The transmitter side of the wireless interface is connected to the resistive sensor bridge. The interface also provides an excitation voltage for the pressure transducers (Figure 3). Let the sensor-transfer characteristics be represented by the transfer function f(p). The sensor bridge has a differential output voltage in the mV range, ratiometric to the supply voltage V_CC (Equation (1)): (1) V P = V B P 1 − V B N 1 = V C C f ( p )

The output voltage V_OUT from the instrumentation amplifier is the sum of the amplified differential input voltage V_P, multiplied by the instrumentation amplifier gain G_IA, and the offset voltage V_OFS: (2) V OUT = G I A V P + V OFS

The instrumentation amplifier gain G_IA is determined and fixed by the resistor R_G. The offset voltage is proportional to the supply voltage and defined by the resistor divider R_OFS1 and R_OFS2 (Figure 3). (3) V OFS 1 = V C C R OFS 2 R OFS 1 + R OFS 2

The amplifier output voltage is connected to the ADC. The reference voltage V_REF is derived from the supply voltage by the resistor divider R_OFS1 and R_OFS2 and is equal to the offset voltage V_OFS: (4) V REF = V OFS = V C C R OFS 2 R OFS 1 + R OFS 2

The 16-bit digital output value from the ADC is proportional to the ratio of the ADC input voltage and the reference voltage (Figure 4): (5) N ADC = 2 16 V INADC V REF

Replacing V_INADC = V_OUT we obtain: (6) N ADC = 2 16 G I A V P + V OFS V REF = N ADC = 2 16 G I A f ( p ) + α αwhere: (7) α = R OFS 2 R OFS 1 + R OFS 2

Equation (6) has no reference voltage, which means the ADC reference voltage could be an arbitrary value as long as it is within the ADC specification required by the ADC. This is true only when the sensor-bridge excitation and the ADC reference voltage are proportional or equal (Equation (4)). Finally, the digital readouts N_ADC are buffered and transmitted via a wireless link (Figure 4).

Digital readouts are transmitted to the receiver. The raw digital data N_DAC feeds the digital-to-analog converter with the same sampling rate as the ADC converter in the transmitter. The applied external reference input voltage V_ref determines the full-scale output voltage of the DAC converter: (8) V DAC = N DAC 2 M V REF (9) V REF = V C C R β R + ( 1 − β ) R = 1 2 V C Cwhere 2^M refers to the DAC resolution. The reference voltage is set to one half of the bridge supply voltage (V_CC/2). The DAC output is connected to a fully differential amplifier. It has a differential input and a differential output (Figure 5).

The differential output voltage is generated by the differential driver with a rail-to-rail output. Its internal common-mode feedback architecture allows its output common-mode voltage to be controlled by the voltage applied to V_M. To implement the fully differential configuration the feedback resistors and attenuator resistors must match perfectly. One option is to select the resistors and sort them into several bins, which creates many problems when it comes to mass production. Another option is to use high-precision resistors, which raises the cost of the implementation. An optimal trade-off between the costs, the mass-production requirements and the performance could be implemented with a thick-film hybrid-circuit technology providing the ultimate match of the feedback network consisting of four resistors that determine the amplifier's closed-loop gain. The amplifier's differential output voltage (Figure 5) is defined as: (10) V ODIF = V O P − V O N

The common-mode output voltage is the average of the two voltages and is defined as: (11) V OCM = V O P + V O N 2

The voltage gain of the single-ended-to-differential output topology can be derived from the signal definitions shown in Figure 3. The setting V_OFS2 = 0 can be written as: (12) V DAC − V A P R G = V A P − V O N R F , V A N = V A P = V O P ( R G R F + R G )

Solving the above Equation (10) gives the gain relationship for V_ODIF/V_DAC: (13) V O P − V O N = V ODIF = V DAC ( R F R G )

An inverting configuration with the same gain magnitude can be implemented by simply applying the input signal to V_OFS2 and setting V_DAC = 0. For a balanced differential input, the gain from V_DAC − V_OFS2 to V_ODIF is also equal to R_F/R_G.

The advantages of the proposed topology can be summarised as follows: -

there is no need for accurate (and costly) voltage references in the transmitter or receiver,

A disadvantage of the presented solution is that it requires a highly matched resistor network. There are other types of amplifiers, which can be deployed in this circuit and are commonly used. One is differential amplifier implemented with singe operational amplifier. True instrumentation amplifiers with three or two operational amplifiers may be implemented. They all amplify differential signals with good rejection of common mode input voltages. The latter two are popular for discrete implementation having lower requirements on resistors. Since our amplifier circuit is implemented in a thick film hybrid circuit technology, the resistor matching is not an issue, because they are all precisely laser trimmed.

The performance of a battery-operated wireless device depends on the energy efficiency. One of the main consumers of the energy in the battery is the RF link. The transmitter's power efficiency could be maximised by minimizing the RF link's active time. The active time starts with the transition from a low power state to the active state. This period is followed by a data-transmission interval. Finally, the RF link needs some time to switch from the active mode back to the sleep mode. The transition intervals are significantly shorter than the active transmission. The main focus in minimizing the RF link's power consumption should be during the active period. The easiest way to reduce the power consumption of the RF transmitter is to reduce the bandwidth of the RF link by sending less data without losing performance.

During the system design, it is necessary to define the required system resolution δ_X and the operating range (x_MAX−x_MIN). Both parameters define the minimum number of bits required to store any value within the operating range: (14) M S > log 2 x MAX − x MIN δ Xwhere M_S is the smallest number of bits.

Another possible solution to reduce the amount of data being transmitted is data compression. However, the lossless compression of a continuous data stream is a challenging task for a resource-limited embedded microcontroller. The compression method should conform to the restrictions imposed on the processing power and the memory resources. The best method to reduce data rate is to use a custom data format with a resolution equal to M_S. The data reduction is then implemented as simple bit-manipulation, where all the processing remains within the microcontroller register file. In our implementation we used half-precision 16-bit floating-point numbers using 1 sign bit, a 5-bit excess-15 exponent and 10 mantissa bits, in accordance with IEEE Std 754-2008 [17].

Replacing a cable with a wireless interface presents new challenges for the field of data integrity. It is not uncommon to be faced with issues relating to the integrity of readouts transmitted via a wireless interface. This wireless interface is usually small in size and has limited computing capabilities. With some safety-critical applications, like healthcare, data integrity ranks high in the core requirements. Wrong decisions caused by invalid data may harm someone's health or even result in the death of a patient. One such example is wireless blood-pressure monitoring. When used, e.g., in a critical-care unit, many decisions are based on instruments' readouts. If the blood pressure displayed by the patient's monitor is wrong, the patient could receive the wrong treatment, resulting in a critical state. In such cases, it is better not to transfer any data at all than present data that might be invalid. With this in mind, three levels of error detection were implemented: sequence-number checking, control-byte error checking and the checksum calculation. The whole data frame structure is shown in Figure 6.

At the upper level, a sequential freshness security service is employed. Sequential freshness maintains an ordered sequence of received frames. When a frame is received, the freshness value is compared with the last known freshness value. If the freshness value is newer than the last known value, the check has passed, and the freshness value is updated to the new value. If the freshness value is not newer than the last known freshness value, the check has failed. This service provides evidence that the received data are newer than the last data received by that device.

The frame control byte (FCB) represents the essential part of an application frame. The bit pattern within the FCB defines the type of payload or serves as a special command, like data-acknowledge, data-acquisition start and stop, etc. The FCB is divided in two 4-bit symbols. The FCB error detection is provided with 4-bit to 8-bit coding. There are only 16 valid byte codes for each 4 bit half of the FCB. Each symbol is coded with an 8-bit code. Finally, the check sum calculation is operated over the complete frame and added at the end of the frame. Each data frame has control structures with a data payload (Figure 6). Some special frames such as reception acknowledge or command strobes have no data payload.

The wireless-sensor interface shown in Figure 2 was implemented with two different wireless technologies. The first set was implemented on IEEE 802.15.4 transceivers based on the CC2400 from TI/Chipcon (Figure 7(a)). The second pair was implemented with standard Bluetooth WT12 modules from Bluegiga (Figure 7(b)).

The main reason for the implementation with two different wireless technologies was their evaluation for industrial and medical applications. They are both some of the most commonly used in a variety of applications. IEEE 802.15.4 is preferred in industrial applications, like ZigBee and similar protocols. Medical applications are more Bluetooth oriented.

The following table presents the main characteristics of the two wireless technologies that are relevant for the selection of a target application. The data gathered in Table 1 could be used as a guideline when selecting the optimum wireless technology. The final decision, however, also depends on other factors, like availability, legal and safety compliance with medical or industrial applications, etc.

In order to evaluate the performance of the developed wireless interface for replacing cables in bridge-sensor applications, a dedicated data-acquisition system was constructed. The clinical evaluation system (Figure 8) schematic is shown in Figure 9. The pressure was generated using a programmable pressure source for laboratory testing, while real live signals from different patients were taken during clinical trial. The calibrated pressure sensor S was used for the reference electrical signal. The output voltage from sensor S was connected to the transmitter unit and served as a reference signal p_T. The same signal was directly connected to the data-acquisition system. The transmitter output signal was wirelessly transmitted to several receiver units simultaneously. All the receiver signals p_R1, p_R2 p_RN were measured with dedicated channels in the DAQ.

The purpose of the study was to determine whether the wireless transmission of pressure signals from the sensor to the data-acquisition system is feasible, safe and as accurate as a conventional cable connection. The analysis was made by comparing pressure-signal pairs p_T and p_Ri (i = 1, …,N). Each signal was sampled and stored in files over a long period of time. The sampling frequency was twice the sampling frequency of the wireless interface, which resulted in huge data files. The gathered data was, therefore, analyzed offline.

As shown in Figure 10, the signal p_R is delayed after the signal p_T. The wireless-data connection is not ideal; it exhibits some error in the time and the amplitude. In addition, the delay time and the amplitude error between the signals may change over time [18]. The main reason for the time-delay variability is the difference in the internal clocks between the transmitter and the receiver unit (Figure 10). The amplitude error is caused by component tolerances in the transmitter acquisition and receiver reconstruction circuits.

The wireless interface was measured with the DAQ system over a one-day period. As mentioned above, the measurement resulted in an enormous amount of data that was stored in huge files. It was not possible to perform the evaluation on a sample-by-sample basis [19]. To handle such long data records, it is necessary to split the long data record into segments of a manageable size. In order to evaluate the quality of the wireless data transmission a dedicated, multiple-step data-extraction and evaluation algorithm was developed. The principle of the algorithm is sketched in Figure 11.

The acquired test-results file contains two sets of data: p_T from the transmitter side and p_R from the receiver side. Both signals were sampled simultaneously, although they are not correctly aligned due to the delay induced by the wireless system. The first step in the algorithm is the extraction of segments that are suitable for analysis. The segment size was determined in a preliminary analysis that considered two criteria. The first one was the trade-off between the number of segments and the computational speed: shorter segments require a shorter processing time. On the other hand, this would result in a larger number of segments, which is more difficult to handle. The second criterion was related to the duration time of the segmented data. The programmable pressure source generated a periodic signal. To keep the analysis consistent at least two input signal periods should be present in a single segment. Consequently, one whole period of the transmitter periodic signal p_T lies between the segment array indexes a and a + N, as shown in Figure 11.

The corresponding samples appear in the receiver signal p_R between indices b and b + N as an approximate and a delayed approximate of the signal p_T. In order to calculate the difference between the two signals, they must be aligned in time. This is done by shifting the output signal back until the shapes fit. In order to determine the actual error induced by the wireless system, the two signals must be perfectly aligned. The index b, which represents the start of the transmitted signal within the received array, is not known. The difference between the indices a and b (see Figure 11) characterizes the time delay and is determined by calculating the cross-correlation between the two signals.

Let the extracted segments of the signals p_T and p_R be represented by the arrays: (15) p T [ i ] = [ p T a , p T a + 1 , … , p T a + N ]and: (16) p R [ j ] = [ p R b , p R b + 1 , … , p R b + N ]where a is the starting index and N is the segment length limiting the transmitter-segment boundaries. The corresponding segment in the receiver signal is denoted by the index b and the equal length N (see Figure 11).

The array segment within the receiver signal array is shifted back in time: (17) p R ′ [ j ] = p R [ j − k ]where the array shift is denoted by the lag difference k. The maximum k is related to the buffering mechanism of the wireless system and is proportional to the buffer width. The signal delay is determined by calculating the normalized cross-correlation between the segments p_T and p′_R at all the expected values of k. The normalized cross-correlation between the two arrays is defined as: (18) ρ = p T ⊗ p R ′

The delay k = b − a is defined as the lag for which the normalized cross-correlation has the largest absolute value ρ_MAX. At this point, the two signals closely resemble each other. In reality, the wireless system adds some errors in amplitude. Some variation in the time delays of the individual segments is also apparent due to the dynamic clock handling of the internal buffering mechanism. The resulting small amplitude errors and time-delay deviations, however, provide sufficient correlation between the pair of the delayed signal, as shown in Figure 12.

The last step, shown in Figure 11, is the evaluation. The result of the evaluation process is a single value, calculated from the aligned signal segments for each evaluated parameter (i.e., amplitude error, time delay).

The first evaluation stems from the mean difference between the signals. The difference array δ[i] is calculated by subtracting the corresponding elements from the aligned signal arrays: (19) δ [ i ] = [ p R c − p T a , p R c + 1 − p T a + 1 , … , p R d − p R b ]

The new array δ[i] is the source for the first evaluator δ̄. It is calculated as an average value of the array δ[i]: (20) δ ¯ = 1 b − a ∑ j = a b δ [ j ]

The signal difference evinces a systematic amplitude error. Its value represents the actual quality of the wireless transmission system. This should be kept within acceptable limits, defined by the required system accuracy.

The second evaluator is the time delay. The difference between the indices a and b is transformed into time. The time between two samples within the signal array is defined by the sampling frequency f_S. The time delay D between the signals of the observed segments is calculated by: (21) D = b − a f S