A low voltage and low power parallel electronically tunable resistor with linear and nonlinear characteristics

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A low voltage and low power parallel electronically tunable resistor with linear and nonlinear characteristics

Roshanak Alavi Fard

^a,ⁿ

, Mohammad Pooyan

^b

aDepartment of Electronic, Islamic Azad University, Qazvin Branch (QIAU), Qazvin, Iran

bShahed University, Tehran, Iran and also with Islamic Azad University, Qazvin Branch (QIAU), Qazvin, Iran

a r t i c l e i n f o

Article history:

Received 17 July 2011 Received in revised form 7 March 2012 Accepted 8 March 2012 Available online 17 April 2012 Keywords:

Dynamic range Linearity OTA Parallel Tunablity

a b s t r a c t

In this paper a bilateral resistive circuit is designed and presented with is work as a positive and negative electronically tunable resistor and has zero DC offset. The proposed topology is designed by paralleling two electronically tunable resistors to obtain lower resistive values and decreasing nonlinearity percent. The proposed topology is low voltage and low power and with proper transcurrent circuit, its current–voltage characteristics can be linear, expansive (square) and compressive (square root). Its supply voltages are71 V and its dynamic range is71 V too. The designed circuit is simulated in an industrial 65 nm CMOS process. The linear version is tunable over the wide resistance range of 7 kO^{–37 G}O^.

1. Introduction

CMOS active resistors are very important blocks in VLSI analog design, mainly used for replacing the large value passive resistors, with great advantage of a much smaller area occupied on silicon.

They have applications in tunable gain amplifiers, artificial neural networks, tunable frequency oscillators, integrated continues time filters with RC high accuracy with tunable time constant, frequency synthesis networks, resistive synthesis networks, current dividers and voltage dividers[1–7]. The traditional realiza- tions of floating resistances were achieved by employing intrinsic device characteristics. However the resulting resistances of these techniques are strongly dependent on device parameters and predetermined[1]. Group of the electronically tunable resistors are according to voltage to current transformer[1–5].

In this paper we propose the new electronically tunable resistor with high tunability that can be positive, negative, linear and nonlinear resistor. The simulations are in HSPICE and MATLAB.

2. Electronically tunable resistor 2.1. Linear electronically tunable resistor

As shown inFig. 1, an OTA has two input voltage terminalsV_þ andV that receives input voltages completely and produces two

output currentsI_OþandI_O proportional to the difference of the input voltages. These currents have the same value but in opposite directions and two output terminals IOþ and IO . IO

output currents are the same but with opposite directions

I_Oþ¼IO ¼I ð1Þ

IOis proportional with the differential OTA input voltages and is explained in the form of below:

IO¼g_mðV_þ V Þ ð2Þ

Gmis OTA transconductance ratio.

Topology of the floating resistor is shown inFig. 2. It is used the OTAs in current mirrors as reference currents. The OTAs receiveXandYinput potentials and produce the output current proportional with the difference of the X and Y for sinks and sources transcurrent circuits. WhenV_þandV are applied to the XandYnodes, respectively, sink transcurrent circuit1 and source transcurrent circuit1 turn on. Sink transcurrent circuit1 sinks the output current of the OTA1 fromXnode and source transcurrent circuit1 sources the output current of the OTA1 to theYnode.

Relectronically¼ðV_þ V Þ

I ¼ 1

gm ð3Þ

As Eq. (3) shows, the resistive value of the electronically tunable resistor at X and Y nodes are proportional to the reciprocal of the OTAs tranconductance. Therefore the value of the electronically tunable resistor is tuned withg_mchanges. This circuit works bilateral as whenV and V_þ are applied to theX andYnodes, respectively, sink transcurrent circuit2 and source transcurrent circuit2 turn on. The source transcurrent circuit2 journal homepage:www.elsevier.com/locate/mejo

Microelectronics Journal

http://dx.doi.org/10.1016/j.mejo.2012.03.008

nCorresponding author.

E-mail addresses:[email protected] (R. Alavi Fard), [email protected] (M. Pooyan).

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sources output current of the OTA2 to the X node and sink transcurrent circuits2 sinks output current of the OTA2 from the Ynode.

Fig. 3shows a cascode current mirror. If instead of transcurrent circuits in block diagram of theFig. 2put cascode current mirror, a linear electronically tunable resistor will obtain. Circuit schematic of the linear electronically tunable resistor is shown in Fig. 4. When V_þ and V are applied to the X and Y nodes, respectively, transistors M1, M2, M3, M4, M5, M6, M7and M8turn on and transistors M₉, M₁₀, M₁₁, M₁₂, M₁₃, M₁₄, M₁₅and M₁₆are off. When V and V_þ are applied to the X and Y nodes, respectively, transistors M1, M2, M3, M4, M5, M6, M7and M8are off and transistors M9, M10, M11, M12, M13, M14, M15and M16turn on. Fig. 5 shows current–voltage characteristics of the positive linear electronically tunable resistor with different values ofgm.

These electronically tunable resistors have physically realized by many factories such as Dallas semiconductor, Analogue device and Texas Instrument. These factory names and their electronically tunable resistors IC products are shown inTable 1.

2.2. Negative electronically tunable resistor

If in block diagram ofFig. 2exchangeXandYterminals of the OTAs, then negative electronically tunable resistor will obtain.

Fig. 6is the block diagram of the negative electronically tunable resistor circuit.

If instead of the transcurrent circuits in block diagram of the Fig. 6 put cascode current mirror, the negative linear electronically tunable resistor will obtain. The relation betweenV_þ and V and the current pass through them, in the negative linear OTA

+

- +

-

Fig. 1.Transconductance amplifier (OTA).

Sink Transcurrent Circuit1

OTA1 OTA2

Source Transcurrent Circuit2 Source Transcurrent

Circuit1

Sink Transcurrent Circuit2 +

- - +

- +

+ - X

Y

Fig. 2.Block diagram of the electronically tunable resistor.

VDD

Iin

IOUT

Fig. 3.Cascode current mirror.

+

- - +

M4 M3

M2 M1

VDD

M10 M9

M12 M11

VDD

M8 M7

M6 M5

- +

M14 M13

M16 M15

OTA OTA

- +

VSS

X

Y

Fig. 4.Circuit of the linear electronically tunable resistor.

Fig. 5.Current–voltage characteristics of the linear electronically tunable resistor.

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electronically tunable resistor obtains from Eq. (4).

I ¼ 1

g_m ð4Þ

The resistive value of the negative electronically tunable resistor is tuned by changinggm. Current–voltage characteristics of the negative electronically tunable resistor are shown inFig. 7.

2.3. Nonlinear electronically tunable resistor

Nonlinear transcurrent circuits are shown inFig. 8. If instead of the transcurrent circuits in block diagram of theFigs. 2 and 6put nonlinear transcurrent circuits, the expansive (kx²) and compressive (k ffiffiffi

px

) electronically tunable resistor will obtain. Resistive values of these nonlinear electronically tunable resistors obtain from (6) and (8).

I¼IOkx² ð5Þ

I ¼ 1

g_mkx² ð6Þ

and

I¼IOk ffiffiffi

px

ð7Þ

I ¼ 1

g_mk ffiffiffi

px

ð8Þ Figs. 9–11are the simulation results of the nonlinear electronically tunable resistors.

The factory names and their electronically tunable resistors IC products.

Factory name IC numbers

Analog device AD5246 Dallas

semiconductor

DS1847, DS1848, DS1848E-010, DS1848E-050, DS1848B- 010,

DS1848B-050, DS1666, DS1666S, DS1667, DS1667-10, DS1667-50,

DS1667-100, DS1667-010, DS3904, DS3905, DS3904U-020, DS3905U-020

Texas instrument

TMP300

OTA1 OTA2

Source Transcurrent Circuit2 Source Transcurrent

Circuit1

Sink Transcurrent Circuit2 +

- +

-

+ + - Y

X

Fig. 6.Block diagram of the negative electronically tunable resistor.

Fig. 7.Current–voltage characteristics of the negative linear electronically tunable resistor.

Iref

VSS VSS VSS

Iin Iout

Iref

VSS

VSS VSS

Iin Iout

Fig. 8.(a) Compressive(square-root) transcurrent circuit, (b) expansive(square) transcurrent circuit[4].

Fig. 9.Current–voltage characteristics of the compressive electronically tunable resistor (k ffiffiffi

px ).

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3. Modified electronically tunable resistor

Silicon resistors are elements can parallel with each other but the electronically tunable resistors which are presented until now can be parallel with itself. The electronically tunable resistor in Fig. 2 can parallel by the same circuit as itself, like silicon resistors.Fig. 12 is the topology of the modified electronically tunable resistor whichXandYare its two input terminals. It is obtained by paralleling twoFig. 2electronically tunable resistors.

The OTA receivesXand Yinput potentials and produces the output current proportional with the difference of theXandYfor sinks and sources transcurrent circuits. When V_þ and V are applied to the X and Y nodes, respectively, sink transcurrent circuit1, source transcurrent circuit1, sink transcurrent circuit2 and source transcurrent circuit2, turn on.

In result currents flowXandYnodes are linearly proportional with the difference of their potentials and ratio of the voltage to Fig. 10.Current–voltage characteristics of the positive expansive electronically tunable resistor (kx²).

Fig. 11.Current–voltage characteristics of the negative expansive electronically tunable resistor (kx²).

Source Transcurrent Circuit3

OTA1 OTA2

Sink Transcurrent Circuit3 Source Transcurrent

Circuit1 +

- + -

- +

- + X

Y

OTA3 OTA4

Circuit2 +

- +

-

- +

- + X

Y

Fig. 12.Block diagram of the modified electronically tunable resistor.

- + - +

M3

M4 M2

M1

VDD

M20 M19

M18 M17

VDD

M8 M7

M 6 M 5

- +

M24 M23

M22 M21

OTA OTA

+ -

VSS

X Y

- + - +

M12 M11

M10 M9

VDD

M26 M25

M28 M27

VDD

M16 M15

M14 M13

- +

M30 M29

M32 M31

OTA OTA

+ -

VSS

X Y

Fig. 13. Circuit of the modified linear electronically tunable resistor.

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Relectronically¼ðV_þ V Þ IþI ¼ 1

2g_m ð9Þ

As Eq. (9) shows, the resistive value of the electronically tunable resistor at X and Y nodes are proportional to the reciprocal of the OTAs tranconductance. Therefore the value of the electronically tunable resistor is tuned withgmchanges. This circuit works bilateral as whenV andV_þ is applied to theXand Ynodes, respectively, sink transcurrent circuit3, source transcurrent circuit3, sink transcurrent circuit4 and source transcurrent circuit4, turn on.

If instead of transcurrent circuits in block diagram of theFig. 7 put cascode current mirror, a linear electronically tunable resistor will obtain. Circuit schematic of the linear electronically tunable resistor is shown inFig. 13. WhenV_þandV are applied to theX and Y nodes, respectively, transistors M1, M2, M3, M4, M5, M6, M₇,M₈, M₉, M₁₀, M₁₁, M₁₂, M₁₃, M₁₄, M₁₅and M₁₆ turn on and transistors M17, M18, M19, M20, M21, M22, M23, M24,M25, M26, M27, M28, M29, M30, M31and M32are off. WhenV andV_þare applied to theXandYnodes, respectively, transistors M1, M2, M3, M4, M5, M6, M7,M8, M9, M10, M11, M12, M13, M14, M15and M16are off and transistors M17, M18, M19, M20, M21, M22, M23, M24,M25, M26, M27, M28, M29, M30, M31and M32turn on.

3.1. DC charachteristics

The modified electronically tunable resistor is a low voltage circuit and V_DDand V_SSareþ1 V and 1 V, respectively.Fig. 14 shows current–voltage characteristics of the positive linear electronically tunable resistor with different values ofgm. As shown in Fig. 14, the electronically tunable resistor is linearized in wide dynamic range from 1 V to 1 V which shows wide linearization of this proposed circuit compare to the electronically tunable resistors presented in[2–9], then this linear electronically tunable resistor is proper for large signal applications. The current–

voltage characteristic of the electronically tunable resistor in[9]

does not pass through the origin while the current–voltage characteristics of the proposed electronically tunable resistor have zero DC offset. InFig. 14 the resistive values of the linear electronically tunable resistor changes from 50.34 M

O

^to

435 M

O

. The nonlinearity percent for the different resistive

values are obtained from (10) and are shown inFig. 15.

Nonlinearity Percent¼9Rreal Rideal9

Rideal 100 ð10Þ

As shown in Fig. 15, maximum nonlinearity percent for the 50.34 MO resistive value is 1.7% and maximum nonlinearity percent for the 435 MOresistive value is 3.6%.

The minimum resistive value obtained from linear electronically tunable resistor is 7.034 k

O

and the maximum resistive value obtained is 37.67 G

O

. The total power dissipation for the 7.034 kO resistive value is obtained is 0.43 mW and for the 37.67 GO ^{is 8.416}10 ¹¹W which shows that the proposed electronically tunable resistor is a low power circuit.

Fig. 16(a) shows the current–voltage characteristics of the Fig. 4electronically tunable resistor circuit for the different values from 12.3 kO^{to 20.7 k}O. Maximum nonlinearity percent for the 12.3 kOresistive value is 24% and maximum nonlinearity percent for the 20.7 kO resistive value is 10.4% which are shown in Fig. 16(b). Fig. 17(a) shows the current–voltage characteristics of the Fig. 13 electronically tunable resistor circuit for the different values from 12.3 kO^{to 20.7 k}O. Maximum nonlinearity percent for the 12.3 kO resistive value is 7.8% and maximum nonlinearity percent for the 20.7 kOresistive value is 2.4% which are shown inFig. 17(b). It is observed that for the equal resistive values theFig. 4 electronically tunable resistor circuit diagram shows more linearity and less nonlinearity percent thanFig. 13 electronically tunable resistor circuit diagram.

3.2. Temperature behavior

For the 967.43 k

O

resistive value, current–voltage characteristics of the electronically tunable resistor in 251C and 3001C are shown inFig. 18. The current–voltage characteristic in 251C is sketched with straight line and the current–voltage characteristic at 3001C is sketched with dashed line. It is observed fromFig. 18 that the current–voltage characteristic at 251C is completely matched the current–voltage characteristic at 3001C and linear electronically tunable resistor shows good temperature behavior.

3.3. Using electronically tunable resistor in a voltage amplifier The linear electronically tunable resistor is used in the voltage amplifier circuit shown inFig. 19. 1 V peak large signal is given to the input of the amplifier. In the circuit of the amplifier the Fig. 14.Current–voltage characteristics of the positive linear electronically tun-

able resistor.

Fig. 15.Nonlinearity percent for the different resistive values shown inFig. 14.

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resistive value of the electronically tunable resistor is set to 9.313 M

O

and feedback resistor Rf is chosen 19.14 M

O

^{. Fourier}

transform of the output signal of the amplifier is shown inFig. 20.

Output signal of the amplifier has 0.99% total harmonic distortion (THD) which shows that the electronically tunable resistor operates with high linearity.

3.4. Frequency response

Fig. 21 shows the frequency response of the amplifier.

Fig. 21(a) shows the frequency response of the amplifier from 0–1 MHz. The resistive value of the amplifier is 7.66 M

O

^{at DC}

frequency and its value is 19.14 M

O

^{at 1 MHz.}Fig. 21(b) shows the frequency response of the amplifier from 1 MHz to 1 GHz. At this frequency range the resistive value of the electronically tunable resistor is constant and is equal to 19.14 M

O

^.

3.5. Negative electronically tunable resistor

If in block diagram ofFig. 12exchangeXandYterminals of the OTAs, then negative electronically tunable resistor will obtain.

Fig. 17. (a) Current–voltage characteristics of theFig. 13circuit diagram electronically tunable resistor for the 12.3 kO^{to 20.7 k}Oresistive values. (b) Nonlinearity percent for different resistive values shown inFig. 17(a).

Fig. 18.Current–voltage characteristics for the resistive value of 967.43 kOⁱⁿ 251C and 3001C.

Fig. 16.(a) Current–voltage characteristics of theFig. 4circuit diagram electronically tunable resistor for the 12.3 kOto 20.7 kOresistive values. (b) Nonlinearity percent for different resistive values shown inFig. 16(a).

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Fig. 22is the block diagram of the negative electronically tunable resistor circuit.

If instead of the transcurrent circuits in block diagram of the Fig. 22 put cascode current mirror, the negative linear electronically tunable resistor will obtain. The relation betweenV_þand V and the current pass through them, in the negative linear electronically tunable resistor obtains from (11).

2I ¼ 1

2g_m ð11Þ

The resistive value of the negative electronically tunable resistor is tuned by changing gm. The first negative-resistance semiconductor devices are the tunnel diode and the Gunn diode.

The resistance values of these devices are fixed, and they can not be changed by varying the control voltage. Another disadvantage of the classical negative-resistance devices is that their parameters, such as the peak current (voltage) can not be easily adjusted to the required circuit specifications. In addition, their current–voltage characteristics with the negative slope do not pass through the origin [10]. While the proposed negative electronically tunable resistor is simply tunable and its current is zero when the voltage is zero. Fig. 23shows current–voltage characteristics of the negative linear electronically tunable resistor with different values of gm. The proposed negative electronically tunable resistor is a low voltage circuit and VDD

andVSSareþ1 V and 1 V, respectively. As shown inFig. 23, the negative electronically tunable resistor is linearized in wide dynamic range from 1 V to 1 V which shows wide linearization of this proposed circuit compare to the negative electronically tunable resistors presented in [10] then this negative electronically tunable resistor is proper for large signal applications.

3.6. Nonlinear electronically tunable resistor

If instead of the transcurrent circuits in block diagram of the Figs. 12 and 22put nonlinear transcurrent circuits, the expansive (kx²) and compressive (k ffiffiffi

px

) electronically tunable resistor will obtain. Resistive values of these nonlinear electronically tunable resistors obtain from (13) and (15).

I¼IOkx² ð12Þ

Fig. 20.Fourier transform of the output signal of the voltage amplifier.

Fig. 21.Frequency response of the amplifier (a) from 0–1 MHz (b) from 1 MHz–

1 GHz.

Vin DUT

VOUT -

+

Fig. 19.Using the electronically tunable resistor in a voltage amplifier.

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Relectronically¼ðVþ V Þ IþI ¼ 1

2g_mkx² ð13Þ

and

I¼IOk ffiffiffi

px

ð14Þ

Relectronically¼ðV_þ V Þ IþI ¼ 1

2g_mk ffiffiffi

px

ð15Þ Figs. 24–26are the simulation results of the nonlinear electronically tunable resistors. The current–voltage characteristics of the nonlinear electronically tunable resistor has the wide dynamic range71 V as its supply voltages are 71 V too, which compare to the nonlinear electronically tunable resistor presented in[4]has wider dynamic range.

4. Conclusion

In this paper a bilateral positive and negative electronically tunable resistor is designed and presented. Resistive value of the electronically tunable resistor can be tuned with changing gm

values. In addition current–voltage characteristics of the electronically tunable resistor can be positive, negative, linear, compressive (k ffiffiffi

px

) and expansive (kx²) that shows high tunability of this electronically tunable resistor. This electronically resistor is designed in industrial 65 nm CMOS process and has71 V supply voltage. Dynamic range of the electronically tunable resistor is 71 V too. This structure has 0.99%THD for 1 V large signal input voltage and high linearity is another property of this design.

Linear electronically tunable resistor can be tuned for the resistive value from 7 k

O

^{to 37 G}

O

and presents proper temperature behavior.

OTA1 OTA1

Circuit2 +

- +

-

- +

- + Y

X

OTA2 OTA1

Circuit2 +

- + -

- +

- + Y

X

Fig. 22.Block diagram of the negative electronically tunable resistor.

Fig. 23.Current–voltage characteristics of the negative linear electronically tunable resistor.

Fig. 24.Current–voltage characteristics of the compressive electronically tunable resistor (k ffiffiffi

px ).

Fig. 25.Current–voltage characteristics of the positive expansive electronically tunable resistor (kx²).

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References

[1] R. Alavi Fard and M. Pooyan, A low voltage and low power highly tunable electronically resistor, Journal of Circuits, Systems and Signal Processing, submitted.

OTAs, AEU—International Journal of Electronics and Communications 62 (2008) 725–731, http://dx.doi.org/http://dx.doi.org/10.1016/j.aeue.2007.09.007.

[3] N. Tadic and D. Gobavic, A voltage controlled resistor in CMOS technology using bisection of the voltage range, Proceedings of the 17th IEEE Conference on Instrumentation and Measurement Technology (IMTC 2000), pp.1704–

1710, Baltimore, May 2000, http://dx.doi.org/10.1109/19.982971.

[4] K.H. Wee, R. Sarpeshkar, An electronically tunable linear or nonlinear MOS resistor, IEEE Trans. Circuits Syst. Regul. Pap. 55 (2008) 2573–2583, http://dx.

doi.org/http://dx.doi.org/10.1109/TCSI.2008.920063.

[5] B. Maundy, S. Gifts, P. Aronhime, Practical voltage/current-controlled grounded resistor with dynamic range extension, Circuits, Devices & Syst. 2 (2008) 201–206, http://dx.doi.org/http://dx.doi.org/10.1049/iet-cds:20070164.

[6] S. Sakurai, A CMOS square-law programmable floating resistor independent of the threshold voltage, IEEE Trans. Circuits Syst. II: Analog Digital Signal Process. 39 (1992) 565–574, http://dx.doi.org/http://dx.doi.org/10.1109/

82.168949.

[7] S.F. Al-Sarawi, A novel topology for grounded-to-floating resistor conversion in CMOS technology, Microelectron. J. 33 (2002) 1059–1069, http://dx.doi.or g/http://dx.doi.org/10.1016/S0026-2692(02)00111-8.

[8] H. Huang, W. Hsieh and K. Chen, Programmable voltage-to-current converter with linear voltage control resistor, IEEE International Symposium On Circuits and Systems (ISCAS 2008), pp. 2310–2313, Seattle, May 2008, http://dx.doi.org/10.1109/ISCAS.2008.4541916.

[9] C. Popa, Improved linearity active resistor with controllable negative resistance, IEEE International Conference on Integrated Circuit Design and Technology (ICICDT’06.2006), pp. 1–4, Padova, August 2006, http://dx.doi.

org/10.1109/ICICDT.2006.220794.

[10] N. Tadic and D. Gobovic, A floating, negative-resistance voltage-controlled resistor, Proceedings of the 18th IEEE Conference on Instrument and Measurement Technology (IMTC2001), pp. 437–442, Budapest, May 2001, http://dx.doi.org/10.1109/IMTC.2001.928856.

Fig. 26.Current–voltage characteristics of the negative expansive electronically tunable resistor (kx²).