Current-mode variable frequency quadrature sinusoidaloscillators using two CCs and four passive components includinggrounded capacitors

Abhirup Lahiri

Received: 9 February 2010 / Revised: 8 November 2010 / Accepted: 26 November 2010 / Published online: 9 December 2010

� Springer Science+Business Media, LLC 2010

Abstract This paper reports realizations of current-mode

quadrature sinusoidal oscillator using only two multiple-

output current conveyors (first or second generation current

conveyor CCI/CCII) and four passive components includ-

ing two grounded capacitors. Therefore, the circuits

employ minimum number of passive components to realize

a second-order sinusoidal oscillator. Three types of circuits

are reported depending on the condition of oscillation and

frequency of oscillation (FO). The circuits have FO con-

trollable by either resistor or capacitor and are suitable to

be used as variable frequency oscillator for different

applications. All the circuits provide two explicit quadra-

ture current outputs from high output impedance terminals.

PSPICE simulation results are included to verify the

workability of the proposed circuits.

Keywords Quadrature sinusoidal oscillator � Current-

mode (CM) � Explicit-current-output (ECO) � Current

conveyors (CCs)

1 Introduction

Sinusoidal oscillators are very important analog circuits

and find numerous applications in communication, control

systems; signal processing, instrumentation and measure-

ment systems (see [1] and references cited therein). Since

the advent of current conveyors, namely the first-genera-

tion current conveyor (CCI) and the second-generation

current conveyor (CCII) by Sedra and Smith in [2, 3];

considerable attention has been given to the realizations of

active RC sinusoidal oscillators using current conveyors

(CCs). Several classes of CC-based sinusoidal oscillators

have evolved depending on the number of passive compo-

nents employed and the tuning laws. Single-resistance-

controlled oscillators (SRCOs) using three resistors and two

capacitors have been found to be minimal in realizing

oscillators providing independent tuning of the condition of

oscillation (CO) and the frequency of oscillation (FO) via

two different resistors [4, 5]. Oscillators using four passive

components (including two resistors and two capacitors) are

classified as minimal (or minimum component) oscillators

and are suitable realizing variable frequency oscillators

(VFOs) [6]. 2R-2C VFOs can be mainly classified under two

types depending on the governing tuning laws as follows:

Type1

CO : C1 ¼ C2 ð1Þ

FO : fo ¼1

2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

C1C2R1R2

r

ð2Þ

Type2

CO : R1 ¼ R2 ð3Þ

FO : fo ¼1

2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

C1C2R1R2

r

ð4Þ

It is clear from (1)–(4) that Type1 oscillators can provide

frequency tuning by means of resistors R1 and R2 and

Type2 oscillators can provide frequency tuning by means

of capacitors C1 and C2. Thus, both type of circuits are

suitable to be used as VFOs. Since realizations of both

voltage-controlled resistors and capacitors are known, both

Type1 and Type2 circuits can be used as voltage-controlled

oscillators (VCOs). 2R-2C VFOs, particularly circuitsA. Lahiri (&)

36-B, J and K Pocket, Dilshad Garden, Delhi, India

e-mail: lahiriabhirup@yahoo.com

123

Analog Integr Circ Sig Process (2012) 71:303–311

DOI 10.1007/s10470-010-9571-8

governed by Type1 tuning laws, have been investigated

extensively by several researchers using different CCs.

Some key works include:

(1) CCII based VFO employing two CCIIs and grounded

capacitors proposed by Horng et al. in [7].

(2) CFOA based version of the circuit in [8] by Bhaskar

et al. in [8].

(3) Differential difference current conveyor (DDCC)

based VFO proposed by Kilinc et al. in [6] (circuit

number 6). The circuit, however, used floating

capacitors which is not desirable from monolithic

integration point of view [9].

(4) Differential voltage current conveyor (DVCC) based

VFO by Agarwal in [10] using grounded capacitors and

capable of providing one explicit-current-output (ECO).

(5) Multiple-output DVCC based VFO proposed by

Horng in [11], which uses two DVCCs and grounded

capacitors and is capable of providing two quadrature

ECOs.

(6) Multiple-output fully-differential second-generation

current conveyor (FDCCII) based VFOs by Horng

et al. in [12] which use a single FDCCII and grounded

capacitors while also providing two quadrature ECOs.

This paper discusses realizations of circuits governed

by both Type1 and Type2 tuning laws.

(7) Using adjustable gain second-generation negative

current conveyor in [13], the authors propose a

2R-2C oscillator and its resistor-less equivalent.

Unfortunately, the circuit used floating capacitors and

the suitability of quadrature outputs is not investigated.

Considering the current interest in the design of current-

mode (CM) circuits, oscillators providing explicit-current-

outputs (ECOs) are highly desirable. Such oscillators can

be used as input sources for CM circuits, e.g. CM filters.

The possibility of quadrature functionality in CM oscilla-

tors is another desirable feature which would make the

oscillators suitable for providing two 90� phase shifted

current outputs signals and which could be fed as inputs to

CM quadrature mixers or single sideband modulators [1,

9]. Although many previously reported 2R-2C VFOs have

capability of quadrature signal generation, but to the best of

the author’s knowledge, only two 2R-2C quadrature

oscillators providing two ECOs have been reported in the

literature: (i) by employing multiple-output DVCCs in [11]

and (ii) by employing multiple-output FDCCII in [12]. An

interesting question arises on whether the CM QOs similar

to that in [11, 12] can be created using CCI/CCII? It can be

argued that CCI and CCII are simpler building blocks as

compared to FDCCII or DVCC. Moreover, several types of

CCI and CCII are also available as the off-the-shelf ICs

(e.g. CCII? is available as CFOA AD844 IC by Analog

Devices [14]) and their dual/multiple-output variants can

also be easily created using commercially available ICs.

But complex building blocks like DVCC are not com-

mercially available yet and their construction using com-

mercially available ICs like AD844 requires several ICs

and matched resistors (e.g. DVCC would require three

AD844 ICs and two matched resistors [15]). Thus, the

motivation of this work is to provide similar oscillators as

in [11, 12] (with same tuning laws), but by using simpler

building blocks, namely the CCI and CCII. Multiple-output

CCs are used which help in current copying and generation

of quadrature ECOs. Both Type1 and Type2 oscillator

circuits are reported and another type of CM QO is also

described with its governed tuning laws other than Type1

or Type2. It is worth mentioning here that very recently a

catalogue of oscillators has been reported using SVA [16]

and resistor-less variants of Type2 oscillators have also

been described (Fig. 3e). The circuits reported here have

been verified using PSPICE simulations and the results are

in correspondence with the theory.

2 Proposed circuit

Type1 circuits are shown in Fig. 1 and are derived using

the SVA as briefed in the Appendix A. The circuit in

Fig. 1a is corresponding to the matrix A2, same as the

circuit in [7, 8], but with quadrature signal functionality.

Using routine circuit analysis, one can derive the following

characteristic equation (CE) for the oscillator circuit

s2C1C2R1R2 þ sR1ðC1 � C2Þ þ 1 ¼ 0 ð5ÞSince R1 is grounded, it can be easily replaced by a

non-linearity cancelled MOSFET working in triode region

Fig. 1 Type1 CM QOs

304 Analog Integr Circ Sig Process (2012) 71:303–311

123

[17, 18] (and thereby simulating a voltage controlled

resistor) to create a voltage controlled oscillator (VCO)

[18]. The marked ECOs in Fig. 1a are related as

Io1 ¼ jk1Io2 where k1 ¼1

xoC2R1

¼ffiffiffiffiffiffiffiffiffiffi

C1R2

C2R1

r

ð6Þ

It is clear from (6) that the ECOs are 90� phase shifted and

have equal amplitudes when k1 = 1. Intuitively, the

quadrature nature of the ECOs can be expected since these

are copies of currents flowing in the capacitor C2 and resistor

R1, respectively. An interesting point can be noted from (6)

that both R1 and R2 should be equal and need to be varied

simultaneously (to vary the frequency) so that the ratio of the

generated quadrature signals k1 remains unity. This would

result in balanced amplitude quadrature output generation

and which can be very desirable in some applications. As an

alternative realization, the circuit in Fig. 1a can also be

created using other CCs. One such example, is shown in

Fig. 1b wherein the DO-CCII- has been replaced by a DO-

ICCII? [19]. Note that ICCII, just like DVCC is not available

commercially, nevertheless the circuit is included as an

alternate realization. The resulting oscillator is governed by

the same CE, CO and FO as in (5), (1) and (2), respectively.

Possible circuit realizations of CM quadrature oscilla-

tors governed by Type2 tuning laws using two CCs are

shown in Fig. 2. The circuits are corresponding to the

matrix B1 (see Appendix A). The circuits have the fol-

lowing characteristic equation

s2C1C2R1R2 þ sC2ðR1 � R2Þ þ 1 ¼ 0 ð7Þ

The marked ECOs in Fig. 2 are related as

Io2 ¼ �jk2Io1 where k2 ¼1

xoC1R2

¼ffiffiffiffiffiffiffiffiffiffi

C2R1

C1R2

r

ð8Þ

As in Type1 oscillators of Fig. 1, if C1 and C2 are same

and varied simultaneously by equal amounts then the ratio

of the generated quadrature signals can be unity.

Another type of oscillator is shown in Fig. 3. This cir-

cuit is derived from the recently reported CFOA based

oscillator in [20] (shown in Fig. 3 of [20]). The circuit is

described by the following CE

s2C1C2R1R2 þ sðC1R1 þ C2R2 � C2R1Þ þ 1 ¼ 0 ð9Þ

Under the condition that C2 ¼ 2C1 ¼ 2C, the CO and

FO are given as

CO : R1� 2R2 ð10Þ

FO : fo ¼1

2pC

ffiffiffiffiffiffiffiffiffiffiffiffiffi

1

2R1R2

r

ð11Þ

The tuning laws are not related to either Type1 or

Type2, but frequency tuning can still be achieved by

varying both C1 and C2, such that C2

C1¼ 2 is maintained. For

example, if C1 and C2 are two variable capacitor banks

(composed of unit capacitors and switched together by

means of a common bit pattern), such that each unit

Fig. 2 Type2 CM QOs

Fig. 3 Type3 CM QOs

Analog Integr Circ Sig Process (2012) 71:303–311 305

123

capacitor of C2 bank is twice the value of the unit capacitor

of C1 bank. The marked ECOs in Fig. 3 are related as

Io1 ¼ jk3Io2 where k3 ¼1

xoC1R1

ð12Þ

3 Non-ideal analysis and discussion

The following non-idealities of the CCs are considered to

analyze their effects on the circuit

(1) The CCs suffer from current and voltage tracking

errors and which deviate the current and voltage

conveyance coefficients from their ideal magnitude of

unity. We use symbols, bij to represent the magnitude

of current conveyance coefficient from x to zj and ai

to represent the voltage conveyance coefficient from

y to x terminal for the ith CC (where i = 1,2,

j ¼ 1; 2; 3; . . .). ci represent the current conveyance

coefficient from y to x terminal for the ith CCI.

(2) The non-zero parasitic resistance Rx appears at the

x terminal of both the CCs and which adds into the

external resistors R1 and R2.

(3) The parasitic capacitance Czijappears between the

high-output impedance zj terminals of the ith CC

and ground and the parasitic capacitance Cyi

appears between the high-input impedance y termi-

nal of the ith CC and ground where (i = 1,2).

Similarly, the parasitic resistance Rzijand Ryi

appear

at zj and y terminals of the ith CC. To alleviate the

effects of the parasitic resistance Rz and Ry at

terminals z and y for circuit in Fig. 1a, the

operating frequency should be chosen such that

fo [ max 12pðC1þCz11

þCy2ÞðRz11

jjRy2Þ;

12pðC2þCy1

ÞRy1

� �

. For

circuit in Fig. 2b, the effects of the parasitic

resistance Rz and Ry can be alleviated by choos-

ing the operating frequency as fo [

max 12pðC1þCz21

þCy1þCy2

ÞðRy1jjRy1jjRz21

Þ;1

2pðC2þCz11þCz22

ÞðRz11jjRz22

Þ

�

Þ.

The aforementioned non-idealities affect both the CO

and FO of the oscillators. For operating frequencies greater

the the lower threshold (as provided above) the effects of

large valued parasitic resistances (Rz or Ry) can be

neglected. Considering other non-idealities, the non-ideal

expressions for the CO and the FO of oscillators are pro-

vided in Table 1.

The results for the CO in Table 1 are very helpful in

realizing practical oscillators. Since the parasitics are not

well controlled and would change with the design of CCs;

considering strict equality of capacitors or resistors for the

CO (e.g. as in (1), (3)), the oscillator may not start-up due

to insufficient open-loop gain. Therefore, sufficient oscil-

lator start-up margins should be taken for design. Other

points to be noted are as follows:

(1) The FO for Type1 circuit in Fig. 1a can still be

independently controlled and tuned via resistors R1

and R2. The external capacitors and resistors can be

kept much larger than the parasitics to minimize the

deviation from the theoretically expected FO.

(2) The non-ideal expressions for Type2 circuits in

Fig. 2, do not exhibit any independence as external

resistor and capacitor terms are present in both CO

and FO. Strictly speaking, only when b11 = 1, the FO

can be tuned independently via capacitors C1 or C2.

However, if b11 is made very close to unity (e.g. by

creating improved current mirrors by cascading), then

the right hand term of the CO can be neglected and

the start-up margin would not be affected much even

if C1 and/or C2 are varied to change the FO.

(3) The non-ideal expressions for Type3 circuits in Fig. 3

have been derived by considering that the operating

frequency fo � C2þCy

2pR2ðC2CyÞ. Under these conditions, Cy

can be neglected and the CE still remains second-

order (if Cy is considered, the CE becomes third-

order). As before, with C2 ¼ 2C1 ¼ 2C, the FO can

be tuned by varying both C1 and C2, such that C2

C1¼ 2

is maintained.

(4) The fo sensitivities for all the external passive

components are no more than 0.5 except for Type3

oscillator with capacitor matching constraint and

where SfoC ¼ �1.

Table 1 Non-ideal CO and FO for oscillators

Circuit CO fo

Type1 Fig. 1a a2c2ðC2 þ Cy1Þ�C1 þ Cz11

þ Cy2 12p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a1a2b11

ðC1þCz11þCy2

ÞðC2þCy1ÞðR1þRx1

ÞðR2þRx2Þ

q

Type2 Fig. 2b a1ðR2 þ Rx2Þ � a2b21ðR1 þ Rx1

Þ� 12p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a2b22þa2b21c1ð1�b11ÞðC1þCz21

þCy1þCy2

ÞðC2þCz11þCz22

ÞðR1þRx1ÞðR2þRx2

Þ

q

ðC1þCz21þCy1

þCy2ÞðR2þRx2

Þc1ð1�b11ÞC2þCz11

þCz22

Type3 Fig. 3b R1ð2� a1Þ� 2R2 � 2Rx1þ ða1 � 2ÞRx2

12pC

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

12ðR1þRx2

ÞðR2�Rx2Þ

q

306 Analog Integr Circ Sig Process (2012) 71:303–311

123

In Table 2, the main features of the reported types of

oscillator circuits here are compared with those of previous

works (restricted to only those dealing with active RC

oscillators).

4 Simulation results

The proposed oscillator circuits have been simulated in

PSPICE using MOSFET implementation of CCI and

DO-CCII-, as shown in Figs. 4 and 5, respectively. Circuit

in Fig. 1a is taken as the design example. The circuit is

implemented with 0.35 lm TSMC CMOS technology [27].

The aspect ratios of the transistors in CCI (of Fig. 4b) and

DO-CCII- are indicated in Tables 3 and 4, respectively and

IB = 50 lA. For Type1 oscillators, the circuit in Fig. 1a is

taken as the design example. It is designed with passive

component values of R1 ¼ R2 ¼ 10 kX, C1 = 100 pF and

C2 = 101 pF. The start-up of oscillations and the steady-

state waveforms for both the ECOs is shown in Fig. 6. The

observed frequency of 149 kHz is in close correspondence

with the theoretical value of 159.1 kHz. The total harmonic

distortion (THD) at both the outputs is less than 0.6%. The

variation of the FO by resistor R1 (and R2 fixed at 10 kX) is

shown in Fig. 7a, the corresponding variation of the output

signal amplitudes is shown in Fig. 7b and the variation of

the THD of current Io1 is shown in Fig. 7c. For Type2

oscillators, the circuit in Fig. 2a is taken as the design

example. It is designed with passive component values of

C1 ¼ C2 ¼ 100 pF, R1 ¼ 10 kX and R2 ¼ 10:1 kX. The

start-up of oscillations and the steady-state waveforms for

both the ECOs is shown in Fig. 8. The observed frequency

is 149.25 kHz and the THD at both the outputs is less than

1.7%. The FO is varied by means of a variable capacitor

bank which consists of 7 unit capacitors each of 5 pF and a

fixed capacitor of Cfix = 65 pF, as shown in Fig. 9. Three

binary bits can be used as control signals and which need to

be converted to thermometric code (n) to switch the seven

capacitors. Simple NMOS transistors with minimum length

and sufficient width to create low resistance switches can

be used. Binary code 000 (equivalent to n = 0) corre-

sponds to all the seven capacitors being OFF and pattern

Table 2 Comparison of features of recently reported ECO oscillators

Circuits Active element

and number

Number.

of passive

elements

ECO Quadrature

ECOs

Independent

FO control

Matching

condition

Figures 1 and 2 in [20] CFOA (2) 5 Yes No Yes Yes

[21] CCI/CCII (2) 5 Yes No Yes Yes

[22] CFOA (1) 6 Yes No No Yes

[23] CFOA (2) 5 Yes No Yes No

[24] DVCC (1) 5 Yes No Yes No

[25] CCII (2) 6 Yes No Yes Yes

[26] CCII-TA (1) 4 Yes Yes Yes No

[9] CDTA (2) 3 Yes Yes Yes No

Proposed CCI/CCII (2) 4 Yes Yes Yes No, yes

for Type3

Fig. 4 Possible MOS implementations of CCI

Analog Integr Circ Sig Process (2012) 71:303–311 307

123

111 (equivalent to n = 7) corresponds to all the seven

capacitors being ON. General expression for the effective

capacitance is given as

C1eff: ¼ Cfix þ nCon þ ð7� nÞCoff ð13Þ

where Con represents the capacitance of the arm which

is switched ON, Con * 5 pF, Coff represents the

capacitance of the arm which is switched OFF (in our

case this capacitance is negligibly small as compared to

the ON capacitance) and n e [0, 1, 2,…, 7] is the ther-

mometric code representing the number of unit capaci-

tors that are ON. The variation of FO with thermometric

code n is shown in Fig. 10a, the corresponding variation

of the output signal amplitudes is shown in Fig. 10b and

the variation of the THD of current Io2 is shown in

Fig. 10c.

5 Concluding remarks

Realizations of variable frequency quadrature sinusoidal

oscillator using two CCs and minimum number of passive

components, namely two resistors and two grounded

capacitors have been demonstrated. As proposed to earlier

such realizations using complex ABBs like multiple-output

FDCCII and DVCC, the proposed circuits here are created

using multiple-output CCI or CCII. Circuit realizations

governed by the most significant CO and FO tuning laws

are provided and are are classified under three types.

Although additional types of tuning laws and correspond-

ing circuit realizations for 2R-2C oscillators are not ruled

out, it is believed that that proposed circuits here along

with those in [11, 12] cover the most significant types of

second-order active RC CM-QOs realizable using only four

passive components.

Appendix A: oscillator synthesis via state variable

method

The method of synthesis of second-order sinusoidal oscil-

lators has been dealt extensively in [5, 16] and here we

restate the important steps. In general, a second-order

oscillator can be characterized by means of the following

matrix equation

dV1

dtdV2

dt

� �

¼ a11 a12

a21 a22

� �

V1

V2

� �

ð14Þ

where V1 and V2 are the state variables and are the voltages

across the two capacitors C1 and C2, respectively. From

(14), the characteristic equation (CE) of the oscillator is

given asFig. 6 Oscillation waveforms of the ECOs for Type1 oscillator in

Fig. 1a: a start-up and b steady-state

Fig. 5 Possible MOS implementation of DO-CCII(-)

Table 3 Transistors widths for CCI

MOSFET W/L (lm/lm)

M3–M4, M8–M9, M13–M15 30/0.5

M1–M2, M5–M7, M10–M12 10/0.5

Table 4 Transistors widths for DO-CCII-

MOSFET W/L (lm/lm)

M3–M4, M8–M9, M12–M13, M16–M18 30/0.5

M1–M2, M5–M7, M10–M11, M14–M15, M19 10/0.5

308 Analog Integr Circ Sig Process (2012) 71:303–311

123

s2 � sða11 þ a22Þ þ ða11a22 � a12a21Þ ¼ 0 ð15Þ

It is evident from (15) that

CO : a11 ¼ �a22 ð16Þ

FO : fo ¼1

2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a11a22 � a12a21

p ð17Þ

Comparing (16) and (17) with the desired tuning laws as in

(1) and (2) for Type1 oscillators and (3) and (4) for Type2,

8 9 10 11 12 13 14 15100

120

140

160

180

200

Resistor R1 (kOhms)

Fre

quen

cy (

kHz)

115 120 125 130 135 140 145 150 155 160 165 17060

80

100

120

140

Operating Frequency

Cur

rent

am

plitu

des

(uA

)

115 120 125 130 135 140 145 150 155 160 165 1700

0.5

1

1.5

Operating Frequency

TH

D o

f cur

rent

Io1

(%)

Theoretical

Simulated

Io2

Io1

(a)

(b)

(c)

Fig. 7 a FO variation with

resistor R1, b amplitude

variation with frequency, c THD

variation with frequency

Fig. 8 Oscillation waveforms of the ECOs for Type2 oscillator in

Fig. 2a: a start-up and b steady-state Fig. 9 Variable capacitor bank for FO tuning

Analog Integr Circ Sig Process (2012) 71:303–311 309

123

we can derive different matrices by appropriately choosing

the parameters aij (where i = 1,2). For Type1 oscillators

the following matrices are possible

A1 ¼1

C1R1

1C1R1

� 1C2ð 1

R1þ 1

R2Þ � 1

C2R1

" #

;

A2 ¼1

C1R1� 1

C1R1

1C2ð 1

R1þ 1

R2Þ � 1

C2R1

" # ð18Þ

A3 ¼� 1

C1R1

1C1R1

� 1C2ð 1

R1þ 1

R2Þ 1

C2R1

;

" #

A4 ¼� 1

C1R1� 1

C1R1

1C2ð 1

R1þ 1

R2Þ 1

C2R1

" # ð19Þ

A total of four different oscillator circuits can be

realized corresponding to each Ak matrix (k = 1, 2, 3, 4),

but it is sufficient to give CC based realization of any one

of the matrix in the class and the rest can be derived by

simple interchange of sign of the output current, i.e. by

utilizing either z ? or z- terminal of multiple current

output CC. For Type2 oscillators the following matrices are

possible

B1 ¼1

C1ð 1

R1� 1

R2Þ � 1

C1R11

C2R20

" #

; B2 ¼1

C1ð 1

R1� 1

R2Þ 1

C1R1

� 1C2R2

0

" #

ð20Þ

B3¼� 1

C1ð 1

R1� 1

R2Þ 1

C1R1

� 1C2R2

0

" #

; B4¼� 1

C1ð 1

R1� 1

R2Þ 1

C1R1

� 1C2R2

0

" #

ð21Þ

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0 1 2 3 4 5 6 7140

160

180

200

Thermometric Code (n)

Fre

quen

cy (

kHz)

145 150 155 160 165 170 175 180 185110

120

130

140

150

Operating Frequency

Cur

rent

am

plitu

des

(uA

)

145 150 155 160 165 170 175 180 1851

1.2

1.4

1.6

1.8

Operating Frequency

TH

D o

f cur

rent

Io2

(%)

Theoretical

Simulated

Io2

Io1

(a)

(b)

(c)

Fig. 10 a FO variation with

thermometric code, b amplitude

variation with frequency, c THD

variation with frequency

310 Analog Integr Circ Sig Process (2012) 71:303–311

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Abhirup Lahiri received Bach-

elor of Engineering (B.E.) degree

from the Division of Electronics

and Communications, Netaji

Subhas Institute of Technology

(erstwhile, Delhi Institute of

Technology), University of

Delhi, India. His research inter-

ests include design of compact

analog circuit solutions using

novel voltage-mode and current-

mode active elements. He has

authored/co-authored several

international journal/conference

papers and has acted as a reviewer

(by editor’s invitation) for international journals and conferences. He is a

member of ACEEE, IAENG and IACSIT.

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