Design method of constant phase-shifter microwave passive integrated circuit in 130-nm BiCMOS technology with bandpass-type negative group delay

Recei ed 29 July 2022, accep ed 18 Augus 2022, da e o publica ion 23 Augus 2022, da e o cu en e sion 12 Sep embe 2022. Digi al Objec Iden i ie 10.1109/ACCESS.2022.3201137 Design Me hod o Cons an Phase-Shi e Mic owa e Passi e In eg a ed Ci cui in 130-nm BiCMOS Technology Wi h Bandpass-Type Nega i e G oup Delay BLAISE RAVELO 1, (Membe , IEEE), MATHIEU GUERIN 2,3, (Membe , IEEE), JAROSLAV FRNDA 4,5, (Senio Membe , IEEE), FRANK ELLIOT SAHOA6, GLAUCO FONTGALLAND 7, (Senio Membe , IEEE), HUGERLES S. SILVA 8,9,10, (Membe , IEEE), SAMUEL NGOHO11, FAYROUZ HADDAD 2,3, (Membe , IEEE), AND WENCESLAS RAHAJANDRAIBE 2,3, (Membe , IEEE) 1School o Elec onic and In o ma ion Enginee ing, Nanjing Uni e si y o In o ma ion Science & Technology (NUIST), Nanjing, Jiangsu 210044, China 2CNRS, Aix-Ma seille Uni e si y, 13007 Ma seille, F ance 3IM2NP UMR7334, Uni e si y o Toulon, 13007 Ma seille, F ance 4Depa men o Quan i a i e Me hods and Economic In o ma ics, Facul y o Ope a ion and Economics o T anspo and Communica ion, Uni e si y o Zilina, 01026 Žilina, Slo akia 5Depa men o Telecommunica ions, Facul y o Elec ical Enginee ing and Compu e Science, VSB—Technical Uni e si y o Os a a, 70800 Os a a, Czech Republic 6Labo a oi e de Physique Nucléai e e Physique de l’En i onnemen (LPNPE), Uni e si é d’An anana i o, An anana i o 101, Madagasca 7Applied Elec omagne ic and Mic owa e Labo a o y, Fede al Uni e si y o Campina G ande, Campina G ande, Pa aíba 58429, B azil 8Ins i u o de Telecomunicações, Uni e sidade de A ei o—Campus Uni e si á io de San iago, 3810-193 A ei o, Po ugal 9Depa amen o de Ele ónica, Telecomunicações e In o má ica, Uni e sidade de A ei o—Campus Uni e si á io de San iago, 3810-193 A ei o, Po ugal 10Depa men o Elec ic Enginee ing, Uni e si y o B asília (UnB), B asília, Fede al Dis ic 70910-900, B azil 11Associa ion F ançaise de Science des Sys èmes (AFSCET), 75013 Pa is, F ance Co esponding au ho : Ma hieu Gue in ([email p o ec ed]) This wo k was suppo ed in pa by he Minis y o Educa ion, You h and Spo s, Czech Republic, unde G an SP2022/5; in pa by he NSFC unde G an 61971230; in pa by he Jiangsu Specially Appoin ed P o esso P og am and Six Majo Talen s Summi o Jiangsu P o ince unde G an 2019-DZXX-022; and in pa by he S a up Founda ion o In oducing Talen o he Nanjing Uni e si y o In o ma ion Science & Technology. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ABSTRACT The minia u iza ion and applica ion de elopmen a e he expec ed challenges on he oday enginee ing design esea ch on bandpass (BP) ype nega i e g oup delay (NGD) ci cui . To o e come his echnical limi , an inno a i e con ibu ion on in eg a ed ci cui (IC) design me hod o BP-NGD applica ion o design cons an phase shi e (PS) in 130-nm BiCMOS echnology is de eloped in he p esen pape . The BP-NGD PS mic owa e passi e IC is opologically consis ed o cascade o CLC- and RLC- esonan ne wo ks. A e he S-ma ix modelling, he syn hesis design equa ions enabling o calcula e each lumped componen alues cons i u ing he BP-NGD PS BiCMOS a e es ablished. The design equa ions a e exp essed knowing he a ge ed speci ica ions as phase shi and ope a ing equency. The BiCMOS design me hodol- ogy including he key s eps as design ule checking (DRC), layou e sus schema ic (LVS) and pos -layou simula ion (PLS) is desc ibed. The minia u ized BP-NGD PS design easibili y is e i ied wi h schema ic and layou simula ions wi h IC CMOS s anda d comme cial so wa e ool. A p oo -o -concep (POC) o 130-nm BiCMOS BP-NGD PS ope a ing a he cen e equency 0=1.9 GHz and bandwid h 1 =0.1 GHz is designed and simula ed. A e DRC, he chip layou o minia u ized BP-NGD PS POC p esen s 0.407 mm2 size. The BP-NGD PS POC exhibi s cons an phase shi no able alue o abou ϕ0= −90◦+/−0.4◦unde S21( 0)=−6+/−1 dB ansmission coe icien wi h good la ness and e lec ion coe icien s (S21( 0) and The associa e edi o coo dina ing he e iew o his manusc ip and app o ing i o publica ion was Wenjie Feng. 93084 This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/ VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui S21( 0)) widely be e han −10 dB. The design obus ness is con i med by 1000- ial Mon e Ca lo unce ain y19 analyses wi h PLS esul s. Because o he po en ial in eg a ion in wi eless senso ne wo ks (WSNs), he BP-NGD20 PS unde s udy is a p omising candida e o he imp o emen o he u u e 5G and 6G anscei e design.21 INDEX TERMS 130-nm BiCMOS echnology, in eg a ed ci cui (IC), design me hod, mic owa e ci cui , passi e22 opology, S-pa ame e model, bandpass (BP) nega i e g oup delay (NGD), BP-NGD applica ion, mic owa e phase23 shi e (PS).24 I. INTRODUCTION25 The echnological and enginee ing e olu ion ends o26 enhance he quali y o human li e and o de elop he mode n27 socie y. To ace up he challenging socie al si ua ion, new28 knowledge leading o na u al p og ess o physical science29 is expec ed. Fu he unde s anding o non- ulga phenom-30 ena can be he mos e icien solu ions agains he socie al31 p oblems. In o he wo ds, ecen esea ch wo ks s a e he32 exis ence o abno mal physical phenomena which equi e33 u he s udy. The nega i e g oup delay (NGD) phenomenon34 belongs among he mos coun e in ui i e physical phenom-35 ena which is s ill no well- amilia o mos o elec onic and36 communica ion enginee s.37 A. STATE OF THE ART ON THE NGD ELECTRONIC38 CIRCUIT DESIGN39 The ascina ing NGD phenomenon was ini ially expe -40 imen ed in dispe si e op ical media p esen ing nega i e41 e ac i e index (NRI) whe e he g oup eloci y can also42 be nega i e [1], [2], [3]. The adio equency (RF) and43 mic owa e NGD phenomenon was alida ed wi h spli ing44 esona o (SRR) s uc u e based NRI me ama e ial ci cui s45 iden i ied om 3-D and 2-D pe iodical bulk ma e ials [4], [5].46 Howe e , he me ama e ial-based mic owa e NGD ci cui s47 ope a e wi h signi ican losses. Fo his eason, he NGD48 ci cui applica ions a e li e ally less de eloped and less49 in es iga ed compa ed o o he elec onic and communi-50 ca ion unc ions as il e , an enna, ampli ie , couple and51 powe combine /di ide . Las wo decades, di e se opolo-52 gies o NGD mic owa e ci cui s we e designed and expe i-53 men ed [6], [7], [8], [9], [10], [11], [12]. I was demons a ed54 ha he NGD ci cui s can be designed by using lumped R,55 L and C opologies and also mic os ip opologies. In addi ion56 o he basic unde s anding o NGD phenomenon meaning, he57 main challenge a his s age was he design o low a enua ion58 and compac NGD mic owa e ci cui [10], [11], [12]. Mo e-59 o e , despi e he p og essi e esea ch wo k om ew g oups60 a ound he wo ld, he NGD enginee ing emains, so a ,61 an un amilia concep o non-specialis RF and mic owa e62 design, manu ac u ing and es enginee s.63 An inno a i e undamen al heo y o NGD ci cui inspi ed64 om il e heo y which is easy o unde s and o g adu-65 a e s uden s and non-specialis elec onic design, ab ica ion,66 es and comme cial enginee s was ini ia ed [13], [14]. The67 NGD ci cui heo y is elabo a ed om ans e unc ion (TF)68 app oach [13], [14]. I is no ewo hy ha he main di e ence69 is he ac ha he il e is cha ac e ized om TF magni ude 70 and he NGD is cha ac e ized om he TF g oup delay (GD). 71 Based on he NGD- il e analogy, he inno a i e classi ica- 72 ion o low-pass (LP) [13], [14], [15], [16], [17], high-pass 73 (HP) [13], [14], [18], [19], [20], [21], bandpass (BP) [4], [5], 74 [6], [7], [8], [9], [10], [11], [12], [13], [14] and s op-band (SB) 75 [13], [14], [21], [22], [23] NGD opologies a e iden i ied. 76 These di e en NGD opology ypes a e cha ac e ized om 77 he equency band(s) whe e he GD is suscep ible o be 78 nega i e. Behind he NGD heo e ical de elopmen , he e a e 79 cu ious ques ions abou he applica ion. 80 B. STATE OF THE ART ON THE NGD CIRCUIT-BASED 81 PHASE SHIFTER (PS) DESIGN 82 Ten a i e RF and mic owa e enginee ing applica ions o 83 NGD ci cui s [24], [25], [26], [27], [28], [29], [30], [31], [32], 84 [33], [34], [35], [36] we e p oposed. Ones o mos ema kable 85 applica ions a e based on he NGD equaliza ion echnique 86 which consis s o cascading posi i e GD (PGD) and NGD 87 ci cui s [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], 88 [34], [35], [36]. The NGD equaliza ion app oach enables 89 na u ally o compensa e delay and elec onic componen 90 undesi able e ec s [25], [26], [27], [28]. By means o BP- 91 NGD elec onic unc ion, he un amilia NGD equaliza ion 92 enables mo e impo an ly o design inno a i e mic owa e 93 phase shi e s (PSs) [29], [30], [31], [32], [33], [34]. The 94 solu ion o RF and mic owa e PS opology can be lexibly 95 designed wi h bo h ac i e [29], [30], [31], [32] and passi e 96 [33], [34], [35] opologies. The main pa icula i y o such 97 PSs is he possibili y o ope a e in b oadband wi h cons an 98 alue o independen ly wi h equency [29], [30], [32], [33], 99 [34]. This inno a i e PS opology can be exploi ed o design 100 Hilbe il e [36] which is in e es ing o design highe pe o - 101 mance anscei e s (Tx-Rx). Fo example, he Hilbe il e 102 is expec ed o be a good echnological candida e o pe o m 103 ope a ion as FFT and iFFT and also o design analog and 104 mixed modula o s and demodula o s o u u e communica- 105 ion on - and back-end sys ems. Mo e ecen s udy [35] 106 highligh s ha by using SB-NGD unc ion, inno a i e design 107 solu ion o s ai PSs can be pe o med. 108 Compa ed o he me ama e ial-based mic owa e PS design 109 [37] and applica ion o on - and back-end e minals [38], 110 [39], [40], u he unde s anding and applica i e s udies 111 o BP-NGD ci cui s a e needed. The echnical challenge 112 slowing down he de elopmen o cons an phase BP-NGD 113 PS is he in eg a ion easibili y in minia u ized Tx-Rx 114 VOLUME 10, 2022 93085 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui sys em. The p ominen solu ion is he design in CMOS115 in eg a ed ci cui (IC) echnology whose he easibili y o 116 LP- [41], [42] and HP- [43] NGD ci cui s we e ecen ly117 heo e ically in es iga ed.118 C. ORIGINALITY AND OUTLINE OF THE PAPER119 The main no el y o he p esen esea ch wo k is desc ibed as120 ollows:121 •The IC-based design me hodology o BP-NGD PS122 cons i u ed by combined capaci i e-induc i e-capaci i e123 ne wo k and BP-NGD passi e lumped ci cui s. The124 no el BP-NGD based PS is designed in 130-nm125 BiCMOS echnology.126 •The heo e ical syn hesis o mula ion and design127 app oach BP-NGD based PS is designed in 130-nm BiC-128 MOS echnology. The undamen al equa ions allowing129 o calcula e he lumped passi e opology in unc ion o 130 he a ge ed ope a ion equency a e es ablished.131 The p esen pape is o ganized in se en main sec ions as132 ollows:133 •Sec ion II ecalls he gene al speci ica ions o he un a-134 milia BP-NGD and posi i e g oup delay (PGD) ideal135 ci cui s.136 •Sec ion III de ines he ideal analysis and also he key137 speci ica ions o he beha io o he p oposed BP-NGD138 PS om he S-ma ix modelling.139 •Sec ion IV examines heo e ically he analy ical140 S-ma ix models o he PGD, BP-NGD and PS lumped141 opologies.142 •Sec ion V e eals he syn hesis equa ions enabling o143 de e mine he R, L and C componen alues om he144 expec ed speci ica ions o he PS unde s udy.145 •Sec ion VI is ocused on he CMOS IC design me hod-146 ology o he BP-NGD PS by using IC simula o 147 Cadence VIRTUOSO. A minia u ized BP-NGD PS148 p oo -o -concep (POC) will be designed and s udied.149 •Sec ion VII examines he e i ica ion esul s om cal-150 cula ion and simula ions. Mon e Ca lo (MC) unce ain y151 analyses (UAs) a e also pe o med o highligh he152 CMOS BP-NGD PS design.153 •Sec ion VIII inalizes he pape wi h conclusion.154 II. GENERAL DESCRIPTION OF BP-NGD155 AND PGD FUNCTIONS156 The gene al heo e ical app oach o analyze he BP-NGD PS157 is in oduced in he p esen sec ion. The in oduced heo y158 is based on S-pa ame e ep esen a ion. The speci ica ions o 159 BP-NGD and also he PS a e de ined.160 A. S-MATRIX MODELLING GENERAL DESCRIPTION161 Ac ing as a mic owa e ci cui , he analysis o he PS s ud-162 ied in his pape is essen ially based on S-ma ix app oach.163 Fig. 1 ep esen s a gene al con igu a ion o wo-po black164 FIGURE 1. Two-po S-pa ame e black box. box modelled by S-ma ix:165 [S(s)]=S11(s)S21(s) S21(s)S11(s).(1) 166 wi h s=jωis he Laplace a iable exp essed in unc ion o 167 angula equency ω=2π . The S-model elabo a ed in he 168 along pape is e e ed o he impedance R0=50.169 Ac ing as a symme ic ci cui , we ha e he magni udes 170 o he e lec ion and ansmission coe icien s exp essed as, 171 espec i ely:172 S11(ω)=|S11(jω)|(2) 173 S21(ω)=|S21(jω)|.(3) 174 In addi ion o he magni udes, he p esen s udy will also 175 conside : 176 • he phase o he ansmission coe icien which is 177 de ined by: 178 ϕ(ω)=a g [S21(jω)](4) 179 • he equency dependen GD esponse which is de ined 180 by: 181 GD(ω)= −∂ϕ(ω) ∂ω .(5) 182 When he las quan i y is nega i e, he S-pa ame e p esen s 183 an un amilia NGD beha io . The nex subsec ion ecalls he 184 main speci ica ions o BP-NGD ype ci cui s. 185 B. SPECIFICATIONS OF TYPICAL BP-NGD FUNCTION 186 A ci cui can be classi ied as ypical BP-NGD unc ion i 187 we can ind an angula equency, ω, om he ansmission 188 coe icien GD espec ing he condi ion:189 GD(ω)<0.(6) 190 An ideal esponse o BP-NGD unc ion can be ep esen ed 191 by: 192 •The cu -o angula equencies, ω1and ω2, as depic ed 193 by Fig. 2(a), as oo s o equa ion: 194 GD(ω)=0.(7) 195 •By aking a eal nega i e pa ame e n, he ideal GD 196 esponse can be nega i e as de ined by: 197 GD(ω1≤ω≤ω2)= n<0.(8) 198 •By aking he maximal e lec ion coe icien 199 0<Amax <1, we ha e he ideal esponse displayed 200 as plo ed in Fig. 2(b): 201 93086 VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui FIGURE 2. (a) GD, (b) e ec ion and (c) ansmission coe icien esponses o ypical BP-NGD unc ion. S11(ω1≤ω≤ω2)=An≤Amax.(9)202 •And by aking he minimal ansmission coe icien 0203 <Bmin <1, we ha e he ideal esponse as shown in204 Fig. 2(c):205 S21(ω1≤ω≤ω2)=Bn≥Bmin.(10)206 Fo he case o BP-NGD ci cui , he bandwid h is de ined by:207 1ω =ω2−ω1.(11)208 To design an ideal PS, he ideal S-ma ix model o BP-209 NGD in equency band [ω1, ω2]wi h:210 S11,NGD(jω)=S22,NGD(jω)≈0.(12)211 The e o e, he BP-NGD S-ma ix can be o mula ed by:212 [SNGD(jω)]=0S21,NGD(jω) S21,NGD(jω) 0 .(13)213 The S-ma ix p esen s he associa ed ansmission coe icien 214 exp essed as:215 S21,NGD(jω)=Bn·exp[j(ϕn−ω· n)](14)216 wi h 0<Bn<1 and ini ial phase shi :217 ϕn=ϕNGD(ω1).(15)218 In opposi e o he p esen case, he PGD ci cui speci ica ions219 will be elabo a ed in he nex sec ion.220 C. SPECIFICATIONS OF THE PGD FUNCTION BEHAVIOR 221 The PGD unc ion ope a es as ypical ue ime delay (TTD) 222 ci cui assumed o wo k in he equency band de ined by 223 limi s ω1and ω2wi h ω1< ω2which is he same as he 224 equency band o he p e iously desc ibed BP-NGD unc- 225 ion. By aking eal posi i e p, he ideal GD diag am can be 226 ep esen ed by Fig. 3 speci ied by:227 GD(ω1≤ω≤ω2)= p>0.(16) 228 The PGD is expec ed o p esen he same speci ica ions 229 in e ms o e lec ion and ansmission coe icien s as he 230 BP-NGD ones plo ed in Fig. 2(b) and Fig. 2(c), wi h Ap=231 Anand Bp=B2 n, espec i ely. The GD diag am shown by 232 Fig. 3 enables o exp ess he phase shi associa ed o he PGD 233 ha wi hin equency band [ω1, ω2]. Acco dingly, he ideal 234 S-ma ix model o PGD unde ideal condi ion:235 S11,PGD(jω)=S22,PGD(jω)≈0.(17) 236 FIGURE 3. GD diag am o PGD unc ion cons i u ing he PS. The associa ed S-ma ix should be:237 [SPGD(jω)]=0S21,PGD(jω) S21,PGD(jω) 0 (18) 238 which p esen s he associa ed ansmission coe icien 239 exp essed as:240 S21,PGD(jω)=Bp·expj(ϕp−ω· p)(19) 241 wi h 0 <Bp<1 and ini ial phase shi :242 ϕp=ϕPGD(ω1).(20) 243 The nex sec ion desc ibes he p oposed PS heo iza ion om 244 he p e iously de ined BP-NGD and PGD cha ac e iza ion. 245 III. GENERAL DESCRIPTION OF THE BP-NGD BASED 246 CONSTANT PS 247 The undamen al heo y o he cons an o independen o 248 equency PS is desc ibed in he p esen subsec ion. The ideal 249 ep esen a ion o he cons i u ing PGD and NGD ci cui is 250 in oduced. The ideal main speci ica ions and he analy ical 251 app oach om he S-pa ame e ope a ion a e de ined. 252 A. S-PARAMETER IDEAL ANALYSIS OF THE BP-NGD 253 FUNCTION BASED PS 254 The BP-NGD PS unde s udy is composed cascaded PGD 255 and NGD ci cui s. The analysis is elabo a ed based on he 256 VOLUME 10, 2022 93087 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui equency domain ep esen a ion. The wo iden ical NGD ci -257 cui s a e in e cala ed by PGD one. The opological solu ion o258 design his PS, we p oposed he wo-po opology in oduced259 by Fig. 4. Since he e lec ion coe icien s a e negligible260 unde condi ions (12) and (17), he S-ma ix modelling o his261 synop ic diag am is he p oduc :262 [S(jω)]=[SNGD(jω)]×[SPGD(jω)]×[SNGD(jω)].(21)263 FIGURE 4. Two-po black box o equency-independen PS cons i u ed by PGD and NGD ci cui s in cascade. Subs i u ing he S-ma ix o equa ion (13) and equa-264 ion (18) in o he p e ious ela ion, i yields he PS ollowing265 ideal model:266 [S(jω)]=0S21(jω) S21(jω) 0 (22)267 whe e he o e all ansmission coe icien ideally exp essed268 as ollows:269 S21(jω)=S21,NGD(jω)·S21,PGD(jω)·S21,NGD(jω).(23)270 I yields he phase shi analy ical exp ession o he nex 271 subsec ion.272 B. PHASE SHIFT ANALYTICAL EXPRESSION273 Subs i u ing he ansmission coe icien s gi en by equa-274 ion (14) and equa ion (19) in o he p e ious one, we ha e:275 S21(jω)=B2 nBpexpj2ϕn+ϕp−ω(2 n+ p).(24)276 I means ha he associa ed phase shi ϕPS (ω)=277 a g [S21(jω)]is gi en by:278 ϕPS (ω)=2ϕn+ϕp−ω(2 n+ p).(25)279 To gene a e a equency independen PS wi hin equency280 band [ω1, ω2], he phase shi mus be exp essed as:281 ϕPS (ω)=ϕ0=Cons an .(26)282 By iden i ica ion coe icien s o equa ions (25) and (26),283 we ha e:284 •The PS GD GDPS (ω)= −∂ϕPS (ω)/∂ω as de ined in285 equa ion (5) becomes:286 GDPS (ω)= p+2 n=0.(27)287 which implies:288 p= −2 n.(28)289 •The independen equency phase alue:290 ϕ0=2ϕn+ϕp.(29)291 Mo e illus a i e comp ehension abou he cons an phase292 shi aspec can be eached wi h g aphical ep esen a ion o 293 phase diag am.294 C. PHASE DIAGRAM ANALYSIS OF THE BP-NGD BASED PS 295 The p e ious analy ical app oach enables o plo he ideal 296 beha io o he BP-NGD PS unde s udy. We also ecall ha 297 he PS is expec ed o ope a e wi hin equency band [ω1, ω2].298 We can deno e ω0∈[ω1, ω2]a pa icula ope a ing angu- 299 la equency. Acco ding o such pa icula cha ac e is ics, 300 we can ealize a equency independen PS illus a ed om 301 algeb aic ope a ion based on PGD and NGD phase plo 302 shown by Fig. 5(a). Following he ideal case beha io , i is 303 no ewo hy ha he BP-NGD PS should p esen :304 •A phase shi equal o cons an ϕPS (ω)=ϕ0which is 305 equal o cons an o does no depend o he equency as 306 s a ed by equa ion (26) and depic ed by Fig. 5(a). 307 •A ze o delay in he wo king equency band o he s udy 308 as s a ed by equa ion (27) and highligh ed by Fig. 5(b). 309 Be o e he in es iga ion o POC, a conc e e design o he 310 p oposed PS wi h RLC-ne wo k based lumped ci cui is 311 in es iga ed in he nex subsec ion. 312 FIGURE 5. (a) Phase and (b) GD esponses o PGD, NGD, and equency-independen PS ideal unc ion. IV. S-PARAMETER MODEL OF PGD AND NGD PASSIVE 313 CIRCUITS UNDER CONSIDERATION 314 The S-pa ame e models o he elemen a y ci cui s cons i u - 315 ing he PGD, NGD and cons an PS ci cui s a e de eloped in 316 his sec ion. 317 A. S-PARAMETER MODELLING OF PGD TOPOLOGY 318 Fig. 6 ep esen s he schema ic o he PGD passi e wo-po 319 ci cui . I ac s as a π- opology composed o wo iden ical 320 Cp-pa allel capaci o s connec ed a he inpu /ou pu accesses 321 and Lp-se ies induc o . This passi e cell can be named 322 CLC-ci cui also in he es o he pape . 323 93088 VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui FIGURE 6. Schema ic o wo-po PGD ci cui cons i u ing he BP-NGD PS unde s udy. The PGD- opology equi alen impedance ma ix is gi en324 by:325 [ZPGD(s)]=1+LpCps21 1 1 +LpCps2 2+Cps(2 +LpCps2).(30)326 The S-ma ix model is calcula ed om Z- o-S ans o m327 ela ionship:328 [SPGD(s)]={[ZPGD(s)]−R0[I2−D]}× {[ZPGD(s)]+R0[I2−D]}−1(31)329 wi h 2-D iden i y ma ix:330 [I2−D]=1 0 0 1 (32)331 Acco dingly, we ha e he e lec ion and ansmission coe i-332 cien exp essions o he ollowing PGD S-ma ix:333 S11,PGD(s)=sLp−R2 0Cp(2 +LpCps2) DPGD(s)(33)334 S21,PGD(s)=2R0 DPGD(s)(34)335 whe e:336 DPGD(s)=(1 +R0Cps)hR0(2 +LpCps2)+Lpsi.(35)337 These analy ical ela ions will be exploi ed o elabo a e he338 analysis and design me hod in he ollowing subsec ion.339 B. BP-NGD S-PARAMETER MODELLING AND NALYSIS340 The BP-NGD opology is comp ised o simple RLC-se ies341 ne wo k as pa allel impedance. The wo-po cell is p esen ed342 by Fig. 7.343 FIGURE 7. BP-NGD passi e cell employed in his pape o design he cons an PS. The equi alen ma ix impedance associa ed o he NGD344 passi e opology is w i en as:345 [ZNGD(s)]=Z(s)×1 1 1 1 (36)346 wi h:347 Z(s)=R+L s +1 C s.(37) 348 The associa ed S-ma ix model is es ablished om Z- o-S 349 ma ix ans o m om ela ionship as exp essed in equa- 350 ion (31). Acco dingly, we ha e he e lec ion and ansmis- 351 sion coe icien exp essions o he ollowing S-ma ix o he 352 NGD passi e cell:353 S11,NGD(s)=−R0 R0+2Z(s)(38) 354 S21,NGD(s)=2Z(s) R0+2Z(s).(39) 355 The model o he PGD and NGD combined cells is elabo a ed 356 in he nex subsec ion. 357 C. π-TOPOLOGY S-PARAMETER MODELLING 358 OF PS CIRCUIT 359 Figs. 8 ep esen he conc e e ci cui o designing PS passi e 360 opology. I is cons i u ed by he combined PGD and NGD 361 ci cui s schema ized by he gene al π- opology shown by 362 Fig. 8(a). The de ailed con igu a ion o he BP-NGD PS 363 ci cui including all he lumped componen s is depic ed by 364 Fig. 8(b). 365 FIGURE 8. (a) Equi alen impedance based π- opology and (b) wo-po black box o equency-independen PS cons i u ed by PGD and NGD ci cui s in cascade. The passi e opology o he PS is composed o wo iden- 366 ical Zp-pa allel impedances connec ed a he inpu /ou pu 367 accesses and Zs-se ies impedance analy ically gi en by:368    Zs(s)=Lss Zp(s)=Z(s) 1+C s Z(s).(40) 369 The BP-NGD PS- opology equi alen impedance ma ix is 370 gi en by:371 [ZPS (s)]=4(s)Zs(s)+Zp(s)Zp(s) Zp(s)Zs(s)+Zp(s)(41) 372 VOLUME 10, 2022 93089 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui wi h:373 4(s)=Zp(s) Zs(s)+2Zp(s).(42)374 By means o Z- o-S ma ix ans o m, we ha e he e lec ion375 and ansmission coe icien exp essions o he ollowing S-376 ma ix o he BP-NGD PS passi e cell:377 S11,PS (s)=Zs(s)Z2 p(s)−R2 0Zs(s)+Zp(s) DPS (s)(43)378 S21,PS (s)=2R0Z2 p(s) DPS (s)(44)379 wi h:380 DPS (s)=R0+2Zp(s) R0Zs(s)+Zp(s)+Zs(s)Zp(s).(45)381 Be o e he design me hodology o BP-NGD PS in CMOS382 echnology, he syn hesis o mulas o lumped componen s383 will be in es iga ed in he ollowing sec ion.384 V. SYNTHESIS FORMULAS OF THE BP-NGD385 CONSTANT PS386 This sec ion desc ibes he main design o mulas es ablished387 om he p e ious analyses. The alues o esis o , induc o 388 and capaci o componen s cons i u ing he BP-NGD PS a e389 add essed in unc ion o he a ge ed speci ica ions.390 A. HYPOTHESES FOR THE PRESENT BP-NGD PS391 ANALYSES392 Fo he sake o he ma hema ical complexi y, le us ake a393 eal posi i e pa ame e A1 as he hypo he ical e lec ion394 loss. The syn hesis o he p oposed PS in he p esen pape 395 is pe o med unde ma ching condi ions o PGD and NGD396 e lec ion coe icien s:397 (S11,PGD(jω)=S22,PGD(jω)=A S11,NGD(jω)=S22,NGD(jω)=A.(46)398 Consequen ly, we expec o ha e he PS access ma ching wi h399 espec o equa ion:400 S11,PS (jω)=S22,PS (jω)=A.(47)401 Based on such hypo hesis, he BP-NGD PS ansmission402 coe icien can be simply app oxima ed by he ollowing403 p oduc :404 S21,PS (jω)≈S21,NGD(jω)·S21,PGD(jω)·S21,NGD(jω).(48)405 Based on such assump ion, he syn heses o ou PS consis 406 in de e mining lumped componen wi h espec o he a -407 ge ed speci ica ions. The design app oach can be explo ed408 om analyses om PGD and NGD ci cui s. The analy ical409 elabo a ion o he las wo ones a e examined in he wo nex 410 subsec ions.411 B. DESIGN EQUATIONS OF THE PGD CIRCUIT412 CONSTITUTING COMPONENTS413 The analysis and syn hesis o he PGD ci cui is elabo a ed in414 he p esen subsec ion.415 1) PGD CIRCUIT ANALYSIS AT THE WORKING FREQUENCY 416 Fi s o all, he PGD ci cui can be analyzed by he exam- 417 ina ion o magni ude o e lec ion coe icien exp essed in 418 equa ion (33) and he phase o ansmission coe icien 419 exp essed in equa ion (34). We can choose as pa icula angu- 420 la equency:421 ω=1 pLpCp .(49) 422 Secondly, i is impo an o unde line ha a his angula 423 equency, he PGD ci cui shown by Fig. 6 is in phase 424 quad a u e:425 ϕPGD(ω0)= −π/2.(50) 426 The PGD ci cui syn hesis consis s p ac ically in de e min- 427 ing he cons i u ing componen s induc o Lpand capaci o 428 Cp o a ge he pa icula ope a ion angula equency and 429 e lec ion coe icien A1 by sol ing equa ions:430 ω=ω0(51) 431 S11,PGD(jω0)=A.(52) 432 In his case, we ha e:433 •The ansmission coe icien w i en in equa ion (34)434 becomes: 435 S21,PGD(jω0)=p1−A2.(53) 436 •The GD de ined in equa ion (5) applied o equa ion (34)437 becomes: 438 GDPGD(ω0)= p(54) 439 which is gi en by:440 p=2√1−A2 ω0.(55) 441 These analy ical equa ions se e o cha ac e ize ou PGD 442 ci cui as desc ibed in he ollowing pa ag aph. 443 2) GRAPHICAL ANALYSIS 444 By using equa ion (55), he a ia ion o he PGD GD and 445 wo king equency p oduc e sus e lec ion coe icien Ais 446 plo ed in Fig. 9(a). We can see ha he p oduc a ia ion is 447 no signi ican when Ainc eases o −40 dB o −10 dB. Con- 448 sequen ly, based on such inc ease o e lec ion coe icien , 449 we see ha he GD-wo king equency p oduc dec eases 450 om 0.318 o 0.302. 451 The ca og aphies o he PGD GD p e sus pai wo k- 452 ing equency a ying om min =0.5 GHz and max =453 2.5 GHz and e lec ion coe icien Ais displayed in Fig. 9(b). 454 In he conside ed ange o pai (A, 0), we emphasized 455 ha pis dec easing om 0.637 ps o 120 ps in e sely o 456 0and A.457 93090 VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui FIGURE 9. Plo s o PGD (a) GD-wo king equency and (c) GD ca og aphy e sus pai (A, 0). 3) SYNTHESIS FORMULAS458 The design equa ions o he PGD ci cui a e es ablished459 by in e sing he equa ion o e lec ion coe icien and GD.460 Acco dingly, he PGD-ci cui syn hesis o mulas de i ed461 om he p e ious equa ions a e:462 Lp=R0 ω0 1+A 1−A(56)463 Cp=q1−A 1+A R0ω0.(57)464 The o he o mulas o calcula ing he o he componen s o 465 he PS a e es ablished om he analysis o he BP-NGD466 ci cui and he PS shown by Fig. 7 and Fig. 8, espec i ely.467 The BP-NGD ci cui analysis a e in oduced in he ollowing468 subsec ion.469 C. ANALYSIS AND SYNTHESIS OF BP-NGD CIRCUIT470 CONSTITUTING COMPONENTS471 As s a ed in [29], [30], [31], [32], [33], [34], [35], and [36],472 he BP-NGD ci cui mus ope a e in opposi e phase o he473 PGD one. The NGD block ideal speci ica ion will be de ined474 in he ollowing pa ag aph.475 The BP-NGD ci cui shown in Fig. 7 was analyzed by he476 examina ion o magni ude o e lec ion coe icien exp essed477 in equa ion (38) and he GD associa ed o he ansmission478 coe icien exp essed in equa ion (39) a he pa icula angula 479 equency:480 ω=1 √LC .(58)481 I should be poin ed ou ha a his angula equency, he 482 NGD ci cui p esen s he phase om equa ion (39) equal o:483 ϕNGD(ω0)=0.(59) 484 In his case, we ha e: 485 •The e lec ion coe icien w i en in equa ion (38)486 becomes: 487 S11,NGD(jω0)=R0 R0+2R.(60) 488 •The ansmission coe icien w i en in equa ion (39) 489 becomes: 490 S11,NGD(jω0)=R0 R0+2R.(61) 491 •The GD de ined in equa ion (5) applied o equa ion (39) 492 becomes: 493 GDNGD(ω0)= n.(62) 494 which is gi en by:495 n=−2R0L R(R0+2R).(63) 496 The BP-NGD ci cui syn hesis equa ions a e es ablished in 497 he ollowing subsec ion. 498 D. ELABORATION OF NGD CIRCUIT COMPONENT 499 SYNTHESIS 500 The NGD ci cui syn hesis is na u ally he calcula ions o he 501 cons i u ing componen s esis o R, induc o Land capaci- 502 o C o a ge : 503 •The pa icula ope a ion angula equency as s a ed in 504 equa ion (51). 505 •The e lec ion coe icien e i ying: 506 S11,NGD(jω0)=A(64) 507 •The GD equalized om equa ion (28) which leads o he 508 equa ion: 509 2R0L R(R0+2R)= p 4(65) 510 Las ly, he NGD-ci cui syn hesis o mulas de i ed om he 511 p e ious equa ions a e:512 R=R0(1 −A) 2A(66) 513 L=R0 8A2ω0 1+A 1−A(67) 514 C=8A2 R0ω0 1−A 1+A.(68) 515 Knowing he esis o syn hesis equa ion, he ansmission 516 coe icien w i en in equa ion (34) becomes:517 S21,NGD(jω0)=1−A.(69) 518 Fu he insigh on he BP-NGD cha ac e is ics can be es ab- 519 lished om hese R, L and C componen syn hesis equa ions. 520 VOLUME 10, 2022 93091 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui E. BP-NGD CIRCUIT BANDWITH VERSUS REFLECTION521 COEFFICIENT522 The analysis o he BP-NGD bandwid h is desc ibed in he523 p esen subsec ion.524 1) ANALYTICAL EXPRESSION525 The GD o he BP-NGD ci cui shown in Fig. 7 can be526 exp essed om he ansmission coe icien in oduced in527 equa ion (39) and de ini ion (5). The NGD cu -o angula 528 equencies a e de e mined by sol ing equa ion (7). Follow-529 ing hese analy ical ac ions, i can be de i ed om syn hesis530 equa ions (66), (67) and (68), he NGD cu -o equencies531 e sus e lec ion coe icien and cen e equency gi en by:532 ω1=ω0 u u 1+8A3(A−2) +Ah1+4(a−1)√λi A+1(70)533 ω2= u u 1+8A3(A−2) +Ah1+4(1 −a)√λi A+1(71)534 wi h:535 λ=1+A+4A2(A−1)2.(72)536 I implies he NGD ela i e BW which is de ined 1ω/ω0=537 1 / 0by o mula:538 1 0 539 = 4A(1 −A)h2A(A−1) +√λi (1 +A)n1+Ah1+4(A−1)h2A2(A−1) +√λiio .540 (73)541 2) GRAPHICAL ANALYSIS542 Fo u he insigh abou he a ia ion o p e iously exp essed543 pa ame e s, g aphical analyses o he NGD ela i e band-544 wid h and ansmission coe icien a e pe o med in he545 p esen pa ag aph when Ainc eases om −40 dB o −10 dB.546 Acco dingly, Fig. 10(a) ep esen s he mono onic a ia ion547 o he NGD BW exp essed by equa ion (70). We ind ha 548 his ela i e equency inc eases almos linea ly om abou 549 4% o 75.4%. Howe e , he ansmission coe icien a ia ion550 dec eases om −3.3 dB o −0.09 dB as wi nessed by in551 Fig. 10(b).552 Be o e he nume ical e i ica ion o he es ablished553 mic owa e heo y easibili y, he nex subsec ion desc ibes554 he design o POC o be in es iga ed and also he associa ed555 me hodology o 130-nm BiCMOS BP-NGD PS.556 VI. METHODOLOGY AND DESCRIPTION OF 130-nm557 BiCMOS BP-NGD PS DESIGN558 The p esen sec ion desc ibes he CMOS design me hodology559 o he BP-NGD PS opology. A POC designed in 130-nm560 BiCMOS echnology by using an IC design and simula ion561 comme cial ool will be in oduced.562 FIGURE 10. Va ia ions o (a) NGD BW and (b) ansmission coe icien e sus e lec ion coe icien a he ope a ion equency. A. DESIGN METHODOLOGY OF THE BP-NGD 563 PS IN CMOS TECHNOLOGY 564 Simila o he CMOS design me hod o NGD ICs in o- 565 duced in [41], [42], and [43], he p oposed BP-NGD PS one 566 should s a om he a ge ed speci ica ions o he inal layou 567 design. The main ac ions behind he design me hodology o 568 BP-NGD PS ICs a e indica ed by he design low depic ed 569 by Fig. 11. The p oposed six p incipal s eps o he CMOS IC 570 design can be desc ibed as ollows:571 •S ep 1: The choice o he BP-NGD PS speci ica ions 572 as phase shi ( ixed o ϕ0= −90◦ o he p esen 573 s udy) wo king equency and e lec ion loss which is 574 linked o he a enua ion. The designe can e e o he 575 speci ica ions plo ed by Figs. 5. 576 •S ep 2: The ideal alues o esis o , induc o and capaci- 577 o cons i u ing he BP-NGD PS IC should be calcula ed. 578 Fo his s ep, he design enginee s can use o mulas (56), 579 (57), (66), (67) and (68). 580 •S ep 3: The p e iously calcula ed alues mus be e i- 581 ied in he componen lib a y o he simula ion so wa e 582 ( o he p esen s udy, Cadence-VURTUOSO ). Then, 583 he easibili y o he BP-NGD PS CMOS IC design 584 should be in es iga ed by he compa ison be ween he 585 calcula ed esul s o S-pa ame e simula ions. 586 •S ep 4: The layou design should begin in he p esen 587 s ep a e schema ic ideal simula ion. The BP-NGD PS 588 CMOS IC mus espec he design ule check (DRC) 589 wi h high Ohmic unsalicided N+poly esis o and sym- 590 me ical high cu en spi al induc o . The DRC ensu es 591 ha he design can be manu ac u ed wi hin he limi s o 592 p oduc ion p ocess. The layou e sus schema ic (LVS) 593 o BP-NGD PS CMOS IC mus be pe o med. The LVS 594 93092 VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui FIGURE 21. His og am o S21a e( ) a e age om he BP-NGD PS MC UA. FIGURE 22. S11max( 0) his og am om he BP-NGD PS MC UA. VOLUME 10, 2022 93099 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui TABLE 6. IC BP-NGD PS mean and s anda d de ia ions om n=1000 ial UAs. TABLE 7. Compa ison o pe o mances o BP-NGD based RF and mic owa e PS. [29], [30], [32], [33], [34], [35]. They a e dedica ed o ope a e822 in RF and mic owa e equencies and implemen ed wi h823 lumped (using R, L, C and ansis o componen s), mic os ip824 and hyb id echnologies. I is wo h o no e ha acco ding825 o he s a e-o - he-a , he e a e di e en opologies BP-NGD826 ci cui -based PS which a e implemen ed ei he wi h passi e827 o ac i e ci cui s. Mos o exis ing PSs we e designed o828 ope a e in single-band [29], [30], [32], [33], [34] and one o 829 hem ope a es in dual-band [35].830 Thep oposed BiCMOS BP-NGD PS p esen sa ema kable831 ad an age in e ms o phase shi and ansmission coe icien 832 la ness’s. Fu he mo e, i is he i s ime ha his pa icula 833 mic owa e PS was designed in minia u e echnology based834 on 130-nm BiCMOS which allows o each physical size835 lowe han 1 mm2.836 VIII. CONCLUSION837 An o iginal esea ch wo k on BP-NGD mic owa e enginee -838 ing applica ion o designing minia u e quad a u e passi e839 PS ope a ing independen ly o he equency is de eloped.840 The in es iga ed PS IC using un amilia BP-NGD unc ion841 is inno a i ely designed in 130-nm BiCMOS echnology.842 The heo e ical app oach based on he S-ma ix modelling843 is elabo a ed. The main p inciple o he BP-NGD PS opology844 is implemen ed om he cascade o PGD and NGD ci cui s.845 The PGD ci cui is cons i u ed by induc o and capaci o 846 which named CLC eac i e ne wo k. The NGD one is com- 847 posed o RLC- esonan ne wo k. The modelling, analysis and 848 syn hesis o BP-NGD and CLC PGD a e in oduced. The 849 syn hesis equa ions enabling o de e mine he lumped ci cui 850 pa ame e s in unc ion o he a ge ed wo king equency, 851 phase shi , GD and e lec ion coe icien a e es ablished. 852 To gene alize he BP-NGD PS concep in BiCMOS ech- 853 nology, he design me hodology o IC including he DRC, 854 LVS and PLS is desc ibed.The design easibili y o he minia- 855 u ized BP-NGD PS is e i ied in 130-nm BiCMOS echnol- 856 ogy by using a s anda d comme cial ool. The ob ained esul s 857 con i m he IC designabili y o he BP-NGD PS. As expec ed, 858 he cons an phase shi o abou −90+/−1◦wi h ou s anding 859 challenging la ness is ob ained. Mo eo e , he PS la ness is 860 e i ied o e 18.4% ela i e bandwid h. Fu he mo e, in e - 861 es ing la ness’s o ansmission coe icien phase and mag- 862 ni ude is e i ied. The obus ness o he PS expec ed du ing 863 he ab ica ion p ocess is expec ed wi h 1000- ial MC UAs. 864 The sensi i i ies o he cons an PS cha ac e is ics a e poin ed 865 ou in unc ion o he ela i e a ia ions o layou IC physical 866 pa ame e s. 867 As ongoing esea ch in con inua ion o he p esen s udy, 868 we a e cu en ly wo king on: 869 •The ab ica ion and es o BiCMOS BP-NGD PS 870 p o o ypes, 871 •The easibili y o BP-NGD PS a highe equencies as 872 W-band, 873 •The in eg a ion and es o mul i-band BP-NGD PS in 874 o phased a ay an enna design [40], [41], [42], [43], 875 •And he eal en i onmen cha ac e iza ion es o minia- 876 u ized CMOS and MMIC PS o he u u e 5G and 6G 877 TxRx mic owa e sys em. 878 REFERENCES 879 [1] B. Séga d and B. Macke, ‘‘Obse a ion o nega i e eloci y pulse p opa- 880 ga ion,’’ Phys. Le . A, ol. 109, pp. 213–216, May 1985. 881 [2] J. N. Munday and W. M. 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Le ., ol. 28, no. 4, pp. 290–292, Ap . 2018. 897 [7] B. Ra elo and S. De Blasi, ‘‘An FET-based mic owa e ac i e ci cui wi h 898 dual-band nega i e g oup delay,’’ J. Mic ow., Op oelec on. Elec omagn. 899 Appl., ol. 10, no. 2, pp. 355–366, Dec. 2011. 900 [8] B. Ra elo, ‘‘Inno a i e heo y on mul iband NGD opology based on 901 eedback-loop powe combine ,’’ IEEE T ans. Ci cui s Sys . II, Exp. B ie s,902 ol. 63, no. 8, pp. 738–742, Aug. 2016. 903 [9] X. Zhou, B. Li, N. Li, B. Ra elo, X. Hu, Q. Ji, F. Wan, and G. Fon galland, 904 ‘‘Analy ical design o dual-band nega i e g oup delay ci cui wi h mul i- 905 coupled lines,’’ IEEE Access, ol. 8, pp. 72749–72756, 2020. 906 93100 VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui [10] G. Liu and J. Xu, ‘‘Compac ansmission- ype nega i e g oup delay907 ci cui wi h low a enua ion,’’ Elec on. Le ., ol. 53, no. 7, pp. 476–478,908 Ma . 2017.909 [11] T. Shao, Z. Wang, S. Fang, H. Liu, and S. Fu, ‘‘A compac ansmission910 line sel -ma ched nega i e g oup delay mic owa e ci cui ,’’ IEEE Access,911 ol. 5, pp. 22836–22843, 2017.912 [12] T. Shao, S. Fang, Z. Wang, and H. Liu, ‘‘A compac dual-band nega-913 i e g oup delay mic owa e ci cui ,’’ Radioenginee ing, ol. 27, no. 4,914 pp. 1070–1076, Dec. 2018.915 [13] B. Ra elo, ‘‘Simili ude be ween he NGD unc ion and il e gain916 beha iou s,’’ In . J. Ci cui Theo y Appl., ol. 42, no. 10, pp. 1016–1032,917 Oc . 2014.918 [14] B. Ra elo, ‘‘On he low-pass, high-pass, bandpass and s op-band NGD RF919 passi e ci cui s,’’ URSI Radio Sci. Bull., ol. 2017, no. 363, pp. 10–27,920 Dec. 2017.921 [15] B. Ra elo, ‘‘Fi s -o de low-pass nega i e g oup delay passi e opology,’’922 Elec on. Le ., ol. 52, no. 2, pp. 124–126, Jan. 2016.923 [16] R. Rand ia si e ana, Y. Gan, F. Wan, W. Rahajand aibe, R. Vauché,924 N. M. Mu ad, and B. Ra elo, ‘‘S udy and expe imen a ion o a 6-dB925 a enua ion low-pass NGD ci cui ,’’ Anal. In eg . Ci cui s Signal P ocess.,926 ol. 110, no. 1, pp. 105–114, Jan. 2022.927 [17] E. J. R. Samba a, A. Jaomia y, S. Ngoho, S. S. Yazdani, N. M. Mu ad,928 G. Chan, and B. Ra elo, ‘‘Low-pass nega i e g oup delay modelling929 and expe imen a ion wi h i-po esis o less passi e c oss-ci cui ,’’ P og.930 Elec omagn. Res. M, ol. 108, pp. 39–51, 2022.931 [18] M. Gue in, F. Wan, K. Go shko , X. Huang, B. Tishchuk, F. E. Sahoa,932 G. Chan, S. Bacca , W. Rahajand aibe, and B. Ra elo, ‘‘High-pass NGD933 cha ac e iza ion o esis i e-induc i e ne wo k based low- equency ci -934 cui ,’’ COMPEL-In . J. Compu . Ma h. Elec . Elec on. Eng., ol. 40, no. 5,935 pp. 1032–1049, Oc . 2021.936 [19] R. Yang, X. Zhou, S. S. Yazdani, E. Samba a, F. Wan, S. Lalleche e,937 and B. Ra elo, ‘‘Analysis, design and expe imen a ion o high-pass neg-938 a i e g oup delay lumped ci cui ,’’ Ci cui Wo ld, o be published, doi:939 10.1108/CW-07-2020-0131.940 [20] S. Fenni, F. Haddad, A. Jaomia y, S. S. Yazdani, F. E. Sahoa, L. Ram-941 i idisoa, M. Gue in, W. Rahajand aibe, and B. Ra elo, ‘‘In es iga ion942 on ou -po mono-capaci o ci cui wi h high-pass nega i e g oup delay943 beha io ,’’ In . J. Ci cui Theo y Appl., ol. 50, no. 2, pp. 478–495,944 Feb. 2022.945 [21] H. Jia, F. Wan, J. F nda, M. Gue in, W. Rahajand aibe, P. Thaku ,946 A. Thaku , B. Agnus, and B. Ra elo, ‘‘No el ee-shaped opology heo y947 o low- and high-pass NGD double- ype unc ion,’’ IEEE Access, ol. 10,948 pp. 28445–28460, 2022.949 [22] M. Gue in, Y. Liu, A. Douye e, G. Chan, F. Wan, S. Lalleche e,950 W. Rahajand aibe, and B. Ra elo, ‘‘Design and syn hesis o induc o less951 passi e cell ope a ing as s op-band nega i e g oup delay unc ion,’’ IEEE952 Access, ol. 9, pp. 100141–100153, 2021.953 [23] S. Fenni, F. Haddad, K. Go shko , B. Tishchuk, A. Jaomia y, F. Ma y,954 G. Chan, M. Gue in, W. Rahajand aibe, and B. Ra elo, ‘‘AC low- equency955 cha ac e iza ion o s opband nega i e g oup delay ci cui ,’’ P og. Elec o-956 magn. Res. C, ol. 115, pp. 261–276, 2021.957 [24] J.-K. Xiao, Q.-F. Wang, and J.-G. Ma, ‘‘Nega i e g oup delay ci cui s958 and applica ions: Feed o wa d ampli ie s, phased-a ay an ennas, con-959 s an phase shi e s, non- os e elemen s, in e connec ion equaliza ion, and960 powe di ide s,’’ IEEE Mic ow. Mag., ol. 22, no. 2, pp. 16–32, Feb. 2021.961 [25] C. D. B oom ield and J. K. A. E e a d, ‘‘B oadband nega i e g oup962 delay ne wo ks o compensa ion o oscilla o s, il e s and communica ion963 sys ems,’’ Elec on. Le ., ol. 36, no. 23, pp. 1931–1933, No . 2000.964 [26] K.-P. Ahn, R. Ishikawa, and K. Honjo, ‘‘G oup delay equalized UWB965 InGaP/GaAs HBT MMIC ampli ie using nega i e g oup delay ci cui s,’’966 IEEE T ans. Mic ow. Theo y Techn., ol. 57, no. 9, pp. 2139–2147,967 Sep. 2009.968 [27] B. Ra elo, S. Lalléchè e, A. Thaku , A. Saini, and P. Thaku , ‘‘Theo y and969 ci cui modeling o baseband and modula ed signal delay compensa ions970 wi h low-and band-pass NGD e ec s,’’ AEU-In . J. Elec on. Commun.,971 ol. 70, no. 9, pp. 1122–1127, Sep. 2016.972 [28] T. Shao, Z. Wang, S. Fang, H. Liu, and Z. N. Chen, ‘‘A ull-passband linea -973 phase band-pass il e equalized wi h nega i e g oup delay ci cui s,’’ IEEE974 Access, ol. 8, pp. 43336–43343, 2020.975 [29] B. Ra elo, M. Le Roy, and A. Pe ennec, ‘‘Applica ion o nega i e g oup976 delay ac i e ci cui s o he design o b oadband and cons an phase977 shi e s,’’ Mic ow. Op . Technol. Le ., ol. 50, no. 12, pp. 3077–3080,978 Dec. 2008.979 [30] B. Ra elo, A. Pé ennec, and M. Le Roy, ‘‘Syn hesis o equency- 980 independen phase shi e s using nega i e g oup delay ac i e ci cui ,’’ In . 981 J. RF Mic ow. Compu .-Aided Eng., ol. 21, no. 1, pp. 17–24, Jan. 2011. 982 [31] B. Ra elo, M. Le Roy, and A. Pé ennec, ‘‘F equency-independen ac i e 983 phase shi e s o UWB applica ions,’’ in P oc. 40 h Eu . Mic ow. Con .,984 Pa is, F ance, Sep. 2010, pp. 1774–1777. 985 [32] B. Ra elo, ‘‘Dis ibu ed NGD ac i e ci cui o RF-mic owa e commu- 986 nica ion,’’ AEU-In . J. Elec on. Commun., ol. 68, no. 4, pp. 282–290, 987 Ap . 2014. 988 [33] Y. Meng, Z. Wang, S.-J. Fang, and H. Liu, ‘‘B oadband phase shi e wi h 989 cons an phase based on nega i e g oup delay ci cui ,’’ P og. Elec omagn. 990 Res. Le ., ol. 103, pp. 161–169, 2022. 991 [34] J. Nebhen and B. Ra elo, ‘‘Inno a i e mic owa e design o equency- 992 independen passi e phase shi e wi h LCL-ne wo k and bandpass NGD 993 ci cui ,’’ P og. Elec omagn. Res. C, ol. 109, pp. 187–203, 2021. 994 [35] B. Ra elo, G. Fon galland, H. S. Sil a, J. Nebhen, W. Rahajand aibe, 995 M. Gue in, G. Chan, and F. Wan, ‘‘O iginal applica ion o s op-band 996 nega i e g oup delay mic owa e passi e ci cui o wo-s ep s ai phase 997 shi e designing,’’ IEEE Access, ol. 10, pp. 1493–1508, 2022. 998 [36] B. Ra elo, ‘‘Nega i e g oup delay based Hilbe il e ,’’ in Nega i e 999 G oup Delay De ices: F om Concep o Applica ions, He o dshi e, U.K.: 1000 Michael Fa aday House, 2018, ch. 7, pp. 173–198. 1001 [37] M. A. An oniades and G. V. Ele he iades, ‘‘Compac linea lead/lag 1002 me ama e ial phase shi e s o b oadband applica ions,’’ IEEE An ennas 1003 Wi eless P opag. Le ., ol. 2, pp. 103–106, 2003. 1004 [38] Y. Li, M. F. Iskande , Z. Zhang, and Z. Feng, ‘‘A new low cos leaky 1005 wa e coplana wa eguide con inuous ans e se s ub an enna a ay using 1006 me ama e ial-based phase shi e s o beam s ee ing,’’ IEEE T ans. An en- 1007 nas P opag., ol. 61, no. 7, pp. 3511–3518, Jul. 2013. 1008 [39] S. S. Oh and L. Sha ai, ‘‘Compensa ed ci cui wi h cha ac e is ics o 1009 lossless double nega i e ma e ials and i s applica ion o a ay an ennas,’’ 1010 IET Mic ow., An ennas P opag., ol. 1, no. 1, pp. 29–38, Feb. 2007. 1011 [40] H. Liu, S. Gao, and T. H. Loh, ‘‘Compac dual-band an enna wi h elec onic 1012 beam-s ee ing and beam o ming capabili y,’’ IEEE An ennas Wi eless 1013 P opag. Le ., ol. 10, pp. 1349–1352, 2011. 1014 [41] B. Ra elo, W. Rahajand aibe, M. Gue in, B. Agnus, P. Thaku , and 1015 A. Thaku , ‘‘130-nm BiCMOS design o low-pass nega i e g oup delay 1016 in eg a ed RL-ci cui ,’’ In . J. Ci cui Theo y Appl., ol. 50, no. 6, 1017 pp. 1876–1889, Jun. 2022. 1018 [42] F. Wan, T. Gu, B. Li, B. Li, W. Rahajand aibe, M. Gue in, 1019 S. Lalleche e, and B. Ra elo, ‘‘Design and expe imen a ion o induc o less 1020 low-pass NGD in eg a ed ci cui in 180-nm CMOS echnology,’’ IEEE 1021 T ans. Compu .-Aided Design In eg . Ci cui s Sys ., ea ly access, 1022 Dec. 23, 2021, doi: 10.1109/TCAD.2021.3136982. 1023 [43] M. Gue in, W. Rahajand aibe, G. Fon galland, H. S. Sil a, G. Chan, 1024 F. Wan, P. Thaku , A. Thaku , J. F nda, and B. Ra elo, ‘‘Theo y and 1025 o iginal design o esis i e-induc i e ne wo k high-pass nega i e g oup 1026 delay in eg a ed ci cui in 130-nm CMOS echnology,’’ IEEE Access,1027 ol. 10, pp. 27147–27161, 2022. 1028 BLAISE RAVELO (Membe , IEEE) is cu en ly 1029 an Uni e si y Full P o esso a NUIST, Nanjing, 1030 China. He is also a Lec u e in ci cui & sys em 1031 heo y, science, echnology, enginee ing and ma h- 1032 ema ics (STEM), and applied physics. He is also 1033 a Pionee o he Nega i e G oup Delay (NGD) 1034 concep abou <0 signal a eling physical space. 1035 This ex ao dina y concep is po en ially use ul o 1036 an icipa ing and p edic ion all kind o in o ma ion. 1037 He was he esea ch di ec o o 11 Ph.D. s uden s 1038 ( en de ended), a pos doc o al esea che , a esea ch enginee , and mas e ’s 1039 in e nships. Wi h U.S., Chinese, Indian, Eu opean, and A ican pa ne s, he is 1040 ac i ely in ol ed and con ibu es on se e al in e na ional esea ch p ojec s 1041 (ANR, FUI, FP7, INTERREG, H2020, and Eu ipides2, Eu os a s). He is he 1042 coau ho o mo e han 370 scien i ic esea ch pape s in new echnologies 1043 published in in e na ional con e ences and jou nals. His esea ch in e es s 1044 include mul iphysics and elec onics enginee ing. He is a membe o IET 1045 Elec onics Le e s Edi o ial Boa d as a Ci cui & Sys em Subjec Edi o . 1046 VOLUME 10, 2022 93101 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui He has been a membe o Scien i ic Technical Commi ee o Ad anced1047 Elec omagne ic Symposium (AES), since 2013. He is anked in Top1048 2% wo ld’s scien is s based on yea s (2020–2021) by S an o d Uni e -1049 si y, USA (h ps://else ie .digi alcommonsda a.com/da ase s/b chxk zyw/3).1050 He has Google Schola H-index (2022)=26 and i10-index (2022)=83.1051 He is also a membe o esea ch g oups, such as URSI, GDR Ondes, and1052 Radio Socie y. He egula ly in i ed o e iew pape s submi ed o publi-1053 ca ion o in e na ional jou nals, such as IEEE TRANSACTIONS ON MICROWAVE1054 THEORY AND TECHNIQUES, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, IEEE1055 TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, IEEE TRANSACTIONS ON1056 INDUSTRIAL ELECTRONICS, IEEE ACCESS,IET CDS, and IET MAP, and books1057 (Wiley, In ech Science).1058 MATHIEU GUERIN (Membe , IEEE) ecei ed1059 he Doc o a e (Enginee ing) deg ee in mic oelec-1060 onics and elecommunica ions om Poly ech1061 Ma seille, in 2010. He was a Resea ch Mas e in1062 in eg a ed ci cui s design wi h he Uni e si y o 1063 Aix-Ma seille, in 2010. He wo ked as he Tech-1064 nical Leade o he Analog and Radio-F equency1065 Design Team, IDEMIA-S a Chip, o i e yea s1066 and designed chips embedded in SIM ca ds and1067 con ac less bank ca ds wi h biome ic ecogni ion.1068 He joined Aix-Ma seille Uni e si y as an Assis an P o esso , in 2020, and he1069 joined he IM2NP Labo a o y, CCSI Team. He is also wo king on me hods1070 o modeling and cha ac e izing ci cui s in analog elec onics. His esea ch1071 in e es s include he design and syn hesis o ci cui s in digi al elec onics.1072 JAROSLAV FRNDA (Senio Membe , IEEE)1073 was bo n in Slo akia, in 1989. He ecei ed he1074 M.Sc. and Ph.D. deg ees om he Depa men o 1075 Telecommunica ions, VSB—Technical Uni e si y1076 o Os a a, Czechia, in 2013 and 2018, espec-1077 i ely. He is cu en ly wo king as an Assis an 1078 P o esso a he Uni e si y o Zilina, Slo akia.1079 He has au ho ed o coau ho ed 32 SCI-E and nine1080 ESCI pape s in WoS. His esea ch in e es s include1081 quali y o mul imedia se ices in IP ne wo ks, da a1082 analysis, and machine lea ning algo i hms.1083 FRANK ELLIOT SAHOA ecei ed he mas e ’s1084 deg ee in elec ical enginee ing om he Uni e -1085 si y o An si anana, Madagasca , in 2004, and1086 he mas e ’s deg ee in nuclea physics, heo e ical1087 physics, and applied physics om he Uni e si y1088 o An anana i o, in 2007. F om 2008 o 2010,1089 he was a DAAD Doc o a e Fellow o he Ins i ü 1090 ü Nuklea e En so gung (I.N.E.), Ka ls uhe Ins i-1091 u e o Technology—Ge many. He de ended his1092 Ph.D. hesis a he Uni e si y o An anana i o,1093 in 2015, whe e he is cu en ly an Assis an P o esso a he Physics Depa -1094 men . His esea ch in e es s include en i onmen al adioac i i y moni o ing1095 using nuclea echniques and nega i e g oup delay (NGD) ci cui s. He is eg-1096 ula ly in ol ed o pa icipa e in in e na ional echnical coope a ion p ojec s1097 suppo ed by IAEA, such as MAG/7/002, MAG/5/014, RAF/5/063, and1098 MAG/5/019.1099 GLAUCO FONTGALLAND (Senio Membe , 1100 IEEE) was bo n in Fo aleza, Cea á, B azil, 1101 in Ma ch 1966. He ecei ed he G adua e and M.S. 1102 deg ees in elec ical enginee ing om he Uni- 1103 e sidade Fede al de Campina G ande (UFCG), 1104 Campina G ande—Pa aíba, B azil, in 1990 and 1105 1993, espec i ely, and he Ph.D. deg ee in 1106 elec onics om he Toulouse Ins i u Na ional 1107 Poly echnique—ENSEEIHT, Toulouse, F ance, 1108 in 1999. 1109 His Ph.D. hesis wo k was nomina ed a he Toulouse Ins i u Na ional 1110 Poly echnique—ENSEEIHT o he Leopold Escande Awa d, in 1999. 1111 F om 2010 o 2012, he was a Visi ing Schola a he Elec oScience Lab- 1112 o a o y, The Ohio S a e Uni e si y (OSU), USA. Cu en ly, he is a Full 1113 P o esso a UFCG, whe e he de elops esea ch on: elec omagne ic mod- 1114 eling, EMC, EMI, ESD, RFID, UWB, p opaga ion, and an ennas o a - 1115 ious applica ions. He has published mo e han 200 pape s in jou nals and 1116 con e ences. 1117 D . Fon galland is a membe o he Sociedade B asilei a de Mic o-ondas 1118 e Op oele ônica (SBMO), Sociedade B asilei a de Ele omagne ismo 1119 (SBMag), Sociedade B asilei a de Mic oele ôncia (SBMic o), and The 1120 applied Compu acional Ele omagne ics Socie y (ACES). He is he Pas 1121 IEEE AP-S Chap e Chai and a membe o he 2020 IEEE AP-S S u- 1122 den Design Con es and 2020 IEEE AP-S Field Awa ds E alua ion. 1123 Since 2019, he has been an Associa e Edi o o IEEE LATIN AMERICA 1124 TRANSACTIONS.1125 HUGERLES S. SILVA (Membe , IEEE) ecei ed 1126 he B.Sc., M.Sc., and Ph.D. deg ees in elec ical 1127 enginee ing om UFCG, B azil, in 2014, 2016, 1128 and 2019, espec i ely. He is cu en ly pu su- 1129 ing he Ph.D. deg ee wi h he Telecommunica- 1130 ions Ins i u e, Uni e si y o A ei o, Po ugal. His 1131 esea ch in e es s include wi eless communica- 1132 ions, digi al signal p ocessing, and wi eless chan- 1133 nel modeling. 1134 SAMUEL NGOHO ecei ed he G adua e deg ee 1135 om ESIGELEC, Rouen, F ance, in 2012, and 1136 he Ph.D. deg ee in hema ic o high equency 1137 elec onics, pho onics and sys ems om he XLIM 1138 Labo a o y, Uni e si y o Limoges, Limoges, 1139 F ance. His Ph.D. subjec conce ned was based 1140 on he design and p oduc ion o in eg a ed op o- 1141 elec onic componen s o high speed elecommu- 1142 nica ions sys ems. He wo ked as an In eg a ion, 1143 Ve i ica ion, Valida ion, and Quali ica ion Engi- 1144 nee o RF/HF p oduc s and sys ems o ci il and mili a y applica ions. 1145 He is cu en ly wo king as a Sys em Enginee a THALES SIX, Genne il- 1146 lie s, F ance. His esea ch in e es s include he p og ess o mic oelec on- 1147 ics, in pa icula in he de elopmen o inno a i e unc ions in eg a ed in 1148 mic owa e de ices o mee he need o densi ica ion and e olu ion o spec a 1149 o u u e communica ions sys ems. He also akes pa wi hin esea ch g oups 1150 in he use o un amilia me hods o esol ing complex sys em as K on’s 1151 me hod. 1152 93102 VOLUME 10, 2022 B. Ra elo e al.: Design Me hod o Cons an PS Mic owa e Passi e In eg a ed Ci cui FAYROUZ HADDAD (Membe , IEEE) ecei ed1153 he mas e ’s deg ee in elec onic enginee ing1154 om ENSEIRB, Bo deaux, F ance, in 2006,1155 and he Ph.D. deg ee in mic oelec onics1156 om Aix-Ma seille Uni e si y (AMU), F ance,1157 in 2009.1158 Since 2010, she has been wi h he In eg a ed1159 Ci cui s Design Team, Ins i u e o Ma e ials,1160 Mic oelec onics and Nanosciences o P o ence1161 (IM2NP), Ma seille, F ance. She is cu en ly an1162 Assis an P o esso a AMU. She co-supe ised eigh mas e ’s and i e1163 Ph.D. s uden s. She is he au ho o coau ho o mo e han 70 pape s1164 published in e e eed jou nals and con e ences. He esea ch in e es s1165 include CMOS analog and RF in eg a ed ci cui s design, ul a-low powe 1166 (ULP), and mul i-s anda ds applica ions. She co-o ganized he In e na ional1167 Con e ences ICECS 2014 and NEWCAS 2021. She was a membe o he1168 echnical p og am commi ee o se e al IEEE in e na ional con e ences.1169 She is a Re iewe o IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS (TCAS),1170 In e na ional Jou nal o Elec onics and Communica ions (AEUE), Applied1171 Sciences jou nal, IET Elec onics Le e s, and o many IEEE con e ences1172 dedica ed o in eg a ed ci cui s (ISCAS, NEWCAS, ICECS, MWSCAS,1173 ICMCS, and SBCCI).1174 WENCESLAS RAHAJANDRAIBE (Membe , 1175 IEEE) ecei ed he B.Sc. deg ee in elec ical engi- 1176 nee ing om Nice Sophia-An ipolis Uni e si y, 1177 F ance, in 1996, he M.Sc. deg ee (Hons.) in elec- 1178 ical enginee ing om he Science Depa men , 1179 Uni e si y o Mon pellie , F ance, in 1998, and he 1180 Ph.D. deg ee in mic oelec onics om he Uni e - 1181 si y o Mon pellie . He is cu en ly a Full P o esso 1182 a he Uni e si y o Aix-Ma seille. Since 1998, 1183 he has been wi h he In o ma ics, Robo ics and 1184 Mic oelec onics Labo a o y o Mon pellie (LIRMM), Mic oelec onics 1185 Depa men . Since 2003, he has been wi h he Ma e ials, Mic oelec on- 1186 ics and Nanoscience Labo a o y o P o ence (IM2NP), Mic oelec onic 1187 Depa men , Ma seille, F ance, whe e he was an Associa e P o esso . Since 1188 2014, he has been a P o esso a Aix-Ma seille Uni e si y, whe e he heads 1189 he IM2NP Labo a o y, In eg a ed Ci cui Design G oup. He is egula ly 1190 in ol ed o pa icipa e and o lead na ional and in e na ional esea ch p ojec s 1191 (ANR, H2020, and FP7 KIC-InnoEne gy). He di ec ed and co-supe ised 1192 15 mas e ’s and 18 Ph.D. s uden s. He is he au ho o coau ho o 11 pa en s 1193 and mo e han 150 pape s published in e e eed jou nals and con e ences. 1194 He is an Expe o ANR and he F ench Agency o Resea ch. His cu en 1195 esea ch in e es s include AMS and RF ci cui design om ansis o o 1196 a chi ec u al le el, ul alow powe ci cui design o sma senso in e ace 1197 and embedded elec onic in bioelec onic and e-heal h applica ions, wi eless 1198 sys ems, design echnique, and a chi ec u e o mul i-s anda d anscei e . 1199 He has se ed on P og am Commi ees o IEEE NEWCAS and ICECS. 1200 He has been and is a Re iewe o con ibu ions submi ed o se e al IEEE 1201 con e ences and jou nals, such as ISCAS, NEWCAS, MWSCAS, ESSCIRC, 1202 ESSDERC, RFIC, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR 1203 PAPERS, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS,1204 and IET Elec onics Le e s.1205 1206 VOLUME 10, 2022 93103