch and other parasitic reactances, to the extent that it may appear to be positive, negative, or accidentally zero. A perturbation series is derived to account for the various contributions, and includes a hitherto undocumented effect of Faraday shield displacement current. Control of parasitics is needed if bridges built by different individuals are to give comparable results.
The data show a linear relationship between phase error and frequency except for a small deviation attributable to a dispersion region in the premeability of the ferrite transformer core. This supports the view that the phase error can be considered as a time delay ocurring primarily in the transformer.
Various phase compensation schemes are proposed and evaluated. These lead to bridge designs with 2-point frequency tracking that can easily achieve a maximum phase error of better than ±0.2° and a maximum magnitude error of better than ±0.3% over the 1.6 MHz to 30 MHz range. A 3-point tracking scheme that gives a maximum phase error of ±0.04° is also demonstrated.
The need for the transformer Faraday shield is investigated. Theory indicates that the effect of the parasitic capacitance from line to detector port is correctable depending on the coupling factor. An unshielded bridge with 2-point frequency tracking gave a maximum phase error of ±0.05°over the 1.6 MHz to 30 MHz range, close to the ±0.03° limit imposed by dispersion effects in the ferrite used.