FAQ3 CAPACITANCE MEASUREMENT

The capacitance measuring system must be able to measure very small inter-electrode capacitances, of the order of 10^-15 Farads (1 fF), in the presence of much larger capacitances to earth of the order of 200,000 fF (mainly due to the screened connecting cables).

The capacitance measurement technique used in PTL equipment is based on the use of an excitation signal in the form of a 1.25MHz square waveform. The excitation signal is applied to one electrode (the SOURCE electrode) and the currents which flow into the remaining (DETECTOR) electrodes (which are held at virtual ground potential) are measured using a synchronous demodulator. These measured currents are proportional to the capacitance between the SOURCE electrode and the DETECTOR electrodes. Back to top

With the current state of capacitance measurement technology, it is possible to measure capacitance changes between 2 unearthed electrodes of 0.2 fF in the presence of stray capacitance to earth of 200pF at a rate of 2000 measurements per second. This sets a practical lower design limit on the smllest capacitance between any pair of electrodes of around 10fF. Sensors with inter-electrode capacitances lower than 10fF will usually produce very noisy and unstable images. Back to top

The capacitance values when the sensor contains air are referred to as "standing capacitances" and their relative values are shown in the figure below for a 12-electrode circular sensor with internal electrodes. Sequential electrodes (adjacent electrodes), have the largest standing capacitances (values for a typical sensor are around 200-500fF), while diagonally opposing electrodes (opposite electrodes) have the smallest capacitances (typically 10-20 fF). Back to top

Relative inter-electrode-pair capacitance values

Many different ECT measurement protocols are possible (see eg Reinecke, 1994), as capacitances can be measured between many combinations of groups of electrodes (which effectively become new "virtual electrodes"). Back to top

No. The measurements for a single frame of data are made sequentially. Consequently, the capacitance data within the frame will be collected at different times and there will be some skewing of the data. Interpolation techniques can be used to de-skew this data if this effect is likely to produce significant errors. Back to top

Most work to-date with circular vessels has used the simplest arrangement (which we refer to as protocol 1) where capacitances are measured between single pairs of electrodes. The measurement sequence for protocol 1 involves applying an alternating voltage from a low-impedance supply to one (source) electrode. The remaining (detector) electrodes are all held at zero (virtual ground) potential and the currents which flow into these detector electrodes (and which are proportional to the inter-electrode capacitances) are measured. A second electrode is then selected as the source electrode and the sequence is repeated until all possible electrode pair capacitances have been measured. This generates M independent inter-electrode capacitance measurements, where:

M = E.(E - 1)/2

and E is the number of electrodes located around the circumference. For example for E = 12, M = 66. Back to top.

Other possible protocols involve grouping electrodes and exciting them in pairs (protocol 2) and triplets (protocol 3) etc. The formula for the number of independent measurements for grouped electrodes is :

M = (E).(E - (2P - 1)) / 2

where P (the protocol number) is the number of electrodes which are grouped together. Back to top

In principle, the use of more complex protocols can generate a larger number of independent measurements for a given electrode size and capacitance measurement sensitivity than the simple single-pair protocol 1. Improved image resolution is therefore achievable, although at the expense of the maximum image frame rate, which falls as the protocol number or number of electrodes increases. Back to top

For a sensor with internal electrodes, the components of capacitance due to the electric field inside the sensor will always increase in proportion to the material permittivity when the sensor is filled uniformly with higher permittivity material. However for sensors with external electrodes, the permittivity of the wall causes non-linear changes in capacitance, which may increase or decrease depending on the wall thickness and the permittivities of the sensor wall and contents. Back to top

Last updated 24-05-2002

Copyright 2001 PTL