PMWIS specification

As shown in Fig. 1, the PMWIS super-heterodyne receiver includes an antenna, an LNA, an RF amplifier, an RF filter to reject out-band harmonics, a mixer with LO, an IF filter, an IF amplifier, a detector diode, and an integrator. The output signal is sent to a video amplifier, an analog to digital converter, and to the computer to create an image [Reference Sani, Mohanna and Askarpour11].

The power received by the antenna is P _a = kΔfT _a, where Δf(Hz) is the bandwidth (equal to the IF bandwidth), T _a(k) is the antenna temperature, and K is the Boltzmann constant (1.38 × 10⁻²³ J/K). This is considered as the signal at the receiver input. The receiver equivalent noise power at the receiver input is P _r = kΔfT _r, where T _r(k) is the receiver noise temperature (due to the thermal noise in the receiver components). In this case, the detector gives an analog output voltage proportional to the received noise power, which can be calculated by equation (1) [Reference Le Vine and Skou12].

(1)$$V_{{\rm out}} = GK\Delta f( {T_r + T_a} ) + V_{{\rm offset}}$$

where, V _offset(V) is the detector offset voltage and G is the receiver gain. To reduce the system noise, the RF amplifier should have low noise and high gain for the detection of very small wave powers. The temperature resolution is defined as the lowest temperature difference which can be detected by the system or the temperature sensitivity of the system is obtained by equation (2) [Reference Tiuri13].

(2)$$\Delta T = ( {T_a + T_r} ) \sqrt {\displaystyle{1 \over {\Delta f\tau }} + {\left({\displaystyle{{\Delta G} \over G}} \right)}^2} $$

where, ΔG/G is the receiver gain fluctuations and τ(s) is the integration time of the low-pass filter after the detector. In order to improve the temperature resolution, the temperature equivalent to the system noise must be reduced and its integration time and bandwidth must be increased. It should be noted that a large increase in integration time will increase the imaging time but also increases the gain fluctuations. In the PMWIS, Δf is the IF bandwidth which in this receiver is 1.5 GHz. An acceptable threshold for ΔT is 0.5 K in most passive imaging systems [Reference Lynch JJ6, Reference Martin, González, Kolinko and Lovberg14]. Therefore, using equation (2) and considering 10 ms for the integration time and ignoring the small gain fluctuations, the temperature resolution of 0.126 K is obtained. In the process of designing the PMWIS, the total gains of the RF and IF amplifiers and the responsivity of the diode should be considered to provide a suitable input power level required for detection. According to Rayleigh–Jeans law, the power level of the received signal for the bandwidth of 1.5 GHz at brightness temperature (T _B) of 273 k is −82.47 dBm, which is very small. Therefore, the RF amplifier must have high gain and low noise characteristics to provide the power level required for the diode detector.

Also, the loss in the IF amplifier, the mixer attenuators, and the filters must be considered. Since the central frequency is 35 GHz, a mixer with LO of 33.5 GHz is used to convert the signal to the IF of 1.5 GHz. Thus, the diode must have an appropriate sensitivity at the frequency of 1.5 GHz, so an RF power detector with a 60 dB dynamic range is employed (LT5534 (https://www.analog.com/media/en/technical-documentation/data-sheets/5534fc.pdf)). It operates in the range of 50 MHz to 3 GHz. Designing an input impedance matching network for the diode is challenging, the wider bandwidth the lower the detector sensitivity. Figure 2(a) shows the matching circuit for the detector diode. Figures 2(b) and 2(c) illustrate the S ₁₁ diagram representing the input impedance matching in both narrowband and wideband modes. Figure 3 indicates the output voltage (volts) of the detector versus the input power in both narrowband and wideband modes. As can be seen in Fig. 3, a suitable sensitivity for the imaging application has been obtained. Therefore, the components of the receiver, operating before the detector, must be designed in such a way that the necessary power is obtained.

Figure 2. (a) Impedance matching circuit designed for the detector diode. (b) s ₁₁ diagram for a wide band. (c) s ₁₁ diagram for a narrow band.

Figure 3. Detector output voltage and measured diagram in terms of input power.

Typically, commercial RF LNA components have a noise figure (NF) of 2.2 dB and a gain of 16 dB at 35 GHz. Therefore, two RF amplifiers are needed to provide the total gain of 32 dB. Additionally, two IF amplifiers with a total gain of 40 dB are utilized. The super-heterodyne receiver is simulated and shown in Fig. 4 and the received power that reached the detector is plotted in Fig. 5.

Figure 4. Super-heterodyne receiver.

Figure 5. Received power to the diode for the temperature of 313 K.

In the simulation, the attenuations of the mixer and the filter are considered. After the detector, an integrator (low-pass amplifier) is employed to eliminate high frequencies and smooth the output having 100 Hz bandwidth. In the image, the voltage difference between the pixels is equivalent to the temperature difference between the regions. The output voltage is plotted in Fig. 6 for a temperature of 313 K. The output voltage is equivalent to the object temperature and includes some ripples in the time duration of the measurement (scanning the object).

Figure 6. The output voltage of the system for a temperature of 313 K.

The amplitude of these ripples depends on the bandwidth of the low-pass filter. To eliminate the ripples, it is necessary to calculate the mean of the voltage in the interval τ(s) for each pixel (scanned region) and map the voltage difference of regions in the scanned object as an image.

Filter design method

Microwave components in communication systems are required to be compact, and show high performance. To implement Ka-band filters with low insertion loss, low cost, and high power capacity, the substrate-integrated waveguide (SIW) [Reference Xu and Wu15] can entirely meet the above requirements, besides, the SIW circuit is fabricated by standard printed circuit board (PCB) process, which is very low weight and easy to integrate with planar circuits. Therefore, SIW technology is employed for designing the millimeter-wave filters of the PMWIS, resonator antenna [Reference Chemweno, Kumar and Afullo16], slot antenna for terahertz application [Reference Ur Rehman Kazim, Abohmra, Ur Rehman, Imran and Abbasi17], etc. As shown in Fig. 7, the waveguide structure can be made by a pair of arrays of metal short circuit rods that act as fences to trap the electromagnetic wave inside. The SIW structure only supports the propagation of TE_n0 electric transverse modes, similar to the TE_n0 mode in rectangular waveguides. The lack of TM modes is useful for the design of the band-pass filter because it can eliminate some unwanted out-of-band harmonics.

Figure 7. SIW structure and equivalent waveguide.

The dimensions of an SIW must be determined to propagate a specific mode. The process of designing and determining SIW parameters is selecting s from the range of 0.05 < s/λ _c < 0.25 and 0.5 < d/s < 0.8 and then placing the parameters d and s in equation (3) and calculating w [Reference Kordiboroujeni and Bornemann18].

(3)$$w = w_{eff} + s( {0.766e^{0.4482d/s}-1.176e^{{-}1.214d/s}} ) $$

At first, the even order Iris filter [Reference Wang, Wong, Sun, Chen, Zhu and Chu19] with direct coupling as shown in Fig. 8(a), and SIW resonators are designed and simulated. Then based on direct coupling, one stage quadruple structure without negative coupling is designed just to obtain a relatively moderate attenuation slope in the stop band. The third-type filter is also realized as one stage quadruple structure, by using a coplanar waveguide (CPW) line; to achieve negative coupling between cavity 1 and 4, it will generate two transmission zeroes (TZs) at each side of the pass band (Fig. 8(b)). Filters of cascaded quadruple structures generate pairs of TZs, the number of which depends on the order of the cascaded structure [Reference Levy20]. Therefore, adjusting different negative coupling coefficients in every block can obtain corresponding pairs of TZs in the stop band. This structure has one negative coupling and three positive couplings [Reference You, Chen, Zhu and Gong21], the dotted line in Fig. 8(b) indicates negative coupling (electric field coupling), and the solid line indicates positive coupling (magnetic field coupling). Same structure filter with cross-couplings improves stop band performance with a steeper attenuation slope. In the negative cross-coupling filter, there exists one non-adjacent electric field coupling by CPW line and three adjacent magnetic field coupling by post-wall irises. CPW line is used to achieve negative coupling to obtain a single pair of TZs at each side of the pass band. Therefore, two controllable zeroes on both sides of the pass band are designed. Finally, a cascaded filter with direct coupling is used in the receiver. The filter is light weight and compatible with PCB manufacturing technology, due to the fact that they use SIW resonators.

Figure 8. (a) Direct coupling and (b) quadruple structure filter with negative couplings (solid line: positive coupling, dashed line: negative coupling).

Firstly, considering the insertion loss L _Ar (dB) = 0.1 dB and a minimum attenuation of stopband L _As (dB) at Ω = Ω_s(Rad/s), the order of the low-pass Chebyshev prototype filter, with the mentioned characteristics, is obtained n = 4 from equation (4) [Reference Hong and Lancaster22]:

(4)$$n \ge \displaystyle{{{\cosh }^{{-}1}\sqrt {( {{10}^{0.1L_{As}}-1/{10}^{0.1L_{Ar}}-1} ) } } \over {{\cosh }^{{-}1}{\rm \Omega }_s}}$$

Since the Iris method is used to design the filter, direct coupling relations must be used to calculate the coupling coefficients and the external quality factor. The fractional bandwidth (FBW) and the central angular frequency (ω ₀) are calculated by the following relations [Reference Matthaei23]:

(5)$${\rm FBW} = \displaystyle{{w_2-w_1} \over {w_0}}$$

(6)$$\omega _0 = \sqrt {w_1w_2} $$

Therefore, the presented external quality factor and the coupling coefficients are [Reference Hong and Lancaster22]:

(7)$$Q_e = \displaystyle{{g_0g_1} \over {{\rm FBW}}}$$

(8)$$K_{ii + 1} = \displaystyle{{{\rm FBW}} \over {\sqrt {g_ig_{i + 1}} }}\quad i = 1, 2, \ldots ,n-1$$

where n is the filter order and g _is are the values of the low-pass prototype filter elements. After calculating the coupling coefficients required for the specified filter specifications, the next important step is to establish a relationship between each of the coupling coefficients with the physical structure of the coupled resonators, to determine the physical dimensions of the filter to be constructed. In order to calculate the coupling coefficient of tuned asynchronous resonators (i.e. the resonant frequency of each resonator is different), regardless of the coupling type, equation (9) is used [Reference Hong and Lancaster22]:

(9)$$k = {\pm} \displaystyle{1 \over 2}\left( {\displaystyle{{\,f_{02}} \over {\,f_{01}}} + \displaystyle{{\,f_{01}} \over {\,f_{02}}}} \right)\sqrt {{\left( {\displaystyle{{\,f_{\,p2}^2 -f_{\,p1}^2 } \over {\,f_{\,p2}^2 + f_{\,p1}^2 }}} \right)}^2-{\left( {\displaystyle{{\,f_{02}^2 -f_{01}^2 } \over {\,f_{02}^2 + f_{01}^2 }}} \right)}^2} $$

where f _0i (i = 1,2) represents the self-resonant frequency of each resonator without having any coupling with its neighboring counterpart and f _pi (i = 1, 2) denotes the two split resonant frequencies when two resonators are coupled to each other. If a particular coupling is considered a positive coupling, then a negative coupling refers to a coupling whose phase response is opposite to the positive coupling phase response. The phase response of a coupling coefficient can be found from the S parameters of the coupling structure. To obtain the external quality factor of a resonator, the resonator can be excited by employing a feed line, so that there is no aperture as a load in it. The state, which is equivalent to a single-aperture network, is called a singly loaded resonator. In this case, the external quality factor is equal to [Reference Pozar24]:

(10)$$Q_e = \displaystyle{{w_0.\tau _{S_{11}}( {w_0} ) } \over 4}$$

where w ₀ is the resonant angular frequency and $\tau _{S_{11}}( {w_0} )$ is the group delay in the resonant frequency. To calculate the group delay, equation (11) is used, in which $\angle S_{11}$ is the phase of S ₁₁.

(11)$$\tau _{S_{11}}( {w_0} ) = \left. {-\displaystyle{{\partial ( {\angle S_{11}\; } ) } \over {\partial w}}} \right\vert _{\,f = f_0} = \left. {-\displaystyle{1 \over {2\pi }}\displaystyle{{\partial ( {\angle S_{11}\; } ) } \over {\partial f}}} \right\vert _{\,f = f_0}$$

Designing the RF filter for PMWIS at 35 GHz central frequency

Having the bandwidth of 1.5 GHz and the central frequency of 35 GHz, the lower and upper cut-off frequencies of the BPF became f ₁ = 34.25 GHz and f ₂ = 35.75 GHz, respectively. By determining the characteristics of the desired filter, the values of the elements of the fourth-degree low-pass prototype filter are calculated. It is necessary to calculate the external quality factor Q _e and the coupling coefficients K. By placing g _i and FBW = 0.042867 in equations (7) and (8), these coefficients will be Q _e = 24.214, k ₁₂ = k ₃₄ = 0.037 and k ₂₃ = 0.029. Using the SIW technology on the 8 mil Rogers 4003 substrate, the physical dimensions of the filter are obtained by simulation and optimization. Firstly, by placing the substrate specifications in the LineCalc tool of ADS software, the specifications of the grounded coplanar waveguide (GCPW) feed line that has an impedance of 50 ohms are determined, and wi. Cw. Cs. li parameters. Then, using the methodology described in section “Designing the RF filter for PMWIS at 35 atz central frequency,” the diameter of the vias and their distances are calculated. The diameter of the short-circuit rods dvia = 0.5 mm and the distance between them is maximally considered as s = 0.9 mm. However, reducing the distance of the vias reduces the physical strength of the filter. Figure 9 and Table 1 show the filter structure and its dimensional parameters.

Figure 9. Designed filter structure.

Table 1. The filters dimensions

The next step is to determine the dimensions of the resonators. The highest filter resonant frequency is 35.75 GHz. By placing the resonant frequency in equation (12), the dimensions of the waveguide resonating at this frequency are obtained w _eff = λ = 4.4575 mm and L _eff = 2.5735 mm. To obtain the equivalent SIW dimensions, equation (3) should be used, in which case w = 4.82788 mm and L = 2.78738 mm are calculated, and after optimization, w ₁ = 4.6575 mm and L ₁ = 2.649 mm [Reference Pozar24]:

(12)$$f_{TE101} = \displaystyle{c \over {2\sqrt {\mu _r\varepsilon _r} }}\sqrt {{\left({\displaystyle{1 \over {w_{eff}}}} \right)}^2 + {\left({\displaystyle{1 \over {L_{eff}}}} \right)}^2} $$

The method of obtaining the optimal values:

The resonant dimensions of 1 and 2 are the same as 3 with 4, respectively, due to the symmetry in this filter. The coupling coefficients k ₁₂, k ₂₃, and k ₃₄ must be calculated in terms of distances w ₁₂, w ₂₃, and w ₃₄, respectively, so k ₁₂ = k ₃₄ and w ₁₂ = w ₃₄. The coupling coefficients k ₁₂ and k ₂₃ are sufficient for the design due to the symmetry structure of the filter. To obtain k ₁₂, the structure of Fig. 10 in HFSS software is swept parametrically versus changing w ₁₂ parameter. The result of the parametric sweep creates several scattering parameter curves | s ₂₁|, which are shown in Fig. 10. By extracting the frequencies f _p1 and f _p2 from these curves, and using equation (9), k ₁₂ can be obtained in terms of w ₁₂. Since the dimensions of resonator 1 are not the same as the dimensions of resonator 2, so the self-frequencies of each resonator are not equal. By calculating the approximate values of the dimensions and optimization method, the precise dimensions can be computed. It can be assumed that the second resonator resonates at the same frequency as the first resonator, thus the values f ₀₁ and f ₀₂ can be considered equal to calculate k ₁₂ in equation (9). From the curves fork ₁₂ = 0.03711, the distance w ₁₂ is 1.73 mm. Performing a similar process, the changes in k ₂₃ can be obtained in terms of the distancew ₂₃. According to simulations similar to w ₁₂, for k ₂₃ = 0.029 the distance of w ₂₃ is 1.615 mm.

Figure 10. Diagram of extracting the k ₁₂ coupling coefficient in terms of w ₁₂.

After that, the external quality factor (Q _e) must be calculated. To observe variations, Q _e of the structure in Fig. 11 must be parametrically swept in terms of L _io. At each step of the parametric sweep, the group delay around the resonant frequency is obtained by placing the phase of S ₁₁ in equation (10). Q _e can then be calculated for different L _io using equation (11). Figure 11 shows the changes in Q _e with respect to L _io. According to Fig. 11, the length of L _io for Q _e = 24.21 is about 0.34 mm. After optimization of the parameters L _io = 0.495.

Figure 11. Simulated changes in external quality factor (Q _e) in terms of L _io.

As mentioned above, it was assumed that the dimensions of the resonators are the same in the calculation of k ₁₂ and k ₂₃, but in the following, the optimization method and accurate calculation of the parameters are described by studying the factors affecting the filter output. The filter specifications can be directed to the desired specifications by setting the four parameters L ₁, L ₂, w ₁₂, and w ₂₃. According to Fig. 12, L ₁ affects the upper cut-off frequency. Therefore, after approximately calculating L ₁, the optimal value of L ₁ can be calculated by partially changing L ₁, as shown in Fig. 12, so that the upper cut-off frequency is 35.75 GHz. Due to the coupling effects in the filter, each parameter has a significant effect on a specific part of the response (according to Fig. 10), and the exact value of each parameter can be determined.

Figure 12. Simulated S-parameter S ₁₁ of cascaded direct coupling filter versus the (a) L ₁, (b) L ₂, (c) w ₂₃, (d) w ₁₂.

After obtaining the dimensions of the filter and optimization, a complete simulation of the filter is performed and the filter output is obtained as shown in Fig. 13(a). More accurately, the connectors also affect the outputs of the filter, so in order to test the filter with the connectors, the dimensions must be optimized with the presence of the connectors. As can be seen in Fig. 13(b), the responses are affected by the presence of the connectors.

Figure 13. Final filter output after optimization (a) without connector and (b) with connector.

The E-field distribution of the optimized structure is shown in Fig. 14 at different frequency. Figure 14(a) shows the distribution of E-field in the pass-band (at 35 GHz). According to Fig. 14(a) the input power transmitted to output port. Figure 14(b) shows the distribution of the E-field out of band (at 33 GHz), that is given the input power is not transmitted to output port.

Figure 14. Electric field distribution for the (a) resonant frequency of cascaded filter with direct coupling at 35 GHz and (b) far away from the resonant mode at 33 GHz.

Next, the square filter and the filter with mutual coupling are simulated and optimized. The diameter of the short-circuit rods dvia = 0.3 mm and the distance between them is maximally considered as s = 0.5 mm. The structure and simulation results of square filters with direct and cross-coupling are shown in Fig. 15. To verify the simulation results, the first filter was built and tested. The filter is implemented on an RO 4003 PCB as shown in Fig. 16.

Figure 15. (a) Structure of quadruple filter with direct coupling. (b) Structure of quadruple filter with cross-coupling. (c) Simulation results of quadruple filter with direct coupling. (d) Simulation results of quadruple filter with cross-coupling.

Figure 16. fabricated cascaded filter with direct coupling and test setup.

The comparison of measured and simulated results is shown in Fig. 17, which indicates the results are almost equal. The use of connectors has altered the measurement results. Moreover, the existing manufacturing technology, which uses a thickness of 35 microns of copper, has caused more losses in the measurement results.

Figure 17. Comparison of measured and simulated results of cascaded filter with direct coupling.

Fabrication of the LNA and the filter

In section “PMWIS specification” a two-stage LNA has been designed, as described in Fig. 4. Taking into account the losses of the connectors and transmission lines as well as some inaccuracies during the construction and soldering, it was estimated that the total gain may be decreased. Therefore, a new LNA employing three amplifiers has been designed and implemented as shown in Fig. 18(a). The simulation and measurement results of the amplifiers along with the filter are shown in Fig. 18(b) According to the datasheet, the input power to the amplifier must be −5 dBm as maximum. Thus, the input power of LNA must be small enough so that, after amplification by the initial two-stage amplifiers, the power transmitted to the third amplifier be less than −5 dBm. Figure 18(b) presents the result of combining amplifiers with the filter as a plot of S ₂₁.

Figure 18. (a) fabricated filter integrated with amplifiers. (b) Gain.

In order to have a light weight, small, and low-cost system with appropriate spatial resolution and temperature, all parts must be assembled on one board. All parts have been implemented with GCPW impedance matching lines in the RF part and microstrip lines in the IF part. Also, in order to be able to measure without the presence of the target and the temperature setup and by the signal generator, the entire components before the detector are placed on one single board and the detector part is placed on a separate board. To test the hot object, the antenna and the detector board must be connected to the main board. The antenna [Reference Sani, Mohanna and Askarpour11] and the detector were implemented in such a way that they can be re-integrated with the main board after the initial test. Figure 19 shows the measurement setup and the system under test.

Figure 19. Experimental setup used for the determination of the final board bandwidth and available power gain.

To test the system of the super-heterodyne receiver front-end of the PMWIS, a signal with a frequency of 35 GHz and a power of −75 dBm is applied to the input part of the board, i.e. RF input, and a signal with a frequency of 33.5 GHz and a power of 13 dBm is applied to the LO of the mixer, i.e. LO input. It should be noted that the loss of the cable is also taken into account here, and due to the 5 dB attenuation of the cable, the power reaches to −80 dBm at the RF input point. In the LO input, the board is directly connected to the signal generator to avoid the cable loss. The bias voltage of the RF and IF amplifiers is 5 volts, which is supplied by the power supply. The IF output point is connected to the network analyzer to measure the power in terms of frequency. The results of IF output in the frequency range of 30–40 GHz considering −80 dBm power input are shown in Fig. 20. Additionally, in Table 2, a comparison has been made between the parameters achieved in this project and some other works.

Figure 20. IF output.

Table 2. Comparison of different works with this project

The triple-stage RF LNA has been implemented having the specification of: RF 34.25–35.75 GHz; bandwidth 1.5 GHz; gain >60 dB; NF <2.3 dB. It has less overall integration time compared to some other works, referenced in Table 2. As a result, the target imaging time is decreased, where by reducing the NF, a suitable temperature resolution can be achieved. By using suitable filters at the RF and IF stages, a bandwidth of 1.5 GHz has been obtained, which is wider than the referenced systems operated at the frequency range.