Assessment of the error in the average current sensed by the unidirectional current pulse transformer

Assessment of the error in the average currentsensed by the unidirectional current pulsetransformer

N. McNeill and N.K. Gupta

Abstract: Advantages of using a current transformer (CT) for current sensing in switched modepower converters are that galvanic isolation is inherent, losses are low, the bandwidth is highand a high-amplitude output signal may be obtained. However, ‘droop’ occurs as a result of themagnetising current drawn. Peak current droop is defined as the instantaneous per-unit shortfallin sensed current at the end of a rectangular pulse. Average current droop is defined as theper-unit shortfall in the average current sensed. The CT inherently operates in a resonant modewhen sensing a unidirectional current pulse. This is advantageous as some of the current–timeproduct lost to the magnetising branch may be recovered thereby alleviating the average currentdroop. Average current droop is investigated when diode rectification is used. Three operatingmodes are identified and described. These are designated the discontinuous magnetising current,continuous magnetising current and discontinuous secondary current modes (DSCM). It isshown that the CT’s core losses may predominately influence the average current droop.Provided the DSCM is avoided, simple correction factors are shown to be appropriate for substan-tially correcting the sensed current to allow for these losses.

1 Introduction

Advantages of using a current transformer (CT) for currentsensing in switched mode power converters are that galva-nic isolation is inherent, losses are low, bandwidth is highand a high-amplitude output signal may be attained [1, 2].Conventional resistive sensing is simple, but if galvanic iso-lation is required this must be added separately. Also, powerdissipation is high. This latter difficulty can be circum-vented by sensing the voltage drop across a magnetic com-ponent’s parasitic resistance [3]. However, circuitry isrequired to extract this signal from the component’s term-inal voltage and the resistance of the (normally copper) con-ductor varies with temperature.

This paper investigates the average current droop in thesignal derived from a unidirectional current pulse transfor-mer when used with diode rectification and without a dis-crete reset voltage clamp circuit. It is noted that, althoughthe CT cannot inherently sense non-return-to-zero dc cur-rents, this may be achieved in many power converter appli-cations by use of the dual CT technique where the outputs oftwo CTs are summed [4].

1.1 Unidirectional current pulse sensing using a CT

Fig. 1 shows a CT (CT1) sensing the current in a switch(TR1) in a boost converter so that current-mode control

# The Institution of Engineering and Technology 2008

doi:10.1049/iet-cds:20070226

Paper first received 28th June and in revised form 16th November 2007

N. McNeill is with the Department of Electrical and Electronic Engineering,University of Bristol, UK

N.K. Gupta is with the School of Engineering and the Built Environment,Napier University, Edinburgh, UK

E-mail: [email protected]

IET Circuits Devices Syst., 2008, 2, (2), pp. 265–276

may be implemented [5–8]. During TR1’s on-time (Ton)the CT’s rectifier diode (D2) conducts and, ideally, theinstantaneous voltage, vout, across the load resistor (RL) isgiven by

vout ¼ipRL

n(1)

where ip is the primary current in the CT and n is its turns ratio

n ¼N2

N1

(2)

A drawback with the CT is that droop (D) results as a pro-portion of the current under measurement is diverted intothe CT’s magnetising branch. Droop is normally definedas the per-unit fall in the sensed current at the end of a rec-tangular current pulse. Droop is problematic in peak currentcontrol schemes as it opposes the effect of slope compen-sation necessary if sub-harmonic oscillations are to beavoided and 100% voltage feed-forward is to be attained[5]. A clamp circuit may be included to connect the second-ary winding across a voltage source during TR1’s off-time(Toff), when resetting the CT’s core material. However, pro-vided D2 can support the resulting peak reset voltage, theclamp circuit may be omitted and the CT can be resetusing its stray capacitances [4]. This has the advantagethat the reset time is reduced as the required Vt product isaccumulated more rapidly and operation at a higher dutyfactor (d) is therefore possible.

Fig. 2a shows a general transformer equivalent circuit.Inter-turn and core-to-winding capacitances, which affectthe high-frequency performance and resetting behaviourof the transformer, are lumped together as Ceq.

The equivalent circuit is simplified here to give that inFig. 2b where, in addition to the ideal transformer, onlythe inductive component of the magnetising branch referred

265

Fig. 1 CT sensing unidirectional current pulse through power device

a Power device deployed in boost converterb Power device (and CT primary) current waveform

to the secondary side (Lm2), the secondary winding resist-ance (Rw) and Ceq are included. As the CT is fed from acurrent source, the primary winding resistance (Rp) andleakage inductance (Lp), both in any case small, areassumed not to affect the voltage developed across Lm/Lm2. The flux excursion in a CT is normally small and theresistive leg (Rm) in parallel with Lm which representscore losses is initially neglected. However, core losses areaddressed subsequently in this paper. The secondaryleakage inductance (Ls) is also neglected as it is assumedthat the CT is constructed with a toroidal core carrying anevenly spaced secondary winding.

Ideally, the CT’s secondary current, i2, is

i2 ¼N1

N2

� �ip (3)

However, (neglecting Ceq) as Lm2, the magnetisingbranch referred to the secondary side, lies in parallel with

266

Rw and RL; it, therefore draws some of this current. If ipundergoes a step change from zero to Ip at t ¼ 0, then, ifit is initially zero, i2 decays according to

i2 ¼N1

N2

� �Ipe�t=t (4)

where the time constant, t, is given by

t ¼Lm2

Rw þ RL

(5)

and Lm2 is given by

Lm2 ¼Aem0mrN

22

le(6)

where Ae and le are the core’s effective area and length,respectively. Rw may be neglected in (5) where it is muchsmaller than RL. i2’s rate of decay can be lessened by

Fig. 2 Transformer equivalent circuits

a General equivalent circuitb Simplified CT circuit with quantities referred to secondary side

IET Circuits Devices Syst., Vol. 2, No. 2, April 2008

reducing RL which consequently increases t. However, v2 isnow reduced and has a smaller signal-to-noise ratio which isundesirable in a power converter where high noise levelsmay be present because of switching transients. If t ismuch greater than Ton, as is normal, then the drop incurrent because of the droop may be approximated aslinear. Therefore

i2 ¼N1

N2

Ip 1 �Rw þ RL

� �Lm2

t

� �(7)

where t ¼ dT ¼ Ton.The per-unit fall in current at the end of a pulse is there-

fore

D ¼Rw þ RL

� �dT

Lm2

(8)

1.2 Active output stage with diode rectification

Instead of the circuit in Fig. 1, the circuit in Fig. 3 may beimplemented [9]. Here, i2 flows into the node at theop-amp’s inverting terminal. The op-amp is in an invertingconfiguration and maintains this terminal at virtually thesame potential as its grounded non-inverting terminal byholding vout equal to i2RF. (The polarity of the connectionsmade here to CT1 is such that vout is positive.) If, initially,the voltage drop across D1 is neglected then each end of thesecondary winding is held at virtually the same potential bythe feedback action of the op-amp, effectively short-circuiting it.

The resistance seen in parallel with Lm2 is now reduced toRw. Consequently, t is now increased from the value givenby (5) to

t ¼Lm2

Rw

(9)

Although the resistance is now reduced the forward voltagedrop (Vf) from D1 is still impressed across the CT’s second-ary terminals. D is now

D ¼nIm2(0)

Ip(10)

where Im2(0) is the secondary magnetising current (im2) atswitch turn-off and represents the shortfall in the secondarycurrent at turn-off. If the voltage drop across Rw is small incomparison with Vf then, as Vf is applied across Lm2 for the


period dT, Im2(0) is given by

Im2(0) ¼VfdT

Lm2

(11)

Putting this into (10) yields

D ¼nVfd

fIpLm2

(12)

TR2 acts as a Class-A amplifier to ensure that sufficientcurrent is driven through RF if the op-amp cannot directlysource this current. RE is included because vout may berequired to go slightly negative during periods when ip iszero in order to satisfy any op-amp offset voltages. RE

allows a negative voltage to appear and prevents theop-amp’s output from going to the negative rail whentrying to source this voltage. The op-amp’s transientresponse when TR1 is turned on and the load current isre-applied to the CT is therefore improved as its outputvoltage has to slew less before settling.

As an alternative to a rectifier diode, synchronous rectifi-cation can be implemented [10] at the cost of added com-plexity. If a MOSFET with a sufficiently low on-stateresistance is used then a voltage much lower than Vf maybe achieved with a consequent reduction in droop.However, apart from the increased circuit complexityincurred, the introduction of the MOSFET’s inter-terminalcapacitances may increase the minimum reset periodrequired.

2 Resonant resetting operation

As described in Section 1, during a current pulse, somecurrent diverts into Lm2. However, when the current pulseends, the energy stored in Lm2 is dissipated either in theform of losses in the CT or externally. Three operatingmodes are identified here. These are designated the discon-tinuous magnetising current mode (DMCM), continuousmagnetising current mode (CMCM) and the discontinuoussecondary current mode (DSCM).

A discrete reset circuit is not used here and D1 is rated tosupport the peak reverse voltage appearing (v2(pk)). Giventhat the energy stored in Lm2 at the end of a current pulseis transferred to Ceq when v2(pk) is reached, then, neglectingcore losses

Lm2I2m2(0) ¼ Ceqv

22(pk) (13)

Fig. 3 Unidirectional current pulse sensing with active load and diode rectification

267

Rearranging (13) and putting in the result in (11) yields

v2(pk) ¼dVf

fffiffiffiffiffiffiffiffiffiffiffiffiffiffiLm2Ceq

p (14)

provided that im2 ¼ 0 at the beginning of the current pulse.The resonant frequency (vr) of the voltage half-cycle is

vr ¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Lm2Ceq

p (15)

Being able to sense average currents in a power converteraccurately even with high peak current droop is useful, asin many applications average current control is adequateor even advantageous [11] compared to peak current control.

2.1 Theory of CT resonant operation with losslessCT core material

With respect to Fig. 4, during a current pulse im2 ramps upand subtracts from i2. When the pulse ends, the half oscil-lation described by (14) and (15) occurs. At t ¼ Tr ¼ p/vr,v2 attempts to change direction and im2 again flows into therectifier diode which now clamps v2. Some of the im2tproduct lost during the pulse is thus returned to the CT’soutput terminals during Toff. The average current droop(Dave) may therefore be less than that predicted from thepeak current droop.

In Fig. 4b, im2 decays to zero before the current pulse isre-applied. The time taken for the decay is denoted as tc.This is DMCM operation. In Fig. 4c im2 has not decayed

268

to zero before the current pulse is re-applied and operationis in the CMCM mode. Although im2 passes through zero inthe CMCM mode, the term discontinuous is used here torefer to a state where im2 is zero for a finite period. Vf1 isthe rectifier diode’s forward voltage drop during thecurrent pulse. Vf2 is the voltage drop seen when the fluxhas reversed and im2 decays linearly. Vf1 is invariablygreater than Vf2 as, during Ton, the diode current comprisesi2 less im2, whereas during Toff only im2 flows. As im2 is typi-cally less than i2 by a factor of ten or more, the diode isoperating at a significantly different point on its v– i charac-teristic. However, for clarity in Fig. 4b, the ratio of Vf1 to Vf2

is exaggerated to be much greater than that likely to beencountered in a practical circuit. It is also noted thatwhereas Vf1 is the external voltage drop, the voltageacross Lm2 is the sum of this voltage and the voltage devel-oped across Rw by i2.

In considering the effect of im2 on Dave over a switchingperiod, Fig. 4 is simplified here to give Fig. 5 by neglectingthe half-oscillation period, Tr, where it is much smallerthan T.

For the DMCM mode, I1 is given by

I1 ¼Vf1dT

Lm2

(16)

For the CMCM mode, I1 and I2 are found from

I1 ¼ I2 þVf1dT

Lm2

(17)

Fig. 4 Operation in DMCM and CMCMs

a Current pulse in CT primary windingb v2 and im2 with discontinuous im2

c v2 and im2 with continuous im2


Fig. 5 Operation in DMCM and CMCMs with oscillatory period omitted for simplicity

a Current pulse in CT primary windingb v2 and im2 with discontinuous im2

c v2 and im2 with continuous im2

and

I2 ¼ �I1 þVf2 1 � dð ÞT

Lm2

(18)

The ratio of Vf1 to Vf2, (kv) is

kv ¼Vf1

Vf2

(19)

Combining (17) and (18) and expressing Vf2 as the ratio ofVf1 given in (19) yields

I1 ¼Vf1T

2Lm2

1 � d

kvþ d

� �(20)

and also:

I2 ¼Vf 1T

2Lm2

1 � d

kv� d

� �(21)

It is noted that, where kv is equal to one, then for d � 0.5, I1is simply given by:

I1 ¼Vf 1T

2Lm2

(22)

At the boundary between the CMCM and DMCM modes

d ¼ dTH ¼1

kv þ 1(23)

where dTH is the threshold duty factor. With respect to (16)and (20) and taking kv as 1 where (20) then simplifies to give


(22), Fig. 6a shows the peak im2 reached plotted against d.The peak core flux excursion (Fig. 6b) is proportional tothis current.

2.2 Effect of magnetising current on averagecurrent droop

2.2.1 Average current droop with discontinuousmagnetising current and lossless core material:The net im2 averaged over one switching cycle (Im2(ave)) iscalculated by summing the areas representing charge inthe current profile in Fig. 5b and dividing by T

Im2(ave) ¼Q1 � Q2

T(24)

As im2 during the interval from dT to tc is negative then Q2 isalso negative, thereby reducing Im2(ave). Q1 is given by

Q1 ¼d2T

2Vf1

2Lm2

(25)

Q2 is given by

Q2 ¼I1tc2

(26)

where tc is given by

tc ¼I1Lm2

Vf2

(27)

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Combining (26) and (27) and putting in (16) for I1 yields

Q2 ¼kvVf1d

2T

2

2Lm2

(28)

Putting (25) and (28) into (24) gives

Im2(ave) ¼d2TVf1

2Lm2

1 � kv� �

(29)

If kv ¼ 1 then no droop results and if kv . 1 then negativedroop results. That is, the im2t product returned into theop-amp’s input during Toff exceeds the im2t product lostduring Ton.

2.2.2 Average current droop with continuous mag-netising current and lossless CT core material: im2

averaged over T is calculated by summing the applicableareas shown in the current profile in Fig. 5c and dividingby T

Im2(ave) ¼�Q1 þ Q2 � Q3

T(30)

Q1 is given by

Q1 ¼1

2I2�� t1 (31)

where jI2j is I2’s magnitude, given by

I2�� ¼ Vf1T

2Lm2

d� 1

kvþ d

� �(32)

t1 is given by

t1 ¼I2�� Lm2

Vf1

(33)

Putting (32) and (33) into (31) gives

Q1 ¼Vf1T

2

8Lm2

d� 1

kvþ d

� �2

(34)

Q2 is given by

Q2 ¼1

2I1 dT � t1� �

(35)

Fig. 6 Magnetising current and core flux excursion againstd for kv ¼ 1

a Peak value of im2

b Peak value of core flux, f

270

Putting (20) and then (33) into (35) gives

Q2 ¼Vf1T

2

8Lm2

1 � d

kvþ d

� �2

(36)

Q3 is given by

Q3 ¼ 1 � dð ÞTI1 þ I2

�� 2

� �(37)

Putting in (20) and (32) into (37) gives

Q3 ¼Vf1T

2

2Lm2

ðd� d2Þ (38)

Finally, (34), (36) and (38) are put back into (30) to yieldIm2(ave)

Im2(ave) ¼Vf1T

2Lm2

(d� d2)1

kv� 1

� �� (39)

Fig. 7 shows the normalised average magnetising currentdrawn against d for kv ¼ 1.1 and 1.2. It is noted that thisis always negative.

2.2.3 Operation in DSCM with lossless CT corematerial: As Ip is reduced or Ton is increased, a point isreached where ip is entirely diverted into Lm2 before theend of the pulse. This is the DSCM mode, shown inFig. 8, and occurs at d ¼ d1

d1 ¼IpLm2

nVfT(40)

The difference between Vf1 and Vf2 is neglected here as theeffect on droop because of entering the DSCM mode istaken as being dominant. Therefore it is assumed thatVf ¼ Vf1 ¼ Vf2.

Above d1 the measured current does not change as noinformation is available because the core flux no longerchanges. Above d1, Dave is

Dave ¼d� d1

d(41)

Fig. 7 Normalised average magnetising current drawn againstd for kv ¼ 1.1 and 1.2


Fig. 8 CT waveforms in DSCM mode

a Current pulse in CT primary windingb Secondary currentc v2 and im2

To avoid DSCM operation, Lm2 has to be sufficiently largesuch that d1 is larger than the worst-case d encountered for agiven Ip.

However, (41) is only appropriate up to that duty factorwhere ip is re-applied after the resonated im2 from the pre-vious pulse has reached zero. Operation above this dutyfactor (d2) is shown in Fig. 9. d2 is derived from

1 � d2

� �T ¼

IpLm2

nVf

(42)

if Tr is small compared to T. (42) may be rearranged to give

d2 ¼ 1 �IpLm2

nVfT(43)

This may be expressed in terms of d1

d2 ¼ 1 � d1 (44)

Dave in this region may be calculated by equating current–time products (charges) as follows. The ideal outputcurrent–time product (Qi) is

Qi ¼ dTIp

n

� �(45)

With respect to Fig. 9b, the actual output is given by

Qactual ¼1

21 � dð ÞT

Ip

nþ I1

� �þ

1

2tc

Ip

nþ I1

� �(46)

This simplifies to give

Qactual ¼1

2

Ip

nþ I1

� �1 � dð ÞT þ tc

(47)


I1 and tc are given by

I1 ¼Ip

n�Vf 1 � dð ÞT

Lm2

(48)

and

tc ¼ I1 þIp

n

� �Lm2

Vf

(49)

Putting (49) into (47) and substituting (48) for I1 gives

Qactual ¼2I2

pLm2

n2Vf

�2Ip

n1 � dð ÞT (50)

Dave is given by

Dave ¼Qi � Qactual

Qi

(51)

Putting (45) and (50) into (51) and rearranging gives

Dave ¼1

d�

2IpLm2

TdnVf

(52)

This may be expressed in terms of d1

Dave ¼1

d�

2d1

d(53)

Although increasing Lm2 avoids DSCM operation, a draw-back is that, for a fixed Ceq, the maximum allowable dutyfactor is reduced as the reset period required by the half-oscillation is now increased.

271

Fig. 9 Effect of reapplying current pulse before resonant magnetising current from previous pulse has reached zero in DSCM

a Current pulse in CT primary windingb Secondary currentc v2 and im2

2.2.4 Effect of CT core losses: CT losses are notaddressed in previous sections. Three approaches may betaken in anticipating Dave. First, the theory in Section2.2.2 is applied where losses are neglected. Secondly, thedroop attributable to variations in kv and d is neglectedand the droop resulting from core losses may be taken asdominant. Thirdly, both the above factors are combined.The second approach is taken here.

The volumetric power loss (Pv) for a ferrite materialunder sinusoidal excitation may be approximated as [12]

Pv ¼ k1 faBd

ac (54)

where Bac is the flux density excursion, f is the excitationfrequency and k1, a and d are constants. The core’s powerloss (Wcore) is

Wcore ¼ PvVe (55)

where Ve is the core’s effective volume. Therefore

Wcore ¼ Vek1 faBd

ac (56)

At a given frequency, the core loss may be expressed as

Wcore ¼ k2Bdac (57)

if Vek1 fa are lumped and expressed as a constant, k2.

Up to dTH, Bac is directly proportional to d. Therefore ford � dTH (57) may be written as

Wcore ¼ k3dd (58)

and above dTH the core losses remain fixed at this level.

272

The power output from the CT is Vf i2(ave). Therefore forkv ’ 1, any core loss is directly manifested as a shortfall inthe sensed current.

The factor ‘d’ here is taken as 2.5 from [12]. However,two points are noted. First, as stated in [12], (54) is onlyappropriate for a limited permutation of frequencies andflux density excursions. Secondly, for simplicity, the fluxdensity excursion is taken as sinusoidal. However, it has aconsiderable harmonic content and a more completemethod of assessing losses is given in [13].

3 Experimentation

3.1 Experimental arrangements

The boost converter circuit in Fig. 10 was used for exper-imentation. A low-pass filter (R1 and C1) was included toobtain vout(ave). The CT is constructed around a FerroxcubeTN9/6/3 core in 3F3 material [14]. vout(ave) is ideally

vout(ave) ¼diL1(ave)RF

n(59)

provided iL1 is continuous. TR1 is an IRF1010E MOSFETand D1 is a 43CTQ100 Schottky diode. D2 is a 1N4148p–n diode. Although a Schottky diode may be preferred forD2 because of its lower Vf, a p–n diode was used as thehigher Vf is useful in accentuating droop for experimentation.

At n ¼ 120 and RF ¼ 120 V a gain of 1 V/A is expected.At the rated Ip (5 A) and given that n ¼ 120 andRw ¼ 0.89 V, the voltage drop across Rw is calculated at37 mV, small in comparison to D2’s forward voltage dropof �0.8 V.


Fig. 10 Converter circuit used for experimentation

The switching frequency was 20 kHz. This relatively lowfrequency was selected as, for the CT used here, this allowsoperation at a high duty factor (�95%) prior to incompletereset resulting. Dynamic op-amp parameters are also lessimportant.

Table 1 lists data from the experimental circuit.

3.2 Experimental results

Fig. 11 shows exemplifying waveforms for DMCM oper-ation. iL1(ave) is 5 A and d is 33%. The values of L1, Vin

and VLOAD in Fig. 10 are selected here such that they

Table 1: Experimental circuit parameters

op-amp feedback resistance

(RF), V

120

emitter resistance (RE), kV 10

op-amp type NE5534AN

CT rectifier diode (D2) 1N4148

bipolar npn transistor used in

location TR2

ZTX651

supply rail voltages (Vcc and

2Vcc), V

+15

R1, kV 10

C1, nF 3.0

core shape TN9/6/3

CT primary winding

configuration

single conductor passed

through core aperture

CT secondary winding

configuration

120 turns of 0.2 mmdiameter

copper wire

core material Curie

temperature, 8C

�200

measured value of Lm2 at

�208C, mH

11.0

measured value of Rw at

�208C, V

0.89


Fig. 11 Waveforms in DMCM

a Principal waveforms (vGS ¼ 20 V/div, v2 ¼ 20 V/div, iL ¼ 5 A/div,time scale: 10 ms/div)b v2 shown in greater detail (vGS ¼ 20 V/div, v2 ¼ 5 V/div, timescale: 10 ms/div)c iL1 and vout shown in greater detail (vGS ¼ 20 V/div, iL ¼ 1 A/div,vout ¼ 1 V/div, time scale: 10 ms/div)

273

allow a visible rate of current change over the switchingperiod.

TR1’s drive signal (vGS) is shown for reference purposes.iL1 is sensed using a high-bandwidth dc current probe. FromFig. 11b it is seen that v2 adopts different levels, Vf1 duringTon and Vf 2 during Toff and before im2 effectively terminates.Termination of conduction is characterised by an oscillationin v2 having a peak amplitude approximately equal to Vf andat the same frequency (�300 kHz) seen during the period Tr

as Lm2 again resonates with Ceq. As expected, the durationof tc exceeds that of Ton as kv is greater than 1. vout(inst) ischaracterised by several phases. During Ton, it is essentiallyproportional to ip, less a component attributable to droop. Att ¼ Ton, it drops to zero during the interval Tr when the resethalf-oscillation occurs. It then rises as im2 decays throughD2, and then reaches zero when im2 has commutated.

Fig. 12 shows exemplifying waveforms for CMCM oper-ation. Again, iL1(ave) ¼ 5 A. However, d is now 67%.

In Figs. 11 and 12 the permutation of input and outputvoltages and L1 allows a discernible rate of change ofcurrent over a switching cycle. However, for subsequent

Fig. 12 Waveforms in CMCM

a Principal waveforms (vGS ¼ 20 V/div, v2 ¼ 20 V/div, iL ¼ 2 A/div,vout ¼ 2 V/div, time scale: 10 ms/div)b v2 shown in greater detail (vGS ¼ 20 V/div, v2 ¼ 10 V/div, timescale: 10 ms/div)c iL1 and vout(inst) shown in greater detail (vGS ¼ 20 V/div, iL ¼ 1 A/div, vout ¼ 1 V/div, time scale: 10 ms/div)

274

measurements L1 is increased so that the current ripple isless than 1%.

Fig. 13 shows vout(ave) for iL1(ave) of 5 and 1 A, respect-ively. The ideal vout(ave) is also shown. The error increasesas ip is reduced. This is expected, as the peak value of im2

upon which the error depends is essentially independentof the magnitude of ip. It is also seen, particularly at 1 A,that a change in the trajectory in the measured current isevident at dTH ’ 60% where the transition from DMCMto CMCM operation occurs. At d ¼ 95% some increaseddistortion is evident as insufficient reset time is availablefor the reset half-oscillation to elapse.

Fig. 14 shows the absolute droop against duty factor for ipbetween 1 and 5 A in 1 A increments. It is essentially inde-pendent of ip. Some offset error is expected in these read-ings as the droop is calculated by subtracting themeasured current from the set current. ip was set usinginstrumentation with a resolution of 1% at the lowestcurrent and therefore a consequent (larger) per-unit errormay appear in the droop calculated in this way.

As core losses are expected to be proportional to d2.5

below dTH, then as d approaches zero, losses are verysmall. (29) giving the droop for lossless CT operation is

Fig. 13 Measured and ideal sensed average output voltage(vout(ave) ) plotted against d for iL1 ¼ 5 and 1 A

a iL1 ¼ 5 Ab iL1 ¼ 1 A


expected to become applicable where Dave becomes slightlynegative. This is consistent with the results in Fig. 14.

3.3 Experimental results at low primary currents

In the diode-rectified CT, the magnitude of im2 is essentiallyindependent of ip. In order to evaluate the behaviour of im2

more accurately, ip is now reduced to accentuate im2’s rela-tive magnitude. Subsequent measurements are taken at500 mA or less. To enhance the resolution of the sensedcurrent, RF was increased from 120 to 1.2 kV, giving anideal vout of 10 V/A.

Fig. 15 shows measured and ideal sensed currents againstd for ip ¼ 100, 300 and 500 mA. The ip against d boundaryat which DSCM operation occurs is marked. This is calcu-lated using (40) and taking Lm2 as 11.0 mH as given inTable 1.Vf is taken as 0.8 V. The measurements exhibiting pla-

teaus approximately centred around d ’ 50% lie belowthe boundary where the ratio of d to ip is too high toavoid DSCM operation.

3.4 Addition of compensating terms to CT outputsignal

Fig. 16 shows the sensed, ideal and compensated averageoutput voltage against d for ip ¼ 500 mA. The changefrom DMCM to CMCM operation (that is, at dTH) occurswhen d is �60%. dTH is higher than that predicted in (23)as losses are significant and it is also affected by the pre-sence of Tr. The voltage is corrected at this duty factor by2.79dTH

2.5, where the empirically determined factor 2.79 is

Fig. 14 Absolute droop expressed as output voltage shortfallagainst d for currents from 1 to 5 A

Fig. 15 Measured and ideal average output voltage (vout(ave))plotted against d for iL1 ¼ 100, 300 and 500 mA


required to give zero error. (vout(ave) represents the sensedcurrent, and as such, the shortfall in vout(ave) represents theloss in output current proportional to core losses asdescribed in Section 2.2.4.) Below dTH a compensatingvoltage of 2.79d 2.5 is added and above dTH a voltage of2.79dTH

2.5 is added.Using this compensation scheme, it is nonetheless

evident that an increasing error is present as d approaches100%. This is attributed to the observation that, as d rises,the average voltage impressed across Lm2 increases slightly.That is, while the primary winding of the CT is conductingduring the period dT, the voltage across Lm2 is given byVf1 þ i2Rw, whereas when the pulse is not present duringToff, this voltage is approximated as Vf2.

4 Conclusions

Factors affecting the average current droop in the signalderived from a UCPT with an active load and without a dis-crete reset circuit have been investigated. It is shown that, atcertain combinations of frequency and flux excursion, corelosses may predominately influence the average currentdroop. Provided that the current pulse being measureddoes not entirely divert into the CT’s magnetising branchbefore it terminates, a simple piece-wise correctionscheme using two measured parameters is appropriate forsubstantially correcting the output signal to allow for corelosses. However, a limitation here is that accurate coreloss data for ferrite materials operating at low flux excur-sions is required. With ferrite core materials, a further limit-ation arises if accuracy is to be obtained over a wideoperating temperature range as the losses are stronglytemperature-dependent.

5 References

1 Mammano, R.: ‘Current sensing solutions for power supplydesigners’. Application Note SLUP114, Unitrode Power SupplyDesign Seminar Handbook SEM1200, 1997, p. 1.1–1.34

2 Billings, K.: ‘Switchmode power supply handbook’ (McGraw-Hill,New York, 1999, 2nd edn.), pp. 3.186–3.191

3 Hua, L., and Luo, S.: ‘Design considerations of time constantmismatch problem for inductor DCR current sensing method’. Proc.21st Annual IEEE Applied Power Electronics Conf. and Exposition2006, March 2006, pp. 1368–1374

4 Ma, K.-W., and Lee, Y.-S.: ‘Technique for sensing inductor and dcoutput currents of PWM dc–dc converter’, IEEE Trans. PowerElectron., 1994, 9, (3), pp. 346–354

Fig. 16 Introduction of compensation to CT output signal(iL1 ¼ 500 mA)

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2

5 ‘Practical considerations in current mode power supplies’. ApplicationNote U-111, Applications Handbook, Unitrode Corporation,Merrimack, NH, 1997, pp. 3.106–3.123

6 Noon, J.P.: ‘UC3855A/B high performance power factorpreregulator’. Application Note U-153, Applications Handbook,Unitrode Corporation, Merrimack, NH, 1997, pp. 3.179–3.193

7 Bryant, B., and Kazimierczuk, M.K.: ‘Modelling the closed-currentloop of pwm boost dc–dc converters operating in CCM with peakcurrent-mode control’, IEEE Trans. Circuits Syst. I, Regul. Pap.,2005, 52, (11), pp. 2404–2412

8 Ridley, R.B.: ‘A new, continuous-time model for current-modecontrol’, IEEE Trans. Power Electron., 1991, 6, (2), pp. 271–280

9 Kassakian, J.G., Schlecht, M.F., and Verghese, G.C.: ‘Principles ofpower electronics’ (Addison-Wesley, Reading, MA, 1991),pp. 597–599

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10 McNeill, N., Gupta, N.K., and Armstrong, W.G.: ‘Active currenttransformer circuits for low distortion sensing in switched modepower converters’, IEEE Trans. Power Electron., 2004, 19, (4),pp. 908–917

11 Dixon, L.: ‘Average current mode control of switching powersupplies’. Application Note U-140, September 1999, TexasInstruments Inc., available at: www.ti.com, accessed December 2006

12 Mohan, N., Undeland, T.M., and Robbins, W.P.: ‘Power electronics:converters, applications and design’ (John Wiley, New York, 1989),pp. 304–322

13 Roshen, W.A.: ‘A practical, accurate and very general core loss modelfor nonsinusoidal waveforms’, IEEE Trans. Power Electron., 2007,22, (1), pp. 30–40

14 TN9/6/3 ferrite toroids and 3F3 material specification data sheets,www.ferroxcube.com


Documents

Assessment of the error in the average current sensed by the unidirectional current pulse transformer