Today, two main sectors of applications are the driving forces of sensor development:

- Driver surveillance
- Sleep monitoring of babys
- Stress monitoring of employees

In many industrial applications as well as in vital parameter sensing, presence detection and vibration analysis, a measurement of the displacement is sufficient. In these cases, the absolute distance between system and target is not of interest, while a highly precise measurement of the relative displacement around a zero point is desired. Therefore, an unmodulated sinusoidal signal with frequency \(f\) is transmitted and reflected by the target. At the receiver, the phase difference \(\Delta\varphi\) between transmit (Tx) and receive (Rx) signal is evaluated. Since it is directly related to the path delay of the electromagnetic wave by \(\Delta\varphi = 2\pi f \cdot \tau\) the displacement \(\Delta x\) can be determined if the speed of light \(c\) is known: $$\Delta x= c \cdot \frac{\tau}{2} = c \cdot \frac{\Delta\varphi}{4 \pi f}$$

In free space applications, \(c\) equals the vacuum speed of light. The factor of two in the equation appears due to the fact that a target displacement by \(\Delta x\) delays both the path from antenna to target and the path from target to antenna. In practical applications, the wavelength (for example 12.5mm at 24 GHz) is much smaller than the absolute distance between system and target and therefore an unknown number of sinusoidal periods occurs between Tx and Rx signal, making an absolute ranging impossible.

However, thanks to the theoretically infinitely small bandwidth of the RF signal, the required bandwidth at the receiver only depends on the speed \(c\) of the moving target, i.e. the occurring Doppler shift. The minimum required bandwidth can be estimated by $$B_\text{min}=\left(\frac{1+\frac{v}{c}}{1-\frac{v}{c}}-1 \right) \cdot f \approx \frac{2vf}{c}.$$

Thus, for a target movement of 1 m/s, a bandwidth of only 160 Hz is sufficient, if a 24 GHz Tx signal is used. The narrow signal bandwidth is a clear advantage of CW radars, since the noise power can be reduced by appropriate filtering and thus leads to a high measurement precision. Moreover, low sampling frequencies lead to low data rates and allow for power- and resource efficient systems. Since no modulation is required, the hardware effort is also small which leads to cost-efficient solutions.

After all, it can be stated that the system topology, with a modulated or unmodulated carrier, strongly depends on the application. A careful trade-off between features and performance has to be made leading to a tailored system for a given scenario.

In this article, a system for vibration analysis is presented. Since a high measurement precision is necessary, a CW system topology was chosen. It leads to a very compact, cost-efficient and lightweight solution to the measurement task.

The proposed system is designed to show the application of radar systems in different scenarios. In this paragraph the building blocks of firmware, RF and baseband are described.

For many applications a high sampling rate might not be necessary but a low power consumption is required. Therefore, the firmware is designed to be adjustable for this case. Since all active components as phase-locked loop (PLL), transceiver, temperature-compensated crystal oscillator (TCXO) and analog amplifiers are integrated in the system in a way that they can be shut down, a high percentage of power can be saved. This principle is called duty-cycling, which means that the microcontroller powers up all active components in the right order to perform the measurement and switches them off immediately afterwards. Shortly after, the microcontroller enters its sleep mode and wakes up again by an internally generated timer interrupt. Consequently, the power consumption is reduced tremendously and the resolution is still the same as in continuous mode. However, keeping Nyquist theorem \(f_\text{sampling}>2f_\text{max}\) in mind, the frequency of the duty cycling should not fall below two times the maximal expected frequency which is generated by the targets vibrations.

As a first part of the hardware, the RF section is explained in detail, as a crucial part of the overall system. The block diagram is depicted in Figure 1. One main component is the the used 24 GHz ultra-wideband transceiver TRX24_007 by SiliconRadar. In this system the bandwidth is a parameter of freedom to find the ideal matching of the used innovative RF transition from microstrip to waveguide which is necessary for the used 3D-printed horn antenna. The output frequency is internally generated by a voltage controlled oscillator (VCO) which is locked by an external PLL, the ADF4158. The PLL receives the fed back and by 8 divided output signal of the VCO and compares it to a known reference which is derived from a TCXO, a temperature stable frequency source.

The output power of the signal can be easily increased by the integrated power amplifier (PA) which adds 4 dBm. This consequently increases the signal-to-noise ratio (SNR) and thus leads to a higher overall precision of the measurement. However, this of course increases the power consumption as well. The RF signal afterwards passes an external hybrid coupler since in this case a monostatic approach is pursued. This means that the same antenna is used for the transmission and receiving path. On the one hand, this reduces cost and size of the system but on the other hand the overall performance depends on the quality of the radar coupler, which cannot be seen as ideal in a real system. As an antenna, a 3D laser-sintered horn antenna is used. The weight is reduced by more than 30% due to the included holes with a diameter small enough to have no influence on the propagation of the electromagnetic wave. The backscattered signal is then guided in the receiver path and inside the transceiver. Before performing the down conversion, the SNR can be further increased by switching on the integrated low noise amplifier (LNA). Finally, four down converted DC voltages are generated and form the differential IQ signal. By using differential signals, the system becomes more tolerant against common mode interferences.

In the next part, the analog baseband circuit is investigated more precisely. The circuit is shown in Figure 2 and is separated in two parts outside and inside of the used microcontroller STM32F373.

The figure shows the circuit for the I or Q channel and starts with a fully differential amplifier which amplifies the signals and still remains the differential behavior. This helps to avoid common-mode distortions and hence optimizes the SNR. Afterwards, a passive low-pass filter is applied to suppress high frequency signal components. However, the filter has to be designed such that the short DC pulses, caused by the duty-cycling and the short RF pulses are still able to pass this filter and are not suppressed. This trade-off between bandwidth and settling time is a key factor for these kind of radar systems. Inside of the microcontroller the differential signals can be further amplified by a programmable gain amplifier (PGA), before being digitized with the integrated 16 bit sigma-delta ADC. The I and Q data is finally transmitted via an FTDI-Interface and universal serial bus (USB) to the host PC where the data is processed in Matlab.

With $$\Delta\varphi=\arctan\left(\frac{Q}{I}\right)$$ the phase difference can directly by calculated. From there on, the relative displacements of the target can be calculated with the already mentioned equation \(\Delta x= c \cdot \frac{\tau}{2} = c \cdot \frac{\Delta\varphi}{4 \pi f}\). After these basic operations a fast Fourier transform (FFT) is applied to calculate for example the vibration frequency of the target or the heart and respiration frequency of a person.

In this article, two major applications of radar sensors in industry and the health/lifescience sector have been presented.

In industrial applications, radar systems can be used to detect tiny displacements. This might be oscillations or vibrations of moving parts and machines. The frequencies and amplitues of these oscillations provide valuable information on the condition of the device, which helps to prevent faults and damages.

In the medical field, changes in heart and respiration rate can be monitored contactlessly. The data can be used to detect tiredness and mental stress of car or truck drivers. Moreover, high-risk patients, such as babys or sick people can be monitored continuously, without affecting the comfort or the daily life.

For both sectors the advantage of radar, that non-conductive materials as clothes, dirt, fog or even mattresses are penetrated is huge. Beside the mentioned applications a further almost infinite number of others are thinkable. Moreover, since the costs for components are rapidly decreasing and microcontrollers become even stronger calculation units, radar and RF systems are one of the key future technologies.

[1]

*, IEEE Microwave Magazine*, vol. 21, iss. 1, pp. 88-95, 2020.

[2]

[3]

*, IEEE Microwave Magazine*, vol. 20, iss. 1, pp. 91-97, 2019.

[4]

*, IEEE Microwave Magazine*, vol. 19, iss. 1, pp. 91-98, 2018.