Design of an Active Differential Mode Current Filter for a Boost
Power Factor Correction AC-DC Converter
Rajib Goswami1, Shuo Wang2 and Yongbin Chu1
1
Power Electronics and Electrical Power Research Laboratory, University of Texas at San Antonio, TX 78249, USA
2
Power Electronics and Electrical Power Research Laboratory, University of Florida, Gainesville, FL 32611, USA
Email: shuowang@ieee.org (Dr. Shuo Wang)
Abstract - The aim of this paper is to introduce a
methodology to design an active DM filter at the input side
of AC-DC converters to cancel current ripples and DM
EMI noise. The boost PFC AC-DC converter’s noise
characteristic was first analyzed. The active filter
topologies are designed based on the identified
characteristics of the AC-DC converters. Several design
issues such as thermal run away, DC offset, stability and
compensation design, and the number of preamplifier
stages are to be addressed in detail. Both simulations and
experiments were conducted to validate the proposed
methodology. It is found that the proposed design
methodology can meet the design objective and the big
stability challenge for the DM active filter of AC-DC
converters.
Index Terms—Boost PFC, DM noise, Electromagnetic
Interference, Active DM current filter, AC/DC converters.
I. INTRODUCTION
Almost all the switching mode power conversion systems
generate conducted electromagnetic interference (EMI) noise
[1]. The EMI can be categorized to differential mode (DM)
and common mode (CM) EMI. The noise flowing between the
power conversion systems and ground is usually called CM
noise and the noise flowing between two power carrying
conductors is called DM noise [2]. Passive LC filters are
widely used in industry to attenuate EMI. However, the size,
weight and cost of the passive EMI filters are always a big
concern for power electronics industry. Because filter
inductors must carry the full load current and DM capacitors
must withstand full AC line voltages, the passive DM filters
can be very big. Hybrid CM filters have been proposed to
reduce the EMI filter size, weight and cost [2]. In a hybrid CM
filter, an active filter attenuates the low frequency (LF) CM
noise and a passive filter attenuates the high frequency (HF)
CM noise. Because the corner frequency of the passive filter
is significantly increased, the CM EMI filter size could be
significantly reduced. However, an EMI filter is composed of
a CM and a DM functional units [3]. The hybrid CM filter can
only reduce the size and weight of the CM functional unit. In
order to further reduce the size of the whole system, the size
and weight of the DM functional unit must be reduced. Most
of the existing techniques address the CM active filter [4-8].
Some literature addresses the DM active filter for DC/DC
applications [9]. On the other hand, the DM active filters
designed for AC-DC converters is deemed to be very
challenging [10] and there are few papers to address this topic.
In this paper, a methodology will be developed to design
This work was sponsored by The Boeing Company.
978-1-4673-7151-3/15/$31.00 ©2015 IEEE
an active DM filter in the AC side of a boost PFC AC-DC
converter. The DM noise model for the boost PFC is first
developed. Based on the developed model, the current
cancellation, voltage cancellation, feedback and feed-forward
active filters are analyzed. The feedback current cancellation
is proposed for DM active filter. Design issues such as thermal
run away, DC offset, stability, compensation design, and the
number of preamplifier stages are addressed in detail.
Solutions are proposed to these issues. Both simulations and
experiments were carried out to validate the proposed
methodology. It is found that the proposed design
methodology can meet design objective and stability challenge
for the DM active filters of AC-DC converters.
II. DM NOISE MODEL OF A BOOST PFC AC-DC
CONVERTER
Boost PFC AC-DC converters have been widely used as
front end converters to offer high power factor to power grid.
The converter works at switching mode which generates lots
of DM and CM noise. Fig.1 shows a typical boost PFC circuit
and an EMI measurement setup with line impedance
stabilization networks (LISNs) connected between the power
line and the converter. The path of DM noise current IDM is
shown in the figure. Based on substitution theory, the DM
noise model can be developed by replacing the MOSFET with
a voltage source which has the same voltage waveform as the
drain to source voltage VDS, and replacing diode with a current
source which has the same current waveform as the diode
current ID.
Based on the superposition theory, the DM noise generated
by VDS can be represented with Fig. 2. It is also found that ID
does not contribute to the DM noise on the AC input side. So
Fig. 2 is the DM noise model for a boost-PFC AC-DC
converter at continuous conduction mode. The DM noise
source impedance is determined by ZCBL//ZLB. For the
prototype used in this paper, CBL is 0.22uF and LB is 400uH.
Within the concerned frequency range from 150kHz to
30MHz, the noise source impedance ZN is determined by ZCBL.
The noise load impedance is LISN’s impedance ZLISN or grid
impedance ZGrid when LISNs are not present.
D1
D2
LB
LISNs
DB
i DM
VAC
CBL
50μH
50μH
0.1μF
1μF×2
50Ω
ID
RL
VDS
VL
CB
0.1μF
50Ω
D3
D4
Fig. 1 DM noise in a Boost PFC AC-DC converter.
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(a) Feedback,
LB
ZLISN or ZGrid
iDM
ZLISN or ZGrid
(b) Feedforward.
VDS
CBL
ZN
ICancel(s)
ZN
ICancel(s)
VN
ZGrid
ZN
iDM
VN
AT(s)
ZGrid
AT(s)
iDM
Feedback
(a)
Fig. 2 DM noise model.
Feedforward
(b)
Fig. 4 Feedback and feed-forward control.
III. ACTIVE FILTER TOPOLOGY DESIGN
In Fig. 3, to reduce DM noise, there are several ways to
design active filters based on the criteria below:
1) Based on noise sensing and cancellation method:
(a) Voltage sensing - voltage injection,
(b) Current sensing - voltage injection,
(c) Voltage sensing - current injection,
(d) Current sensing - current injection.
VCancel(s)
ZGrid
iDM
VN
ZGrid
AT(s)
V-V
iDM
ZN
ICancel(s)
(b)
ICancel(s)
VN
V-I
VN
I-V
AT(s)
(c)
ZN
iDM A (s)
T
(a)
ICancel(s)
ZGrid
VCancel(s)
ZN
For feedforward control, to achieve a good cancellation,
the active filter's gain AT(s) should be as close to unity as
possible. It has a strict requirement on the values of key
components. For feedback control, the active filter's gain AT(s)
should be as big as possible. Feedforward control does not
improve the unity gain bandwidth of the active filter over
feedback control due to the fixed unity gain-bandwidth for a
given operational amplifier. It can improve the magnitude of
gain at the pass-band, but that improvement is very much
dependent on the accuracy of the component values used in
the design [1]. Hence, due to the flexibility of the feedback
control, it is selected in this paper.
Because the current sensing - current injection is
employed, for the convenience of analysis, it is better to
represent the noise source with a Norton equivalence in Fig.5.
ZN
ZGrid
VN
ZGrid
iDM
AT(s)
Fig. 5.Noise source with Norton equivalence.
Fig. 3. DM active filter topology.
For the active filter using voltage injection method, a
voltage transformer is needed in series with AC power line. It
must therefore carry full converter currents. Furthermore, the
transformer magnetizing inductance must be big enough to
reduce the magnetizing current supplied from the active filter
so as to reduce the power loss of the active filter. Because of
this, the transformer is big and heavy which contradicts active
filter's objective: filter size and weight reduction. Because of
this, voltage injection should be avoided.
For the DM noise sensing, a current transformer is a
simple way to directly sense DM noise current. It is also
possible to eliminate the influence of CM noise current with a
proper current transformer structure.
DM noise voltage on power line can also be sensed for
active filters. However, the sensed voltage includes not only
the information of the DM noise of the boost PFC converter
but also the information of grid impedance and the voltage
noise flowing from the grid. It does not directly represent the
DM noise information of the boost PFC converter. It
complicates the filter design. Because of this, current sensing
is the best choice.
Based on analysis above, current sensing and current
injection should be used for the active filter.
In Fig. 4, the control strategy of the active filters incudes:
IN
Feedback
I-I
(d)
2) Based on control scheme:
iDM
ZN
AT(s)
The current gain GCL(s) from IN to iDM in Fig. 5 is given by
(1):
GOL ( s )
G (s) ,
(1)
G (s) =
= OL
CL
1 + AT ( s )GOL ( s ) 1 + T ( s )
ZN
where, G ( s) =
and T ( s ) = AT ( s )GOL ( s ) . T(s) is
OL
Z N + Z Grid
the loop gain. To ensure stability, T(s) must have sufficient
gain and phase margin.
The current insertion gain GIS(s) in Fig. 5 is defined as the
iDM with active filter to that without active filter. It is given by
(2) as,
1
1
.
(2)
G ( s) =
=
IS
1 + AT ( s )GOL ( s )
1 + T ( s)
GIS(s) should be as small as possible. Because of this,
active filter’s gain AT(s) should be as big as possible. It should
also have enough bandwidth. GOL(s) should be also as close to
unity as possible to achieve small GIS(s). It means ZN>>ZGrid.
Because in Fig. 2, ZN is small impedance, it is therefore
not good for the active current filter implementation in Fig. 5.
Because of this, a DM inductor LDM is added between the
boost PFC converter and the active filter. Furthermore, a DM
capacitor CR is added between the active filter and the power
grid to reduce grid impedance so that new source impedance
and new load impedance meet condition (ZLDM+ZN)
>>ZCR//ZGrid. This means GOL(s)≈1. So GIS(s)≈1/(1+AT(s)).
Fig. 6 shows this modification.
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CR
ZGrid
ICancel(s)
IN
ZN
AT(s)
iDM
both EMI noise frequency component and power line
frequency component.
One of the biggest differences between the active filter of
an AC-DC converter and a DC-DC converter is the active
filter of an AC-DC converter must avoid to inject line
frequency currents because the line frequency currents are not
the DM noise currents to be suppressed. Because of this, a
high pass filter is integrated with the CT. In Fig. 9, CHP is
added between CT and the load resistor RCT. LCT, CHP and RCT
forms a high pass filter with an I-V transfer function,
LDM
Feedback
Fig. 6.Final optimal topology for a feedback, I-I DM active filter.
IV. ACTIVE DM EMI FILTER DESIGN
A. Insertion Gain GIS(s) and Current Gain GCL(s) with LISNs
In a standard EMI noise test setup, there are two LISNs as
shown in Fig. 1 between power grid and the power converter.
Based on the CISPR 16 EMI standard, for DM noise from
150kHz to 30MHz, LISNs can be approximately modeled as a
resistance RLISN=100Ω in parallel with an inductance
LLISN=100μH as shown in Fig. 7.
50μH
100μH
ZLISN(s)
Fig. 7 LISN Equivalent Impedance Model for DM
After the insertion of LISN model between power line and
CR, the active filter topology can be shown as in Fig. 8.
LDM
LLISN R
C
LISN
R
iDM
ICancel(s)
ZN
AT(s)
IN
Fig. 8. LISNs are inserted between power line and CR.
The
equivalent
impedance
on
grid
side
1 . As discussed in the last section, due to the
|| sLLISN ||
sC R
small impedance of CR, GOL(s) is very close to unity and hence
after LISNs' impedance is paralleled with CR, GOL(s) is still
close to unity from 150kHz to 30MHz,
1
1
(3)
G (s) ≈ G (s) ≈
=
CL
IS
1 + T ( s)
·
¸¸
¹
(4)
2
1
and Q = 1
RCT
LCT CHP
LCT
C HP
LCT CHP
RCT
Vin(s)
The line frequency current usually has a high magnitude to
deliver power to the AC-DC converter. ωc must be high
enough so that the high pass filter has a high attenuation to
line frequency current component. At the same time, to
maintain a high loop gain T(s) or low GIS(s) within the
concerned frequency range above 150kHz, ωc must be below
150kHz or the first noise spike after 150kHz. There is around
3.4 decades between 60Hz and 150kHz. The high pass filter
also introduces phase shift which needs to be considered for
the stability of the active filter. Hence, careful compensation is
needed to shape the gain and phase of AT(s).
2) Cancellation of CM Noise while Current Sensing
Feedback
LISN
§ s
s
+¨
ω c Q ¨© ω c
,
Fig. 9. Current transformer with a 2nd order high pass filter.
100Ω
50Ω
50Ω
1+
2
· RCT
¸¸
¹ n
IDM(s)/n
0.1μF
0.1μF
is R
where, ω =
c
LISN
Model for DM in
Impedance 150kHz-30MHz
ZLISN(s)
50μH
1μF×2
Vin ( s )
=
I DM ( s)
§ s
¨¨
© ωc
In this paper, only the reduction of DM noise is considered
so the performance of active filter in reducing DM noise is the
focus. The AC-DC converter also generates CM noise which
circulates between the power-line and the ground. Hence,
when the current is sensed using a CT, it senses both the CM
and DM currents. In Fig. 10, the current sensed by a typical
CT is connected to a single power line. The sensed primary
current iprim includes both DM and DM noise: iprim=iDM+iCM.
Line 1
1 + AT ( s)
Noise
Receiving
End
Based on (3), the active filter's noise attenuation
performance and stability are determined by T(s). T(s) should
be analyzed and designed.
B. Active Filter Circuit Design
Toroidal current transformer
Sensed Primary Current =iDM + iCM
iDM
iDM
iCM
Noise
Source End
iCM
Line 2
1) Current Transformer Integrated with a High Pass Filter
A toroidal current transformer (CT) with a turn ratio n is
designed to sense the DM current. The magnetizing
inductance of the secondary is LCT. The sensed current has
Fig. 10 Noise current sensing using a current transformer.
A simple current sensing technique can be applied to
cancel the CM noise current from the sensed current. In Fig.
11, this CT arrangement technique has been shown.
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Line 1
Noise
Receiving
End
Toroidal current transformer
Sensed Primary Current =2×iDM
iDM
iCM Noise
Source End
iDM
iCM
The amplifier has a preamplifier stage (for voltage
amplification) and a current amplifier stage. The preamplifier
stage is composed of a wide bandwidth operational amplifier
and the current amplifier stage is a class AB amplifier.
b)
Line 2
Fig. 11 Cancelling CM noise from the sensed noise current.
In the arrangement as shown in Fig. 11, the line 1 goes
through the CT's toroidal core in exactly the same manner as
in a typical CT and the noise current flows through it is
iDM+iCM . The difference in this arrangement is that the line 2
is also made to pass through it in the reverse direction so that
iDM-iCM also passes through the toroidal core. Hence, due to
this arrangement the total current sensed by the CT is,
iprim=2×iDM. The sensed iCM is canceled. . The CT’s I-V
transfer function of (4) is now modified as follows,
2
§ s · R
2 × ¨¨ ¸¸ CT
Vin ( s)
(5)
© ωc ¹ n
=
2
I DM ( s)
§ s ·
s
+ ¨¨ ¸¸
1+
ωcQ © ωc ¹
The first advantage of this arrangement is that, it does not
sense CM noise which will be dealt with a dedicated CM
hybrid filter. The second advantage is that it increases the DM
current by twice (6 dB) which eventually increases the loop
gain. The stability issue for both low and high frequencies
needs to be considered carefully with this increased loop gain.
Number of Preamplifier Stages
More than one stage preamplifiers can increase the open
loop gain of the amplifier. It leads to increased -3dB
bandwidth. However, the open loop gain of an operational
amplifier usually has a single pole within the concerned
frequency range. One stage preamplifier introduce -π/2 phase
shift. m stage cascaded preamplifiers introduce -mπ/2 phase
shift. Because the output of CT has almost no phase shift
within the concerned frequency range, with more than one
stage preamplifiers, the AT(s) will have more phase shift
which causes stability issues. Because of this, a single stage
preamplifier is preferred.
Class AB Amplifier Design
c)
A class AB amplifier is used in the output stage of the
active filter circuit to have a higher current injection capacity.
A typical configuration is shown In Fig. 13(a).
+VCC
RB1
ID
Iin
V1
3) Amplifier Design
Fig. 12 shows the amplifier block diagram. It includes preamplifier stage and current amplifier stage.
-VCC
Current amplifier
Preamplifier
RB1
ID
Iin
V2
Iout
V1
T2
IC
IRB1
+
T1
VBE -
+ RE1
V
-D
V2
Iout
RE2
RB2
Zload
T2
-VCC
(b)
Fig. 13 Class AB Amplifier (a) Typical, (b) with emitter resistors
Cinj
Rinj
Rinj
(b)
Fig. 12. Amplifier configuration: (a) current feedback and (b) voltage feedback.
a)
T1
+
V
-D
(a)
Current amplifier
Cinj
(a)
+
VBE -
Zload
RB2
Preamplifier
+VCC
IC
IRB1
DC Offset Issues
In Fig. 12, the voltage amplifier (b) instead of current
amplifier (a) is employed here because the current amplifier
may have output DC offset issues. This is because the current
amplifier regulates the output current so the output voltage
may have DC offsets due to the unbalanced charge on the
capacitor Cinj in the injection network or load impedance. The
charge on the capacitor will build up and may finally saturate
the output and then the active filter cannot work properly. The
voltage amplifier regulates the output voltage, there is no
output DC offset issues. Although voltage amplifier is used, it
can still inject currents as the output voltage is added to the
injection network and the load impedance.
A class AB amplifier has an npn and a pnp transistor with
equal base to emitter voltage. The two transistors should have
a very high bandwidth and does not reduce the active filter’s
bandwidth for the specified EMI frequency range. They
should have enough current injection capacity and have
sufficient power rating for the desired conditions. ZDT6753,
npn-pnp complementary pair was chosen in the design. The
two transistors in ZDT6753 have very similar features. It has a
typical transition frequency (bandwidth) of 175MHz and
hence does not have adverse effects in the concerned EMI
frequency range. For biasing the amplifier, different biasing
techniques has been analyzed. It is found that, as the supply
voltage ±VCC can be fixed to a certain value, a simple diode
bias would the advantage of having less number of
components and simplicity of design. From the IC-VBE(ON)
curve of the transistor as shown in Fig. 14, the turn-on baseemitter voltage, VBE(ON)=0.545V. It corresponds to a
collector current, IC at 0.6mA. For having a good high
frequency performance 1N4148 signal diodes are used for
biasing. The voltage across diode, VD should be slightly
higher than VBE, so it was chosen as VD=0.57V. From the IDVD curve of diode, as shown in Fig. 15, VD corresponds to a
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diode current, ID=0.3mA. To handle high injection current, the
current in bias should be high enough, so two bias diodes are
in parallel. Now, IRB1 ≈ 0.6mA.
0.01
0.009
0.008
IC (A)
0.006
0.004
0.003
X= 0.545
Y= 0.0006
0.001
0
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
VBE(Volt)
Fig. 14 IC-VBE(ON) curve of the transistor.
-3
x 10
ID (A)
4
Rescaled and Redrawn
From Diode Datasheet
3
Z Load
1
X= 0.57
Y= 0.0003
I inj
Vout
0.45
0.5
0.55
0.6
0.65
0.7
≈
0.75
1
+ Rinj
sCinj
1
+ Rinj
sCinj
(6)
sC inj
1
=
§ 1
· 1+ s
¨
+ Rinj ¸
ω inj
¨ sCinj
¸
©
¹
Here ωinj=1/(RinjCinj).
VD (Volt)
D. Component Parameter and Compensation Design
Fig. 15 ID-VD curve of the bias diode.
With the relationship, R = VCC − VD , the value of RB1 can
B1
Active filter’s open loop transfer function is,
I inj
Vin Vout I inj .
I RB1
be calculated. The value of RB1 is dependent on the bias
voltage or supply voltage, VCC. Hence, the value of VCC needs
to be chosen first. VCC needs to be chosen considering the
highest magnitude of the injected current, so that the
amplifier’s output voltage V2 is still smaller than VCC for that
magnitude of injected current.
d)
§ 1
·
+ Rinj ¸ ≈
Z Load = Z CR || ( Z LDM + Z N ) + ¨
¨ sCinj
¸
©
¹
§ 1
·
= Z LISN || Z CR || ( Z LDM + Z N ) + ¨
+ Rinj ¸ ≈
¨ sC
¸
inj
©
¹
The transfer function from the output voltage of class AB
amplifier to injection current is therefore,
(7)
2
0
0.4
IC
The current injection network consists of an injection
capacitor Cinj and a small resistor Rinj. The injection capacitor
is needed for the isolation of active filter from high voltage
AC power line and the resistor is needed to ensure stable
impedance and a constant gain on pass-band. The load
impedance of the class AB amplifier is the impedance of the
injection network in series with the impedance between two
power lines as shown in Figs 6 and 8.
The load impedance is given by (6) for without LISNs and
(7) for with LISNs. Due to the small impedance of CR, the
load impedance of the class AB amplifier is mostly
determined by injection network if the injection network is
properly designed.
X= 0.57
Y= 0.002
0.002
5
ID IS
I C I SD , where VT is thermal
C. Current Injection Network Design
0.005
6
the following relation, R =
E
VT ln
voltage, ID is diode current, ISD is diode saturation current, IC
is collector current and IS is BE junction saturation current, I
The class AB amplifier configuration with the emitter resistors
is shown in Fig. 13 (b).
Rescaled and Redrawn
From Transistor Datasheet
0.007
value of emitter resistors, RE1 and RE2 can be done based on
Thermal Runaway Issue for the Class AB Amplifier
For the class AB amplifier, the two transistors have power
loss which generates heat and increases device temperature.
When the transistor temperature increases, the transistor base
to emitter (BE) junction voltage drops. However, the BE bias
voltage is not reduced. This causes the transistor to enter linear
region. As a result, there is more current flowing through two
transistors and generating higher conduction power loss. This
in turn further increases the device temperature until the
transistors are killed.
Two emitter resistors RE1 and RE2 are added to the class
AB amplifier. They provide a negative feedback to stabilize
the BE junction bias voltage. They were proved to be an
efficient solution to thermal runaway issue. Choosing the
AT ( s) =
I DM
=
I DM
×
Vin
×
(8)
Vout
Hence, compensation can be designed for Vout/Vin to
achieve desired gain and stability. n, LCT and RCT are designed
based on primary currents, magnetic core characteristics and
the desired loop gain. CT should be designed to make sure that
the CT core does not get saturated for the designed current and
desired inductance. In this paper, the current transformer was
designed to have 10 turns and the chosen value for the high
pass filter inductor is 1mH. The CT was made with
ZW41610TC core from the Magnetics Company and has
around 0.96mH with 10 turns. CHP can be determined based on
the attenuation required at the line frequency. These three
values determine ωc and Q in equation (4).
The injection pole frequency, ωinj is determined by Rinj and
Cinj. Rinj should be small to limit the power loss and also the
conditions of (6) and (7) should be satisfied. From (7) and (8),
Rinj also influence active filter’s loop gain 1/Rinj above ωinj.
Hence, to obtain enough gain at the pass-band, Rinj should not
be too big too. The choice of Cinj is dependent on the allowable
60Hz leakage current flowing through the Cinj. It is due to the
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fact that at line frequency (60 Hz for the case under
consideration) the impedance of Cinj is typically much higher
than Rinj (due to the small value of Rinj). Hence, the impedance
of Cinj determines the leakage current at line frequency due to
the drop of line voltage across the injection network. High
leakage 60Hz current causes power loss to class AB amplifier.
To limit the leakage current the value of Cinj needs to be small
(high impedance). To keep a constant ωinj, a small Cinj requires
a big Rinj. Hence, there is a tradeoff between the choices of
these two values.
The preamplifier can be designed to have the desired gain
at pass-band and also to have sufficient phase and gain
margin. It is assumed that the operation amplifier can be
approximated with unity gain-bandwidth Aωop, where A is the
open loop gain and ωop is the open loop single pole corner
frequency. Another requirement for the operational amplifier
is to have a high operating voltage. This is necessary to make
sure that the operational amplifier is not saturated even when
the maximum injection current is reached. This high operating
voltage condition decreases the possibility of using a low
voltage, high bandwidth operational amplifier. For the
compensation design, a simple non inverting topology with a
single amplifier stage has been chosen. Combining all the
individual parts the chosen voltage amplifier current injection
active filter circuit is shown in Fig. 16. In Fig. 16, for the
simple non inverting topology, voltage gain of the amplifier is
given by, Vout/Vin=1+ZF/ZG.
For AT(s) in (8), the Vin/IDM in (5) and Iinj/Vout in (7) have
three zeros at the origin. At high frequencies, these zeros at the
origin are cancelled by the poles in (5) and (7).Operational
amplifier’s pole will be the only pole at high frequencies. High
frequency compensation design would be discussed in a later
section.
Low frequency instability could happen before 150kHz
when loop gain is higher than unity and there is not enough
phase margins. Hence, low frequency compensation design
should focus on the frequency below 150kHz when loop gain
is
still
smaller
than
unity.
In
the
design,
1 , for implementing those
1 and
Z F = RF +
Z G = RG +
sCF
sCG
compensation pole and zero at low frequencies. Hence, at low
frequencies, the voltage gain of the amplifier becomes,
s
1+
ωCMP1
Vout
(9)
= AOP ×
s
Vin
1+
ωCMP 2
1
where, AOP = C F + C G ,and ω CMP 2 =
,
C G RG
CF
ω CMP1 = ω CMP 2 × AOP ×
RG
RG + RF
The zero at ωCMP1 needs to be placed very close to CT’s
corner frequency ωc as shown in Fig. 17, so that the magnitude
continues to rise at 40dB/dec and at the same time, the phase
is compensated. This high rate is important if a high gain is
needed for the EMI frequency range. The remaining pole at
ωCMP2 has to be placed in between ωc and ωinj, so that there is
sufficient gain and phase margin. In the high frequency range
(>150kHz), for a more accurate model, the model is modified
to include operational amplifier’s internal output resistance R0
and its open loop transfer function characteristics becomes as
follows,
Z
1+ F
(10)
Vout
ZG
=
Vin
s ­§ Z F · § Z F ·§ R0 · § R0 ·½
¸ + ¨1 +
¸¨
¸+¨
¸¾
1+
®¨1 +
Aω op ¯¨© Z G ¸¹ ¨© Z G ¸¹¨© Z Load ¸¹ ¨© Z G ¸¹¿
At low frequencies, (10) can be approximated using (9)
and hence the pole placements hold alright. Considering (10)
and plugging in all the different transfer functions of (8), the
final loop gain of the active filter becomes,
2
AT ( s ) =
I inj
I DM
§ s · R
2 × ¨¨ ¸¸ CT
© ωc ¹ n × sCinj ×
=
2
s
s
§ s ·
s
1+
1+
+ ¨¨ ¸¸ 1 + ω
inj
Aωop
ωc Q © ωc ¹
1+
ZF
ZG
­§
Z F · § Z F ·§ R0
¸ + ¨1 +
¸¨
®¨¨1 +
Z G ¸¹ ¨© Z G ¸¹¨© Z load
¯©
· § R0
¸¸ + ¨¨
¹ © ZG
·½
¸¸¾
¹¿
(11)
+VCC
T1
RB1
CHP
Isec
LCT
RE1
Vin
RCT
ZG
RE2
ZF
RB2
RLISN
Vout
LLISN
CT
CInj
T2
RInj
-VCC
IPrim
LDM
CR
ZN
ICancel
IN(s)
Fig. 16 Active filter circuit connected in the Feedback configuration.
dB
+20
|AT(s)|
-60
ωCMP 2
20dB/dec
ωinj
ωop '
40dB/dec
60dB/dec
ωc , ωCMP1
Radian
Frequency
ωinj
Fig. 17. Loop gain AT(s).
Fig. 17 shows the loop gain with all the corner frequencies
described above. ωop’ which is not directly shown but can be
derived from (11), is caused by the pole ωop of the operational
amplifier in (11).
E. Design of Operational Amplifier and Related Component
While choosing operational amplifier, the conditions as
presented before needs to be satisfied. The operational
amplifier can be selected based on its internal structures:
voltage feedback amplifiers (VFAs) or current feedback
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F. Loop Gain Adjustment for High Frequency Stability
The operational amplifier AD829 can be approximated
using a single pole until a very high frequency. But if the pass
band (150kHz-30MHz) gain needs to be increased, careful
high frequency compensation is required. This compensation
is needed due to the fact that the operational amplifier has
parasitic poles and zeros at high frequency. Hence, the gain
needs to be adjusted to fall below zero dB (unity gain) before
the phase becomes affected by those parasitic poles and zeros.
This can be done by adding a very small valued capacitor
CFCMP in parallel with ZF. ZF is now modified as,
§
1 ·
1
. With this compensation method
¸¸ ||
Z F 1 = ¨¨ RF +
sC F ¹ sCFCMP
©
a pole-zero pair is added and enough phase and gain margin
can be ensured at high frequencies. With the stated
1
, and the
configuration, the pole is placed at ω
PCMPH =
RF C FCMP
§ R + RF
= ωPCMPH ¨¨ G
© RG
In this design a 10pF CFCMP capacitor is used.
zero is placed at
ω ZCMPH
where, ω
ZCMPH
the low frequency spectrum with and without the active filter
in section V below.
Magnitude(dB)
30
With CFCMP
10
0
-10 5
10
6
10
Frequency
10
7
10
7
Phase(Degree)
100
0
-100
-200 5
10
6
10
Frequency
Fig. 18 Comparison of Loop Gain without and with the Compensation
Capacitor.
V. EXPERIMENTAL RESULTS
A prototype was developed with a pass band gain of 20dB
following the methodology developed above. The prototype
was first tested using a signal generator and an RF amplifier as
the noise source. Then the prototype was used for a boost PFC
AC-DC converter to reduce its DM noise. The simulations
and the experiments fully validate the proposed design
technique above.
120
Without Active Filter
With Active Filter
100
80
60
40
20
·.
¸¸
¹
The measured loop gain with and without the CFCMP
capacitor for the circuit in Fig. 16 are compared in Fig. 18.
The loop gain was measured using network analyzer Agilent
4395A. The loop gain was calculated from the measured Sparameters. It is shown that the designed circuit has a good
pass-band gain and has sufficient phase margin (no stability
issue) when CFCMP capacitor is used. The frequencies lower
than 100kHz is not shown in this measurement due to the
frequency limitation of the network analyzer Agilent 87511.
The low frequency stability was also ensured by using a
square wave generator as the noise source, Vds and checking
Without CFCMP
20
dbuA
amplifiers (CFAs). Both of them have their advantages and
disadvantages. The good thing about CFAs is that they can
have higher bandwidth as compared to VFAs. But in CFAs,
the condition of single pole approximation for the transfer
function is not applicable, as their structure is more different.
Moreover they tend to have more offset voltages as compared
to VFAs. Hence, a VFA is preferable here. While choosing
between different VFA's, the single pole approximation should
hold for the chosen operational amplifier. The supply voltage
of the operational amplifier needs to be high enough so the
operational amplifier's output should not get saturated even for
the highest amplitude of the output voltage. Another thing to
consider is that the operational amplifier should have both
positive and negative supply voltage due to the circuit
topology chosen as shown in Fig. 16 (a single power supply
with a DC bias to the amplifier may also be a choice). In this
design AD829 VFA is chosen, as this operational amplifier
has a high bandwidth and meets those criterions stated above.
Based on the operational amplifier's performance the value of
RG, CG and RF, CF needs to be chosen using (9). If the chosen
resistor values are too big or too small the operational
amplifier's performance becomes bad due to the internal
circuit structure of the operational amplifier. In this work,
RG=100Ÿ, RF=1000Ÿ, CG=69nF, CF=22nF are used.
0 5
10
6
10
Frequency(Hz)
10
7
Fig.19 Measured DM noise with and without active DM filter for a
square wave noise source from 100kHz to 30MHz.
In Fig. 19 the noise is generated using a signal generator
and an RF amplifier. In the measurement, CR is 0.2μF and LDM
is 180μH. The square wave noise which has high frequency
harmonics was fed to the active filter. In Fig. 19, the noise
spectrum without the active filter is shown by black lines and
the noise after the addition of the active filter is shown by grey
lines. It is seen that the active filter is working as expected
and reduced the noise by around 20dB in the pass-band. After
around 12MHz, it cannot cancel the EMI noise which is also
expected from the measured loop gain of Fig. 18 as loop-gain
is almost equal to the inverse of the insertion gain as predicted
by (2).
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To validate that the designed active filter will have reduced
performance below 150kHz, the square wave’s frequency is
adjusted to 10kHz. Fig. 20 shows the measured spectra from
10kHz to 500kHz. It clearly shows that due to the high pass
filter integrated with the active filter, the active filter has
reduced performance below 150kHz. It has negligible noise
reduction performance for 10kHz noise.
90
Without Active Filter
With Active Filter
80
70
60
dbuA
50
40
30
20
10
0
-10 4
10
5
Frequency
10
VI. CONCLUSION
In this paper, a FB current cancellation active DM filter is
proposed, implemented, and tested, and techniques to improve
the performance of active filters are explored. This paper
focuses primarily on the challenges of implementing the FB
circuit topology for the case of AC-DC converters. It begins
with introducing the DM EMI noise model for a boost PFC
AC-DC converter. It describes the constraints and impedance
requirements for the successful implementation of the active
filter. It also discussed the choice of active filter topologies.
Then it develops the steps for the active filter hardware design
and describes the constraints for choosing the individual
components. Based on the proposed design methodology of
this paper, a prototype active filter circuit has been
implemented. The developed active filter circuit can ensure
stability as well as maintain a particular gain requirement,
which are big challenges in case of active filter design for ACDC converters. The prototype was tested using a square wave
noise source and also with a boost PFC AC-DC converter. The
developed technique was validated with experiments.
Fig. 20. Measured DM noise with and without active DM filter for a square
wave noise source from 10kHz to 500kHz.
In Fig. 21, the measured DM noise for a boost PFC ACDC converter is presented. The noise spectrum without the
active filter is shown by black lines and the noise with the
active filter is shown by broken grey lines. The PFC has a
variable switching frequency due to its control scheme. In
both measurements, all the CM and DM capacitors of the
existing EMI filter of the boost PFC converter were removed
(only the boost PFC capacitor CBL was not removed). The
value of CR is 0.2μF and LDM, the leakage inductance of a CM
inductor, is around 300μH. They meet the stated impedance
condition as found from (2) and (6).
90
Without Active Filter
With Active Filter
80
70
dbuA
60
50
40
30
20
10
0 5
10
6
Frequency
10
Fig. 21 Measured DM noise with and without active DM filter for a boost
PFC AC-DC converter source
For the boost PFC converter under consideration, the noise
spectrum becomes very low at frequencies above 1MHz and
after this frequency it becomes difficult to measure the
improvement due to active filter, as it becomes close to
background noise. It is shown that the results meet the
designed pass band gain (not include LDM and CR’s
attenuation) when the noise is measurable below 1MHz and it
also operated free of instability.
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