Grounded Voltage Controlled Positive Resistor with Ultra Low Power Consumption

In this work, a new CMOS based grounded voltage controlled positive resistor (GVCPR) with one control voltage is proposed. The proposed GVCPR employs only five CMOS transistors, one operated in triode region and others operated in saturation region or OFF. One of the main properties of the proposed GVCPR is its ultra low power consumption; however, a single active component matching condition is needed. A number of SPICE simulation results using IBM 0.13 μm SIGE013 level-7 CMOS process parameters such as its performance analysis and verification in tunable voltage-mode first-order all-pass filter and high-Q & high-gain voltage-mode multiple-feedback second-order band-pass filter are included to confirm the theory. The superior performance of the proposed GVCPR is also proven by numeric Figure of Merit calculation. DOI: http://dx.doi.org/10.5755/j01.eee.20.7.8023


I. INTRODUCTION
Electronically tunable resistors are widely used in analog signal processing.The application of tunable resistors can be found in telecommunications, electronics and measurements such as active RC filters with variable cut-off frequencies, controlled oscillators, variable gain amplifiers, voltage or current dividers, and voltage or current to frequency converters.In VLSI technology, a resistor can be achieved in silicon technology by using poly silicon of diffusion areas [1].However, resistors of practical values on silicon wafer suffer from limited values and high variability due to process variations.Moreover, its resistance values are not variable, and therefore, they are generally replaced by active resistors [2].Our detailed literature survey given in Table I shows that during the last three decades several grounded voltage or current controlled positive resistor realizations were reported that in standard CMOS technology can be electronically controlled externally via control voltage(s) [3]- [9].As a main disadvantage of these realizations is high power dissipation.The configurations in [10] and [11] employ respectively four and two bipolar junction transistors (BJTs).However, in practice the BJT-based circuits are less preferred due to their temperature dependence.In [12], the controlled grounded resistor is made up of a junction gate field-effect transistor (JFET) and an active building blocks such as voltage buffer (VB) and second/generation current conveyor (CCII).
In this work, a new CMOS based grounded voltage controlled positive resistor (GVCPR) with one control voltage is proposed.The proposed GVCPR employs only five CMOS transistors, one operated in triode region and others operated in saturation region or OFF.The circuit is supplied by voltages equal to the threshold voltages of the used IBM 0.13 μm SIGE013 level-7 CMOS technology.Hence, one of the main advantages of the proposed GVCPR is its ultra low power consumption.However, the proposed GVCPR needs a single active component matching condition.A number of SPICE simulation results and numerical Figure of Merit calculation are included to confirm the theory and superior performance of the proposed GVCPR.

II. PROPOSED GROUNDED VOLTAGE CONTROLLED POSITIVE RESISTOR
Symbol of the proposed CMOS based GVCPR is given in Fig. 1 where -VTP and -VTN are positive and negative power supply voltages, respectively.Also, Vc is control voltage of the proposed CMOS based GVCPR.Apart from these, VTP and VTN are respectively threshold voltages of PMOS and NMOS transistors [13].From Fig. 1, impedance of the proposed GVCPR is defined as follows ( ).
In fact, the equivalent input resistance of the GVCPR is a function of the control voltage Vc.The proposed CMOS GVCPR is depicted in Fig. 2. The transistor M2 is operated in linear region (VGS2 -VTN2 > VDS2 = │Vin│), which has the following drain current, iD2, for all where kN2 is the transconductance parameter of the M2 transistor and VTN2 is the threshold voltage with body effect [13].For the proposed GVCPR in Fig. 2, it is assumed that all the transconductance parameters are equal.In other words, kP1 = kN2 = kN3 = kN4 = kN5 = k.Routine analysis of the proposed GVCPR in Fig. 2, the following input current is found For Vin > 0, M2 and M3 are ON while M1, M4 and M5 are OFF thus the following drain currents are obtained After combining equations from ( 3) to ( 7), the following input resistance is evaluated It is important to note that one should select Vc > VTN2 in addition to VGS2 -VTN2 > │Vin│ for proper operation of the proposed GVCPR.

III. SIMULATION RESULTS
To verify the theoretical study, the behavior of the proposed GVCPR shown in Fig. 2 has been verified by SPICE simulations.In the design, transistors are modeled by the IBM 0.13 μm SIGE013 level-7 CMOS process parameters (VTN = 0.0408721 V, N = 451.7567843cm 2 /(Vs), VTP = 0.2178731V, P = 100 cm 2 /(Vs), TOX = 3.2 nm) [14].The aspect ratios of all the NMOS (M2-M5) and PMOS (M1) transistors in Fig. 2 are chosen as 6.5 m/1.04 m and 19.5 m/1.04 m, respectively.In the GVCPR, a DC voltage equal to Vb = -0.75V is connected to the bulk of the transistor M2, while the bulk of other transistors are connected to their corresponding sources to prevent body effect.The -0.75 V voltage is standard voltage (VSS) of the used IBM 0.13 μm SIGE013 CMOS technology and can be easily found in a system that is realized with technology.First of all, the performance of the GVCPR was tested by DC analysis.The I -V characteristics are shown in Fig. 3, that were performed by applying input currents to resistor and obtaining the corresponding voltages on the same terminal.The proposed circuit was varied by control voltage values Vc = {0.5;0.525; 0.564; 0.63; 0.78; 1.27} V and it behaves as a resistor with equivalent values of Req between 1.75 k to 500  by 250  decrement.Similarly, the value of Req versus control voltage Vc is depicted in Fig. 4. It can be again seen that the obtained resistance changes from 1.75 k to 500  by varying Vc from 0.5 V to 1.3 V by 10 mV increment.In Fig. 7, distortion characteristics of the GVCPR for Vc = {0.63;0.78; 1.27} V (Req  1 k, 750 , 500 ) are depicted, where sinusoidal input currents with f = 100 MHz and different magnitudes are applied to the circuit separately to find out total harmonic distortion (THD) of the corresponding voltages on the same terminal.For Req  1 k it can be seen that an input with amplitude of 50 A yields THD value of 3.87%.The power consumption versus applied various control voltages for the proposed GVCPR is shown in Fig. 10, where the Vc is increased from 0.5 V to 1.3 V by 10 mV step size.From the simulation results, it can be seen that the proposed resistor consumes ultralow power (around 176 nW) and the results are in good agreement with the theory.

IV. APPLICATION EXAMPLES
In this section, the performance of the proposed GVCPR in Fig. 2 is tested in more complex circuits such as in tunable voltage-mode (VM) first-order all-pass filter (APF) and high-Q and high-gain VM multiple-feedback (MFB) secondorder band-pass (BP) filter.

A. Tunable VM First-Order All-Pass Filter
First of all, to demonstrate the usefulness of the proposed GVCPR, it was used in VM first-order APF, which is shown in Fig. 11 [15].An APF (phase shifter) is a useful analog signal processing unit, which finds wide application areas in control or measurement systems in order to shift phases of the signals while keeping their amplitudes unchanged.Assuming R1 = R2, routine analysis yields the following voltage transfer function (TF) for the circuit in Fig. 11   and phase response from TF ( 9) is given as The pole frequency of the VM first-order APF is calculated as Hence, the proposed GVCPR can be with advantage used for tuning the f0 of the filter via control voltage Vc.
In order to confirm the performance of the proposed GVCPR, the behavior of the VM first-order APF shown in Fig. 11 has also been verified using SPICE software.In simulations the passive element values were chosen as R1 = R2 = 1 kΩ, C = 53 pF, and the ADA4899-1 [16] ultralow noise and distortion unity-gain stable high speed voltage feedback op amp was used with DC power supply voltages equal to ±5 V. Fig. 12 shows the ideal and simulated gain and phase responses illustrating the electronic tunability of the filter example.The pole frequency is varied for f0  {1.9; 3; 4; 5.8} MHz via control voltage Vc = {0.5;0.63; 0.78; 1.27} V of the proposed GVCPR, respectively.Similarly, possibility of tuning the pole frequency f0 via Vc is shown in Fig. 13, where the control voltage was increase from 0.5 V to 1.27 V by 10 mV step size.Finally, to illustrate the time-domain performance, transient analysis was performed to evaluate the voltage swing capability and phase errors of the filter as it is demonstrated in Fig. 14.A sine-wave input of 100 mV amplitude and frequency of 3 MHz was applied to the filter while keeping the passive element values as listed above and setting Vc = 0.63 V (Req  1 kΩ).Note that the output waveform is in 90 degree phase shift with the input one.The total harmonic distortion (THD) at this frequency is found as 3.48 %.

B. High-Q and High-Gain VM MFB Second-Order Band-Pass Filter
As a second test, the proposed GVCPR is used in high-Q and high-gain VM infinite-gain MFB second-order BP filter, which is given in Fig. 15 [12].Routine circuit analysis yields the following VM TF for the circuit where Rp = R1 Req.
The natural angular frequency 0, quality factor Q, and centre frequency gain H0 can be derived from (12) as follows: In SPICE simulations again the ADA4899-1 [16] ultralow noise and distortion unity-gain stable high speed voltage feedback op amp was used with DC power supply voltages equal to ±5 V and passive component values were chosen as C1 = C2 = 20 pF, R1 = 1 kΩ, and R2 = 120 kΩ.
To demonstrate the utility of the proposed GVCPR, its value in the filter given in Fig. 15 was changed via control voltage Vc = {0.5;0.63; 0.78; 1.27} V and magnitude responses are depicted in Fig. 16.It can be seen that as Vc increases (Req decreases), 0 and Q increase, which is consistent with the expected theory.
where the related values were taken from Table I and the results are depicted in Fig. 17.Note that due to limited information in some of the listed references the FoM is calculated and compared only for GVCPRs in [4] and [7]- [9].Here it is worth noting that for the proposed GVCPR the highest value of FoM denotes superior circuit performance.

VI. CONCLUSIONS
In this study, a new CMOS based GVCPR with one control voltage is proposed.The proposed GVCPR employs only five CMOS transistors, one operated in triode region and others operated in saturation region or OFF.One of the main properties of the proposed GVCPR is its ultra low power dissipation.Nevertheless, the proposed GVCPR requires a single active component matching constraint.A number of SPICE simulation results verify the claimed theory well as expected.

Fig. 1 .
Fig. 1.Symbol of the proposed grounded voltage controlled positive resistor.

For
Vin < 0, M3 is OFF while M1, M2, M4 and M5 are ON thus the following drain currents are obtained 3

Fig. 3 .
Fig. 3.I -V characteristics of the proposed GVCPR for different values of control voltage Vc.

Fig. 4 .
Fig. 4. Controllability of the Req with respect to the control voltage Vc.

Figure 5 Fig. 5 .FrequencyFig. 6 .
Figure 5 illustrates the time-domain performance of the GVCPR with value equal to Req  1 k (Vc = 0.63 V), in which transient analysis was applied from 100 ns to 200 ns by 50 ps step sizes for sinusoidal input currents at f = 100 MHz and three different magnitudes Iin = {15; 30; 45} μA.Fast Fourier Transform (FFT) characteristics of the

Fig. 7 .
Fig. 7. Distortion characteristics of the proposed GVCPR for three different values of Req against applied input currents at f = 100 MHz.

Fig. 8 .Fig. 9 .
Fig. 9. Output voltage noise variation of the proposed GVCPR for three different values of Req versus frequency.

Fig. 10 .
Fig. 10.Total power dissipation of the proposed GVCPR versus control voltage Vc.

FrequencyFig. 12 .Fig. 13 .
Fig. 12. Electronical tunability of the pole frequency of the VM first-order all-pass filter by the proposed GVCPR.

Fig. 14 .
Fig. 14.Time-domain responses of the VM first-order all-pass filter at 3 MHz.

FoM (A/m 2 )
Fig. 17.Performance comparison of grounded voltage controlled positive resistors listed in TableI.

TABLE I .
COMPARISON OF PREVIOUSLY PUBLISHED GROUNDED VOLTAGE OR CURRENT CONTROLLED POSITIVE RESISTORS.