All industrial and medical EM flow meters operate on the principle of EM induction.
The fundamental design structure of such devices is similar. Any EM flow meter consists of an electromagnet, transducers (electrodes), input and output systems. The input system is the power supply unit of the electromagnet, which can be either DC or AC. The output system conditions the measured total voltage signal from the electrodes, processes the signal and then stores or displays the results. It mainly consists of signal conditioning and signal processing sub-systems. The signal conditioning sub-system performs the following functions: (1) impedance transformation, (2) amplification and (3) filtering of unwanted signals. The signal processing sub-system discriminates the
flow signal from unwanted signals, if they have the same frequency, by methods that will be described later in this section.
Early designs of EM flow meters used permanent magnets or DC-powered electromagnets for the generation of a uniform magnetic field. This meant that the flow signal was in the form of a DC potential difference. However, polarisation normally occurs at the surface of the electrodes due to electrochemical effects between the electrodes and the conductive fluid, blood vessel wall or skin surface [9]. Polarisation also creates a DC potential which is hard to differentiate from the DC flow potential difference. Moreover, the DC flow induced signal is typically very small and requires significant amplification by a direct-coupled amplifier. The amplitude of the DC offset due to polarisation is usually much larger than the flow induced voltage signal and therefore, it causes the amplifier to saturate (exceeds its dynamic operating range).
For these reasons, DC-powered electromagnets (or permanent magnets) are not desirable. Alternating current (AC) methods overcome this problem as the detected flow induced signal becomes an AC potential difference and any DC offsets can be minimised considerably by using an AC-coupled amplifier [127]. The AC-coupled amplifier combines a high-pass filter and an amplifier. The alternating current can be sinusoidal, square-wave or trapezoidal. Each one of these excitation source methods has certain advantages over the others as will be described below.
Normally, the physiological potential difference signal Δ measured by a two-electrode or multi-electrode AC flow metering system is mathematically given by
Δ = + + ( )+ ( )+ Eq. 2-54
The first term of the right-hand side of Eq. 2-54 is the flow induced potential. is the calibration factor of the device which is related to the geometry of the flow cross section, and the size and shape of electrodes. and are the mean values of magnetic flux density and the conductive liquid velocity, respectively.
From Faraday’s law of induction, a transformer emf is induced in any conducting loop in the presence of a time-varying magnetic field as was shown in Section 2.5.2. The conductive liquid (blood), the electrodes and the connecting cables form a conductive loop. Therefore, this transformer emf superimposes on the flow induced voltage signal, and it is given by the term ⁄ . For a sinusoidal AC magnetic field, the transformer emf has a similar frequency and waveform to the flow induced signal. It is also proportional to the excitation frequency of the electromagnet, unlike the flow induced signal. The transformer emf can be minimised by careful design of the electrodes and the cabling. The cables connecting the electrodes should always be positioned in parallel with the plane of the magnetic field. However, in practical devices, this is hard to achieve and therefore, there will always be some magnetic flux cutting the cabling loops. Additionally, twisted-pair cables reduce the transformer emf as this minimises the area of the cable loops that the magnetic flux can get into and there is also a cancelling effect as induced potentials are in opposite directions.
Yet, the transformer emf is not usually fully eliminated using the methods suggested above and other methods must be utilised to ensure the transformer emf does not interfere with the flow induced signal measurement. One method for removing the transformer emf from the measured signal is by sensing it at the electrodes using a
“pickup” coil [124]. Then, the signal from the “pickup” coil is used to subtract the transformer emf from the total signal at the input of the amplifier.
Alternatively (or additionally), a PSD method can be utilised to distinguish the induced emf from the transformer emf for a sinusoidal AC excitation as they are out of phase by 90° from each other as seen in Eq. 2-24. In other words, if the excitation current is a cosine wave, then the waveform of the magnetic field will also be a cosine wave. The flow induced signal is in phase with the magnetic field, and consequently it will have the same phase as the current [127, 144, 145]. However, the transformer emf will be a sine wave. Note that sine and cosine waves are sinusoids of different phases. The PSD allows the flow induced signal to be separated from the transformer emf. This is a method whereby the measured signal is multiplied by a reference signal. The reference signal is in phase with the flow induced signal. Then, the resultant output is averaged over time. As a result, the output is a DC value which corresponds to the root mean square (RMS) value of the AC flow induced signal. This method has been implemented in EM flow metering using analogue and digital electronics [146-149].
In this research, a PSD method was utilised to discriminate the flow induced signal from the transformer emf. There are two schemes that are available in the literature to perform PSD. The first scheme is as briefly described above and the other scheme relates to the use of Discrete Fourier Transform (DFT) [150]. This method has not been implemented before in the application of EM blood flow metering. It requires a high-speed data acquisition device to sample the total measured signal and the reference signal. The reference signal can be the coil current as it is in phase with the magnetic field. The DFT is applied to both signals to obtain their magnitude and phase.
Subsequently, the in-phase component, i.e. the flow induced voltage signal, can be determined. This method is described in greater detail in Chapter 6.
There is another method used to discriminate between the sinusoidal flow signal and the
also relies on the fact that the transformer emf is 90° out of phase with the flow signal.
When the transformer emf is at zero-crossing point, the flow induced signal is at maximum (negative or positive). If a portion of the total measured signal is sampled at the zero-crossing point of the transformer emf, this portion of the signal is only related to the liquid flow. This method can be implemented using an amplifier that is controlled by a timing circuit. In the literature such an amplifier is called a ‘gated’ amplifier and is controlled by a control circuit which uses the excitation signal of the electromagnet as a reference signal to generate the timing sequence for sampling [151, 152]. Note that this method can also be achieved by using microcontrollers or DAQ devices and a numerical software such as MATLAB. Both methods, i.e. the PSD and sampling rely on phase integrity from the input of the measuring system to its output to ensure accurate extraction of the flow induced voltage signals.
The transformer emf is sinusoidal if the electromagnet excitation signal is a sine wave.
However, if the power source of the electromagnet is a square waveform, the transformer emf appears as a voltage spike (transient) with a time constant = ⁄ (where is the inductance of the electromagnet and is the DC resistance of the electromagnet coil) as illustrated in Figure 2.34. Such a flow meter is referred to as a square-wave EM flow meter. This voltage spike appears when the polarity of the excitation signal changes ( ). Thus, the flow induced voltage signal is measured after the voltage spike transient has died away. This can be achieved by a time-delay insertion during the sampling of the flow induced voltage signal. This requires the ‘on’
period of the magnetic field to be long enough to allow the transient to pass and then, the flow induced signal is recorded. However, this means that the excitation frequency has to be low. The advantages of the square-wave excitation are (1) the process of
the sinusoidal excitation and (2) the inductive impedance is also much lower (function of frequency) which means that more current can be supplied to the electromagnet for the same voltage source, and this results in the generation of a stronger magnetic field.
However, low frequency signals are more sensitive to RF and mains interferences and usually have a poor signal to noise (SNR) ratio. Furthermore, low frequency excitation means that the electronics in the signal conditioning sub-system have a slower transient response and therefore, take significant amount of time to reach a steady-state value.
In terms of power efficiency, the square-wave excitation is more efficient than the sine-wave excitation. In the square-sine-wave flow meter, the electromagnet is seen as a resistive (DC) load and therefore, the total power consumed is due to copper losses ( R), i.e.
active power. However, in the sine-wave flow meters, the electromagnet is seen as inductive load, and therefore the power consumed is the vector sum of the active power (copper loss) and reactive power due to the reactance of the electromagnet, which is mainly inductance in the case of an electromagnet. Nevertheless, this reactive power can be reduced significantly using a technique known as Power Factor Correction (PFC).
Figure 2.34: (a) Excitation voltage of the electromagnet (b) Measured voltage signal containing the
PFC refers to a method that can be used to reduce the reactive power withdrawn from the power supply [153]. This is achieved by placing a capacitor in parallel with the inductive load. The value of the capacitor is determined by setting the reactance of the electromagnet ( ) equal to the reactance of the capacitor ( ), i.e. = . It is found to be a useful technique as it lowers the current requirement for the power source of the electromagnet.
The term ∑ ( ) in Eq. 2-54 accounts for the sum of transformer emfs that are of the same waveform as the flow induced signal; however, they are not 90o out of phase as will be explained below. The sources of these emfs can be from:
· The coupling between the electromagnet coil and the electrode leads
· Magnetic flux getting into tissues, the interface between the electrode and the electrolyte or/and the input measurement system.
The impedance elements in those sources, i.e. tissues, electrode/electrolyte interface and the input measurement system will alter the phase relationship between the transformer and motional emfs, so that it is no longer 90° out of phase. This means that some of the transformer emfs generated by those sources will be in phase with the flow induced signal and therefore, they cannot be fully distinguished from the flow induced voltage signal using PSD. However, with proper magnetic and electrostatic shielding methods [154, 155], the use of cavity electrodes [127] and transformer emf nulling (calibrating the device when there is no flow) [127], these sources of error can be reduced to a minimum. Note that these emfs are not significant for square-wave flow meters as they will appear as voltage spikes (refer to Figure 2.34) and will elapse after a time period of about 5 approximately where = ⁄ .
The next error term, ∑ ( ), is due to mains interference, DC offset and biopotentials.
Mains interference refers to the 50 Hz frequency component and its harmonics, i.e.
100 Hz and 150 Hz [156]. Polarisation occurs at the interface between the electrode and skin, vessel wall or conductive liquid. As a result, a DC offset is generated which can be in the range of a few hundreds of millivolts. Biopotentials include electrocardiogram (ECG) signals, i.e. heart potential (0.01 Hz to 3.5 Hz) and electromyogram (EMG) signals, i.e. muscle potentials (2 Hz to 500 Hz) [157]. All these error components, if not minimised, can reduce the SNR and make the flow induced signal difficult to measure.
Moreover, the amplifier of the measurement system has a very large gain because the flow induced signals are usually in the microvolt range. If these error signals are not minimised, they will be amplified and can cause the amplifier to exceed its dynamic operating range (saturation).
Normally, these error signals appear at the input of the measurement system as common mode. Hence, it is necessary that the input of the amplifier of the measurement system should have a high common mode rejection ratio (CMRR) to reject these potentials efficiently. These potentials can also become differential due to the imbalance of the impedance of the electrodes and associated cables. Unwanted differential potential can be eliminated by the use of differential RC filters. The polarisation offset is a potential at DC, i.e. 0 Hz, and can be eliminated by using high-pass filters. Using the sine-wave excitation for the electromagnet allows a specific frequency to be selected, avoiding mains frequency and its harmonics. This frequency can be discriminated from all other unwanted signals by the PSD method described above. Hence, the SNR of the flow induced voltage signals will be high. This is an advantage of the sine-wave excitation over the square-wave method.
The last term, , in Eq. 2-54 is associated with the internal ‘intrinsic’ noise of the electronics. All electronic components such as resistors, reactances, amplifiers and transistors generate noise. The noise source can either be modelled as voltage or current noise. There are 4 main types of noise: (1) thermal (Johnson noise), (2) shot noise, (3) flicker noise and (4) Burst ‘popcorn’ noise [158]. Thermal noise is associated with the thermal movement of charge carriers. It is normally considered to be white noise, i.e. its power spectral density is constant throughout the frequency spectrum. The shot, flicker and burst noises are associated with amplifiers, i.e. transistors, PN junctions and the fabrication process. Datasheets of amplifiers usually state the value of two parameters, i.e. the input-referred voltage and current to model the total noise generated in the amplifier. These noise levels vary at different frequencies and bandwidths.
Noise analysis can be simplified if the dominant noise sources are determined. The total voltage noise of a circuit is the square root of the sum of all noises. This total noise can be critical in high-gain and/or high-frequency analogue circuits. It is important to be aware of this error to ensure that the flow induced potential signals have good SNR.
Careful design and selection of components reduces the effect of the noise associated with electronic components.