Design Method of Constant Phase-Shifter Microwave Passive Integrated Circuit in 130-nm BiCMOS Technology With Bandpass-Type Negative Group Delay

The miniaturization and application development are the expected challenges on the today engineering design research on bandpass (BP) type negative group delay (NGD) circuit. To overcome this technical limit, an innovative contribution on integrated circuit (IC) design method of BP-NGD application to design constant phase shifter (PS) in 130-nm BiCMOS technology is developed in the present paper. The BP-NGD PS microwave passive IC is topologically consisted of cascade of CLC- and RLC-resonant networks. After the S-matrix modelling, the synthesis design equations enabling to calculate each lumped component values constituting the BP-NGD PS BiCMOS are established. The design equations are expressed knowing the targeted specifications as phase shift and operating frequency. The BiCMOS design methodology including the key steps as design rule checking (DRC), layout versus schematic (LVS) and post-layout simulation (PLS) is described. The miniaturized BP-NGD PS design feasibility is verified with schematic and layout simulations with IC CMOS standard commercial software tool. A proof-of-concept (POC) of 130-nm BiCMOS BP-NGD PS operating at the center frequency <inline-formula> <tex-math notation="LaTeX">$f_{0}=1.9$ </tex-math></inline-formula> GHz and bandwidth <inline-formula> <tex-math notation="LaTeX">$\Delta f=0.1$ </tex-math></inline-formula> GHz is designed and simulated. After DRC, the chip layout of miniaturized BP-NGD PS POC presents 0.407 mm<sup>2</sup> size. The BP-NGD PS POC exhibits constant phase shift notable value of about <inline-formula> <tex-math notation="LaTeX">$\varphi _{0}= - 90^{\circ }+$ </tex-math></inline-formula>/−0.4° under <inline-formula> <tex-math notation="LaTeX">$S_{21}(f_{0})= -6$ </tex-math></inline-formula>+/−1 dB transmission coefficient with good flatness and reflection coefficients (<inline-formula> <tex-math notation="LaTeX">$S_{21}(f_{0})$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$S_{21}(f_{0})$ </tex-math></inline-formula>) widely better than −10 dB. The design robustness is confirmed by 1000-trial Monte Carlo uncertainty analyses with PLS results. Because of the potential integration in wireless sensor networks (WSNs), the BP-NGD PS under study is a promising candidate for the improvement of the future 5G and 6G transceiver design.


3) 174
In addition to the magnitudes, the present study will also 175 consider: 176 • the phase of the transmission coefficient which is 177 defined by: • the frequency dependent GD response which is defined 180 by: When the last quantity is negative, the S-parameter presents 183 an unfamiliar NGD behavior. The next subsection recalls the 184 main specifications of BP-NGD type circuits.

186
A circuit can be classified as typical BP-NGD function if 187 we can find an angular frequency, ω, from the transmission 188 coefficient GD respecting the condition: An ideal response of BP-NGD function can be represented 191 by:

192
• The cut-off angular frequencies, ω 1 and ω 2 , as depicted 193 by Fig. 2(a), as roots of equation: • By taking a real negative parameter t n , the ideal GD 196 response can be negative as defined by: ) 198 • By taking the maximal reflection coefficient 199 0 < A max < 1, we have the ideal response displayed 200 as plotted in Fig. 2(b):

206
For the case of BP-NGD circuit, the bandwidth is defined by:

208
To design an ideal PS, the ideal S-matrix model of BP-209 NGD in frequency band [ω 1 , ω 2 ] with: 211 Therefore, the BP-NGD S-matrix can be formulated by:

213
The S-matrix presents the associated transmission coefficient 214 expressed as: 216 with 0< B n <1 and initial phase shift:

218
In opposite to the present case, the PGD circuit specifications 219 will be elaborated in the next section.

221
The PGD function operates as typical true time delay (TTD) 222 circuit assumed to work in the frequency band defined by 223 limits ω 1 and ω 2 with ω 1 < ω 2 which is the same as the 224 frequency band of the previously described BP-NGD func-225 tion. By taking real positive t p , the ideal GD diagram can be 226 represented by Fig. 3 specified by: The PGD is expected to present the same specifications 229 in terms of reflection and transmission coefficients as the 230 BP-NGD ones plotted in Fig. 2(b) and Fig. 2(c), with A p = 231 A n and B p = B 2 n , respectively. The GD diagram shown by 232 Fig. 3 enables to express the phase shift associated to the PGD 233 that within frequency band [ω 1 , ω 2 ]. Accordingly, the ideal 234 S-matrix model of PGD under ideal condition: 235 S 11,PGD (jω) = S 22,PGD (jω) ≈ 0.
(17) 236 The associated S-matrix should be: which presents the associated transmission coefficient 239 expressed as: with 0 < B p < 1 and initial phase shift: The next section describes the proposed PS theorization from 244 the previously defined BP-NGD and PGD characterization. 245

247
The fundamental theory of the constant or independent of 248 frequency PS is described in the present subsection. The ideal 249 representation of the constituting PGD and NGD circuit is 250 introduced. The ideal main specifications and the analytical 251 approach from the S-parameter operation are defined.  Substituting the S-matrix of equation (13)

279
To generate a frequency independent PS within frequency 280 band [ω 1 , ω 2 ], the phase shift must be expressed as:

289
• The independent frequency phase value:

291
More illustrative comprehension about the constant phase 292 shift aspect can be reached with graphical representation of 293 phase diagram.

C. PHASE DIAGRAM ANALYSIS OF THE BP-NGD BASED PS 295
The previous analytical approach enables to plot the ideal 296 behavior of the BP-NGD PS understudy. We also recall that 297 the PS is expected to operate within frequency band [ω 1 , ω 2 ]. 298 We can denote ω 0 ∈ [ω 1 , ω 2 ] a particular operating angu-299 lar frequency. According to such particular characteristics, 300 we can realize a frequency independent PS illustrated from 301 algebraic operation based on PGD and NGD phase plot 302 shown by Fig. 5(a). Following the ideal case behavior, it is 303 noteworthy that the BP-NGD PS should present:

304
• A phase shift equal to constant ϕ PS (ω) = ϕ 0 which is 305 equal to constant or does not depend to the frequency as 306 stated by equation (26) and depicted by Fig. 5(a).

307
• A zero delay in the working frequency band of the study 308 as stated by equation (27) and highlighted by Fig. 5(b). 309 Before the investigation of POC, a concrete design of the 310 proposed PS with RLC-network based lumped circuit is 311 investigated in the next subsection.

314
The S-parameter models of the elementary circuits constitut-315 ing the PGD, NGD and constant PS circuits are developed in 316 this section.

317
A. S-PARAMETER MODELLING OF PGD TOPOLOGY 318 Fig. 6 represents the schematic of the PGD passive two-port 319 circuit. It acts as a π-topology composed of two identical 320 C p -parallel capacitors connected at the input/output accesses 321 and L p -series inductor. This passive cell can be named 322 CLC-circuit also in the rest of the paper. 323 93088 VOLUME 10, 2022 The PGD-topology equivalent impedance matrix is given .

326
The S-matrix model is calculated from Z-to-S transform 327 relationship: Accordingly, we have the reflection and transmission coeffi-332 cient expressions of the following PGD S-matrix:

335
where: These analytical relations will be exploited to elaborate the 338 analysis and design method in the following subsection. The equivalent matrix impedance associated to the NGD 344 passive topology is written as: The associated S-matrix model is established from Z-to-S 349 matrix transform from relationship as expressed in equa-350 tion (31). Accordingly, we have the reflection and transmis-351 sion coefficient expressions of the following S-matrix of the 352 NGD passive cell: The model of the PGD and NGD combined cells is elaborated 356 in the next subsection.
Figs. 8 represent the concrete circuit for designing PS passive 360 topology. It is constituted by the combined PGD and NGD 361 circuits schematized by the general π-topology shown by 362 Fig. 8(a). The detailed configuration of the BP-NGD PS 363 circuit including all the lumped components is depicted by 364 Fig. 8(b).

FIGURE 8. (a) Equivalent impedance based π -topology and (b) two-port black box of frequency-independent PS constituted by PGD and NGD circuits in cascade.
The passive topology of the PS is composed of two iden-366 tical Z p -parallel impedances connected at the input/output 367 accesses and Z s -series impedance analytically given by: The BP-NGD PS-topology equivalent impedance matrix is 370 given by: with:

374
By means of Z-to-S matrix transform, we have the reflection 375 and transmission coefficient expressions of the following S-376 matrix of the BP-NGD PS passive cell: Before the design methodology of BP-NGD PS in CMOS 382 technology, the synthesis formulas of lumped components 383 will be investigated in the following section. First of all, the PGD circuit can be analyzed by the exam-417 ination of magnitude of reflection coefficient expressed in 418 equation (33) and the phase of transmission coefficient 419 expressed in equation (34). We can choose as particular angu-420 lar frequency: Secondly, it is important to underline that at this angular 423 frequency, the PGD circuit shown by Fig. 6 is in phase 424 quadrature: The PGD circuit synthesis consists practically in determin-427 ing the constituting components inductor L p and capacitor 428 C p to target the particular operation angular frequency and 429 reflection coefficient A 1 by solving equations: In this case, we have:

433
• The transmission coefficient written in equation (34) 434 becomes: • The GD defined in equation (5) applied to equation (34) 437 becomes: which is given by: These analytical equations serve to characterize our PGD 442 circuit as described in the following paragraph.

443
2) GRAPHICAL ANALYSIS 444 By using equation (55), the variation of the PGD GD and 445 working frequency product versus reflection coefficient A is 446 plotted in Fig. 9(a). We can see that the product variation is 447 not significant when A increases to −40 dB to −10 dB. Con-448 sequently, based on such increase of reflection coefficient, 449 we see that the GD-working frequency product decreases 450 from 0.318 to 0.302.

451
The cartographies of the PGD GD t p versus pair work-452 ing frequency varying from f min = 0.5 GHz and f max = 453 2.5 GHz and reflection coefficient A is displayed in Fig. 9(b). 454 In the considered range of pair (A, f 0 ), we emphasized 455 that t p is decreasing from 0.637 ps to 120 ps inversely to 456 f 0 and A.   As stated in [29], [30], [31], [32], [33], [34], [35], and [36], 472 the BP-NGD circuit must operate in opposite phase of the 473 PGD one. The NGD block ideal specification will be defined 474 in the following paragraph.

475
The BP-NGD circuit shown in Fig. 7 was analyzed by the 476 examination of magnitude of reflection coefficient expressed 477 in equation (38) and the GD associated to the transmission 478 coefficient expressed in equation (39) at the particular angular 479 frequency:

481
It should be pointed out that at this angular frequency, the 482 NGD circuit presents the phase from equation (39)  In this case, we have:

485
• The reflection coefficient written in equation (38) 486 becomes: • The GD defined in equation (5) applied to equation ( which is given by: . (63) 496 The BP-NGD circuit synthesis equations are established in 497 the following subsection. • The GD equalized from equation (28) which leads to the 508 equation: Lastly, the NGD-circuit synthesis formulas derived from the 511 previous equations are: Knowing the resistor synthesis equation, the transmission 516 coefficient written in equation (34)  The GD of the BP-NGD circuit shown in Fig. 7 can be 526 expressed from the transmission coefficient introduced in 527 equation (39) and definition (5). The NGD cut-off angular 528 frequencies are determined by solving equation (7). Follow-529 ing these analytical actions, it can be derived from synthesis 530 equations (66), (67) and (68), the NGD cut-off frequencies 531 versus reflection coefficient and center frequency given by: 533

564
Similar to the CMOS design method of NGD ICs intro-565 duced in [41], [42], and [43], the proposed BP-NGD PS one 566 should start from the targeted specifications to the final layout 567 design. The main actions behind the design methodology of 568 BP-NGD PS ICs are indicated by the design flow depicted 569 by Fig. 11. The proposed six principal steps of the CMOS IC 570 design can be described as follows: BiCMOS technology is investigated in the present subsection.

614
The different steps of workflow indicated by Fig. 11 were 615 followed during the design.

616
The BP-NGD PS specifications are arbitrarily chosen in 617 order to highlight the microwave CMOS IC design feasibility 618 study. The main specifications including the consideration of 619 the investigation frequency band are indicated in Table 1. The 620 IC design focuses first on the BP-NGD and PGD circuits. 621 Then, the combined circuit is designed to analyze the PS 622 behavior. As result, Fig. 12 represents the schematics of the 623 PGD, NGD and PS POC designed in the environment of the 624 ADS electronic and RF/microwave simulation tools from 625 Keysight technologies .  Table 2.

TABLE 2. Parameters of the PGD and NGD circuits constituting the PS.
The BiCMOS BP-NGD PS design is described in the 632 following subsection.

635
The CADENCE VIRTUOSO design of the PS schematic is 636 displayed in Fig. 13. The STMicroelectronics 130-nm BiC-637 MOS manufacturing process was chosen as main reference 638 for the present microwave PS design because of its compo-639 nent integration potential in the range of desired specification 640 values.

641
Due to the relatively large size of the components, expen-642 sive manufacturing processes such as 28 nm-FDSOI are 643 not needed. Fig. 14 Table 3 and Table 4, respectively. 662 The minimal resonance frequency is also indicated.

665
The present section deals with the numerical verification 666 and state of the art study of the BP-NGD PS topology. The 667 frequency dependent BP-NGD PS behavior will be discussed. 668 The compared and obtained results are from:   The corresponding GDs are displayed by Fig. 15(b) which 701 shows NGD from f 1 = 1.456 GHz to f 2 = 2.48 GHz 702 with GD NGD (f 0 ) ≈ −61 ps. The NGD effect compensates 703 the PGD which presents GD CLC (f 0 ) ≈ 165 ps. Fig. 16(a) 704 confirms that the CLC and NGD circuits are matched to 705 S 11CLC,NGD (f 0 ) ≈ −13 dB around the expected working fre-706 quency. Both circuits present transmission coefficients better 707 than S 21CLC,NGD (f 0 ) > −2 dB as illustrated by Fig. 16(b) 708 confirms that the CLC and NGD circuits. The results of the 709 combined CLC and NGD circuits designed in 130-nm BiC-710 MOS IC technology with parameters indicated by Table 2 and 711  Table 3 are examined in the next subsection.  GDs are plotted in Fig. 17(b). A good agreement between 725 the 130-nm BiCMOS designed BP-NGD PS POC and ideal 726 ones (MATLAB calculation and ADS simulation) PSs 727 and GDs are obtained.

728
As expected, they confirm undeniably the constant PS 729 behavior with GD less than 10 ps around the working fre-730 quency. A good correlation of the behavior of the indepen-731 dent frequency phase shift around the working frequency 732 f 0 = 1.9 GHz is shown in Fig. 17(a). Table 4 Table 2 and Table 3,  The last case MC UA of BP-NGD PS POC UA is focused on 798 the reflection coefficient. The analysis is based on the assess-799 ment of maximum S 11max = max[S 11 (f)]. Fig. 22 depicts the 800 histogram and DSP of S 11ave . We can emphasize that mean 801 value is of about −9.1 dB over the standard deviation of 802 about 1.1 dB. This result enables to state that our BiCMOS 803 PS presents a risk of unmatching if the physical parameters 804 varied over +/−5% relative variation. 805

806
Based on the previous results, Table 5 addresses the summary 807 of the MC UAs. We recall that the statistical run was repeated 808 with 1000 trials.

809
The last explored table indicates the mean values and 810 standard deviations of the four previously discussed specific 811 characteristics analyzed. Less relative variation of physical 812 parameters should be expected to ensure BP-NGD phase shift 813 respecting the criteria of microwave circuits in f low−PS = 814 1.7 GHz and f high−PS = 2.05 GHz.

816
Similar to the investigation on unfamiliar BP-NGD circuit 817 design, the relevance of the proposed BiCMOS BP-NGD PS 818 can be understood with bibliographic study. Table 6 addresses 819 a comparison of performances of unfamiliar BP-NGD circuit-820 based frequency independent PSs available in the literature 821 VOLUME 10, 2022     [29], [30], [32], [33], [34], [35]. They are dedicated to operate  [30], [32], [33], [34] and one of 829 them operates in dual-band [35].   The PGD circuit is constituted by inductor and capacitor 846 which named CLC reactive network. The NGD one is com-847 posed of RLC-resonant network. The modelling, analysis and 848 synthesis of BP-NGD and CLC PGD are introduced. The 849 synthesis equations enabling to determine the lumped circuit 850 parameters in function of the targeted working frequency, 851 phase shift, GD and reflection coefficient are established.

852
To generalize the BP-NGD PS concept in BiCMOS tech-853 nology, the design methodology of IC including the DRC, 854 LVS and PLS is described. The design feasibility of the minia-855 turized BP-NGD PS is verified in 130-nm BiCMOS technol-856 ogy by using a standard commercial tool. The obtained results 857 confirm the IC designability of the BP-NGD PS. As expected, 858 the constant phase shift of about −90+/−1 • with outstanding 859 challenging flatness is obtained. Moreover, the PS flatness is 860 verified over 18.4% relative bandwidth. Furthermore, inter-861 esting flatness's of transmission coefficient phase and mag-862 nitude is verified. The robustness of the PS expected during 863 the fabrication process is expected with 1000-trial MC UAs. 864 The sensitivities of the constant PS characteristics are pointed 865 out in function of the relative variations of layout IC physical 866 parameters.

867
As ongoing research in continuation of the present study, 868 we are currently working on:

869
• The fabrication and test of BiCMOS BP-NGD PS 870 prototypes,

871
• The feasibility of BP-NGD PS at higher frequencies as 872 W-band,

875
• And the real environment characterization test of minia-876 turized CMOS and MMIC PS for the future 5G and 6G 877 TxRx microwave system.