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.
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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
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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·expj(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
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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
nBpexpj2ϕn+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
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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)=sLp−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
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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
0Zs(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)
R0Zs(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 A1 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 A1 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
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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.
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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
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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
