Current-mode control to enhance closed-loop ... - Semantic Scholar
Current-mode control to enhance closed-loop performance of asymmetrical half-bridge DC–DC converters Byungcho Choi and Wonseok Lim Abstract: Asymmetrical half-bridge (ASHB) DC–DC converters exhibit fourth-order power stage dynamics. When the conventional voltage-mode control is adapted to ASHB DC–DC converters, fourth-order power stage dynamics impose certain constraints on the voltage feedback compensation design, and the resulting design offers only limited performance for closed-loop controlled converters. It is demonstrated that current-mode control can be adapted to ASHB converters to enhance their closed-loop performance in the presence of fourth-order power stage dynamics. The principles, performance and experimental results of the current-mode control adapted to ASHB converters are presented in comparison with those of the conventional voltagemode control.
1
Introduction
Recently, bridge-type pulse-width modulated (PWM) converters operating with asymmetrical duty ratios [1, 2] have received increasing research attention due to their circuit characteristics, which offer zero-voltage switching conditions for active switches without any penalty of an increased conduction loss. As an example of such converters, Fig. 1 shows an asymmetrical half-bridge (ASHB) DC–DC converter [3,4] combined with a PWM feedback controller. In addition to the circuit components usually found in conventional half-bridge DC–DC converters, the power stage of an ASHB DC–DC converter utilises a clamp capacitor CC and magnetising inductor Lm to accommodate PWM operation with asymmetric duty ratios. The clamp capacitor and magnetising inductor introduce an additional resonance to the small-signal transfer functions of the power stage and ASHB converters thus exhibit fourth-order power stage dynamics [5]. This paper shows that conventional voltage-mode control suffers from the detrimental effects of fourth-order power stage dynamics and offers only limited performance for closedloop controlled ASHB converters. The current research demonstrates that current-mode control can nullify the adverse effects of fourth-order power stage dynamics and enhance the closed-loop performance of ASHB converters. This paper presents the theoretical and experimental details on the principles, benefits and performance of current-mode control adapted to ASHB converters, in comparison with those of conventional voltagemode control. To verify analytical results of the paper, an experimental ASHB converter was built and its frequencyr IEE, 2004 IEE Proceedings online no. 20040987 doi:10.1049/ip-epa:20040987 Paper first received 25th February 2004 and in revised form 20th July 2004. Originally published online: 29th October 2004 The authors are with the School of Electrical Engineering and Computer Science Kyungpook National University, 1370, Sankyuk-Dong, Buk-Gu, Taegu 702-701, Korea
416
VCc − d VS
1−d
Cc
i L Lf
n:1:1 im
Cf
R
VO
Lm
CSN X
Y
SW −
se Ts = 5µs
PWM Z2(s ) − E/A
Z1(s )
5.0V
Fig. 1 Asymmetrical half-bridge DC–DC converter combined with PWM feedback controller
and time-domain responses were compared with theoretical predictions. Table 1 shows the operating conditions and circuit components of the experimental ASHB converter. 2 Small-signal dynamics and limitations of voltage-mode control
2.1
Small-signal power stage dynamics
Figure 2a shows the small-signal model of the ASHB converter [5] obtained by averaging and linearising the power stage dynamics of the converter. The resistances RCc, RLf and RCf are the equivalent series resistances of the respective reactive components, and the dependent sources shown in the dotted box in Fig 2a represent the small-signal dynamics of the complementary-driven switch pair and centre-tapped transformer. Expressions for these smallsignal sources are given in Table 1. The duty-ratio-to-output transfer function can be derived from Fig. 2a and IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
Table 1: Operating conditions, power stage components, steady-state circuit variables, and transfer functions of experimental ASHB converter Operating conditions
Vs ¼ 40–60 V, Vo ¼ 5.0 V, fs ¼ 200 kHz, R ¼ 0.5 O 0:36V=ms for voltage - mode control Se ¼ 0:10V=ms for current - mode control
Circuit components
Lf : 4.6 mH (esr ¼ 0.02 O), Cf : 194 mF (esr ¼ 0.03 O), CC: 6 mF (esr ¼ 0.2 O), n ¼ 3.0, Lm ¼ 18.3 mH
Steady-state variable
VS ¼ 48 V, IM ¼ 1.91A, IL ¼ 10 A, D ¼ 0.21, VCc ¼ 10 V
Small-signal sources
i^sw ¼ D i^m þ ðIM þ IL =nÞ d^ þ ðD=nÞi^L ; v^sw ¼ D v^s þ VS d^ i^pri ¼ ðð2D 1Þ=nÞi^L þ ð2IL =nÞd^ v^rec ¼ ðð1 2DÞ=nÞv^Cc þ ðD=nÞv^s þ ððVS 2VCc Þ=nÞd^
Transfer functions
ð1 þ s=oesr ÞDn ðsÞ ð1 þ s=ocr ÞDn ðsÞ ; G id ðsÞ ¼ Kid Dd1 ðsÞDd2 ðsÞ Dd1 ðsÞDd2 ðsÞ ð1 þ s=oesr ÞDn ðsÞ ð1 þ s=ocr ÞDn ðsÞ ; G is ðsÞ ¼ Kis G vs ðsÞ ¼ Kvs Dd1 ðsÞDd2 ðsÞ Dd1 ðsÞDd2 ðsÞ ð1 þ s=oesr Þð1 þ s=ozp Þ ð1 þ s=oesr Þ ; Z q ðsÞ ¼ Kq Z p ðsÞ ¼ Kp Dd1 ðsÞ Dd1 ðsÞ G vd ðsÞ ¼ Kvd
where Dn ðsÞ ¼ 1 þ s=ðQn on Þ þ s 2 =o2n Dd1 ðsÞ ¼ 1 þ s=ðQd1 od1 Þ þ s 2 =o2d1 Dd2 ðsÞ ¼ 1 þ s=ðQd2 od2 Þ þ s 2 =o2d2 with pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=ðLm Cc Þ ¼ 135 kr=s pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1=ðLf Cf Þ ¼ 33:5 kr=s pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1=ðLm Cc Þ ¼ 95:4 kr=s
on ffi od1 od2
1 o1 ¼ 2:9 Lm 2Dð12DÞ=ðRn 2 Þ þ RCc Cc n RLf þ R ¼ o1 ¼ 1:62 ðRLf RCf þ RLf R þ RCf RÞCf þ Lf d1 1 ¼ o1 ¼ 8:74 RCc CC d2
Qn ¼ Qd1 Qd2
oesr ¼ 1=ðCf RCf Þ ¼ 172 kr=s; ocr ¼ 1=ððR þ RCf ÞCf Þ ¼ 9:7 kr=s; ozp ¼ RLf =Lf ¼ 4:35 kr=s
2ð1 2DÞVs R 2ð1 2DÞVs 2Dð1 DÞR ¼ 17:8; Kid ¼ ¼ 36:6; Kvs ¼ ¼ 0:1 nðRLf þ RÞ nðRLf þ RÞ nðRLf þ RÞ 2Dð1 DÞ RLf R R ¼ 0:21; Kp ¼ ¼ 0:02; Kq ¼ ¼ 0:96 Kis ¼ nðRLf þ RÞ RLf þ R RLf þ R Kvd ¼
where
subsequently factored to an approximation:
Gvd ðsÞ
^vo Kvd d^
DðsÞ
IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
2ð1 2DÞ VS R nðRLf þ RÞ ! 1 s s 2 DðsÞ ¼ 1 þ þ Qd1 od1 od1 ! 1 s s 2 1þ þ Qd2 od2 od2 Kvd ¼
2 1 þ osesr 1 þ Q1n osn þ osn ð1Þ
ð2Þ
ð3Þ
417
RL f
vCc R Cc CC i m vsw Lm
i sw vs
i pri
Lf
iL
RCf
v rec
Cf
R vo
vs
Gvs (s)
iO
Z p (s)
vo
io
G vd (s)
d a d 1 +1
−1
Tm (s)
d 2
Fm
−3
cr
n
Kvd
−2
G id d 1
G vd
, rad/s
−4 −2
Fv (s) a
−1
esr
magnitude , dB
magnitude, dB
K id
d
G vd
−1
b
d 2 Tm
z 2 −1
z 1 ,rad/s
0dB
−3
Fig. 2 Small-signal power stage model and transfer functions of ASHB converter
n −1
esr
p 1
a Small-signal power stage model b Asymptotic plots for transfer functions
−2 p 2
b
The derivation steps and accuracy of (1) have already been presented in [5]. The expressions for the corner frequencies and damping factors of the transfer function are shown in Table 1, along with those of the other forthcoming power stage transfer functions. As addressed in [5], the first quadratic term in (3) is a result of the resonance between Lf and Cf, and the second quadratic term is due to the secondary resonance between the magnetising inductor Lm and the clamp capacitor Cc. The duty-ratio-to-inductor current transfer function can also be derived from Fig. 2a as 2 s 1 s s 1 þ 1 þ ocr Qn on þ on ^iL ð4Þ Gid ðsÞ Kid DðsÞ d^ where Kid ¼
2ð1 2DÞVS nðRLf þ RÞ
ð5Þ
Figure 2b shows asymptotic plots for 7Gvd (s)7 and 7Gid (s)7 of the experimental ASHB converter. The expressions and values for DC gains and corner frequencies of the transfer functions are given in Table 1.
2.2
Limitations of voltage-mode control
When the switch SW in Fig. 1 is placed at position Y, the feedback control becomes the conventional voltage-mode control. Figure 3a shows a small-signal block diagram representation of the voltage-mode controlled ASHB converter. The gain block Gvs ðsÞ is the open-loop input– output voltage transfer function and Zp(s) is the open-loop output impedance of the power stage, while Fm is the modulator gain of PWM block and Fv(s) ¼ Z2(s)/Z1(s) denotes the voltage feedback compensation of the feedback controller. Expressions for the power stage transfer functions are shown in Table 1, while expressions for Fm and Fv(s) are given in Table 2. Figure 3b shows the asymptotic plot for 7Gvd(s)7 and the loop gain, 7Tm(s)7 ¼ 7Gvd(s) Fv(s)Fm7. The asymptotic plot for 7Tm(s)7 418
Fig. 3
Voltage-mode control
a Small-signal block diagram representation b Asymptotic plots for 7Gvd(s)7 and loop gain, 7Tm(s) ¼ Gvd(s)Fv(s)Fm7
is constructed assuming a three-pole two-zero circuit Fv ðsÞ ¼
Kv ð1 þ s=oz1 Þð1 þ s=oz2 Þ sð1 þ s=op1 Þð1 þ s=op2 Þ
ð6Þ
for the voltage feedback compensation and also assuming that the feedback compensation parameters were selected according to the guidelines given in [5]. The loop gain shown in Fig. 3b reveals the limitations of the voltage-mode control adapted to an ASHB pconverter. Around the ffiffiffiffiffiffiffiffiffiffiffi secondary resonance at od2 = Lm Cc , the loop gain undergoes an additional phase delay of 1801 and the phase of the loop gain drops rapidly to 2701. Thus, to ensure stability with the presence of the secondary resonance, voltage-mode control must place the 0 dB crossover frequency of the loop gain at frequencies well before od2. This constraint places an upper limit on the feedback gain and hinders further enhancement of the closed-loop performance. In addition, (2) indicates that the DC gain of Gvd(s) is a nonlinear function of operating conditions of the ASHB converter. Since voltage-mode control employs Gvd(s) as the only feedback signal for the controller, changes in Gvd(s) directly propagate to closed-loop transfer functions, thereby making the converter performance sensitive to the changes of the operating conditions. In particular, since the DC gain of Gvd(s) is critically influenced by the input voltage of the converter [5], the loop gain characteristics vary substantially even when the input voltage changes within the specified limit. The shortcomings and limited performance of voltage-mode control, such as a narrow control bandwidth and sensitivity to the operating conditions, will become apparent in Section 4, where the performance of voltagemode control is compared with that of current-mode control. IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
Table 2: Summary of control schemes
Voltage-mode control
Feedback controller
Loop gain and closed-loop performance
Gain blocks: 1 Kv ð1 þ s=oz1 Þð1 þ s=oz2 Þ ¼ 0:56; Fv ðsÞ ¼ Fm ¼ Ts Se sð1 þ s=op1 Þð1 þ s=op2 Þ
Tm ðsÞ ¼Gvd ðsÞFv ðsÞFm Gvs ðsÞ Gio ðsÞ ¼ 1 þ Tm ðsÞ Zp ðsÞ Zo ðsÞ ¼ 1 þ Tm ðsÞ
Compensation parameters: Kv ¼ 1500; oz1 ¼ 0:8 od1 ¼ 26:8 krad=s oz2 ¼ 1:2 od1 ¼ 40:2 krad=s op1 ¼ oesr ¼ 172 krad=s op2 ¼ 1:7oesr ¼ 292 krad=s
T1 ðsÞ ¼ Ti ðsÞ þ Tv ðsÞ
Gain blocks: 1 ¼ ¼ 0:27; Ri ¼ 0:41 ðSn Sf þ 2Se ÞTs K 0 ð1 þ s=o0z Þ Fv0 ðsÞ ¼ v sð1 þ s=o0p Þ
0 Fm
T2 ðsÞ ¼
with 0 Ti ðsÞ ¼ Gid ðsÞRi Fm 0 Tv ðsÞ ¼ Gvd ðsÞFv0 ðsÞFm Z ðsÞGvd ðsÞ Zp ðsÞ þ Ti ðsÞ Zp ðsÞ q Gid ðsÞ Zo ðsÞ ¼ 1 þ T1 ðsÞ
Compensation parameters: Kv0 ¼ 60 000; o0z ¼ 0:9; od1 ¼ 30:2 krad=s o0p ¼ oesr ¼ 172 krad=s
Current-mode control
As shown in Fig. 1, current-mode control is implemented by sensing the diode current using a current sensing network (CSN) and feeding this to the PWM block with SW at position X. Among many candidates for current feedback signal [6], the secondary diode current is selected because it provides full benefits of the peak current-mode control [7] with a simple CSN design. While the primary switch current can be used as an alternative feedback signal, the resulting control scheme could complicate the analysis and design of current-mode control because the switch current contains the magnetising inductor current as well as the reflected output filter current. Figure 4a shows the small-signal block diagram of the current-mode controlled ASHB converter. The gain block Ri represents the gain of the CSN and Fm0 is the PWM gain for current-mode control. The expressions for the power stage transfer functions appearing in Fig. 4a are given in Table 1, and the smallsignal gain blocks for current-mode control are presented in Table 2. The sampling effect and feedforward gains of current-mode control, which do not cause significant impacts on the low-and mid-frequency dynamics of a properly-designed current-mode controlled converter [8], are not included in Fig. 4a for the simplicity of ensuing discussions. Figure 4b illustrates the principles of current-mode control based on the asymptotic plots of two individual feedback loops associated with the respective feedback signals. The current loop, Ti ðsÞ ¼ Gid ðsÞRi Fm0 , represents the feedback loop created by the diode current feedback. The CSN gain, Ri, can be chosen to place the 0 dB crossover frequency of Ti at high frequencies, typically 1/ 3-1/5 of the switching frequency [7]. The voltage loop, Tv ðsÞ ¼ Gvd ðsÞFv0 ðsÞFm0 , denotes the feedback loop associated with the output voltage feedback. The asymptotic plot for 7Tv(s)7 is constructed assuming a two-pole onezero circuit Fv0 ðsÞ ¼
Kv0 ð1 þ s=o0z Þ sð1 þ s=o0p Þ
IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
ð7Þ
vs
Gvs (s)
io
Zp (s)
vo
Gvd (s) d
iL
Gis(s)
Tv (s)
Z q(s) Gid (s) Ti (s)
B
Ri Fv (s )
Fm
A
a Tv magnitude , dB
3
Tv ðsÞ 1 þ Ti ðsÞ
z d1 −2 Ti +1 −1 cr 0dB
,rad/s
d2 −3 n −4 −1 −2
p = esr
magnitude , dB
Current-mode control
T1 'z d 1 −2 Ti d2 cr +1 Tv n −2 T2 −1 −1 −4 0dB ,rad/s 'p = esr
b
Fig. 4
−2 c
Current-mode control
a Small-signal block diagram b Individual feedback loops c Overall loop gain and outer loop gain
for the voltage feedback compensation. The parameters for Fv0 ðsÞ can be selected as outlined below: place o0z as high as possible, yet not exceeding od1 place o0p at oesr to cancel the effects of oesr adjust Kv0 to trade-off stability margins and closed-loop performance. Justifications for these selections will be provided later in this Section. Two useful loop gains can be identified from the smallsignal block diagram of Fig. 4a. While the loop gain measured at point A in Fig. 4a is defined as the overall loop 419
Gvd ðsÞFv0 ðsÞFm0 Gid ðsÞRi Fm0
for frequencies where 7Ti7c1. Accordingly, the power stage dynamics influencing both Gvd(s) and Gid(s) will not show in T2 due to canceling of their effects. Since the effects of the secondary resonance between Lm and Cc commonly appear in both Gvd(s) and Gid(s), T2 is unaffected by the secondary resonance, as illustrated in Fig. 4c. This distinctive advantage of current-mode control allows the feedback compensation to be designed, independently from the secondary resonance, to enhance the closed-loop performance of the converter. In addition, since Gvd(s) and Gid(s) both contain a common term 2(12D)Vs in their DC gain, the effects of the input voltage and duty ratio are cancelled in T2. Accordingly, current-mode control maintains the same loop gain characteristics even for applications where the converter’s input voltage is varied widely. By employing an additional feedback from the inductor current, current-mode control effectively nullifies all the detrimental effects of the secondary resonance and offers significant improvements in the converter’s performance. In voltage-mode control, the feedback gain is critically limited by the presence of the secondary resonance, and the converter’s performance thus becomes unsatisfactory and changes widely as the operating conditions are varied. In current-mode control, in contrast, the feedback gain can be increased independently from the secondary resonance, to achieve an enhanced closed-loop performance that will remain the same regardless of potential changes in the operating conditions. 4
Performance of current-mode control
This Section presents the performance of the current-mode control employed to the experimental ASHB converter operating with VS ¼ 48 V and R ¼ 0.5 O. To highlight the merits of current-mode control, the performance of the current-mode-controlled converter is presented in parallel with that of the voltage-mode controlled converter.
4.1
Loop gain
Figure 5 shows the outer loop gain, T2, of the current-mode controlled converter in comparison with the loop gain, Tm, of the voltage-mode controlled converter. The reasons for 420
40
current-mode control
magnitude, dB
20 0 voltage-mode control −20 −40 , ,
−60
theory measurement
50 0 voltage-mode control
−50 phase, deg
gain T1(s), the loop gain measured at point ‘ B’ is referred to as the outer loop gain T2(s) [7]. Fig. 4c shows asymptotic plots for 7T17 and 7T27 along with the two individual feedback loops. Being a vector sum of individual feedback loops, T1 ¼ Ti+Tv, the overall loop gain illustrates the design strategy for current-mode control. By designing 7Tv7c7Ti7 at low frequencies and 7Ti7c7Tv7 at high frequencies, current-mode control can increase the feedback gain while locating the crossover frequency of T1 at higher frequencies with good phase margin. The asymptotic plot for the outer loop gain is constructed using the relationship of T2 ¼ Tv/(1+Ti). Selection of the feedback compensation parameters for Fv0 ðsÞ can now be explained using 7T27. The purpose of the compensation zero, o0z in (7), is to allow T2 to cross over the 0 dB line with a –20 dB/dec slope. In earlier publications [9, 10], it has been shown that the location of o0z also determines the speed of transient responses. Accordingly, o0z can be placed at high frequencies to achieve a fast response, yet not exceeding od1 to avoid being a conditionally stable system [9]. The compensation pole o0p is placed at oesr to maintain a –20 dB/dec slope for a wider frequency range. The outer loop gain can be approximated to T2 TTvi ¼
−100
current-mode control
−150 −200 −250 −300 −350
102
,
theory
,
measurement 103
104
105
frequency, Hz
Fig. 5
Loop gains of experimental ASHB converter
selecting T2 for comparison with Tm are: Only for the outer loop gain T2, the definitions for the phase margin and gain margin become consistent with those of Tm. Since 7T17c7T27 for all frequencies, T2 can be used as a conservative measure for comparison. The feedback compensation parameters were deliberately chosen in a way that both current-mode control and voltage-mode control result in the same 0 dB frequency at 7 kHz. Compensation parameters for both control schemes are shown in Table 2. The analytical predictions and experimental measurements are presented in parallel in Fig. 5. As demonstrated in Fig. 5, current-mode control offers the superior loop gain characteristics with enhanced phase margin and substantial gain boost. The phase margin of current-mode control exceeds 651 while that of voltagemode control falls below 451. Current-mode control exhibits 20 dB gain boost at low and high frequencies, compared with voltage-mode control. Figure 5 also indicates that current-mode control can further increase the feedback gain without degrading the stability margins, while voltage-mode control has little room to increase the feedback gain owing to the rapid phase drop caused by the secondary resonance pffiffiffiffiffiffiffiffiffiffi ffi at od2 1= Lm Cc . Fig. 5 confirms that current-mode control effectively nullifies the detrimental effects of the secondary resonance and allows the controller to be optimised independently from the power stage dynamics. Figure 6 compares the loop gains of the ASHB converter when its input voltage is varied between 40 VoVSo60 V. As predicted in Section 2.2 and demonstrated in Fig. 6a, the loop gain of voltage-mode control is directly influenced by the change in the input voltage. In contrast, the outer loop IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
0
40 Vs =60
−20
Vs =50 Vs =40
0
magnitude , dB
magnitude, dB
20
−20 −40 theory measurement
−60
voltage-mode control
−40 −60 current-mode control
−80
−100
theory measurement
−120
a
102
103
104
105
frequency , Hz 60
magnitude, dB
40
Fig. 7 Input–output voltage transfer function of experimental ASHB converter
Vs : 40V, 50V, 60V
20
converter is given by
0
^vo Zp ðsÞ ¼ Zo ðsÞ ^io closedloop 1 þ Tm ðsÞ
−20 −40
theory measurement
−60 102
for voltage-mode control and
103
104
105
Zo ðsÞ¼
frequency,Hz
Loop gains with different input voltages
a Tm of voltage-mode control b T2 of current-mode control
gain T2 shown in Fig. 6b confirms that current-mode control effectively offsets the change in the input voltage and maintains the same loop gain characteristics.
Input–output voltage transfer function
From Fig. 3a, the input–output voltage transfer function of voltage-mode control can be derived as ^vo Gvs ðsÞ ð8Þ ¼ Gio ðsÞ ^v 1 þ T ðsÞ s closedloop
m
Similarly, the input-to-output voltage transfer function of current-mode control can be derived from Fig. 4a as vd ðsÞ Gvs ðsÞ þ Ti ðsÞ Gvs ðsÞ Gis ðsÞG Gid ðsÞ Gio ðsÞ¼ ð9Þ 1 þ T1 ðsÞ Using the power stage transfer functions given in Table 1, (9) can be simplified to Gio ðsÞ¼
Gvs ðsÞ 1 þ T1 ðsÞ
ð10Þ
Based on the fact that 7T17c7T27c7Tm7, a significant improvement in 7Gio7 is expected for the current-mode controlled converter. Figure 7 compares the input–output voltage transfer functions of the converter. As a direct benefit of the improved loop gain characteristics, currentmode control provides an additional 40 dB attenuation up to mid frequencies, compared with voltage-mode control.
4.3 Output impedance and load transient response The output impedance of the closed-loop controlled ASHB IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
ð12Þ
1 þ T1 ðsÞ
0
-20 magnitude , dB
4.2
Z ðsÞGvd ðsÞ Zp ðsÞ þ Ti ðsÞ Zp ðsÞ q Gid ðsÞ
for current-mode control. Figure 8 shows predictions of (11) and (12) in comparison with the experimental data. The experimental output impedances reveal the influence of the low-frequency measurement noise and effects of the dynamic impedances of active and passive switches that were not accounted for in the model.
b
Fig. 6
ð11Þ
current-mode control
-40
voltage-mode control
-60 theory -80
measurement 102
103
104
105
frequency ,Hz
Fig. 8
Output impedance of experimental ASHB converter
The transient response of the output voltage of a closedloop controlled converter due to its load change is closely related to its output impedance characteristics [9, 10]. The maximum value of output impedance determines the size of the undershoot or overshoot of the output voltage. The peaking in the output impedance causes an oscillatory behaviour in the transient response of the output voltage. Figure 9 shows the simulated and measured load transient responses of the experimental converter. An averaged model of the ASHB converter [5] was used for 421
current,A voltage,V
10 8 6
load current
5.0 4.8 4.6
output voltage
voltage,V
current,A
a 10
6
8 6
This work was supported in part by the HY-SDR Research Center at Hanyang University, Seoul, Korea, under the ITRC Program of IITA, Korea, and in part by the Basic Research Program of the Korea Science and Engineering Foundation under Grant R12-2002-055-02001-0.
5 4.8 4.6
output voltage
d
Load transient responses
a Simulation of current-mode control (100 ms/div) b Simulation of voltage-mode control (100 ms/div) c Measurement of current-mode control (100 ms/div) d Measurement of voltage-mode control (100 ms/div)
simulations and an electric load was used for experiments. Owing to a smooth output impedance curve with smaller peak value, the current-mode controlled converter exhibits a well damped transient behaviour with small undershoot. In contrast, owing to an output impedance curve showing a peaking with larger peak value, the voltage-mode controlled converter reveals an oscillatory behaviour with larger undershoot. 5
Conclusions
ASHB DC–DC converters are a fourth-order system due to the secondary resonance between the clamp capacitor and the magnetising inductor of the transformer. The voltagemode control adapted to fourth-order ASHB converters was found to offer only limited performance for the closedloop controlled converter. This paper has demonstrated that current-mode control can overcome the adverse effects of the secondary resonance
422
Acknowledgments
load current
c
Fig. 9
b
and enhance the closed-loop performance of ASHB converters. By nullifying the influence of the secondary resonance using a current feedback loop, current-mode control can improve loop gain characteristics, input–output voltage transfer function, and load transient response. It has also been found that the closed-loop performance of current-mode controlled ASHB converters remains the same regardless of the potential changes in operating conditions.
7
References
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IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
1
Introduction
Recently, bridge-type pulse-width modulated (PWM) converters operating with asymmetrical duty ratios [1, 2] have received increasing research attention due to their circuit characteristics, which offer zero-voltage switching conditions for active switches without any penalty of an increased conduction loss. As an example of such converters, Fig. 1 shows an asymmetrical half-bridge (ASHB) DC–DC converter [3,4] combined with a PWM feedback controller. In addition to the circuit components usually found in conventional half-bridge DC–DC converters, the power stage of an ASHB DC–DC converter utilises a clamp capacitor CC and magnetising inductor Lm to accommodate PWM operation with asymmetric duty ratios. The clamp capacitor and magnetising inductor introduce an additional resonance to the small-signal transfer functions of the power stage and ASHB converters thus exhibit fourth-order power stage dynamics [5]. This paper shows that conventional voltage-mode control suffers from the detrimental effects of fourth-order power stage dynamics and offers only limited performance for closedloop controlled ASHB converters. The current research demonstrates that current-mode control can nullify the adverse effects of fourth-order power stage dynamics and enhance the closed-loop performance of ASHB converters. This paper presents the theoretical and experimental details on the principles, benefits and performance of current-mode control adapted to ASHB converters, in comparison with those of conventional voltagemode control. To verify analytical results of the paper, an experimental ASHB converter was built and its frequencyr IEE, 2004 IEE Proceedings online no. 20040987 doi:10.1049/ip-epa:20040987 Paper first received 25th February 2004 and in revised form 20th July 2004. Originally published online: 29th October 2004 The authors are with the School of Electrical Engineering and Computer Science Kyungpook National University, 1370, Sankyuk-Dong, Buk-Gu, Taegu 702-701, Korea
416
VCc − d VS
1−d
Cc
i L Lf
n:1:1 im
Cf
R
VO
Lm
CSN X
Y
SW −
se Ts = 5µs
PWM Z2(s ) − E/A
Z1(s )
5.0V
Fig. 1 Asymmetrical half-bridge DC–DC converter combined with PWM feedback controller
and time-domain responses were compared with theoretical predictions. Table 1 shows the operating conditions and circuit components of the experimental ASHB converter. 2 Small-signal dynamics and limitations of voltage-mode control
2.1
Small-signal power stage dynamics
Figure 2a shows the small-signal model of the ASHB converter [5] obtained by averaging and linearising the power stage dynamics of the converter. The resistances RCc, RLf and RCf are the equivalent series resistances of the respective reactive components, and the dependent sources shown in the dotted box in Fig 2a represent the small-signal dynamics of the complementary-driven switch pair and centre-tapped transformer. Expressions for these smallsignal sources are given in Table 1. The duty-ratio-to-output transfer function can be derived from Fig. 2a and IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
Table 1: Operating conditions, power stage components, steady-state circuit variables, and transfer functions of experimental ASHB converter Operating conditions
Vs ¼ 40–60 V, Vo ¼ 5.0 V, fs ¼ 200 kHz, R ¼ 0.5 O 0:36V=ms for voltage - mode control Se ¼ 0:10V=ms for current - mode control
Circuit components
Lf : 4.6 mH (esr ¼ 0.02 O), Cf : 194 mF (esr ¼ 0.03 O), CC: 6 mF (esr ¼ 0.2 O), n ¼ 3.0, Lm ¼ 18.3 mH
Steady-state variable
VS ¼ 48 V, IM ¼ 1.91A, IL ¼ 10 A, D ¼ 0.21, VCc ¼ 10 V
Small-signal sources
i^sw ¼ D i^m þ ðIM þ IL =nÞ d^ þ ðD=nÞi^L ; v^sw ¼ D v^s þ VS d^ i^pri ¼ ðð2D 1Þ=nÞi^L þ ð2IL =nÞd^ v^rec ¼ ðð1 2DÞ=nÞv^Cc þ ðD=nÞv^s þ ððVS 2VCc Þ=nÞd^
Transfer functions
ð1 þ s=oesr ÞDn ðsÞ ð1 þ s=ocr ÞDn ðsÞ ; G id ðsÞ ¼ Kid Dd1 ðsÞDd2 ðsÞ Dd1 ðsÞDd2 ðsÞ ð1 þ s=oesr ÞDn ðsÞ ð1 þ s=ocr ÞDn ðsÞ ; G is ðsÞ ¼ Kis G vs ðsÞ ¼ Kvs Dd1 ðsÞDd2 ðsÞ Dd1 ðsÞDd2 ðsÞ ð1 þ s=oesr Þð1 þ s=ozp Þ ð1 þ s=oesr Þ ; Z q ðsÞ ¼ Kq Z p ðsÞ ¼ Kp Dd1 ðsÞ Dd1 ðsÞ G vd ðsÞ ¼ Kvd
where Dn ðsÞ ¼ 1 þ s=ðQn on Þ þ s 2 =o2n Dd1 ðsÞ ¼ 1 þ s=ðQd1 od1 Þ þ s 2 =o2d1 Dd2 ðsÞ ¼ 1 þ s=ðQd2 od2 Þ þ s 2 =o2d2 with pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=ðLm Cc Þ ¼ 135 kr=s pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1=ðLf Cf Þ ¼ 33:5 kr=s pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1=ðLm Cc Þ ¼ 95:4 kr=s
on ffi od1 od2
1 o1 ¼ 2:9 Lm 2Dð12DÞ=ðRn 2 Þ þ RCc Cc n RLf þ R ¼ o1 ¼ 1:62 ðRLf RCf þ RLf R þ RCf RÞCf þ Lf d1 1 ¼ o1 ¼ 8:74 RCc CC d2
Qn ¼ Qd1 Qd2
oesr ¼ 1=ðCf RCf Þ ¼ 172 kr=s; ocr ¼ 1=ððR þ RCf ÞCf Þ ¼ 9:7 kr=s; ozp ¼ RLf =Lf ¼ 4:35 kr=s
2ð1 2DÞVs R 2ð1 2DÞVs 2Dð1 DÞR ¼ 17:8; Kid ¼ ¼ 36:6; Kvs ¼ ¼ 0:1 nðRLf þ RÞ nðRLf þ RÞ nðRLf þ RÞ 2Dð1 DÞ RLf R R ¼ 0:21; Kp ¼ ¼ 0:02; Kq ¼ ¼ 0:96 Kis ¼ nðRLf þ RÞ RLf þ R RLf þ R Kvd ¼
where
subsequently factored to an approximation:
Gvd ðsÞ
^vo Kvd d^
DðsÞ
IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
2ð1 2DÞ VS R nðRLf þ RÞ ! 1 s s 2 DðsÞ ¼ 1 þ þ Qd1 od1 od1 ! 1 s s 2 1þ þ Qd2 od2 od2 Kvd ¼
2 1 þ osesr 1 þ Q1n osn þ osn ð1Þ
ð2Þ
ð3Þ
417
RL f
vCc R Cc CC i m vsw Lm
i sw vs
i pri
Lf
iL
RCf
v rec
Cf
R vo
vs
Gvs (s)
iO
Z p (s)
vo
io
G vd (s)
d a d 1 +1
−1
Tm (s)
d 2
Fm
−3
cr
n
Kvd
−2
G id d 1
G vd
, rad/s
−4 −2
Fv (s) a
−1
esr
magnitude , dB
magnitude, dB
K id
d
G vd
−1
b
d 2 Tm
z 2 −1
z 1 ,rad/s
0dB
−3
Fig. 2 Small-signal power stage model and transfer functions of ASHB converter
n −1
esr
p 1
a Small-signal power stage model b Asymptotic plots for transfer functions
−2 p 2
b
The derivation steps and accuracy of (1) have already been presented in [5]. The expressions for the corner frequencies and damping factors of the transfer function are shown in Table 1, along with those of the other forthcoming power stage transfer functions. As addressed in [5], the first quadratic term in (3) is a result of the resonance between Lf and Cf, and the second quadratic term is due to the secondary resonance between the magnetising inductor Lm and the clamp capacitor Cc. The duty-ratio-to-inductor current transfer function can also be derived from Fig. 2a as 2 s 1 s s 1 þ 1 þ ocr Qn on þ on ^iL ð4Þ Gid ðsÞ Kid DðsÞ d^ where Kid ¼
2ð1 2DÞVS nðRLf þ RÞ
ð5Þ
Figure 2b shows asymptotic plots for 7Gvd (s)7 and 7Gid (s)7 of the experimental ASHB converter. The expressions and values for DC gains and corner frequencies of the transfer functions are given in Table 1.
2.2
Limitations of voltage-mode control
When the switch SW in Fig. 1 is placed at position Y, the feedback control becomes the conventional voltage-mode control. Figure 3a shows a small-signal block diagram representation of the voltage-mode controlled ASHB converter. The gain block Gvs ðsÞ is the open-loop input– output voltage transfer function and Zp(s) is the open-loop output impedance of the power stage, while Fm is the modulator gain of PWM block and Fv(s) ¼ Z2(s)/Z1(s) denotes the voltage feedback compensation of the feedback controller. Expressions for the power stage transfer functions are shown in Table 1, while expressions for Fm and Fv(s) are given in Table 2. Figure 3b shows the asymptotic plot for 7Gvd(s)7 and the loop gain, 7Tm(s)7 ¼ 7Gvd(s) Fv(s)Fm7. The asymptotic plot for 7Tm(s)7 418
Fig. 3
Voltage-mode control
a Small-signal block diagram representation b Asymptotic plots for 7Gvd(s)7 and loop gain, 7Tm(s) ¼ Gvd(s)Fv(s)Fm7
is constructed assuming a three-pole two-zero circuit Fv ðsÞ ¼
Kv ð1 þ s=oz1 Þð1 þ s=oz2 Þ sð1 þ s=op1 Þð1 þ s=op2 Þ
ð6Þ
for the voltage feedback compensation and also assuming that the feedback compensation parameters were selected according to the guidelines given in [5]. The loop gain shown in Fig. 3b reveals the limitations of the voltage-mode control adapted to an ASHB pconverter. Around the ffiffiffiffiffiffiffiffiffiffiffi secondary resonance at od2 = Lm Cc , the loop gain undergoes an additional phase delay of 1801 and the phase of the loop gain drops rapidly to 2701. Thus, to ensure stability with the presence of the secondary resonance, voltage-mode control must place the 0 dB crossover frequency of the loop gain at frequencies well before od2. This constraint places an upper limit on the feedback gain and hinders further enhancement of the closed-loop performance. In addition, (2) indicates that the DC gain of Gvd(s) is a nonlinear function of operating conditions of the ASHB converter. Since voltage-mode control employs Gvd(s) as the only feedback signal for the controller, changes in Gvd(s) directly propagate to closed-loop transfer functions, thereby making the converter performance sensitive to the changes of the operating conditions. In particular, since the DC gain of Gvd(s) is critically influenced by the input voltage of the converter [5], the loop gain characteristics vary substantially even when the input voltage changes within the specified limit. The shortcomings and limited performance of voltage-mode control, such as a narrow control bandwidth and sensitivity to the operating conditions, will become apparent in Section 4, where the performance of voltagemode control is compared with that of current-mode control. IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
Table 2: Summary of control schemes
Voltage-mode control
Feedback controller
Loop gain and closed-loop performance
Gain blocks: 1 Kv ð1 þ s=oz1 Þð1 þ s=oz2 Þ ¼ 0:56; Fv ðsÞ ¼ Fm ¼ Ts Se sð1 þ s=op1 Þð1 þ s=op2 Þ
Tm ðsÞ ¼Gvd ðsÞFv ðsÞFm Gvs ðsÞ Gio ðsÞ ¼ 1 þ Tm ðsÞ Zp ðsÞ Zo ðsÞ ¼ 1 þ Tm ðsÞ
Compensation parameters: Kv ¼ 1500; oz1 ¼ 0:8 od1 ¼ 26:8 krad=s oz2 ¼ 1:2 od1 ¼ 40:2 krad=s op1 ¼ oesr ¼ 172 krad=s op2 ¼ 1:7oesr ¼ 292 krad=s
T1 ðsÞ ¼ Ti ðsÞ þ Tv ðsÞ
Gain blocks: 1 ¼ ¼ 0:27; Ri ¼ 0:41 ðSn Sf þ 2Se ÞTs K 0 ð1 þ s=o0z Þ Fv0 ðsÞ ¼ v sð1 þ s=o0p Þ
0 Fm
T2 ðsÞ ¼
with 0 Ti ðsÞ ¼ Gid ðsÞRi Fm 0 Tv ðsÞ ¼ Gvd ðsÞFv0 ðsÞFm Z ðsÞGvd ðsÞ Zp ðsÞ þ Ti ðsÞ Zp ðsÞ q Gid ðsÞ Zo ðsÞ ¼ 1 þ T1 ðsÞ
Compensation parameters: Kv0 ¼ 60 000; o0z ¼ 0:9; od1 ¼ 30:2 krad=s o0p ¼ oesr ¼ 172 krad=s
Current-mode control
As shown in Fig. 1, current-mode control is implemented by sensing the diode current using a current sensing network (CSN) and feeding this to the PWM block with SW at position X. Among many candidates for current feedback signal [6], the secondary diode current is selected because it provides full benefits of the peak current-mode control [7] with a simple CSN design. While the primary switch current can be used as an alternative feedback signal, the resulting control scheme could complicate the analysis and design of current-mode control because the switch current contains the magnetising inductor current as well as the reflected output filter current. Figure 4a shows the small-signal block diagram of the current-mode controlled ASHB converter. The gain block Ri represents the gain of the CSN and Fm0 is the PWM gain for current-mode control. The expressions for the power stage transfer functions appearing in Fig. 4a are given in Table 1, and the smallsignal gain blocks for current-mode control are presented in Table 2. The sampling effect and feedforward gains of current-mode control, which do not cause significant impacts on the low-and mid-frequency dynamics of a properly-designed current-mode controlled converter [8], are not included in Fig. 4a for the simplicity of ensuing discussions. Figure 4b illustrates the principles of current-mode control based on the asymptotic plots of two individual feedback loops associated with the respective feedback signals. The current loop, Ti ðsÞ ¼ Gid ðsÞRi Fm0 , represents the feedback loop created by the diode current feedback. The CSN gain, Ri, can be chosen to place the 0 dB crossover frequency of Ti at high frequencies, typically 1/ 3-1/5 of the switching frequency [7]. The voltage loop, Tv ðsÞ ¼ Gvd ðsÞFv0 ðsÞFm0 , denotes the feedback loop associated with the output voltage feedback. The asymptotic plot for 7Tv(s)7 is constructed assuming a two-pole onezero circuit Fv0 ðsÞ ¼
Kv0 ð1 þ s=o0z Þ sð1 þ s=o0p Þ
IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
ð7Þ
vs
Gvs (s)
io
Zp (s)
vo
Gvd (s) d
iL
Gis(s)
Tv (s)
Z q(s) Gid (s) Ti (s)
B
Ri Fv (s )
Fm
A
a Tv magnitude , dB
3
Tv ðsÞ 1 þ Ti ðsÞ
z d1 −2 Ti +1 −1 cr 0dB
,rad/s
d2 −3 n −4 −1 −2
p = esr
magnitude , dB
Current-mode control
T1 'z d 1 −2 Ti d2 cr +1 Tv n −2 T2 −1 −1 −4 0dB ,rad/s 'p = esr
b
Fig. 4
−2 c
Current-mode control
a Small-signal block diagram b Individual feedback loops c Overall loop gain and outer loop gain
for the voltage feedback compensation. The parameters for Fv0 ðsÞ can be selected as outlined below: place o0z as high as possible, yet not exceeding od1 place o0p at oesr to cancel the effects of oesr adjust Kv0 to trade-off stability margins and closed-loop performance. Justifications for these selections will be provided later in this Section. Two useful loop gains can be identified from the smallsignal block diagram of Fig. 4a. While the loop gain measured at point A in Fig. 4a is defined as the overall loop 419
Gvd ðsÞFv0 ðsÞFm0 Gid ðsÞRi Fm0
for frequencies where 7Ti7c1. Accordingly, the power stage dynamics influencing both Gvd(s) and Gid(s) will not show in T2 due to canceling of their effects. Since the effects of the secondary resonance between Lm and Cc commonly appear in both Gvd(s) and Gid(s), T2 is unaffected by the secondary resonance, as illustrated in Fig. 4c. This distinctive advantage of current-mode control allows the feedback compensation to be designed, independently from the secondary resonance, to enhance the closed-loop performance of the converter. In addition, since Gvd(s) and Gid(s) both contain a common term 2(12D)Vs in their DC gain, the effects of the input voltage and duty ratio are cancelled in T2. Accordingly, current-mode control maintains the same loop gain characteristics even for applications where the converter’s input voltage is varied widely. By employing an additional feedback from the inductor current, current-mode control effectively nullifies all the detrimental effects of the secondary resonance and offers significant improvements in the converter’s performance. In voltage-mode control, the feedback gain is critically limited by the presence of the secondary resonance, and the converter’s performance thus becomes unsatisfactory and changes widely as the operating conditions are varied. In current-mode control, in contrast, the feedback gain can be increased independently from the secondary resonance, to achieve an enhanced closed-loop performance that will remain the same regardless of potential changes in the operating conditions. 4
Performance of current-mode control
This Section presents the performance of the current-mode control employed to the experimental ASHB converter operating with VS ¼ 48 V and R ¼ 0.5 O. To highlight the merits of current-mode control, the performance of the current-mode-controlled converter is presented in parallel with that of the voltage-mode controlled converter.
4.1
Loop gain
Figure 5 shows the outer loop gain, T2, of the current-mode controlled converter in comparison with the loop gain, Tm, of the voltage-mode controlled converter. The reasons for 420
40
current-mode control
magnitude, dB
20 0 voltage-mode control −20 −40 , ,
−60
theory measurement
50 0 voltage-mode control
−50 phase, deg
gain T1(s), the loop gain measured at point ‘ B’ is referred to as the outer loop gain T2(s) [7]. Fig. 4c shows asymptotic plots for 7T17 and 7T27 along with the two individual feedback loops. Being a vector sum of individual feedback loops, T1 ¼ Ti+Tv, the overall loop gain illustrates the design strategy for current-mode control. By designing 7Tv7c7Ti7 at low frequencies and 7Ti7c7Tv7 at high frequencies, current-mode control can increase the feedback gain while locating the crossover frequency of T1 at higher frequencies with good phase margin. The asymptotic plot for the outer loop gain is constructed using the relationship of T2 ¼ Tv/(1+Ti). Selection of the feedback compensation parameters for Fv0 ðsÞ can now be explained using 7T27. The purpose of the compensation zero, o0z in (7), is to allow T2 to cross over the 0 dB line with a –20 dB/dec slope. In earlier publications [9, 10], it has been shown that the location of o0z also determines the speed of transient responses. Accordingly, o0z can be placed at high frequencies to achieve a fast response, yet not exceeding od1 to avoid being a conditionally stable system [9]. The compensation pole o0p is placed at oesr to maintain a –20 dB/dec slope for a wider frequency range. The outer loop gain can be approximated to T2 TTvi ¼
−100
current-mode control
−150 −200 −250 −300 −350
102
,
theory
,
measurement 103
104
105
frequency, Hz
Fig. 5
Loop gains of experimental ASHB converter
selecting T2 for comparison with Tm are: Only for the outer loop gain T2, the definitions for the phase margin and gain margin become consistent with those of Tm. Since 7T17c7T27 for all frequencies, T2 can be used as a conservative measure for comparison. The feedback compensation parameters were deliberately chosen in a way that both current-mode control and voltage-mode control result in the same 0 dB frequency at 7 kHz. Compensation parameters for both control schemes are shown in Table 2. The analytical predictions and experimental measurements are presented in parallel in Fig. 5. As demonstrated in Fig. 5, current-mode control offers the superior loop gain characteristics with enhanced phase margin and substantial gain boost. The phase margin of current-mode control exceeds 651 while that of voltagemode control falls below 451. Current-mode control exhibits 20 dB gain boost at low and high frequencies, compared with voltage-mode control. Figure 5 also indicates that current-mode control can further increase the feedback gain without degrading the stability margins, while voltage-mode control has little room to increase the feedback gain owing to the rapid phase drop caused by the secondary resonance pffiffiffiffiffiffiffiffiffiffi ffi at od2 1= Lm Cc . Fig. 5 confirms that current-mode control effectively nullifies the detrimental effects of the secondary resonance and allows the controller to be optimised independently from the power stage dynamics. Figure 6 compares the loop gains of the ASHB converter when its input voltage is varied between 40 VoVSo60 V. As predicted in Section 2.2 and demonstrated in Fig. 6a, the loop gain of voltage-mode control is directly influenced by the change in the input voltage. In contrast, the outer loop IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
0
40 Vs =60
−20
Vs =50 Vs =40
0
magnitude , dB
magnitude, dB
20
−20 −40 theory measurement
−60
voltage-mode control
−40 −60 current-mode control
−80
−100
theory measurement
−120
a
102
103
104
105
frequency , Hz 60
magnitude, dB
40
Fig. 7 Input–output voltage transfer function of experimental ASHB converter
Vs : 40V, 50V, 60V
20
converter is given by
0
^vo Zp ðsÞ ¼ Zo ðsÞ ^io closedloop 1 þ Tm ðsÞ
−20 −40
theory measurement
−60 102
for voltage-mode control and
103
104
105
Zo ðsÞ¼
frequency,Hz
Loop gains with different input voltages
a Tm of voltage-mode control b T2 of current-mode control
gain T2 shown in Fig. 6b confirms that current-mode control effectively offsets the change in the input voltage and maintains the same loop gain characteristics.
Input–output voltage transfer function
From Fig. 3a, the input–output voltage transfer function of voltage-mode control can be derived as ^vo Gvs ðsÞ ð8Þ ¼ Gio ðsÞ ^v 1 þ T ðsÞ s closedloop
m
Similarly, the input-to-output voltage transfer function of current-mode control can be derived from Fig. 4a as vd ðsÞ Gvs ðsÞ þ Ti ðsÞ Gvs ðsÞ Gis ðsÞG Gid ðsÞ Gio ðsÞ¼ ð9Þ 1 þ T1 ðsÞ Using the power stage transfer functions given in Table 1, (9) can be simplified to Gio ðsÞ¼
Gvs ðsÞ 1 þ T1 ðsÞ
ð10Þ
Based on the fact that 7T17c7T27c7Tm7, a significant improvement in 7Gio7 is expected for the current-mode controlled converter. Figure 7 compares the input–output voltage transfer functions of the converter. As a direct benefit of the improved loop gain characteristics, currentmode control provides an additional 40 dB attenuation up to mid frequencies, compared with voltage-mode control.
4.3 Output impedance and load transient response The output impedance of the closed-loop controlled ASHB IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
ð12Þ
1 þ T1 ðsÞ
0
-20 magnitude , dB
4.2
Z ðsÞGvd ðsÞ Zp ðsÞ þ Ti ðsÞ Zp ðsÞ q Gid ðsÞ
for current-mode control. Figure 8 shows predictions of (11) and (12) in comparison with the experimental data. The experimental output impedances reveal the influence of the low-frequency measurement noise and effects of the dynamic impedances of active and passive switches that were not accounted for in the model.
b
Fig. 6
ð11Þ
current-mode control
-40
voltage-mode control
-60 theory -80
measurement 102
103
104
105
frequency ,Hz
Fig. 8
Output impedance of experimental ASHB converter
The transient response of the output voltage of a closedloop controlled converter due to its load change is closely related to its output impedance characteristics [9, 10]. The maximum value of output impedance determines the size of the undershoot or overshoot of the output voltage. The peaking in the output impedance causes an oscillatory behaviour in the transient response of the output voltage. Figure 9 shows the simulated and measured load transient responses of the experimental converter. An averaged model of the ASHB converter [5] was used for 421
current,A voltage,V
10 8 6
load current
5.0 4.8 4.6
output voltage
voltage,V
current,A
a 10
6
8 6
This work was supported in part by the HY-SDR Research Center at Hanyang University, Seoul, Korea, under the ITRC Program of IITA, Korea, and in part by the Basic Research Program of the Korea Science and Engineering Foundation under Grant R12-2002-055-02001-0.
5 4.8 4.6
output voltage
d
Load transient responses
a Simulation of current-mode control (100 ms/div) b Simulation of voltage-mode control (100 ms/div) c Measurement of current-mode control (100 ms/div) d Measurement of voltage-mode control (100 ms/div)
simulations and an electric load was used for experiments. Owing to a smooth output impedance curve with smaller peak value, the current-mode controlled converter exhibits a well damped transient behaviour with small undershoot. In contrast, owing to an output impedance curve showing a peaking with larger peak value, the voltage-mode controlled converter reveals an oscillatory behaviour with larger undershoot. 5
Conclusions
ASHB DC–DC converters are a fourth-order system due to the secondary resonance between the clamp capacitor and the magnetising inductor of the transformer. The voltagemode control adapted to fourth-order ASHB converters was found to offer only limited performance for the closedloop controlled converter. This paper has demonstrated that current-mode control can overcome the adverse effects of the secondary resonance
422
Acknowledgments
load current
c
Fig. 9
b
and enhance the closed-loop performance of ASHB converters. By nullifying the influence of the secondary resonance using a current feedback loop, current-mode control can improve loop gain characteristics, input–output voltage transfer function, and load transient response. It has also been found that the closed-loop performance of current-mode controlled ASHB converters remains the same regardless of the potential changes in operating conditions.
7
References
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IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005
