Realization of current-mode biquadratic filter employing multiple output OTAs and MO-CCII

Accepted Manuscript Regular paper Realization of current- mode biquadratic filter employing multiple output OTAs and MO-CCII Karima Garradhi, Néjib Hassen, Thouraya Ettaghzouti, Kamel Besbes PII: DOI: Reference:

S1434-8411(17)31059-2 http://dx.doi.org/10.1016/j.aeue.2017.08.027 AEUE 52023

To appear in:

International Journal of Electronics and Communications

Received Date: Revised Date: Accepted Date:

30 April 2017 15 July 2017 20 August 2017

Please cite this article as: K. Garradhi, N. Hassen, T. Ettaghzouti, K. Besbes, Realization of current- mode biquadratic filter employing multiple output OTAs and MO-CCII, International Journal of Electronics and Communications (2017), doi: http://dx.doi.org/10.1016/j.aeue.2017.08.027

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Title page with author details

Realization of current- mode biquadratic filter employing multiple output OTAs and MO-CCII

PhD. Karima GARRADHI [email protected] Micro-electronics and instrumentation laboratory University of Monastir Monastir, Tunisia

Prof. Néjib HASSEN [email protected] Micro-electronics and instrumentation laboratory University of Monastir Monastir, Tunisia

PhD. Thouraya ETTAGHZOUTI [email protected] Micro-electronics and instrumentation laboratory University of Monastir Monastir, Tunisia

Prof. Kamel BESBES [email protected] Micro-electronics and instrumentation laboratory University of Monastir Monastir, Tunisia Centre for Research on Microelectronics and Nanotechnology of Sousse, Technopole of Sousse, Tunisia

Karima GARRADHI was born in Nabul, Tunisia, in 1988. She received the applied license. from the Faculty of Sciences of Monastir in 2011, the M.S. degree from at the same University at the Microelectronic and Instrumentation Laboratory in 2013. Actually, she is preparing the Ph.D degree. She is interested to the implementation of low voltage low power integrated circuit design. Néjib HASSEN was born in 1961 in Moknine, Tunisia. He received the B.S. degree in EEA from the University of Aix-Marseille I, France in1990, the M.S. degree in Electronics in 1991 and the Ph.D. degree in 1995 from the University Louis Pasteur of Strasbourg, France. From 1991 to 1996, he has worked as a researcher in CCD digital camera design. He implemented IRDS new technique radiuses CCD noise at CRN of GOA in Strasbourg. In 1995, he joined the Faculty of Sciences of Monastir as an In 1995, he joined the Faculty of Sciences of Monastir as an Assistant Professor of physics and electronics Since 1997, he has worked as researcher in mixedsignals neural networks. Currently, he is professor of microelectronics and electronics to ISIMM University of Monastir. He is focusing on the implementation low voltage - low power mixed and analog circuits

Thouraya ETTAGHZOUTI was born in Tozeur, Tunisia, in 1983. She received the B.S. degree from the Faculty of Sciences of Monastir in 2008, the M.S. degree from at the same University at the Microelectronic and

Instrumentation Laboratory in 2010. Actually, she is preparing the Ph.D degree. She is interested to the implementation of low voltage low power integrated circuit design.

Kamel BESBES was born in Monastir, Tunisia, in 1960. He received the B.S. degree from the Faculty of Sciences of Monastir in 1985, the M.S. degree from the Ecole Centrale de Lyon, Lyon, France, in 1986, the Ph.D. degree from the Institut National des Sciences Appliquées de Lyon (INSA), Lyon, in 1989, and the Doctorat d’Etat degree from the Faculty of Sciences of Tunis, Tunisia, in 1995. In 1989, he joined the Faculty of Sciences of Monastir as an Assistant Professor of physics and electronics. He is now a Professor and the Dean of the Faculty and the Head of the Microelectronics and Instrumentation Laboratory. His research work and interest are focused on microelectronics, modeling, and instrumentation.

filters [3, 4], voltage-controlled oscillators (VCOs) [5] and continuous-time sigma-delta modulators [6] which is an amplifier whose differential input voltage produces an output current with a constant transconductance. These analog systems often require low power, fast settling time and high dynamic range. For this reason, several techniques have been proposed in the litterateur to improve the linearity performance of MOS transconductor such as: crossing-coupling of multiple differential pair [7], adaptive biasing [8], source degeneration using resistors or MOS transistors [9], constant drain-source voltages [10], bulk driven [11] and super class-AB linear operation [12]. Among the previously mentioned techniques, a source degeneration (passive or active) is probably the simplest and most effective solution for realization of low-voltage and low-power OTA [13]. Furthermore, this technique as successfully been used as the input stage of transconductance amplifier to allow a wide input linear range under low power supply voltage operation. In this paper, a novel low voltage low power operational transconductance amplifier circuit using active or passive source degeneration and a second generation current conveyor CCII– using double outputs OTA have been realized. Based on the two multiple current output OTAs (MO-OTAs), one OTA, one MO-CCII and two grounded capacitors, a new SIMO current-mode biquadratic filter is implemented. 2. Proposed operational transconductance amplifier OTA 2.1 Circuit Description 2.1.1 OTA without source degeneration Without considering the resistor R, the proposed circuit OTA is presented in Fig.1. It presents an active element which can convert an input voltage to an output current with transconductance coefficient Gm. It can be characterized by the following expression:

I out  I out  I 2  I1  (Vin  Vin ) Gm

(1)

This circuit is composed by four wide swing low-voltage cascode current mirrors and NMOS differential pair (M1, M2) adjusted by Mc with bias voltage Vb1 which is implemented by two transistors (NMOS (Me) and PMOS (Md)).

Realization of current-mode biquadratic filter employing multiple output OTAs and MO-CCII Abstract—This paper presents a low voltage low power operational transconductance amplifier circuit. By using a source degeneration technique, the proposed realization powered at ±0.9 V shows a high DC gain of 63 dB with a unity gain frequency at 3.5 MHz, a wide dynamic range and a total harmonic distortion of -60 dB at 1 MHz for an input of 1Vpp. According to the connection of negative current terminal to positive voltage terminal of double output OTA circuit, a second generation current conveyor (CCII-) has been realized. This circuit offers a good linearity over the dynamic range, an excellent accuracy and wide current mode of 56 MHz and voltage mode of 16.78 MHz cut-off frequency f-3 dB. Thereafter, new SIMO current-mode biquadratic filter composed by OTA and CCII as active elements and two grounded capacitors is implemented. This filter is characterized by (i) independent adjusting of pole frequency and quality factor, (ii) it can realize all simulations results without changing the circuit topology, (iii) it shows low power consumption about 0.24mW. All simulations are performed by Cadence (Cadence Design Systems) technology Tower Jazz 0.18 μm TS18SL. Keywords—Operational Transconductance Amplifier (OTA), Second generation current conveyor, Dynamic Range, Low-Voltage Low-Power, source-degeneration, Current-mode, Biquadratic filter. 1. Introduction The utilization rate of portable electronic systems such as medical equipment, wireless communication devices and consumer electronic has received a considerable increase. For that, the design of low-power circuit remains the most important goal. The minimization of supply voltage and decreased dimensions of the components were the principle parameters to lower the consumption and enhance performance. Today, OTA is important building block in many analog systems with linear input-output characteristics. It is widely used in analog circuits such as including multipliers [1, 2], continuous-time-

The current mirrors are characterized by low input impedance and high output impedance, which are described by the following expressions [14].

ro10a  ro9 a  ro10a ro9 a g m9 a 1  g m10a ro10a (1  ro9 a g m9 a ) g m10a

Rin 

(2)

Rout  g m9 ro9 ro10

(3)

Assuming that all transistors are operated in the saturation region, the relationship between input voltages (Vin+ , Vin) and output currents (I1, I2) is given by the following expression: Vid  Vin  Vin   VGS 2  VGS 1 

2I 2

n



2 I1

n

(4)

Where Vin+ and Vin- present respectively the non-inverting and inverting input voltage and

 n   n Cox (

W )1, 2 is the transconductance parameter of transistors (M1, M2) with µ, Cox, W and L are L

the mobility, channel capacitance per unit area, channel width, and channel length respectively. The bias current ISS of transistor Mc is given as following:

I SS  I1  I 2

(5)

Based on Eqs (4) and (5), the expressions of currents I 1 and I2 are shown as follows:

I1 

I SS 1  V2   n I SS Vid (1  n id ) 2 2 4 I SS

(6)

I2 

I SS 1  V2   n I SS Vid (1  n id ) 2 2 4 I SS

(7)

Therefore, the differential output current can be expressed as:

I out   I out  I 2  I1   n I SS  Vid   n I SS

 nVid2 1 4 I SS

 1  Vid   n I SS ( n )  Vid3 8 I SS

(8)

In Eq. 8 the higher order terms have been neglected. Hence, the transconductance Gm can be written as:

Gm 

I out   n I SS Vid

(9)

2.1.2 OTA using passive source degeneration In order to improve the performances of pervious circuit, we have used passive source-degeneration technique by adding two resistors at the input differential pair which is illustrated in Fig.1.

Fig. 1. OTA with passive source degeneration

The differential input voltage is shown by the following equation:

Vid  Vin  Vin 

2I 2

n



2 I1

n

 RI out

(10)

The expressions of currents I1 and I2 have become as follows:

I1 

I SS 1  (V  RI out ) 2   n I SS (Vid  RI out ) (1  n id ) 2 2 4 I SS

(11)

I2 

I SS 1  (V  RI out ) 2   n I SS (Vid  RI out ) (1  n id ) 2 2 4 I SS

(12)

The differential output current can be expressed as:

I out   I out  I 2  I1   n I SS  (Vid  RI out ) 1 

 n (Vid  RI out ) 2 4 I SS

(13)

  n I SS  (Vid  RI out ) Therefore, the transconductance Gm can be written as:

Gm' 

I out Gm  Vid 1  Gm R

(14)

When Gm   n I SS is the transconductance of OTA without source degeneration. 2.1.3 OTA using active source degeneration The circuit OTA using active source degeneration is shown in Fig.2. In this circuit, the two passive resistors of source degeneration have been replaced by two NMOS transistors Ma and Mb operated in the triode region which is polarized by Vb2. The circuit diagram for the baising voltage generator (V b2) is realized by two transistors PMOS (Mf) and NMOS (Mg).

Fig. 2. OTA using active source degeneration (Transistors biased on triod region)

The expressions of the differential current output and transconductance are similar to the expressions of previous circuit (Fig.1) except that the expression for R can be written as:

R

1  n Cox (W / L)(Vgs  VT )

(15)

2.2 Dynamic study of Circuit 2.2.1 OTA without source degeneration The differential input voltages Vin+ and Vin- are shown in the following equations:

Vin 

1 [ I 2 (roc  ro 2  roc g m 2 ro 2 )  I1 (roc  roc g m 2 ro 2 )  Vgs3 ] g m 2 ro 2

(16)

Vin 

1 [ I1 (roc  ro1  roc g m1ro1 )  I 2 (roc  roc g m1ro1 )  Vgs3a ] g m1ro1

(17)

Based on two expressions (16) and (17), the differential input voltage can be expressed as:

Vin  Vin 

1 [ I 2 (roc  ro 2  roc g m 2 ro 2 )  I1 (roc  roc g m 2 ro 2 )  Vgs3 ] g m 2 ro 2

1 [ [ I1 (roc  ro1  roc g m1ro1 )  I 2 [roc  roc g m1ro1 ]  Vgs3a ] g m1ro1

(18)

Considering the characteristics of the transistors M1 and M2 are identical, the differential input voltage can be expressed as:

Vin  Vin 

1 [ro1 I out  (Vgs3a  Vgs3 )] g m1ro1

(19)

Where, the gate-source voltages of transistors M3 and M3a are shown respectively in the following equations:

Vgs3   I 2 (

ro5  ro3  ro3 ro5 g m5 I ) 2 g m3 ro3 (1  ro5 g m5 ) g m3

Vgs3a   I1 (

ro5a  ro3a  ro3a ro5a g m5a I ) 1 g m3a ro3a (1  ro5a g m5a ) g m 3a

(20)

(21)

Substituting the expressions Vgs3a and Vgs3 in Eq. 19 and considering the products gmiri much greater than 1, the output current and the transconductance Gm can be expressed as:

I out   I out  g m1Vid

(22)

Gm  g m1Vid

(23)

2.2.2 OTA using passive source degeneration The differential input voltage Vin+ and Vin- are given by the following expressions:

Vin 

1 [ I 2 (roc  ro 2  roc g m 2 ro 2  R(1  ro 2 g m 2 ))  I1 (roc  roc g m 2 ro 2 )  Vgs3 ] (24) g m 2 ro 2

Vi n  

1 [ I1 (roc  ro1  roc g m1ro1  R(1  ro1 g m1 ))  I 2 (roc  roc g m1ro1 )  Vgs3a ] g m1ro1

(25)

Based on two expressions (24) and (25), the differential input voltage can be expressed as:

Vin  Vin 

1 [ I 2 (roc  ro 2  roc g m 2 ro 2  R(1  ro 2 g m 2 ))  I1 (roc  roc g m 2 ro 2 )  Vgs3 ] g m 2 ro 2

1  [ I1 (roc  ro1  roc g m1ro1  R(1  ro1 g m1 ))  I 2 (roc  roc g m1ro1 )  Vgs3a ] g m1ro1

(26)

Considering the characteristics of the transistors M1 and M2 are identical, therefore the differential input voltage can be expressed as:

Vin  Vin 

1 [ro1 I out  R(1  g m1 r01 ) I out  (Vgs3a  Vgs3 )] g m1ro1

(27)

The expressions Vgs3a and Vgs3 are like the previous expressions as indicated in Eq. 20 and Eq. 21. By using the approximation 1  g mi r0i  g mi ri , and the characteristics of the transistors M3 and M3a are identical, the output current can be expressed as:

I out   I out 

g m1 Gm Vid  Vid 1  g m1 R 1  Gm R

(28)

Hence, the characteristics of OTA using passive source degeneration are given by the following expressions:

G 'm 

Gm 1 GmR

(29)

g m9 ro9 ro10  g m 6 ro 6 ro 4 g m9 ro9 ro10  g m6 ro 6 ro 4

(30)



The transconductance:



Output resistor:

Rout 



Differential Mode Gain:

A md  R out G 'm 



Switching Frequency:

FC 

Gain Bandwidth Product:

Gm' 1  g m1 R GBW   2C 2 Cg m1



g m9 ro9 ro10  g m6 ro6 ro 4 g m1  g m9 ro9 ro10  g m6 ro6 ro 4 (1  g m1R )

g m9 r09r010  g m6 r06r04 1  2 CRout 2 C g m9 r09r010  g m6 r06r04

(31)

(32)

(33)

Dynamic and static studies show that the OTA circuit using passive or active source degeneration possesses high linearity compared to OTA circuit without using source degeneration. Although, the disadvantage of this configuration is the large resistor value needed to achieve a wide linear input range. In which Gm = 1/R, the obtained transconductance is restricted to small values. The comparisons between different proposed circuits OTAs are given respectively in Tab. I. TABLE I.

Comparison between OTA without/with source degeneration technique

Parameter

OTA without source degeneration

OTA using passive source degeneration

G 'm  Transconductance

Gm and 1 N

OTA using active source degeneration

G 'm 

Gm and N=Gm×R 1 N

W Gm  Cox I SS ( ) L

N= Gm×R

R=1/(µnCox(w/L) (Vgs-VT)

Consumption

ISS

2(1+N) ISS

2(1+N) ISS

Aspect ratio of transistor

W L

W (1  N ) L

W (1  N ) L

3. Realization of CMOS CCII– Based on CMOS DO-OTA A negative second generation current (CCII–) has been implemented based on double outputs OTA circuit (DO-OTA) using active source degeneration where the terminal of negative output current is connected to the terminal of positive input voltage, as shown in Fig.3.

This circuit has three terminal devices X, Y and Z where the input voltage applied to terminal Y is perfectly conveyed to X terminal and the input current applied at X terminal is conveyed to the Z terminal with negative sign. The relationship between voltage and current terminals are given by the following matrix:

 I Y  0 V   1  X   I Z  0

Y

+ Gm+ - -

Z

0 0 1

VX VY

IX

0 0 0

VY  I   X YZ 

X CCII-

IY

Y

Z

VZ IZ

X Fig. 3. Block diagrams of CCII– based on DO-OTA.

4. Simulation Results The performances of the three proposed circuits OTAs and the second generation current conveyor CCII- are verified by Cadence (Cadence Design Systems) technology Tower Jazz 0.18μm TS18SL. These circuits are operated at ± 0.9V supply voltage, capacitive load of 1pF, resistor of 30 kΩ and a bias voltages values Vb1 and Vb2 are -0.4V, 0.4V respectively. The transistors aspect ratios of the three OTAs are given respectively in Tab. II. TABLE II. Aspect ratios of the transistors Transistors

M1, M2 Mc M3, M4, M5, M6 M3a, M4a, M5a, M6a M9, M10, M9a, M10a Ma, Mb M11, M12, M11a, M12a M13, M14, M13a, M14a Md Me Mf Mg

OTA without source degeneration W(μm) /L(μm) 15/5 30/5 10/1 10/1 5/1 10/1 5/1 1/1 13/1

4.1 Measurement Results of CMOS DO-OTA

OTA with Active source degeneration W(μm) /L(μm) 15/5 30/5 10/1 10/1 5/1 8/10 10/1 5/1 1/1 13/1 6/1 10/1

OTA with Passive source degeneration W(μm) /L(μm) 15/5 30/5 10/1 10/1 5/1 10/1 5/1 1/1 13/1

The DC transfer characteristics of the three proposed OTAs are shown in Fig. 4, which are achieved by varying the input voltage from -0.9V to +0.9V. It is understood that the OTA using active/passive source degeneration has a good linearity (-0.7V, 0.7V) in compared to OTA without source 0

2

4

6

8

10

0

2

4

6

8

10

degeneration. 15,0µ

10

15,0µ 10

O T A_ w ithout S _ R O T A_ us ing P as s iv e S _ R O T A_ us ing Ac tiv e S _ R

10,0µ

10,0µ

8

8

5,0µ

O u tp u t C u rre n t (A )

0,0 4

-5,0µ

O u tp u t C u rre n t (A )

5,0µ 6

6

0,0

4

-5,0µ

O T A_ w ithout S _ R O T A_ us ing Ac tive S _ R O T A_ us ing P as s ive S _ R

2

-10,0µ

-10,0µ

-15,0µ

0

-0,8

-0,4

0,0

0,4

0,8

2

-15,0µ -0,8

-0,4

Differential input voltage (V)

0

(a) 2

4

6

0,0

0,4

0,8

0

Differential input voltage (V)

8

10

0

(b)

2

4

6

8

10

Fig. 4. DC transfer characteristics of the proposed OTAs : (a) Iout+ (b) Iout10

0,0

100,0µ 8

OT A_ w ithout S _ R OT A_ us ing P as s ive S _ R OT A_ us ing Ac tive S _ R

60,0µ

6

4

40,0µ

-20,0µ

Transconductance (S)

Transconductance (S)

80,0µ

10

8

-40,0µ 6

-60,0µ

OT A_ w ithout S _ R OT A_ us ing P as s ive S _ R OT A_ us ing Ac tive S _ R

-80,0µ

20,0µ

4

2 2

-100,0µ

0,0 0

-0,8

-0,4

0,0

0,4

Differential input voltage (V )

(a)

0,8

-0,8

-0,4

0,0

0,4

0,8

Differential input voltage (V )

(b)

Fig. 5. The simulated transconductance of the proposed OTAs : (a) Gm+ ( b) Gm-

From these characteristic, the transconductance Gm of the three OTAs are plotted. As a result, the OTA using active/passive source degeneration has a wide dynamic range in the interval [-0.7V, 0.7V] and present a maximum value of 22.32µS (Fig.5) compared to that of conventional one.

0

The frequency responses and phase margin of the three OTAs are shown in Fig.6.a, Fig.6.b respectively. The OTA using active/passive source degeneration reached an open loop gain of 63 dB with transition frequency at 3.5 MHz and phase margin of active /passive source degeneration of 95 degree, 86 degree respectively. For OTA without source degeneration, we noted a relatively gain of 73dB with transition 0

2

4

6

8

0

10

2

4

6

8

10

frequency at 15 MHz and phase margin of 71 degree. 100

50

10

10

0 8

6

0

4

OT A_ us ing P as s ive S _ R OT A_ w ithout S _ R OT A_ us ing Ac tive S _ R

-50

2

-100

-50

P h a s e m a rgin (de g)

O p e n lo o p re s p o n s e (d B )

50

8

-100 6

-150 -200

OT A_ w ithout S _ R OT A_ us ing P as s ive S _ R OT A_ us ing Ac tive S _ R

-250

4

-300 2

-350 0

100

1k

10k

100k

1M

10M

100M

1G

-400 100

F requenc y (Hz)

1k

10k

100k

1M

10M

100M

1G

F requenc y (Hz)

(a)

(b)

Fig. 6. (a) Open loop frequency response of the three OTAs (b) Phase margin of the three OTAs

4.2 Monte Carlo To investigate the sensitivity on the transconductance, linearity, open loop gain and GBW performances of the proposed circuit (OTA using active source degeneration), Monte Carlo simulations are performed for random value with 100 runs. All Monte - Carlo simulations incorporate ±3σ variation, where σ is the standard deviation of the parameter. TABLE III. . Sensitivity on the performances of the proposed OTA to process variation and mismatch Type Average Standard deviation (σ) Variation rate (%)

Gm (µS) 22.33 0.27 3.63

Linearity (µA) 10.79 0.14 3.89

GBW (MHz)) 3.06 0.275 27

Open loop Gain (dB) 62.52 4.5 21.59

Fig.7 depicts the results for Gm, linearity , open loop gain and GBW distribution of the proposed OTA. Tab. III shows the sensitivity on the performances of the proposed OTA to process variation and

0

mismatch. As results, the Monte Carlo simulation shows that GBW is very sensitive to process variation compared to other performance. As far as, the variation rate indicates the percentage impact of process variation and defects on the performances of the proposed circuit and is calculated through the Eq.34.

Variation rate  0

2

4

6

8

10

3 *1000 Mu

2

4

6

8

(34)

10

10

25 20

0

2

20

4

6

8

10

6

6

10

4

4

5

0

2

2

0 21,5

22,0 4

2

6 22,5

23,0 1 0

8

10,4

T rans c onduc tanc e (µS ) 0

2

4

6

(a)

10,6

10

10,8

11,0

0

11,2

Output c urrent (µA)

0 0

8

8

15

5

0

N =100 Mu =10.79µA S td Dev =149nA

8

N.o o f s a m p le

No o f s a m p le

15

10

10

N =100 Mu = 22.33µS Std Dev =270.9nS

2

4

6

8

10

(b)

10

10

10 10

25

8

Mu= 3.06 MHz Std Dev =275.88 kHz

6

N.o of s a m ple

20 N.o of s a m ple

8

N = 100

25

8 8

20

N = 100 Mu = 62.52dB S td Dev = 64.5dB

6

15

15

6

4 4

10

4

10 4

2 2

5

2

5 2

0 2,2

2,4

2,6

2,8

3,0

3,2

3,4

G B W (MHz)

3,6

00

0

0 45

50

55

60

65

70

75

Open 0 loop gain (dB )

(c) (d) Fig. 7. Monte-Carlo histogram . (a) Transconductance (b) DC transfer characteristics with 0.5V input voltage (C) GBW (d) Open loop gain: with : mu = mean; std Dev: sigma (σ) ; N: number of iterations = 100

4.3 Measurement Results of CMOS CCII– In voltage mode, the CCII- assured good linearity over the rail to rail dynamic range (±0.9V) with the maximum offset voltage is 0.02mV (Fig.8.b).

Frequency response of the voltage gain between terminals X and Y of the CMOS CCII– is shown in (Fig.9.a). The cut-off frequency f-3dB at 16.78 MHz is obtained. The voltage gain is 1. In current mode, a good linearity is obtained over the interval [-15µA, 15µA] (Fig. 8.a). The AC current gain between terminals X and Z of the CMOS CCII– has been plotted in Fig.9.b. The cut-off frequency 0

2

4

6

8

0

10

2

4

6

8

10

f-3dB has been found at 56 MHz and the current gain is 1. 20,0µ

0,6

10,0µ

O u pu t v olta ge V x (V )

O u tpu t c u rre n t Iz (A )

15,0µ

5,0µ 0,0 -5,0µ

-10,0µ -15,0µ

10

-10,0µ 2

0,0

10,0µ

Intput c urrent Ix (A ) 4 6

8

8

0,4 0,2

8

6

0,0 6

-0,2

4

-0,4 4

-0,6 -0,8

-20,0µ -20,0µ 0

10

0,8

20,0µ

2

2

-0,8

-0,6

-0,2

0,0

0,2

0,4

0,6

0

0,8

Input voltage Vy (V)

0

10

-0,4

(a)

(b) 0

2

4

6

8

10

Fig. 8. DC characteristics of second generation current conveyor circuit: (a) current mode (b) voltage mode 10

10

0

0

C u rre n t G a in (dB ) IdB (z ) )

V olta ge ga in (dB ) ,V dB (x )

10

-10

-20

-30

-40

-10

10M

8

-20 6 6

-30 4

-40 -50

4

2 2

-60 -70

1M

8

0

100M

F requenc y(Hz)

(a) Fig. 9.

10M

100M

1G

F requenc y (Hz )

(b)

(a) Frequency response of second generation current conveyor circuit: (a) voltage mode, (b) current mode

In Tab. IV, the simulated performances of OTA without/with source degeneration (passive or active) along with some of the recent works are summarized. TABLE IV. Performance comparison with previously reported work

0

Our circuit Performance design

OTA

OTA

OTA

OTA

[15]

[16]

[17]

[18]

0.18 1.5 126

0.18 1.8 450

0.35 3.3 1000

32.5

40

5 110 ±0.5

40 ±0.9

OTA without source degeneration

OTA with Passive source degeneration

OTA with Active source degeneration

0.18 ±0.9 80.86 63 86 3.5 22.32 ±0.7 154 112 137 63 1 12.71 -13.1

0.18 ±0.9 80.7 63 95 3.5 22.16 ±0.7 172 116 140 63 1 12.58 -13.18

0.18 1.8 600.5 40.9 91

GBW (MHz) Transconductance (μS) Linear range (V) PSRR+ (dB) PSRR- (dB) CMRR (dB) Input Noise Density (nV/√Hz @frequency(MHz) Positive slew rate (V/μS) Negative slew rate (V/μS)

0.18 ±0.9 78.48 76 71 15 100 ±0.1 151 108 123 34 1 12.79 -13.36

69.5 76 107.5 96 1

94.8 1

28

THD (dB) @voltage peak-peak @frequency(MHz) Capacitive load (pF)

-40.45 1 1 1

-60.52 1 1 1

-60.75 1 1 1

-50.6 0.9 10 10

-63 0.35 1 50fF

-61 0.5 5

Technology CMOS (µm) Supply voltage (V) Power consumption (µW) DC gain (dB) Phase margin(degree)

-57 1.6 0.001

5. Application Analogues filters have played a very important role specifically in the field of telecommunications that is why many research workers are interested in improving this type of applications. Some current- mode biquad filters based on OTA and CCII have been reported [19-20]. According to the number of input and output terminals, the circuit configuration of filter can be given into three types (i) single input and single output (SISO) [21], (iii) single input and multi-outputs (SIMO) [22-23] and (ii) multi-inputs and multi-outputs (MIMO) [24-25]. In our case, a new SIMO current-mode biquadratic filter based on OTA and CCII (Second-generation current conveyor) as active element is presented. The circuit configuration is composed by two MO-OTAs, one SO-OTA, one MO-CCII and two grounded capacitors as shown in Fig.10. The SIMO filters can simultaneously realize low pass, band pass, high pass and notch filters without changing the circuit topology. It is characterized by active and passive sensitivities less than unity and an adjustment independently between pole frequency and quality factor.

5.1 Theoretical results The voltages VC2 and VC1 are given by the following expressions:

VC 2   VC1 g m1

VC1 

1 C2 p

(35)

I in g g C1 p  m1 m 2  g m3 C2 p

(36)

Therefore, based on two expressions (35) and (36), the transfer function TLP (s) and TBP (s) for the current output ILP (s) and IBP (s) can be expressed as:

I LP   g m 2 VC 2  g m 2 g m1 VC1

1 c2 p

I BP  g m3 VC1

with

TLP ( s) 

g m1 g m 2 I LP ( s)  2 I in ( s) s C1C 2  sC2 g m 3  g m1g m2

(37)

TBP ( s) 

sC2 g m3 I BP ( s)  2 I in ( s) s C1C 2  sC2 g m 3  g m1g m2

(38)

Depending on the currents of I HP  I in  I LP  I BP , I BR (s)  I in (s)  I BP (s) and I AP (s)  I BR (s)  I BP (s) the high-pass, band-stop and all-pass transfer functions can be respectively realized as the following:

THP ( s) 

I HP ( s) s 2 C1C 2  2 I in ( s) s C1C 2  sC2 g m 3  g m1g m2

(39)

TBR ( s) 

I BR ( s) s 2 C1C 2  g m1g m2  2 I in ( s) s C1C 2  sC2 g m 3  g m1g m2

(40)

TAP ( s) 

2 I AP ( s) s C1C 2  sC2 g m 3  g m1g m2  2 I in ( s) s C1C 2  sC2 g m 3  g m1g m2

(41)

Consequently, five different circuit transfer functions can easily be realized by picking suitable current outputs. This filter additionally needs no component matching conditions to realizing their transfer functions. The pole frequency ( 0 ) and the pole quality factor ( Q0 ) of the filter can be given as follows:

0 

g m1 g m 2 C1C2

Q0 

1 g m3

g m1 g m 2C1 C2

(42)

From Eq. 42, the pole frequency can be adjusted without modifying the quality factor by making equal the two capacitors (C1,C2) and the two transconductances (gm1,gm2). Similarly, the quality factor can be adjusted by transconductance gm3 without affect a pole frequency variation. Therefore, the pole frequency and the quality factor are orthogonally controlled. Based on the sensitivity expression S xy 

x y  , via Eq. 42, we can calculate the sensitivities to circuit y x

elements which are given respectively as follows:

S

1 Qo Q Q   S o S o S o S o  g m1 gm2 C1 g m1 gm2 2

1 Q   S o S o S o  C2 C1 C2 2

S

o g m3

0

S

Qo  1 (43) g m3

Therefore, all the active and passive sensitivities are equal or less than unity in magnitude.

Iin

x

-

z-

CCII- zzy

Iin Iin

C1

VC1

gm1 +

+

C2

+

VC2

gm2 -

+ + -

-

gm3 ILP

+

+ + + +-

IBP

IHP IBR

IAP

Fig. 10. Biquadratic circuit configuration.

5.2 Simulation Results of Filter To test the functioning of proposed current mode filter, we have fixed the capacitors to C1=C2=11pF and the transconductances to gm1=gm2=22.32µS and gm3= 44.64 µS. The simulation results are in good agreement with the theoretical calculations. The center frequency is given by 300 kHz (Fig.11.a). Simulated gain and phase responses of the proposed all pass filter are given in Fig.11.b. Theoretically, it is possible to control the quality factor Q0 while keeping f0 fixed to 300kHz by only modifying gm3 value with C1=C2= 11pF (see Table. V) (Fig 12.a). Fig.12.b shows the simulation results for control of f0 while keeping Q0=1 with modifying the values of transconductance g m1 and gm2 with C1=C2= 11pF (see Tab. V).

0

2

4

6

8

10

20

20

0

0

160 8

-20

C u rre n t G a in (dB )

-20 -40 AP BR HP BP LP

-60 -80

-40

120

6

80

gain phas e

-60

40

4

-80

0 2

-100

-40

-120

-100 10k

100k

1M

10M

P h a se (d e g re e )

C u rre n t G a in (dB )

200

10

1k

0

10k

100k

1M

-80 10M

F requenc y(Hz )

F requenc y (Hz)

(a)

(b)

Fig. 11. (a) Simulation results of the current mode biquadraticfilter (b) Gain and phase responses of the proposed all pass filter

TABLE V.

The gm1, gm2 values for controlling of Q0 and for controlling f0.

f0 300 kHz 600 kHz 1MHz

Fixed Q0 gm1 (μS) 22.32 44.64 66.96

gm2 (μS) 22.32 44.64 66.96

Q0 1 2 3

Fixedf0 gm1 (μS) gm2 (μS) 22.32 22.32 22.32 22.32 22.32 22.32

gm3 (μS) 22.32 11.16 7.44

In the order to test the time-domain of the proposed filter, a sinusoidal input with a 5µA amplitude (peak) and 300 kHz frequency is applied on the terminal I in. The simulation result is presented in Fig.13.a. The THD variation of band pass filter according to different values of input current amplitude is shown in Fig 13.b. For a amplitude less than 5 µA the total harmonic distortion THD has been found to be of lower than 2% with 300 kHz frequency. The result of Monte-Carlo analysis, using 100 runs shows the statistical analysis results for the bandwidth of the BP filter in Fig.14. The mean value is 299.32 kHz for the center frequency with a standard deviation σ= 4.92kHz. The variation rate of the BP filter is equal 4.93% . To estimate our proposed filter, we compared it with some of the recent works presented in the literature as shown in Tab.VI.

0

2

4

6

8

0

10

0

2

4

6

8

10

0

1 10

C u rre n t g a in (d B )

C u rre n t ga in (dB )

8

-40 Q=1 Q=2 Q=3

-25

8

6

fo =1MHZ

6

fo =600K Hz

-50

4

fo =300K Hz

4

2

-80 100

1k

10k

100k

1M

-75 100

10M

F requenc y (Hz)

2

1k

10k 100k F re qu e n c y (Hz )

0

(a)

1M

10M

0

(b)

Fig. 12. (a) Simulation results for control of Q0 while keeping f0 fixed (300kHz) for band pass filter. 0

0

2

2

4

6

8

10

(b) Simulation results for control of f0 while keeping Q0 (=1) fixed for band pass filter 4

6

8

10

6,0µ 4,0µ

10

10

Iin IBp+

10 8

8

T HD (% )

8

0,0 -2,0µ

6

6 6

4

4 4

2

-4,0µ

2 2

0

-6,0µ 0,0

2,0µ

4,0µ

6,0µ

8,0µ

10,0µ

0

2

T ime(S )

2,0µ 4

0

4,0µ

6,0µ

8,0µ

0

10,0µ

Input C urrent (A)

6

8

(a)

10

(b)

Fig. 13. (a) Time-domain input and output signal waveforms of the BP response with amplitude 5µA and fo=300 kHz (b) Dependence of output current total harmonic distortion on input current amplitude of the 0 2 of proposed 4 6 8 10 band-pass filter configuration 10 30 25

N.o of s a m ple

C u rre n t (A )

2,0µ

20

10

N= 100 Mu= 299. 32 kHz S td Dev= 4.92 kHz

8

8 6 6

15

4 4

10

2

5

2 0

0 285

290

295

300

305

310

315

0

F requenc y(kHz)

Fig. 14. Mismatch and process variation on the bandwidth of the BP filter with 100runs

TABLE VI. Comparative study of different implementation of current mode biquadratic filters

Performance design Input/ Output Type Supply voltage (V) Power consumption (mW) Capacitive load (pF). Center frequency(kHZ) No of Active element No. of R+C No. of input terminals Orthogonal control of ω0 and Q Matching Condition required THD (% ) Input current (µA ) @frequency (kHz)

[26] 2017 SIMO

OTA 4

[27] 2016 SIMO ±3 10 8 10000 OTA 4

VDTA 2

80 189.9 CCII 3

0+2 1 Yes

0+2 1 Yes

0+2 3 Yes

No

No

Yes

1.3 16

2 80 1000

[28] 2013] ±1.5 2

[29] 2011 MISO ±1.65

[30] 2013 MISO ±1.5 1.87 1nF 547.29 CCCII 2

[31] 2010 MISO ±1.25

[33] 2005 MISO

OTA 4

[32] 2009 MISO ±1.65 30.95 50 1000 OTA 5

0+2 3

0+2 3 Yes

0+2 3 Yes

0+2 3 No

Our Work SIMO ±0.9 0.24 11 300 OTA+CCII 3+1 0+2 1 Yes

3+2 5 Yes No

Yes

Yes

Yes

Yes

No

0.027

1nF OTA 7

2 5 300

6. Conclusion This paper discusses the approach of low voltage and low power OTA design using a source degeneration (passive or active) technique to improve the linearity performance of MOS transconductor which offers a large differential input voltage capability and a wide Gm adjustment range. The resulting topology achieves a good input range with a high DC gain of 63dB in ±0.9V supply voltage. Based on this circuit, we have implemented a novel low-voltage (LV) low power (LP) second generation current conveyor (CCII–). Finally, we have proposed a current-mode biquadratic filter based on the two multiple current output OTAs (MO-OTAs), one OTA, one MO-CCII and two grounded capacitors. The simulation results of proposed filter are verified with cadence technology Tower Jazz 0.18μm TS18SL. It has a good accuracy with the theoretical results where the center frequency can reach the 300 kHz.

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