·Table of Contents ·Methods and Instrumentation  Essential Variables in ETT. Stepinski, Uppsala University, Signals and Systems, Uppsala, SwedenContact 
Fig 1: Block diagram of EC instrument 
Impedance bridge is the simplest possible EC instrument and a classical input circuit of electronic EC instruments. Indeed, impedance bridge and a cathode tube display were used as the first EC instruments, [2].
Impedance bridge has two functions, firstly, it converts coil impedance to an amplitudephase modulated sine voltage, and secondly, it performs coil balancing. The first function is required for simple coils that are used rather seldom today (mostly in applications with space limitations). However, this circuit is also very useful for probes, especially those employing differential pickups. The importance of impedance bridge results from its second function, probe balancing. Balancing operation is required for any type of probes and coils, both absolute and differential. During balancing coil impedance is compensated which results in shifting operating point from the impedance diagram to the origin of coordinates. This operation for coils is performed using either a balancing coil or a reference coil. Balancing of absolute probes and coils compensates the signal on the surface of defectfree specimen, while balancing of differential probes compensates probe unsymmetry. Generally, balancing makes possible amplification of the modulated signal to enable sensing its small variations in response to the detected flaws. Balancing is a very essential function of the EC instrument since it affects its linearity and dynamic range.
Asymmetric input.
Many modern instruments have a simple asymmetric input suitable for internally balanced differential probes. An internally balanced probe has a number of windings connected in this way that their output should be very small (theoretically zero) if the probe is placed in the air or on a surface of a defect free specimen. Compensating the residual unbalance signal is performed by adding sine and cosine waves to the probe output and requires sophisticated digital circuits estimating their amplitudes to minimize the unbalance, [3]. Total cancellation is usually impossible due to the presence of harmonic components in the probe output signal.
Since automatic balancing circuits are rather complicated and expensive many manufactures resign of direct balancing and replace it with DC compensation after the phase detectors. Such solution should work properly unless the unbalance signal and the gain are not too high. A high unbalance signal amplified before the demodulation may namely result in saturation of some circuits before or in the detectors. This in turn will cause distortion of the modulated signal and substantial errors at the output of the detectors. This is a very important issue since the user generally does not have access neither to the unbalance signal from the probe nor to the signal at the detector input. In practice the user may be not aware when this problem occurs. This means that using such instruments requires very well designed and manufactured probes that do not produce significant unbalance signal. This is even more important when using multiplefrequency systems that excite probes at several frequencies simultaneously.
To conclude discussion on matching probes to the input circuits we can name two essential parameters: probe unbalance signal for internally balanced probes and type of balancing circuit in the EC instrument.
Modern EC instruments employ amplitudephase detectors that suppress the carrier frequency and produce a vector (point) defined by the amplitude A(x) and the phase f(x) in the screen.
However, not many users are aware that different circuits can be used for this purpose and although all of them should operate properly in nominal conditions, they behave differently if the signal V_{SIG}(t,x) is not a perfect sine wave. Below, we will present a short description and an analysis of three main detector types and compare their performance using numerical simulations.
Multiplying detector
Theoretically, amplitude demodulation should be performed by multiplying the input signal V_{SIG}(t,x) by the reference signals sin(wt) and cos(wt) followed by lowpass filtering for suppressing the second harmonic of the carrier frequency. This operation is normally performed on an analog signal by means of analog multipliers. Input signal V_{SIG } in such detector is applied to two analog multipliers together with the reference sine and cosine waves. A direct product of the multiplication takes respectively the form of a sine wave with double frequency and a DC component proportional to A(x)cos{f(x)} for the sine reference, and A(x)sin{f(x)} for the cosine reference. This means that if the double frequency terms are suppressed by lowpass filtering, the DC components will become directly the inphase and the quadrature components of the input signal V_{SIG}. This is theory, in practice V_{SIG} is never a pure modulated sine, it contains certain amount of harmonic components that introduce errors at the output. Also, real analog multipliers produce a considerable amount of noise at the output. To analyse these effects we have performed numerical simulations of different detector structures and compared the results.
Detector with diode ring
The demodulation operation can be made in a simpler way, to eliminate multipliers a square wave can be used instead of the V_{REF},[3]. The square waves must have the same phase as the reference signals. The multiplication with a square wave can be realised using a simple diode ring. The diode ring operates as a full wave rectifier and switching points of the diodes are controlled by the reference V_{REF}. Using diodes simplifies the detector circuit and enables its proper operation for higher carrier frequencies that can reach several MHz in some EC applications. Such detector is simple and robust, it is not sensitive to noise due to averaging by the lowpass filter that follows the diode ring.
Sampling detector
Sampling detector operates on a very simple principle, the input signal is sampled at time instants depending on the detector phase. This detector is simple but sensitive to noise, which means that it requires a noise free pure sine wave for proper operation. It consists a sampleandhold (SH) circuit synchronised by the reference signal, [3]. The SH circuit samples the input signal in time instants defined by the reference.
If V_{SIG} is a pure sine the_{ }output of the SH can be expressed as
This detector has the highest gain of all detector circuits and the lowest ripple. A disadvantage is that it detects all harmonic components as well as the fundamental frequency. It is also very sensitive to electronic noise present in the input signal.
Digital simulations
To compare performance of the above mentioned detector circuits we simulated them in Matlabä and tested for a signal containing various amounts of distortion of the type caused by a saturation operation on the carrier. The distortion was modelled using tanh function normalised in amplitude to obtain a linear dependence for small amplitudes
(1) 
The amount of distortion in the signal was automatically evaluated using the following definition
(2) 
Fig 2: EC carrier with unit amplitude, frequency 10 Hz and harmonic distortion 2 %.Difference between sine and the distorted carrier (upper panel). The distorted carrier and sine (middle panel).Logarithm of the power spectrum of the distorted carrier (lower panel). 
Fig 3: Detection of circle in the complex plane, using carrier with harmonic distortion 2 %.Detector output in the left column and detector error in the right column.Multiplying detector (upper row).Diode ring detector (middle row).Sampling detector (lower row).  Fig 4: Detection of a straight line in the complex plane, using carrier with harmonic distortion 3 %. Detector output in the left column and detector error in the right column.Multiplying detector (upper row).Diode ring detector (middle row).Sampling detector (lower row). 
Fig 5: Eddy current pattern from a differential probe filtered by two different HP filters 
A good way of characterising probes is measuring their response to a specific artificial discontinuity, for instance a drilled hole. Such a response can be acquired using a computer controlled XYscanner and an EC instrument. Below, we present an example of such response acquired for probe KD2, manufactured by ESR Rohman scanned over an aluminium plate with a 1 mm hole drilled from the surface. The probe was excited with frequency 500 kHz. The response presented in Figure 6, often referred to as Point Spread Function (PSF), provides an important information about probe type, its spatial sensitivity and spatial resolution. Based on PSF we can also evaluate probe symmetry and predict its response to different discontinuities. Generally, sensitivity pattern of differential probes is highly asymmetric, they have well pronounced sensitivity maximum in one direction. Absolute probes are insensitive to scanning direction but their response to a small defect depends on the location of this defect respective probe centre.
Fig 6: Quadrature component of the response of a differential probe KD2 to a hole in Al plate. 3D presentation (left) and false colour image (right). 
Fig 7: Response of a differential probe KD2 to a hole in Al plate. Maximum sensitivity in the probe centre (left) and the response 1mm from the probe centre (right). 
This means that this probe which is characterised by high spatial resolution and sensitivity requires relatively high scanning density. It should be noted that the spatial responses of EC probes depend not only o their geometry but also to some degree on the test frequency. Summarising, we will include as an essential parameter PSF (point spread function) of the EC probe used for the inspection.
EC Instrument Function  Essential Variable 
Probe 

Input circuit 

Detector 

Filters 

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