Analyss, Desgn, and Smulaton of a Noel Current Sensng Crcut Louza Sellam Electrcal and Computer Engneerng Department US Naal Academy Annapols, Maryland, USA sellam@usna.edu obert W. Newcomb Electrcal and Computer Engneerng Department The Unersty of Maryland College Park, Maryland, USA newcomb@umd.edu Abstract Ths paper nestgates the behaor of a noel acte current sensng crcut based on the crcut proposed by Macej Kokot. The crcut s a modfcaton of an opamp low sde current sensor whereby the output snks the current to ground through a resstor. Supportng analyss, desgn equatons, as well as Multsm smulaton results are ncluded. Keywords: Current Sensors, OpAmp Crcuts, Desgn, Smulaton, Multsm ntroducton A current sensor s a dece that detects and conerts current to an easly measured output oltage, whch s proportonal to the current through the measured path. There are a wde arety of sensors, and each sensor s sutable for a specfc current range and enronmental condton. No one sensor s optmum for all applcatons. Current measurement, current sensng, or the montorng of current flow nto and out of electronc crcuts s a fundamental requrement n a wde range of electronc applcatons. Typcal applcatons that beneft from current sensng nclude battery lfe ndcators and chargers, current and oltage regulators, DC/DC conerters, ground fault detectors, handheld communcatons deces, medcal dagnostc equpment, motor speed controls and oerload protecton, battery chargers, and batteryoperated crcuts for whch one must know the rato of current flow nto and out of a rechargeable battery. As more applcatons become portable, the demand ncreases for dedcated current montors that accomplsh ther task n a small package and wth low bas current [][]. A partcular current sensng crcut of nterest s the one proposed by Kokot n [5] whereby by combnng the adantages of lowsde and hghsde current sensors, t s possble to come up wth a smple current sensor wth a return current and zero nput oltage. The crcut uses two opamps confgured so that the top opamp snks the current to the output of the second opamp, whle the latter returns an equal current. We pont out that [5] does not prode any analyss or desgn method for mplementng the crcut or to support the clams aboe. n ths paper we present a noel a current sensng crcut, deelop a desgn method through analyss, as well as smulate the crcut. Specfcally, we dere the condtons on the resstors to guarantee that the return current matches the nput current, on the one hand, and, on the other hand, that the sensed current at the output s also the same as the nput current. Further, we examne the condtons on the nput sgnal to preent the opamps from saturatng. Also, the nondeal case of the effect of small oltage perturbaton at the nonnertng termnal of the top opamp on the sensed current s examned. 2 Basc Current Sensors There are two types of current sensng crcuts: passe and acte. Current sensng resstor s of the passe type, and s the most commonly used. t can be consdered a currenttooltage conerter, where nsertng a resstor nto the current path, the current s conerted to oltage n a lnear way (Ohm s law). The man adantages of current sensng resstors nclude low cost, hgh measurement accuracy, measurable current range from ery low to medum, and the capablty to measure DC or AC currents. The dsadantages nclude the ntroducton of an addtonal resstance nto the measured crcut path, whch may ncrease source output resstance and result n undesrable loadng effect, power loss due to dsspaton []. Therefore, current sensng resstors are rarely used
beyond the low and medum current sensng applcatons. Two technques for acte current sensng applcatons are used: lowsde current sensng and hghsde current sensng. Each technque has ts own adantages and dsadantages, dscussed n more detal n the followng sectons. n both methods current s conerted to a proportonal oltage that s readly measurable. f battery current montorng. Fgure 2 shows a hghsde current sensng whereby the sensng or probng resstor s nserted n the current path. The crcut uses a currenttooltage dfferental amplfer to measure the resultng oltage drop. Typcally, the sensed oltage sgnal s amplfed by subsequent op amp crcuts to get the measurable output oltage. Adantages nclude elmnatng ground dsturbance, load connects system ground drectly, detects the hgh load current caused by accdental shorts. The drawback s that t must be able to handle ery hgh and dynamc common mode nput oltages, n addton to complexty and hgher costs []. V0 Vof p p Fgure : Lowsde Currenttooltage Conerter. VoKV K// 2. A Smple Lowsde Current Sensng As shown n Fgure, a smple lowsde current sensor s the typcal operatonal amplfer currenttooltage conerter n whch the opamp snks the ncomng current through the feedback resstor. n general, lowsde current sensng connects the sensng or probng resstor between the load and (rtual) ground. Normally, the sensed oltage sgnal s so small that t needs to be amplfed by subsequent op amp crcuts (e.g., nonnertng amplfer) to get the measurable output oltage. Adantages nclude low nput common mode oltage, ground referenced nput and output, smplcty and low cost. Dsadantages nclude ground path dsturbance, load s lfted from system ground snce t adds undesrable resstance to the ground path, and hgh load current caused by accdental short goes undetected. Consderng the adantages, lowsde current sensng are used where short crcut detecton s not requred, and ground dsturbances can be tolerated [2]. 2.2 A Smple Hghsde Current Sensng Hghsde current sensng s typcally selected n applcatons where ground dsturbance cannot be tolerated, and short crcut detecton s requred, such as motor montorng and control, oercurrent protecton and supersng crcuts, automote safety systems, and Fgure 2: Hghsde Dfferental Amplfer Current to Voltage Conerter. A Noel Current Sensng Crcut Comparng the two sensng crcuts of Fgures and 2, we note that n the frst crcut the nput oltage drop s on the order of mcroolts to mllolts, dependng on the qualty of the C, but the measured current flows nto the sensng node wth no return current to the crcut. Wth ths method one can only measure currents flowng to ground. n the second crcut, howeer, the same current flowng n flows out of the crcut, but a sgnfcant oltage drop occurs at the nput across resstance p. A crcut that combnes the benefts of a return current and zero nput oltage s shown n Fgure [5]. The crcut operates n a somewhat smlar way as the crcut n Fgure n the sense that the top opamp snks the nput (measureable) current. Howeer, the bottom opamp output sources back an equal outgong current. n Secton, we analyze the behaor of ths crcut, namely dere the condtons on the resstors to guarantee that the return current matches the nput current, on the one hand, and, on the other hand, that the sensed current at the output s also the same as the nput current.
Further, we examne the condtons on the nput sgnal to preent the opamps from saturatng. Except for the thrd case, we assume deal opamps, meanng currents nto the opamp termnals are zero, and the oltage dfference between the opamp termnals s also zero. Note that ths s not always the case because the crcut uses both poste and negate feedback. Usng () to sole for 2 and substtutng ts expresson n () and (2) ges: ( 0 02) ( 0 02) and 0 ( ) ( ) () n order for the two currents n () to be equal, t s requred that 2. 0 2 ooo2.2 Condtons to force the sensed and the nput currents to be the same Defnng 0 0 02 Law, we get: and on usng () and Ohm s ( ) ( ) (5) 2 0 2 o 2 From (5), to achee o, we requre 2. Combnng ths condton and the preous result yelds the general condton that all four resstors must be equal n order for the sensed current to be the same as the nput current whch s equal to the return current.. Condtons to aod opamp saturaton Fgure : A Noel Current Sensng Crcut.. Condtons to force the return and the nput currents to be the same By rtue of the deal characterstcs of the opamps, 2,, o, and 2. By Ohm s Law, we hae 02 () 0 0 (2) 0 2 2 02 2 () Snce the output of the opamps cannot exceed the ral oltages Vs and Vs, and also for testng purposes a oltage source wth nternal resstance would be connected at node whle would be grounded, t follows that 2 and become rtual grounds, and. Also snce 0 02 V V 0 s s ( ) ( ) ( ) (6). Effect of perturbaton n on the nput current We keep the same set up as n secton. aboe. For analyss purposes, we assume the opamps deal, except.
for a dsturbance whch causes to deate from 2 (0) by an amount δ, so that δ. Ths n turn wll cause the nput current to deate by a certan amount, whch s determned by substtutng n (). The resultng current s then gen by: ' δ. (7) Note that ths perturbaton has no effect on the sensed and return current whch are stll gen by () and (). As seen n (7), n order to mnmze the deaton of the nput current, has to be large, but stll n the kω range. Ths way the nput, return and sensed currents are kept the same. Smulaton esults Multsm smulatons both n DC (though we do not nclude the results here) and AC (transent analyss n Multsm) were conducted on the crcut of Fgure, wth the ndcated alues for the resstances and nput sgnal, the choce of whch was dctated by the condtons dered n secton. The opamps were a par of 7 s (though other Cs may be used) based symmetrcally wth ± 5V. The graphs of Fgure 5 show the plots of the nput and sensed currents whch are equal. Fgure 6 shows the plots of the nput and returned currents, whch are equal but out of phase snce they flow n opposte drectons. Though not shown here, currents through,,, and are all equal, thus erfyng the analyss and desgn equatons. 5 Dscusson Though the smulaton results show that the crcut performs accordng to the theory, physcal lmtatons of the deces wll undoubtedly affect the results, especally f the alues of the resstances are not chosen properly. For nstance, alues of,,, and n the Ohm range lead to the saturaton of the opamps, as the dfferental termnal nput oltage deates from zero. Also the frequency response of the deces lmts the oerall frequency response for the crcut. Though the effect of the frequency of the nput sgnal on the dscrepancy between the nput, sensed and output currents was not analyzed here, a Multsm smulaton was done, and the results are shown n Fgures 7 and 8. t s noted that een beyond the cutoff frequency of the opamps, the magntudes of the nput and sensed currents reman the same. That s not the case of the phase whch starts to deate around 0 khz, whch ncdentally s also aboe the cutoff. Smlar behaor s obsered wth the return current also, as llustrated n Fgure 8. Vpk khz 0 GND kω node 2 node2 2 VCC 5V Fgure : Smulated Crcut wth nput oltage appled to node a the source resstance, and node connected to ground. Fgure 5: Plots of the nput and sensed currents. 7 5 VDD 5V VDD GND 7 5V 5V 5 VCC U 6 7 C2 6 7 Out2 Out
Fgure 6: Plots of the nput and return current whch here s the same as (). Fgure 8: Magntude plot of the nput current compared to the return current. 6 eferences [] obert F. Coughln and Frederck F. Drscoll, Operatonal Amplfers and Lnear ntegrated Crcuts, 5th ed., Prentce Hall, 998, pp.25 9. [2] Nel Zhao, Wenshua Lao, and Henr Sno HghSde Current Sensng wth Dynamc ange: Three Solutons, Analog Dalogue, 200, pp. 5. [] B. Yuan and X. La, Onchp CMOS Current sensng for DCDC Bucj conerter, Electroncs Letters, Vol. 5, No. 2, 2009, pp. 020. [] B. Gaann et al., MAGFET based current sensngfor power ntegrated crcuts, Mcroelectroncs elablty, Vol, No., 200, pp. 57758. [5] Macej Kokot, Measurng small currents wthout addng resste nserton loss, EDN Europe. Fgure 7: Frequency response comparng the magntude and phase of the nput current to the sensed current