Research ArticleA Controllable Constant Power Generator in 0.35μm CMOSTechnology for Thermal-Based Sensor Applications

Milena Zogović Erceg

Faculty of Electrical Engineering, University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Montenegro

Correspondence should be addressed to Milena Zogović Erceg; milena.zogovic@gmail.com

Received 1 September 2017; Revised 26 November 2017; Accepted 6 December 2017; Published 4 March 2018

Academic Editor: Belén Calvo

Copyright © 2018 Milena Zogović Erceg. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

A CMOS controllable constant power generator based on multiplier/divider circuit is presented. It generates constant power for awide range of the resistive loads. For the generated power of 5mW, and the resistance range from 0.5 kΩ to 1.5 kΩ, the relative errorof dissipated power is less than 0.6%. For single supply voltage of 5V, presented controllable constant power generator generatespower from 0.5mW to 7.8mW, for the load resistance dynamic range from 3 up to 15, while the relative error of generated power isless than 2%. The frequency bandwidth of the proposed design is up to 5MHz. Through the detailed analysis of the loop gain, it isshown that the circuit has no stability problems.

1. Introduction

The circuit which generates constant power for variable resis-tive loads finds application in various types of thermal-basedsensors, such as mass flow meters, anemometers [1], ACpower meters, gas monitoring [2, 3], plant water status mon-itoring [4], seepage meters [5], and other flowmetersintended for very slow fluids. Thermal-based flow sensorsare very attractive because of their simple construction. Theybasically consist of constant power generator and sensing ele-ment. The surrounding fluid transfers heat to/from sensingelement depending on its flow rate. As the temperature ofthe sensing element is changed, its resistance is changed,and the constant power generator changes the voltage dropacross the sensing element to keep constant power. Measur-ing the voltage change across the sensing element, it is possi-ble to extract the information about the fluid flow rate. So, thequality of the constant power generator as a part of thethermal-based sensor is very important. Controllable con-stant power generator is the circuit which generates constantpower dissipation over a range of resistive loads. The controlof the generated power is provided by control voltage or con-trol current. The range of resistive loads has to be as large aspossible for the particular generated power. In that sense, the

quality of constant power generators is determined by theload resistance dynamic range, defined as the ratio of thelargest load resistance to the smallest load resistance(RLmax/RLmin), for the particular value of dissipated power.The other important characteristic of the constant powergenerator is the value of generated power for a given loadresistance, depending on specific application. The relativeerror of generated power over the range of load resistance isthe key quality parameter of the constant power generator.Low-supply voltage of constant power generator is criticalfor many applications as a consequence of the general trendin electronics. The ratio of the largest voltage drop acrossthe resistive load and supply voltage (VLmax/VDD) can beused as a quality indicator of constant power generators.One of the main problems in constant power generatordesign is its stability caused by feedback loops.

There are several designs of constant power generators,developed mostly in BiCMOS and bipolar technologies. ACMOS controllable constant power generator based on theresistive mirror [1] has the range of generated power from0.48mW to 10.8mW, and the load resistance dynamic rangeup to 28, with the relative error of generated power less than2.2% and the supply voltage of 10V. The constant power gen-erator presented in [1] uses four operational amplifiers OP97

HindawiJournal of SensorsVolume 2018, Article ID 3747325, 12 pageshttps://doi.org/10.1155/2018/3747325

which are designed in a complementary bipolar technology,while the rest of the circuit is realized using n-channel MOS-FETs. Hence, the circuit [1] can be considered as a BiCMOStechnology design. The controllable constant power genera-tor [3], based on CMOS translinear loop, has a load resis-tance range from 470Ω to 1.47 kΩ and is able to generatepower up to 11mW, with the supply voltage of ±5V andthe relative error of generated power up to 3%. The circuitpresented in [3] uses off-chip operational amplifier LM301designed in a complementary bipolar technology, while therest of the circuit is realized in a CMOS technology. Hence,the circuit [3] can be considered as a BiCMOS technologydesign. Controllable constant power generator [4–6] canchange the dissipated power by a factor of 1 : 1000, usingthe log-antilog circuit with bipolar junction transistors.This controllable constant power generator uses eightOPA4227 operational amplifiers designed in a complemen-tary bipolar technology. Consequently, the circuit [4–6] canbe considered as a bipolar technology design. The control-lable constant power generator [7] in BiCMOS technologyachieves load resistance range of 1 : 50, with generatedpower up to 100mW. The microcontroller-based solution[9] can achieve large resistance dynamic range and largepower dynamic range, but at the price of reduced frequencybandwidth. The CMOS design proposed in [10] for smallvariations of the resistive load has a large relative error ofthe generated power.

Taking into account that the existing designs of con-trollable constant power generators are designed mostlyin BiCMOS and bipolar technologies and that CMOStechnology is the most popular and the cheapest technol-ogy so far, the goal of this work is the design of fully inte-grated controllable constant power generator in a pureCMOS technology. This paper presents controllable con-stant power generator in 0.35μm CMOS technology basedon current-mode multiplier/divider circuit [8]. The gener-ated power can be adjusted by two control currents whichare the input currents of the multiplier/divider circuit.Through the detailed analysis and simulations, it is shownthat proposed design is able to generate constant powerover a large range of the load resistance. The mathematicalmodel for the loop gain of the controllable constant powergenerator shows that circuit has no stability problems for awide range of resistance for the particular generatedpower. The influence of the process parameter variationsand the temperature variations to the proposed design isalso analyzed.

2. Circuit Description

2.1. Basic Principle. The main purpose of the constant powergenerator is to maintain the constant power dissipationacross the resistive load:

PL = ILVL = const, 1

where PL is the generated power across the resistive load,IL is the current flowing through the resistive load, andVL is the voltage across the resistive load. Generated

power has to be independent of the load resistance. Also,it is desirable to have the possibility to control generatedpower easily.

The basic principle of the controllable constant powergenerator with a novel method for achieving a constantpower dissipated on the resistive load is shown in Figure 1.It consists of multiplier/divider circuit, second generationcurrent conveyor (CCII), load resistor RL, reference resistorRREF, and two DC current sources I1 and I2. The outputcurrent IL of the multiplier/divider circuit is flowing throughthe resistive load RL. The voltage VL across the resistive loadis transferred via CCII to the resistor RREF. So, the outputcurrent I3 of the CCII is given by

I3 =VL

RREF2

On the other hand, the output current of the multiplier/divider circuit is given by

IL =I1I2I3

3

So, the generated power PL can be expressed as

PL = ILVL = RREFI1I2 = const 4

The generated power is independent of the load resis-tance RL and can easily be adjusted by changing control cur-rents I1 and/or I2.

2.2. Complete Circuit Schematic. The multiplier/divider cir-cuit [8] is shown in Figure 2. It is based on the CMOS trans-linear principle. The circuit can be divided into two parts.The first part gives the current which is proportional to thesquare root of the product of two input currents (geometricmean) at its output. The second stage performs squarer/divider operation. The MOSFETs M1, M2, M3, M4, M1a,M2a, M3a, and M4a have long enough channels of 3μm, sothe channel length modulation effect can be neglected inthe analysis. Assuming a good enough matching of MOS-FETs forming the translinear loops (Vt1 =Vt2 =Vt3 =Vt4,Vt1a=Vt2a=Vt3a=Vt4a, β1 =β2 =β3 =β4, and β1a=β2a=β3a=β4a) and a simple quadratic model for the drain currentof the MOSFET operated in the saturated region, it can beshown [8] that the output current IL of the multiplier/dividercircuit is given by

IL =I1I2I3

5

The second-order effects of the multiplier/divider cir-cuits, such as channel length modulation effect and thethreshold voltage mismatching effect, are analyzed in [8]. Itis stated that the channel length modulation effect can beneglected for the long channel MOSFETs. On the other hand,the threshold voltage mismatching effect could affect theperformances of the multiplier or divider circuit, assuming

2 Journal of Sensors

that the multiplier and divider are analyzed separately. Onthe other hand, if the multiplier and divider are used simulta-neously within the multiplier/divider circuit, the thresholdvoltage mismatching effect is compensated [8]. The bodyeffect of the n-channel MOSFETs in a real n-well CMOSimplementation can be solved using n-channel MOSFETswith their own p-wells assuming a twin well technology.

The complete circuit schematic of the proposed control-lable constant power generator with a novel method forachieving a constant power dissipated on the resistive loadis shown in Figure 3. The output current of the multiplier/divider circuit is flowing through the resistive load RL. Thecurrent I3 is obtained as the output current of the CCII.The voltage VL across the resistive load RL is transferredvia input stage of the CCII, so the current at terminal Xof this CCII is VL/RREF. The differential input stage of theCCII is formed by the MOSFETs M12 and M13, with theactive cascoded load (MOSFETs M14, M15, M16, and M17).

The differential input stage is biased by MOSFET M11and biasing voltage VB3. The output current is transferredby the two output cascoded current mirror (MOSFETsM18, M19, M20, M21, M22, and M23). So, the current at theoutput of the CCII is I3 =VL/RREF. To change the directionof the current I3, the wide-swing current mirror is used.This current mirror consists of MOSFETs M24, M25, M26,and M27 and biasing voltage VB4. The current IL flowingthrough the resistive load RL is mirrored by the currentmirror formed by the MOSFETs M6a, M8a, M9, and M10.The current mirror formed by the MOSFETs M28, M29,M30, and M31 is used to sum currents I3 and IL and todivide the sum of the currents by four. In that aim, thechannel widths of the MOSFETs M28 and M30 are four timeslarger than the channel widths of the MOSFETs M29 andM31. The direction of the resulting current is changed usingthe cascoded current mirror formed by MOSFETs M32, M33,M34, and M35.

I1I2/I3

VDD

I1

I2 I3

IL

RL

RREF

Y

X

ZCCII

Figure 1: The principle of operation of the proposed controllable constant power generator.

VDD

VB1VB2

I2

I1

IL

I3

M2

M1 M3

M4 M4a

M3a

M2a

M7a M8a

M5a M6a

M1a

M7

M5

M8

M6

(I1+I2)/4 (I3+IL)/4

Figure 2: Multiplier/divider circuit schematic [8].

3Journal of Sensors

DC current source I1 (I2) is realized by using CCII. Its dif-ferential input stage is formed by the MOSFETs M37 and M38(M50 and M51), with the active cascoded load MOSFETs M39,M40, M41, andM42 (M52, M53, M54, andM55). The differentialinput stage is biased byMOSFETM36 (M49) and biasing volt-age VB3. The current at terminal X of this CCII is VC1/R1(VC2/R2), and it is multiplied by the factor of eight by thetwo output cascoded current mirror MOSFETs M43, M44,M45, M46, M47, and M48 (M56, M57, M58, M59, M60, andM61). So, the output current of this current source isI1 = 8VC1/R1 (I2 = 8VC2/R2). To change the direction of thecurrent I2, the wide-swing current mirror is used. This cur-rent mirror consists of MOSFETs M62, M63, M64, and M65and biasing voltage VB4. The current mirror formed byMOS-FETs M66, M67, M68, and M69 is used to sum currents I1 andI2 and to divide the sum of the currents by four. In that aim,the channel widths of the MOSFETs M66 and M68 are fourtimes larger than the channel widths of the MOSFETs M67and M69. The direction of the resulting current is changedusing cascoded current mirror formed by MOSFETs M70,M71, M72, and M73.

The generated power of the proposed controllable con-stant power generator is given by

PL = 64VC1R1

VC2R2

RREF 6

3. Stability Analysis

Controllable constant power generators usually suffer fromstability problems [1, 3]. The range of resistive loads and

the range of generated power are often reduced as a conse-quence of this problem [1, 3]. The stability analysis of theproposed controllable constant power generator is per-formed through the derivation of the loop gain Aβ(s). Inthe small-signal analysis, the CCII, whose voltage input Yis connected to the active terminal of the resistive load(the output of the multiplier/divider circuit), is modelledas shown in Figure 4 [11, 12]. Capacitance CX is the inputcapacitance at terminal X of the CCII, resistance RX is theinput resistance at terminal X of the CCII, capacitance CYis the input capacitance at terminal Y of the CCII, capaci-tance CZ1 is the output capacitance at terminal Z1 of theCCII, resistance RZ1 is the output resistance at terminal Z1of the CCII, capacitance CZ2 is the output capacitance at ter-minal Z2 of the CCII, and resistance RZ2 is the output resis-tance at terminal Z2 of the CCII. The terminal X of the CCIIis connected to the active terminal of the resistor RREF. Theterminal Y of the CCII is connected to the active terminal ofthe resistive load RL. The terminal Z1 of the CCII is con-nected to the source of the MOSFET M2a, and the terminalZ2 of the CCII is connected to the drain of the MOSFETM9. Current mirrors within multiplier/divider circuit aremodelled as simple ones.

The loop gain Aβ(s) of the proposed controllable con-stant power generator is given by

Aβ s ≈gm1aRL

gm2a RX + RREF

gm4ag2m28 + gm2ag

2m34

gm4ag2m28 + gm1ag

2m34

∏2i=1 1 + s/ωZi

∏3i=1 1 + s/ωpi

,

7

M7 M8

Multiplier/divider circuit CCII

M5

M2 M4

M3

M72

M70

M73

M71

M68 M69M31

M29

M30M37

VC1VC2

VB3 VB3

M38 I1

M36M28M66 M67

M35

M33

M34 M41 M42M46 M47 M48 M54 M55 M59 M60

DC current source I2DC current source I1

M61

M58M57M56M53M52

M50 M51 M64 M65

M63VB4M62M49

M45M44M43M40

M39M32

M1

M6

VB1

M4a M2a

M1a

M7a M8a M10 M16 M17

M15

M13M12

M11

Y X

M18

M21 M22

M19

M26

M24RREF

M27

M25

I3

R2R1

I2

IL RL VB4VB3

VB2

M23VDD

M20M14M9M6aM5a

M3a

Figure 3: Complete circuit schematic of the proposed controllable constant power generator.

4 Journal of Sensors

where the zeroes ωzi and the poles ωpi are

where gm1a, gm2a, gm3a, gm4a, gm28, and gm34 are the trans-conductances of the saturated MOSFETs M1a, M2a, M3a,M4a, M28a, and M34a, respectively, C1 is the parasitic capaci-tance at the drain of the MOSFET M4a, C2 is the parasiticcapacitance at the gate of the MOSFET M1a, C3 is the para-sitic capacitance at the drain of the MOSFET M6a, and C4 isthe parasitic capacitance at the drain of the MOSFET M9. Itis calculated that the DC loop gain ranges from|Aβ(s=0)|≈0.01, for the lower limit of the resistive loads,to |Aβ(s=0)|≈0.3, for the upper limit of the resistive loads,for appropriate generated powers. The parasitic capacitancesC1, C2, C3, and C4 are in the order of 1 pF, while the parasiticcapacitances CX, CY, CZ1, and CZ2 are in the order of 100 fF.The transconductances of saturated MOSFETs are calcu-lated as gmi = (2βiIDi)

1/2.

The absolute value of the loop gain frequency character-istic |Aβ(jω)|, for the lower limit of the resistive loads and forthe appropriate generated powers, is shown in Figure 5. Thefrequency of the first zero ωz1 is about 150MHz, the fre-quency of the next pole ωp2 is about 200MHz, the frequencyof the next pole ωp1 is between 300MHz and 400MHz, thefrequency of the next pole ωp3 is in the order of 10GHz,and the frequency of the last zero ωz2 is in the order of

100GHz. The absolute value of the loop gain frequency char-acteristic |Aβ(jω)|, for the upper limit of the resistive loadsand for the appropriate generated powers, is shown inFigure 6. The frequency of the first pole ωp1 is between30MHz and 130MHz, the frequency of the next zero ωz1 isabout 150MHz, the frequency of the next pole ωp2 is about250MHz, the frequency of the next pole ωp3 is in the orderof 10GHz, and the frequency of the last zero ωz2 is in theorder of 100GHz. As the absolute value of the loop gain fre-quency characteristic |Aβ(jω)| never reaches the value of0 dB, the system is stable.

4. Simulated Results

The circuit is designed and simulated using PSpice withBSIM3 version 3.1 transistor model for TSMC 0.35 μm n-well CMOS process obtained by MOSIS. The circuit is singlesupplied by VDD=5V. Biasing voltages have the followingvalues: VB1 = 3V, VB2 = 3.1V, VB3 = 0.8V, and VB4 = 1.9V.Resistances have the following values: R1 = 8 kΩ, R2 = 8 kΩ,and RREF = 1.25 kΩ.

The current IL flowing through the resistive load as afunction of the voltage VL across the resistive load, for the

ωZ1 =1

RREFCX, 8

ωZ2 =gm4a CZ2 + C4 + gm28 + 1/RZ2 C1

C1 CZ2 + C4, 9

ωp1 =1

RL CY + C3, 10

ωp2 =1

RXRREF/ RX + RREF CX, 11

ωp3 =gm28 gm28 + 1/RZ2 gm2a + 1/RZ1 C1 + gm28gm4a gm28 + 1/RZ2 CZ1 + C2 + gm28gm4a gm2a + 1/RZ1 CZ2 + C4

gm28 gm28 + 1/RZ2 CZ1 + C2 C1 + gm4agm28 CZ1 + C2 CZ2 + C4 + gm28 gm2a + 1/RZ1 CZ2 + C4 C1, 12

Y Y′

CCII(ideal)

CCII (real)

CY

CX

RXX X′

Z1′

RZ1 CZ1

RZ2 CZ2

Z1

Z2Z2′

Figure 4: Small-signal model of the second generation current conveyor [11, 12].

5Journal of Sensors

generated power PL=5mW, is shown in Figure 7. The resis-tance RL is changed from 400Ω to 2.2 kΩ. Larger values ofthe voltage across the resistive load (corresponding to largerresistive load) are out of the input voltage range of the CCII,whose input is connected to the active terminal of the resis-tive load, for a given supply voltage. For larger values of thecurrent flowing through the resistive load (corresponding tosmaller resistive load), the multiplier/divider circuit showslarger errors caused by the channel length modulation ofthe MOSFET M1a. The current IL flowing through the resis-tive load increases rapidly with the decrease of the resistiveload RL due to square-hyperbolic dependence between them,IL=√PL/√RL. The source-to-gate voltage VSG7a of the MOS-FET M7a also increases rapidly, and the drain-to-source volt-age VDS1a of the MOSFET M1a decreases rapidly.

Generated power PL of 5mW of the proposed controlla-ble constant power generator for variable load resistances500Ω<RL< 1.5 kΩ is shown in Figure 8. Relative error ofgenerated power is −0.6%<EL< 0.1%. The generated poweris calculated (6), and the system is calibrated for the loadresistance of 1 kΩ.

Generated powers PL= {0.5mW, 1mW} of the proposedcontrollable constant power generator for variable load

resistances 1 kΩ<RL< 15 kΩ are shown inFigure 9.Generatedpowers PL= {2mW, 3mW, 4mW, 5mW, 6mW, 7mW,8mW, 9mW} of the proposed controllable constant powergenerator for variable load resistances 400Ω<RL< 5.5 kΩare shown in Figure 10. Table 1 shows summarized results

|A𝛽(j𝜔)| (dB)

0𝜔z1 𝜔p2 𝜔p1 𝜔p3 𝜔z2

𝜔, log (rad.s−1)

Figure 5: The absolute value of the loop gain frequency characteristic of the proposed controllable constant power generator, for the lowerlimit of the resistive loads and for the appropriate generated powers.

|A𝛽(j𝜔)| (dB)

0𝜔p1 𝜔z1 𝜔p2 𝜔p3 𝜔z2

𝜔, log (rad.s−1)

Figure 6: The absolute value of the loop gain frequency characteristic of the proposed controllable constant power generator, for the upperlimit of the resistive loads and for the appropriate generated powers.

V2 (RL)1.2 V 1.6 V 2.0 V 2.4 V 2.8 V 3.2 V 3.6 V

−I (RL)

1.0 mA

2.0 mA

3.0 mA

4.0 mA

Figure 7: Current IL flowing through the resistive load versusvoltage VL across the resistive load of the proposed controllableconstant power generator, for generated power PL= 5mW. Thecurrent −I(RL) is, in fact, the current IL. The voltage V2(RL) is thevoltage VL.

6 Journal of Sensors

of the proposed controllable constant power generator. Therange of resistive load RL, for different values of dissipatedpower PL, as well as the values of corresponding control volt-ages VC1 and VC2 is shown. The main demand was that therelative error of generated power is |EL|< 2%. For smallergenerated power 0.5mW≤PL≤ 4mW, the load resistancedynamic range is larger. It ranges from 15 (1 kΩ≤RL≤ 15 kΩ,for PL=0.5mW) to 7 (0.4 kΩ≤RL≤ 2.8 kΩ, for PL=4mW).

For larger generated power 5mW≤PL≤ 9mW, the load resis-tance dynamic range is smaller. It ranges from 5.5 (0.4 kΩ≤RL≤ 2.2 kΩ, for PL=5mW) to 2.4 (0.5 kΩ≤RL≤ 1.2 kΩ, forPL=9mW).

For smaller generated powers, the minimal value of theload resistance is limited by the input voltage offset of theCCII whose input is connected to the active terminal of theresistive load. That offset voltage is not constant over the allinput voltage range of the current conveyor. Small absolutechange of the offset voltage produces large enough relativechange of the current I3 that leads to the larger relative errorof the generated power.

The main limitation for load resistance dynamic range,for all generated powers, is the supply voltage that directlyaffects the input voltage range of the CCII whose input isconnected to the active terminal of the resistive load andthe output current range of the multiplier/divider circuit.With larger supply voltage, it also would be possible togenerate larger powers, as well as the larger range of gener-ated powers.

In order to prove that the proposed controllable constantpower generator is not particularly influenced by the processparameter variations, Monte Carlo simulations have beenperformed. The following process parameters have beenchanged within Monte Carlo simulations: carrier mobility,threshold voltage (for the source-to-bulk voltage VSB=0),body effect coefficient, and channel length modulation coeffi-cient of all MOSFETs, as well as the resistances R1, R2, andRREF. These values have been changed for 10% related tothe nominal values for 100 runs. The nominal value of thegenerated power of PL=5mW is changed with processparameter variations from 4.5mW to 5.6mW for the loadresistance 500Ω<RL< 1.5 kΩ. By analyzing the individualinfluence of a certain process parameter variations, it canbe shown that the change of the generated power is domi-nantly caused by the variations of the resistances R1, R2,and RREF. Although there is a change in the value of the gen-erated power, it is important to stress that the relative error ofthe generated power is not affected by the process parametervariations. The absolute values of these relative errors rangefrom 0.02% to 2.65% only. These relative errors are calculated

RLvar0.6 K 0.8 K 1.0 K 1.2 K 1.4 K0.5 K 1.5 K

−V2 (RL)⁎I (RL)

4.96 mW

4.98 mW

5.00 mW

5.02 mW

Figure 8: Generated power PL versus load resistance RL of theproposed controllable constant power generator, for controlvoltages VC1 = 1.5V and VC2 = 2.67 V. The current −I(RL) is, infact, the current IL. The voltage V2(RL) is the voltage VL.

RLvar2 K 4 K 6 K 8 K 10 K 12 K 14 K1 K 15 K

−V2 (RL)⁎I (RL)

0 W

0.5 mW

1.0 mW

1.3 mW

Figure 9: Generated powers PL= {0.5mW, 1mW} versus loadresistance RL of the proposed controllable constant powergenerator. The current −I(RL) is, in fact, the current IL. The voltageV2(RL) is the voltage VL.

RLvar1.0 K 2.0 K 3.0 K 4.0 K 5.0 K0.4 K 5.5 K

−V2 (RL)⁎I (RL)

0 W

4 mW

8 mW

12 mW

Figure 10: Generated powers PL= {2mW, 3mW, 4mW, 5mW,6mW, 7mW, 8mW, 9mW} versus load resistance RL of theproposed controllable constant power generator. The current−I(RL) is, in fact, the current IL. The voltage V2(RL) is the voltage VL.

Table 1: Values of generated power PL, resistive load RL, controlvoltages VC1 and VC2, for relative error of generated power|ER|< 2%.

PL [mW] RL [kΩ] VC1 [V] VC2 [V]

0.5 1 <RL< 15 0.67 0.6

1 1 <RL< 10 1.33 0.6

2 0.5 <RL< 5.5 0.6 2.67

3 0.4 <RL< 3.7 0.9 2.67

4 0.4 <RL< 2.8 1.2 2.67

5 0.4 <RL< 2.2 1.5 2.67

6 0.4 <RL< 1.8 1.8 2.67

7 0.4 <RL< 1.6 2.1 2.67

8 0.4 <RL< 1.4 2.4 2.67

9 0.5 <RL< 1.2 2.7 2.67

7Journal of Sensors

related to the power generated for the load resistanceRL=1kΩ for each corresponding run. Distribution of theserelative errors in the form of a histogram is shown inFigure 11. The absolute value of the relative error is less than0.5% in 28% runs, less than 1% in 73% runs, and less than1.5% in 95% runs.

In order to investigate the temperature influence to theproposed design, the generated power PL=5mW of the con-trollable constant power generator for variable load resis-tance 0.5 kΩ<RL< 1.5 kΩ with the temperature used as aparameter T∈{−20°C, −10°C, 0°C, 10°C, 20°C, 30°C, 40°C,50°C, 60°C, 70°C, 80°C} has been simulated. Two types ofthe simulations have been performed. In the first one shownin Figure 12, the resistances R1, R2, and RREF are constant,that is, temperature independent. In the second type shownin Figure 13, the temperature influence to the resistancesR1, R2, and RREF is modeled by using the linear temperaturecoefficient α=− 3×10−3/K. This is the typical value of the lin-ear temperature coefficient of the resistor made by using ahigh resistivity poly in a standard 0.35 μm CMOS technol-ogy. The relative error is calculated related to the powergenerated for the load resistance RL=1kΩ at T=27°C. Forthe temperature-independent resistance R1, R2, and RREF(Figure 12), the absolute value of the relative error is up to8%. On the other hand, for the temperature-dependent resis-tances R1, R2, and RREF (Figure 13), the absolute value of therelative error ranges is up to 12%. It is clear that the proposedcontrollable constant power generator is dominantly influ-enced by the temperature variations of the resistances R1,R2, and RREF compared to the influence of the temperaturevariations of the active components. In order to reduce thetemperature influence to the proposed design, according tothe relation (6), either the resistors RREF and R1, or RREFand R2 have to be of the same type, while either the resistorR2 or the resistor R1 has to be designed with predeterminedtemperature coefficient (e.g., zero temperature coefficient).To that aim, either the resistor R2 or the resistor R1 can bedesigned as a composite one [13–15] with predetermined(zero) temperature coefficient. With this composite resistor,it can be expected that the overall temperature influence tothe proposed controllable constant power generator will be

similar to that shown in Figure 12 or even smaller. For thespecific application of the proposed design in the plant tissuehumidity measurements in the open arable field, the temper-ature range of interest is from 0°C to 50°C. In that case, theabsolute value of the relative error is up to 3.5% for thetemperature-independent resistances R1, R2, and RREF andup to 8% for the temperature-dependent resistances R1, R2,and RREF.

Simulations of the frequency response of the CCIIM11-M23 (Figure 3) are shown in Figures 14 and 15. TheDC biasing voltage at the terminal Y of the CCII is used asa parameter and is changed from 0.7V to 3.28V with a stepof 0.43V. This DC biasing voltage corresponds to the DCvoltage VL across the resistive load RL for the generated pow-ers 0.5mW<PL< 9mW and corresponding load resistancerange. The load at the terminal Z is presented by the wide-swing current mirror M24-M27, with the drain of the MOS-FET M27 connected to the supply voltage source VDD. TheCCII has been optimized to achieve the gain-peaking lessthan 3 dB in the frequency responses for all ranges of theDC biasing voltage at the terminal Y of the CCII. The fre-quency voltage transfer characteristic vx/vy is shown inFigure 14. The bandwidth ranges from 39MHz (VY=0.7V,PL=0.5mW) to 125MHz (VY=3.28V, PL=9mW). Thefrequency transconductance transfer characteristic iz/vy isshown in Figure 15. The bandwidth ranges from39MHz (VY=0.7V, PL=0.5mW) to 137MHz (VY=3.28V,PL=9mW).

In order to prove that the proposed controllable constantpower generator is stable, simulations of the transientresponse to a step change of the load resistance RL have beenperformed. The voltage-controlled resistor [12, 16] is used asthe resistive load RL in order to simulate the step change ofthe resistance, Figure 16. The voltage follower within thevoltage-controlled resistor is designed similar to that in[12], but with MOSFETs only. The resistors within the resis-tive voltage divider have the same resistances, R3 =R4. Theload resistance is a step changed from RL=0.707 kΩ toRL=1.299 kΩ, as the control voltage is a step changed fromVC=2.5V to VC=1.6V. The rise time and the fall time ofthe load resistance are 28 ns and 19ns, respectively. The volt-age VL across the voltage-controlled resistor (resistive loadRL) is shown in Figure 17. The product of the voltage VLand the current IL of the voltage-controlled resistor is con-stant and equal to PL=VLIL=5mW. It can be seen that thereis no overshoot in the transient responses which confirms theunconditional stability of the proposed design predicted bythe mathematical model expressed by (7), (8), (9), (10),(11), and (12) and Figures 5 and 6. In addition, it can be esti-mated that the largest frequency bandwidth in the consideredexample is up to 5MHz.

5. Discussion and Conclusions

Proposed controllable constant power generator based onmultiplier/divider circuit is designed and simulated in0.35μm CMOS technology. It is possible to generate smallpower from 0.5mW to 1mW for load resistance from2.5 kΩ to 10 kΩ (variation from −50% to 100%, for the load

0.0 0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

20

Num

ber o

f run

s

Absolute value of the relative error ER (%)

Figure 11: Distribution of the absolute value of the relative error ER.

8 Journal of Sensors

RLvar0.6 K 0.8 K 1.0 K 1.2 K 1.4 K0.5 K 1.5 K

T = −20°CT = −10°CT = 0°CT = 10°CT = 20°CT = 30°CT = 40°C

T = 50°C

T = 60°CT = 70°CT = 80°C

... −V2 (RL)⁎I (RL)

4.6 mW

4.8 mW

5.0 mW

5.2 mW

5.4 mW

Figure 12: The generated power PL= 5mW of the proposed controllable constant power generator versus load resistance for temperaturesT∈{−20°C, −10°C, 0°C, 10°C, 20°C, 30°C, 40°C, 50°C, 60°C, 70°C, 80°C}, with temperature-independent resistors. The current −I(RL) is, infact, the current IL. The voltage V2(RL) is the voltage VL.

RLvar0.6 K 0.8 K 1.0 K 1.2 K 1.4 K0.5 K 1.5 K

... −V2 (RL)⁎I (RL)

4.4 mW

4.6 mW

4.8 mW

5.0 mW

5.2 mW

T = 20°C

T = 10°C T = 70°C

T = 80°C

T = −10°C

T = 30°C T = 60°C

T = 40°CT = 50°C

T = 0°C

T = −20°C

Figure 13: The generated power PL= 5mW of the proposed controllable constant power generator versus load resistance for temperaturesT∈{−20°C, −10°C, 0°C, 10°C, 20°C, 30°C, 40°C, 50°C, 60°C, 70°C, 80°C}, with temperature-dependent resistors. The current −I(RL) is, infact, the current IL. The voltage V2(RL) is the voltage VL.

Frequency10 Hz 100 Hz 1.0 KHz 10 KHz 100 KHz 1.0 MHz 10 MHz 100 MHz 1.0 GHz

DB (V(RREF:2))

−40

−20

0

10

Figure 14: The frequency voltage transfer characteristic vx/vy. The voltage V(RREF:2) is, in fact, the voltage vx.

9Journal of Sensors

Frequency10 Hz 100 Hz 1.0 KHz 10 KHz 100 KHz 1.0 MHz 10 MHz 100 MHz 1.0 GHz

DB (ID(M26))

−100

−80

−60

−50

Figure 15: The frequency transconductance transfer characteristic iz/vy. The current ID(M26) is, in fact, the current iz.

VDD

I1

I2 I3

R3

R4VC

1M1VCR

RREF

X

Y

ZCCII

I1I2/I3

Figure 16: The circuit used for simulations of the transient response to a step change of the load resistance RL using voltage-controlled resistor.

Time0 s 100 ns 200 ns 300 ns 400 ns 500 ns 600 ns 700 ns 800 ns

V (M1vcr:d)

1.8 V

2.0 V

2.2 V

2.4 V

2.6 V

Figure 17: The output voltage of the controllable constant power generator for step change of the resistive load from RL= 0.707 kΩ toRL= 1.299 kΩ. The voltage V(M1vcr:d) is, in fact, the output voltage of the controllable constant power generator in this analysis.

10 Journal of Sensors

resistance RL=5kΩ), with the relative error of generatedpower less than 1.2%. These results are shown in Table 2.Also, it is possible to generate larger power from 1mW to7.8mW for load resistance from 0.5 kΩ to 1.5 kΩ (variationof ±50%, for the load resistance RL=1kΩ), with the relativeerror of generated power less than 2%. These results areshown in Table 3. The circuit is optimized for 5V singlesupply. The ratio of the largest voltage drop across the resis-tive load and the supply voltage (VLmax/VDD) is 68%, whichis a better result than 58% in [1], 40.6% in [3], and 44% in[4–6]. The supply voltage and power dissipation of the cir-cuit are limiting factors in many applications, especially inthe open field, powered by the solar cells. For different appli-cations, where power consumption of the circuit is not criti-cal, it would be possible to generate larger power, with widerload resistance dynamic range, with a higher value of thesupply voltage.

Compared to the design presented in [1], proposed con-trollable constant power generator, for the load resistancerange from 500Ω to 1.5 kΩ, has the smaller range of gener-ated power, with the same level of relative error, but withthe 5V single supply, compared to 7V single supply. Thedesign presented in [1] has larger load resistance dynamicrange, but with 10V single supply. Compared to the designpresented in [3], proposed controllable constant power gen-erator, for the load resistance range from 500Ω to 1.5 kΩ,has the smaller range of generated power, but the smaller rel-ative error with the 5V single supply, compared to ±5V sup-ply voltage. The proposed controllable constant powergenerator also has larger load resistance dynamic range forthe particular generated power, compared to the design pre-sented in [3]. The largest relative error of the proposed designis 6 times smaller than in [10] for the same load resistancerange, for the generated power 0.5mW<PL< 12mW. Thefrequency bandwidth of the proposed controllable constantpower generator is approximately 500 times larger thanin [1] and more than 6400 times larger than in [9]. The

performance comparison between the proposed controlla-ble constant power generator and controllable constantpower generators presented in [1, 3], for resistive load0.5 kΩ<RL< 1.5 kΩ is given in Table 4. The proposeddesign has no stability problems for all generated powersover a wide range of the resistive loads. Based on achievedresults, it can be concluded that the controllable constantpower generator can be used in various thermal-based sen-sor applications.

Conflicts of Interest

The author declares that there is no conflict of interestregarding the publication of this paper.

Acknowledgments

This work has been supported by the Ministry of Science ofMontenegro and the HERIC project through the BIO-ICTCentre of Excellence (Contract no. 01-1001).

References

[1] N. Tadić, M. Zogović, and D. Gobović, “A CMOS controllableconstant-power source for variable resistive loads using resis-tive mirror with large load resistance dynamic range,” IEEESensors Journal, vol. 14, no. 6, pp. 1988–1996, 2014.

[2] G. Ferri and V. Stornelli, “A high precision temperaturecontrol system for CMOS integrated wide range resistive gassensors,” Analog Integrated Circuits and Signal Processing,vol. 47, no. 3, pp. 293–301, 2006.

[3] S. S. W. Chan and P. C. H. Chan, “A resistance-variation toler-ant constant-power heating circuit for integrated sensor appli-cations,” IEEE Journal of Solid-State Circuits, vol. 34, no. 4,pp. 432–439, 1999.

[4] A. J. Skinner and M. F. Lambert, “A log-antilog analog controlcircuit for constant-power warm-thermistor sensors-application to plant water status measurement,” IEEE SensorsJournal, vol. 9, no. 9, pp. 1049–1057, 2009.

[5] A. J. Skinner and M. F. Lambert, “Evaluation of a warm-thermistor flow sensor for use in automatic seepage meters,”IEEE Sensors Journal, vol. 9, no. 9, pp. 1058–1067, 2009.

[6] A. J. Skinner, A. K. Wallace, and M. F. Lambert, “A null-buoyancy thermal flow meter with potential application to

Table 2: Values of generated power PL and corresponding relativeerror ER, for resistive load 2.5 kΩ<RL< 10 kΩ.

PL (mW) ER (%)

0.5 −0.8 <RL< 1.21 −0.9 <RL< 0.5

Table 3: Values of generated power PL and corresponding relativeerror ER, for resistive load 500Ω<RL< 1.5 kΩ.

PL (mW) ER (%)

2 −2 <RL< 1.53 −1.95 <RL< 0.64 −1.9 <RL< 0.355 −0.6 <RL< 0.16 −0.1 <RL< 0.37 −0.7 <RL< 0.27.8 −1 <RL< 2

Table 4: Performance comparison between the proposedcontrollable constant power generator and previous controllableconstant power generators.

[1] [3] This work∗

|ER (%)|max 2.2 3 2

PLmin (mW) 0.48 — 2

PLmax (mW) 10.8 11 7.8

RLmin (kΩ) 0.5 0.5 0.5

RLmax (kΩ) 1.5 1.5 1.5

Supply voltage (V) 7 ±5 5

VLmax/VDD (%) 58 40.6 68

f−3 dB (kHz) 10 — 5000∗Simulated.

11Journal of Sensors

the measurement of the hydraulic conductivity of soils,” IEEESensors Journal, vol. 11, no. 1, pp. 71–77, 2011.

[7] http://Maximintegrated.com. February, 2017 https://www.maximintegrated.com/en/app-notes/index.mvp/id/4470.

[8] A. J. Lopez-Martin and A. Carlosena, “Current-mode multi-plier/divider circuit based onMOS translinear principle,”Ana-log Integrated Circuits and Signal Processing, vol. 28, no. 3,pp. 265–278, 2001.

[9] P. Asimakopoulos, G. Kalsas, and A. G. Nassiopoulou, “Amicrocontroller-based interface circuit for data acquisitionand control of a micromechanical thermal flow sensor,” Jour-nal of Physics: Conference Series, vol. 10, no. 10, pp. 301–304,2005.

[10] C. A. Leme, I. Filanovsky, and H. Baltes, “CMOS stabilizedDC power source,” Electronics Letters, vol. 28, no. 12,pp. 1153–1155, 1992.

[11] B. Wilson, “Performance analysis of current conveyors,”Electronics Letters, vol. 25, no. 23, pp. 1596–1598, 1989.

[12] N. Tadić and H. Zimmermann, “Low-power BiCMOS opticalreceiver with voltage-controlled transimpedance,” IEEE Jour-nal of Solid-State Circuits, vol. 42, no. 3, pp. 613–626, 2007.

[13] M. Wit, Temperature Independent Resistor, 1995, PatentUS5448103.

[14] B. R. Gregoire and U.-K. Moon, “Process-independent resistortemperature-coefficients using series/parallel and parallel/series composite resistors,” in 2007 IEEE International Sympo-sium on Circuits and Systems, New Orleans, LA, USA, 2007.

[15] Y.-H. Chiang and S.-I. Liu, “A submicrowatt 1.1-MHz CMOSrelaxation oscillator with temperature compensation,” IEEETransactions on Circuits and Systems-II: Express Briefs,vol. 60, no. 12, pp. 837–841, 2013.

[16] N. Tadić and D. Gobović, “A voltage-controlled resistor inCMOS technology using bisection of the voltage range,” Pro-ceedings of the 17th IEEE Instrumentation and MeasurementTechnology Conference [Cat. No. 00CH37066], vol. 50,2001no. 6, 2001.

12 Journal of Sensors

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