A new cascade ΣΔ modula o o low- ol age
wideband applica ions
A. Mo gado, R. del Río, J. M. de la Rosa
This le e p esen s a new cascade ΣΔ modula o a chi ec u e wi h uni y signal ans e
unc ion ha a oids he need o digi al il e ing in he e o cancella ion logic. The
combina ion o hese wo aspec s make i highly ole an o noise leakages, e y obus o
non-linea i ies o he ci cui y and especially sui ed o low- ol age implemen a ions a low
o e sampling. Beha io al simula ions a e p esen ed ha demons a e he highe e iciency
o he p oposed opology compa ed o exis ing cascades in ended o wideband
applica ions.
In oduc ion: Many new communica ion sys ems ha e a isen in ecen yea s ha demand
o high-bandwid h ΣΔ modula o s (ΣΔMs) in low- ol age echnologies [1]-[3]. Since
o e sampling mus be es ic ed o low alues in wideband applica ions, a usual design
choice in o de o achie e he equi ed pe o mance is o employ mul i-s age noise shaping
(MASH) a chi ec u es wi h mul i-bi quan iza ion. These ΣΔ opologies ci cum en he
s abili y p oblems o high-o de loops, bu a e sensi i e o quan iza ion noise leakages
caused by misma ches be ween he analog and digi al signal p ocessing in he ΣΔ cascade
[4].
An al e na i e ΣΔM a chi ec u e ha educes he sensi i i y o noise leakages o adi ional
cascade ΣΔMs is he so-called S u dy MASH (SMASH) modula o , ecen ly p esen ed in [1].
© IET (The Ins i u ion o Enginee ing and Technology). This ma e ial is p esen ed o ensu e imely dissemina ion o
schola ly and echnical wo k. Copy igh and all igh s he ein a e e ained by au ho s o by o he copy igh holde s. All
pe sons copying his in o ma ion a e expec ed o adhe e o he e ms and cons ain s in oked by each au ho 's copy igh .
In mos cases, hese wo ks may no be epos ed wi hou he explici pe mission o he copy igh holde .
This opology, which is illus a ed in Fig. 1 in he case o a 2-2 cascade, eplaces he e o
cancella ion logic equi ed in adi ional MASH modula o s o p ope ly combine he s ages
ou pu s by di ec eedback pa hs om he 2nd-s age ou pu o he 1s -s age inpu (ma ked in
Fig. 1 wi h ⊗ o cla i y). The modula o ou pu can be hus ob ained om he di ec digi al
sub ac ion o he wo s ages ou pu s, wi h no need o digi al il e ing o he s ages ou pu s
and he e o e, he subsequen elimina ion o ma ching equi emen s be ween analog and
digi al il e ing.
This le e p esen s a no el ΣΔ cascade in ended o high-speed low- ol age applica ions
which ex ends he unde lying p inciple o SMASH ΣΔMs o he implemen a ion o uni y signal
ans e unc ions (STFs) —i.e., —, while ci cum en ing he p oblems de ec ed
in he o me ones. On he one hand, by using uni y STFs, in eg a o s ideally p ocess
quan iza ion e o only, so ha he ole ance o ampli ie s non-linea i ies is la gely inc eased
[2] [3]. On he o he , by modi ying he s a egy o combine he s ages ou pu s, digi al il e ing
can s ill be a oided, while inc easing he obus ness and he simplici y o he ΣΔM.
P oposed Cascade Topology: The SMASH modula o in Fig. 1 su e s om se e al
d awbacks associa ed o he di ec eedback pa h om he 2nd-s age ou pu o he i s
s age, namely:
• I equi es, a leas , one ex a highly linea digi al- o-analog con e e (DAC) in he
added eedback pa h o he 1s -s age inpu .
STF z() 1=
• I is e y sensi i e o misma ching e ec s in he added eedback pa hs wi h espec
o he 1s -s age analog coe icien s, which causes low-o de noise leakages.
The p oposed modula o a chi ec u e, depic ed in Fig. 2, ci cum en s he abo e-men ioned
d awbacks by means o he ollowing s a egies:
• On he one hand, he p oposed a chi ec u e p ese es he appealing ea u es o
implemen ing uni y STFs, such as high o e load le els and elaxed ou pu swings
and non-linea i ies o he ampli ie s [2] [3].
• On he o he hand, eedback pa hs om he 2nd-s age ou pu o he i s s age a e
emo ed by di ec ly eeding he modula o ou pu back o he i s s age inpu . No e
ha , a he same ime, he digi al sub ac ion o he quan ize s ou pu s is pe o med
inside he 1s -s age loop. This s a egy elimina es he need o , a leas , one ex a
eedback pa h, so ha he numbe o linea DACs equi ed is no inc eased.
Howe e , a DAC wi h a ull scale la ge han ha o he analog- o-digi al con e e s
(ADCs) in he cascade ( and ) is equi ed in o de o accoun o he
summa ion o he digi al ou pu s o he s ages. Al hough, as will be shown in he nex
sec ion, he loca ion o he digi al adde helps o conside ably inc ease he
obus ness o misma ches o he p oposed cascade, hanks o he addi ional
il e ing ob ained o noise leakages.
Conside ing a linea model o he quan ize s in Fig. 2, i can be shown ha he Z-domain
B1B2
ans o m o he modula o ou pu is gi en by:
(1)
whe e s ands o he inpu signal and is he quan iza ion e o o he second
s age. No e ha −con a y o he SMASH modula o in Fig. 1− he quan iza ion e o o he
i s s age, , is cancelled, while a oiding any digi al il e ing. In addi ion, using a scaling
ac o ha is a powe o 2 will help o educe he powe o he 2nd-s age quan iza ion e o
a he ou pu and will equi e only a shi egis e be o e he digi al sub ac ion. This scaling
s a egy can no be di ec ly applied o he SMASH modula o , since in ha case, he ou pu
will be gi en by:
(2)
hus educing he powe o a he ou pu , bu no ha o .
Simula ion esul s: The pe o mance o he p oposed modula o (Fig. 2) has been
compa ed o adi ional 2-2 cascades and o he SMASH modula o (Fig. 1) by beha io al
simula ion using SIMSIDES, a Simulink-based ime-domain simula o o ΣΔ modula o s [5].
All opologies ope a e wi h an o e sampling a io o 16, 4-bi in e nal quan ize s and a 1-V
e e ence ol age o compa ison pu poses wi h da a epo ed in [1].
Yz() Xz() 1d⁄1z1–
–()
4
E2z()⋅⋅–=
Xz() E2z()
E1z()
d
Yz() z2– Xz() 1z1–
–()
4
E1z()⋅1d⁄1z1–
–()
4
E2z()⋅⋅–+⋅=
E2z() E1z()
Fig.3 depic s he Signal o Noise and Dis o ion Ra io (SNDR) achie ed by he di e se
modula o s e sus he inpu le el when conside ing quan iza ion e o s only. No e ha he
o e load le el o he p oposed cascade is conside ably la ge compa ed o he SMASH and
also imp o es ha o adi ional cascades. As shown in Fig.3, he a ainable SNDR peak can
be inc eased by ope a ing he p oposed opology wi h .
Table 1 shows bo h he o e load le els and he ou pu swing equi emen s o he ampli ie s
along he cascades. No e ha he combined usage o uni y STFs and mul i-bi quan iza ion
leads o a ema kable elaxa ion o he ou pu swing o he p oposed modula o compa ed
o MASH and SMASH opologies, wha simpli ies i s low- ol age implemen a ion.
The sensi i i y o noise leakages due o misma ches has been s udied o he di e se
a chi ec u es on he basis o a Mon e Ca lo simula ion. Fig.4 shows he SNDR a -6dBFS
ob ained o he SMASH modula o and he cascade p oposed in Fig.2 o a 50- un Mon e
Ca lo simula ion conside ing a s anda d de ia ion o 0.1% in all capaci o s. No e ha
misma ches a he addi ional eedback pa hs (⊗) a e esponsible o a la ge a ia ion o he
esolu ion in he SMASH opology, wha esul s in i s un eliable p ac ical implemen a ion.
Howe e , he loca ion o he digi al summa ion o he s ages ou pu s inside he 1s -s age loop
esul s in addi ional il e ing and p o ides he p oposed cascades wi h a la ge immuni y o
misma ches. As shown in Fig.4, he low sensi i i y o misma ches is s ill main ained despi e
using a scaling o ob ain la ge SNDRs.
Fig. 5 compa es he SNDR ob ained o he di e se ΣΔ s uc u es agains he ampli ie gain
d1>
d1>

in he in eg a o s o a -6dBFS inpu le el. No e ha he equi ed ampli ie gain in he
adi ional MASH wi h and he SMASH o achie e a SNDR o 95dB a e 50dB and
40dB, espec i ely. These alues a e elaxed o 30dB o he p oposed cascade wi h .
Thanks o he implemen a ion o uni y STFs, he p oposed cascade p o es o ha e also
conside ably la ge ole ance o non-linea i ies in he ampli ie gain. Fig. 6 shows he SNDR
o he di e se opologies agains he gain non-linea i y o a -6dBFS inpu le el. Fo all
s uc u es he ampli ie s gain is assumed o be 55dB and non-linea i ies a e con empla ed
in ampli ie s o he i s modula o s age. No e ha non-linea i y equi emen s a e also g ea ly
elaxed o he p oposed a chi ec u e.
Conclusions: A no el opology o cascade ΣΔ modula o has been p oposed. This
a chi ec u e is capable o achie ing la ge SNDRs a low o e sampling wi h e y elaxed
ou pu swing and gain demands in he ampli ie s, so ha i is especially sui ed o wideband
applica ions in low ol age scena ios. I s e iciency elies upon wo main s a egies, namely:
he educ ion o he e o cancella ion logic o a single digi al adde ha is placed inside he
1s -s age ΣΔ loop, and he implemen a ion o uni y STFs in bo h cascade s ages. Beha io al
simula ion esul s p o e he highe e iciency and obus ness o misma ches o he p oposed
cascade compa ed o exis ing ones.
d1=
d1=
Re e ences
1 Magha i, N., Kwon, S., Temes, G. C., and Moon, U.: ‘S u dy MASH ΔΣ modula o ’,
Elec on. Le ., 2006, 42, (13), pp. 1269-1270.
2 Sil a, J., Moon, U., S eensgaa d, J., and Temes, G. C.: ‘Wideband low-dis o ion del a-
sigma ADC opology’, Elec on. Le ., 2001, 37, (12), pp. 737-738.
3 Sil a, J., Moon, U., and Temes, G. C.: ‘Low-dis o ion del a-sigma opologies o MASH
a chi ec u es’. P oc. 2004 In . Sym. Ci cui s and Sys ems., Vancou e , Canada, 2004, 1,
pp. 1144-1147.
4 No swo hy, S. R., Sch eie , R., and Temes, G. C. (Eds.): ‘Del a-Sigma Da a Con e e s:
Theo y, Design and Simula ion’ (IEEE P ess, 1997)
5 Ruíz-Amaya, J., de la Rosa, J.M., Fe nández, F.V., Medei o, F., del Río, R., Pé ez-Ve dú,
B., Rod íguez-Vázquez, A.: ‘High-le el Syn hesis o Swi ched-Capaci o , Swi ched-
Cu en and Con inuous-Time ΣΔ Modula o s Using SIMULINK-Based Time-Domain
Beha io al Models’, IEEE T ans. Ci cui s and Sys . I, 2005, 52, pp. 1795-1810.
Au ho s' a ilia ions:
A. Mo gado, R. del Río and J. M. de la Rosa (Ins i u o de Mic oelec ónica de Se illa - IMSE-
CNM (CSIC/Uni e sidad de Se illa). Edi . CICA-CNM, A da. Reina Me cedes s/n, 41012-
Se illa, SPAIN).
E-mail: [email p o ec ed]
Table cap ions:
Table 1 O e load le els and ou pu swing equi emen s.
Figu e cap ions:
Fig. 1 SMASH modula o [1]
Fig. 2 P oposed opology
Fig. 3 SNDR e sus inpu ampli ude
Fig. 4 Mon e Ca lo simula ion esul s o capaci o s misma ching e ec s
Fig. 5 SNDR e sus ampli ie ini e gain
Fig. 6 E ec o he ampli ie non-linea i y on he SNDR
Figu e 6
102
101
100
90
92
94
96
98
100
SNDR, dB
Non-linea i y o he ampli ie gain, %
P oposed d = 1
MASH d = 1
SMASH