Chapter 9

Realization of OTA-C filters using OTA-based FP AA

9.1 Introduction

Signi Cicant attention has been paid to active continuous-time filters over the last

three decades. Tens of thousands of journal articles and conference papers may have been

published and presented over the yeurs. The changes in technology hnvc required new

approaches. Thus as cheap, readily available integrated circuit operational amplifiers

(Op-Amps) replaced their discrete circuit (based on vacuum tubes), it became feasible lo

consider actjve-RC ti lter circuits using large numbers of Op-Amps, and new improved

architectures emerged (61,63.65).

Similarly the development of integrated operational transconductance amplifiers

(OT A) led to new filter configurations which reduced the number of resistive

components, and allowed transconductance-mode rather than voltage-mode. This givt:s

rise to OT A-C filters, using only active devices and capacitors, making it more suitable

for integration (63,65-66).

The demands on filter circuits have become ever more stringent as the world of

electronics and communications has advam;ed. For cxnmple, greater demands on

bandwidth uti lization have required much higher performance in filters in Lerms of their

attenuation characteristics, and particularly in the transition region between passband and

stopband. This in tum has required filters capable of exhibiting high quality factor but

having low sensitivity to component changes, and offering dynamically stable

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performanc~. In addition, the conLinuing increase in the operating frequencies of modem

circuits and systems increases the need for active filters that can perform at these higher

frequencies; an area where the Q-enhanccd LC active filter emerges.

9.2 Types of Analog filters

9.2.1 Active-RC Filters

Acclvc- RC filters how been around for some time as a means Of overcoming the

disadvantages nssociated with low-frequency pussive RLC fillers (of which the use of

inductors is one). They offer the opportunity to integrate complex filters on-chip, and do

not have the problems that the relatively bulky. lossy. and expenc;ive inductora bnns in

particuJar their stray magnetic fields that can provide unwanted coupling in a circuit or

system [45).

The Sallcn and Key circuit, shown in Fig. 9.1, (which uses a voltage amplifier,

resistors, and capacilors) is one of the most popular and enduring active-RC filter

architectures. It has been around for about 48 years. Active-RC filters have been widely

used in various low frequency applications in telecommunication networks, signal

processing circuits, communication systems, control, and instrumentation systems.

However, they cannot work at higher frequencies due to OpAmp frequency limitations

and are not suitable for full integration if large resistors arc n:quired. They are also not

electronically tunable and usually lmw complex structures. The most successful approach

to overcome these drowbacks is to replace the conventional OpAmp in active-RC filters

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Cl

Rt 2 R7 3 5

Vo

4 XOP1 :, r RB

0

RA

Figure 9.lSallen and Key circuit

by an OTA giving rise to OT/\-C filters. Programmable high-frequency active filters can

therefore be achieved by incorporating the OT A. OT A-C filters also have simple

structures, and can operate up to several hundreds of Miiz [65,67].

9.2.2 Switched-Capacitor Filters

Another type of filter, called the switched-capacitor filtt::r, has become widely

available in monolithic form. The switched-capacitor Apprm1ch overcomes some vf the

problems inherent in standard active filters, while adding some interesting new

capabilities.

Integrated switched-capacitor filters need no external capacitors or inductors, and

their cutoff frequencies are set to a typical accuracy of ::1:0.2% by an external clock

frequency. This allows consistent, repeatable filter designs using inexpensive crystal-

controlled oscillators, or filters whose cutoff frequencies are variable over a wide range

simply by changing the clock frequency. In addition, switched-capacitor filters can have

low sensitivity to temperature changes.

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Switched-capacitor filters are clocked, sampled-data systems; the input signal is

sampled at a high rate and is processed on a discrete-time, rather than a continuous basis.

This is a fundamental difference between switched-capacitor filtt:rs and conventional

active and passive filters which ore also referred to "continuous time" litters.

The operation of switched-capacitor fillers is basecl on the ability of on-chip

capncilors and MOS switches to simulate resistors . The values of these on-chip capacitors

can be closely matched to oLher capacitors on the IC, resulting in integrated filters whose

cutoff frequencies are proportional to. and delt!nnined only by, the external clock

fre4ucncy. Now. lhese in 1c grntcd filters a rc ncurly olways bascu on swte-vnrluble uclivc

filter topologies, so they are also active filters , but nonnal tenninology reserves the name

" active filter" for filters built using non-switched or continuous active filter techni4ues.

The primary weakness of switched-capacitor filters is that they have more noise at their

ourput:J both ram.lom noise anti clock feedthroug11 than that of stanc.tarc.t acuve filter

circuits [65].

9.2.3 OT A-C Filters

ln recent years OTA-based high frequency integrated circuits, filters and systems

hnvc been widely investigated. This is due to their simplicity, electronic tunnbility nnd

suitability for high frequency operation due to open loop configuration.

The OTA has been implemented widely in CMOS und bipolar and also in

BiCMOS and GoAs technologies. The typical values of transconductanccs are in the

rungc of tens 10 hundreds of µS in CMOS and up to mS in bipolar technology. The

CMOS OT A, for example, can work typicully in the frequency range of SOMHz to

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several I OOMHz. Linearization techniques make the OT A able to handle input signals of

the order of volts with nonlinearities of a fraction of one pcrccnl.

Although OT A-C filters have the potential to operate at rt!latively high

frcyuencic:s the liuc::,ar range of the used transconductance limits the dynamic range. Also

the OTA-C filtt:rs become very power hungry ut Gll7 range. At high fn:quencics

sensitivity to parasitic components becomes very prominent r65}.

9.3 Elementary Transcondutor Building Blocks

With gm-C filters we need n variety of clememnry building blocks wi1h which the

filtcr:s are constructed [45]. As the name "gm-C filters" suggests, we wish to employ only

transconductors and capacitors as basic components [68]. In general. there arc two design

approaches. The first approach begins with a synthesized prototype design and the

necessary transfonnation to obtnin the lumped-element prototype. Ba:scd on lhis

prototype design, each passive element is replaced by its active equivalent. for instance,

an inductor is replaced by n gyrator, which can be implemented using transconductors

and capacitors. Capacitors in lwnped design are nonnally not replaced since they can be

readily implemented in intebrrated circuits. Source and load resistances are replaced by

self-feedback transconductors. Thus Gyrator filters are an alternative for active

implementations of the LC band pass ladder. This realization implies the replacement of

all the inductors and the resistors with active structures that emulate their functionality . Jn

addition, it is helpful to have a way to realize or simulate resistors because these are

difficult to implement with sufficient accuracy and over an udequate range of

values[63,65,67).

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9.3.I Resistors

There is generally little need for resistors in the area of gm-C filters with the

notable exception of source and load resistors in doubly tem1inatcd LC ladders. We need

at least lwo resistors in a lossless ladder. For sensitivity design, source and load resistor

should be incorporated into the design strategy (45).

To realize a resistor, the difli:rcntial tnmsconductance was taken to connect two

inputs to two different voltages and feed the output back to the input as shown in Fig. 9.2.

Always paying attention that feedback is negative, the two equations (9. 1) and (9.2) art:

obtain

Ii= lo = I::. gm• (Vl-V2) (9.1)

Thu!:, the resistor is

R -(VI- V2)fl = II gm ('>.2)

We should be ct:nain to 1m1intain the negative feedback when fonning the gm-

based resistor. If the feedback connection becomes positive, we simulate a negative

resistor. Vi I Ii = - R = - l I gm, in a differential form. Such a resistor is used, for

instance, to compensate the transconductor losses or to illuminntc inductor losst:.c; when

very smnll but real spiral- wound inductors are used on ICs for filters at the high

frequencies.

Figure 9.2 Active implementation of a resistor using "gm" module with one terminal grounded

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The implementation of a floating resistance is more complicated since two

different reference voltages must be created. Therefore, a 1.:ommon practice is lo

transform the input voltage source to an input current source (64). The transformation is

shown in Fig. 9.3. It can be seen that the noating source resistance hos been transformed

into a grounded resistance that can be implemented with the structure from Fig. 9.2. The

input current Iin • is detennined by forcing the equivalence of the two circuits. The

functionality of the sources is equal if the current and the voltage drop on the input

impedance of the LC network are the sume after the transformation (64]. Then it holds

true.

r . Zv: = [' . R~Zr.,~ m R Z 1

' 1 R Z S + l <" lt: + LC (9.3)

R. 11:1 .. 1,.

! v,I \

z~, c ) (

Cl)

b )

Figure 9.3 a) Transformation of the input voltugc source to un input current and

b) The OTA-C implementation

Relation (9.3) results that the equivalent input current source must be scaled with

the reciprocal of the source resistance RS and will be equal to Vin/RS. The

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transformation yields the OTA-C structure from the fi g. 9.3 (h), where the fir:>l

transconductance amplifier implements the sculeu current source.

An advantage of the I/gm resistors is that the resisturs are dectronically variable

because they depend on a bias current (or voltage). A traditional integrated resistor.

implemented say, as n diffused or a deposi ted layer, does not offer this possibility. It is

most helpful in gm-C filter design to have the " resistors" technologically match and track

the active devices. The OTA-based resistor offers a resistance of 19.2 K Olun to 11.07 M

Oluns for transconductance of OT A varying from 0.45 uAN to 7. 7 uAIV.

9.3.2 Gyrators

Another element t11at must be replaced in the uctive implcmenwtion is the

inductance. Inductors are implcmcn1.:d by using an Impedance conversion. The

impedance conversion is u procedure in which an impt.:dan~ 7. is inverted and mirrored

to the input of nn active structure. The inversion ond the impedance mirroring is

implemented with a gyrator whose input current is proporlional to the output voltage and

the output current is proportional to the input voltage through a conversion factor r, called

the gyration resistance [66 j. The general structure of a gyrator as n two-pon and the

equivalent input resistance are shown in Fig. 9 .4.

Figure 9.4 Cen ernl s tructure of a gyrator represented as n two-port

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The equations of the circuit. shown in Fig. 9.3, can be written as follows.

{

~,:: : ~ r 11

1,

v; =-I~ . z (9.4)

The input impedance of the structure is proportional with the reciprocal of the impedance

Z and with the squared gyration resistance. lt re~ults:

I . ,.J I , I ' z ... - T. = z (9.5)

Creating a floating node whose voltage is referenced to the cvound does the

inversion of floating impedance. This procedure can be con:;idered as the replacement of

the Z impedance ground connection from Fig. 9.4 with a floating voltage. The

transformation is done by using a second gyrator that creates the floating nodes at the

terminals of Z, as shown in the Fig. 9.5. It ctm be dcmonstruted that both the input and the

output impedances of the circuit are equal to r /Z. From the analysis it results that nn

inductance cnn be implemented by the inversion of a capacitance. In the OTA-C design

techniques the gyrators are realized as a pair of transconductance amplifiers connected in

a feedback loop. The structures used to simulate the functionality of a grounded and a

noating inductance is presented in Fig. 9.6 and Fig. 9.7. Ilcrc 1hc gyrution r<:sistancc is

equal to I/gm. The value of capacitance can be calculated according Lo Lhis equation: C =

gm2.L. The OT A-based inductor offers nn inductance of 7.6ml1 to 33H for

trw1sconductance of OTA varying from 0.45 uAN to 7.7 uAIV and programmable

capacitor array having a capacitance from 0.45pF to S.75pF.

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I . v

1 ..

1. Z r~ V.~V:

Figure. 9.5 The inversion of a floating impedance with two gyrntors

.ZQ + + g.,

c I ...-·' c

¢ ~-·1 .--·' + + g,,, ._ -

...........

Figure 9.6 The OT A-C Implementation of a grounded inductance

c

Z. ---~ Q

...... ··

~~ .......... ~__.__::_ + >----+--.--

...........

~~~.+~

+ ~

i:

Figure 9. 7 The OT A-C implementation of a floating inductance

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9 .4 hnplcmentation of 6th order Butterworth Band-Pass filter

A 6th order Butterworth Band-pass filter hnving fo llowing specifications.

Center frequency = 51.961 Kl lz.,

Bandwidth= 60KHz.

Stopband = 24dD,

Jnput Impedance = 300K Ohm

and Output Impedance = 300K Ohm.

The prototype of 61h order filter is shown in Fig.9.8. Fig.9.9 shows the realizution

of basic components like ' register', ' floating inductor' and ' grounded inductor' [65-66]

The Gm-c realization of 61h order Butterworth band-pass filter is presented in

Fig.9.10. in which each OTA is realized using on~ cross-coupled OTA. The capadto1

value also includes pnrasitic capacitance uf switches and connectioni:. The

transconductance of ench OTA is adjusteu individually. By adjusting the analog voltage

Vetri, one can change the center frequency of the filter. The Fig. 9.11 shows

implementation of 6th order Butterworth band pass filtt:r in our fPAA using clusters. In

Fig. 9.11 , red lines show used OT As.

dpolo , dpo6o 3 dipole 5

R1 L 1 C1 L3 C3 ~--~~~

L2

Rl• 300K R2 • 300K

Cl • 11.79859 pf

C2• J7 .66919pF C3 • ll .79859pF

ll • 795.145mH

l2• 5J0.937mH l3 • 795.14SmH

Figure 9.8 Prototype of 611' order Buttcnvorth bond-pass filter

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The above structure of 61h order Butterworth Band-pass filter will be

implemented.

L 'b~~f(f

R=-2._ g,,,

c L = -g;_

c L =-

R!

Figure 9.9 Realization of register, floating inductor and grounded inductor

F igure 9.10 Gm-C realization of 6'h order Butterworth ba nd-pass filter

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" . . '

Cluster-1

Cluster-4

Cluster-2 Cluster-3

Cluster-5

.figure 9.11 Implementation of 6' ~ order Butterworth band-pass filter

9.5 Implementation of 121h o rder Butte rworth Bandpas." filter U!jiog FPAA

A 12"' order Ruuerworth Band-pass filter having following ~-pecifications.

Center frequency = 51. 96 1 K Hz.

Bandwidth = 60K.H7.,

Stop band "" 24dB,

Input lmpedwicc '" 300K Ohm,

Output lmpedance - 300K Ohm.

The prvloi.ype filter is shown in fig. 9.12.The Gm-c realization of 12lh order

Butterworth band-pass filter is presented in Pig.9.13 Titis realization implies the

replacement of aJI the inductors and the resistors with gm-C structures that emulate their

functionality. The transconductance of each OTA is adjusted individunlly. By adjusting

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the analog voltage Vetri, one can change the center frequency of filter. The Fig. 9.14

shows implementation of 12th order Butterworth band pass filter in our FPAA using

clusters. In Fig. 9.14, red lines show used OT As.

dipole 5 dipole 7 dipole 9

L6

<ipole 6

"R1• 8001< R2 · !DOI< C1 • U.71411 pF C2 • 12.-..;pl' ca c e.10498of' C4 • 17 JJ745CllDF

C5 •~ ce s Uf611pF

R2 L1 =411.7ClmH l2 • TIIO.H1ml I U • 1.597df l.4 • 6411..«emH L6• 1,12!iH l6-2.0CiU1

dipole 10

Figure 9.12 Prototype of 12•h order Buttcrwo1-th baud-pass filter

Figure 9 . 13 Gm-C realization of 121h order Butterworth bond-pa.ss filter

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Cluster 1 Cluster~ C'lu.;ter 3 Cluster 4

Clus ter .=' Cluster 6 Clu:> te1 -

Figure 9.l 4 Implementation of 12•h order Butterworth band pass filter in FP AA

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