Calculating External Components

AND8332/D
Calculating External
Components
Prepared by: Stef Servaes
ON Semiconductor
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APPLICATION NOTE
Scope
Additional proprietary handshaking is implemented as a
fifth class to program with an external resistor.
The ON Semiconductor vertical N−channel DMOS
device is inherently robust for fast transients. This results in
cable ESD levels of 2 kV (on the RJ45 connector) and HBM
ESD levels of 2 kV.
The PWM controller facilitates single−ended SMPS
power supply topologies such as fly−back and forward
converters. The control scheme is based on peak current
control. This control allows line feed−forward,
cycle−by−cycle current limitation and simple feedback
compensation.
The inrush current limit, operational current limit,
operating frequency and soft start time are programmable,
depending on the requirements of the application.
This application note attempts to give a step−by−step
approach to the implementation of a stable power supply. All
aspects of the process from converter architecture to the
PCB layout guidelines are explained, while trying to
minimize the mathematics necessary to perform the steps.
Converter transfer functions are not deduced as literature on
these topics is widely available.
An isolated fly−back topology is described in this
document. Other topologies are discussed in separate
application notes.
Although the document mostly references the NCP1081,
the discussed principles and calculations for the external
components are equally valid for the NCP1080, NCP1082
and NCP1083.
This document describes how to calculate external
component values for the NCP1080, NCP1081, NCP1082
and NCP1083 integrated PoE−PD and DC−DC converter
controller and elaborates on implementation details, without
delving into theoretical details. Examples are illustrated
with the use of the supplied calculation scripts.
Introduction
The NCP108x are robust, flexible and highly integrated
solutions targeting demanding medium− and high−power
Ethernet terminals. The combination of an enhanced
PoE−PD fully compliant with the IEEE 802.3af and IEEE
802.3at specifications for the NCP1081 with a highly
efficient SMPS, in a single device, offer new opportunities
for the design of products directly supplied over Ethernet
lines. Elimination of the need for any local power adaptor or
power supply drastically reduces the overall installation and
maintenance cost.
ON Semiconductor’s unique process and design
enhancements allow the NCP1081 to power PoE systems
with up to 40 W. The NCP1080 is designed to support power
levels up to 15.4 W, according to the IEEE 802.3af
specification.
The hot swap PD switch and programmable current limit
are designed for high power applications. The handshaking
for power requirements for the IEEE 802.3at standard
supports Type 1 and Type 2 classification with Layer 1
single and dual events as well as Layer 2 classification.
© Semiconductor Components Industries, LLC, 2011
May, 2011 − Rev. 0
1
Publication Order Number:
AND8332/D
AND8332/D
CURRENT MODE CONTROL, ISOLATED FLY−BACK CONVERTER
0.1uF
VPORTP
Bridge1
Magnetics1
0.1uF
1-TX+/BI_DA+
2-TX-/BI_DA3-RX+/BI_DB+
4-NC/BI_DC+
5-NC/BI_DC6-RX-/BI_DB7-NC/BI_DD+
8-NC/BI_DD-
Cline
Zline
0.1uF
Bridge2
RJ45
Magnetics2
VPORTN
0.1uF
Optional ground coupling
capacity. Do not equip.
Cpd, multiple footprints to
allow precise adjustment and
ESR tuning
Cpd1 Cpd2
Cgnd
Cpd3
Csn2
Rbw
T1
Dbw
VPORTP
Cf1
VDDH
CLASS
Rinrush
Rled
Led
Rfb3
VDDL
INRUSH
Rbias1
Rilim1
Cvddl
ILIM1
Cfb2
NCP1081
Csn1
nClassAT
UVLO
U2
Rbias2
Q1
Rgate
Rfb1
GATE
Rdet2
TEST2
CS
TEST1
FB
OSC
COMP
SS
VPORTN1
VPORTN2
1
Cout1 Cout2
Rclass
Rdet1
Vout
L1
Dsec
Cvddh
VPORTP
Cout, multiple footprints to
allow precise adjustment and
ESR tuning.
Rsn2
Rsn1
Rsl
ARTN
RTN
Rcs
Cfb1
TL431
Rfb2
VPORTN
Css
Rosc
Figure 1. Isolated Fly−back Converter with Bias Winding and Diode Bridge
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Cf2
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AND8332/D
Figure 2. Primary Circuitry of the Flyback Converter Using Active Rectification for Better Overall Efficiency
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AND8332/D
PoE−PD SIDE DESIGN
The Isolated Fly−back Converter with Bias Winding and
diode bridge is shown in Figure 1. The primary circuitry can
use also the active rectification bridge for better overall
converter efficiency(Figure 2).
We will calculate or decide on the values for the
components listed in Table 1.
Detection and UVLO Setting
During the detection phase the input impedance of the PD
device is measured by the PSE and should, according to
IEEE 802.3af/at, be included between 23.75 kW and
26.25 kW. The NCP108x can either use its internal under
voltage lockout setting of 37.5 V, or an external resistor
divider can be used to tune the UVLO. The NCP108x will
not allow operation of the power converter unless the sensed
line voltage is above the UVLO pin limit (internal or
external). Rdet or the sum of Rdet1 and Rdet2 should hence be
25.5 kW. The UVLO limit, Vuvlo_on, should be configured to
the low−line design parameter of the converter. In most
cases this will be 36 V. Use Equation 1 to calculate Rdet1 and
Rdet2.
Table 1. LIST OF COMPONENTS
Name
Description
Cout1,2
DC−DC output capacitor
Cpd1,2,3
DC−DC input capacitor
Rcs
Resistor for current sensing
Rsl
Resistor for extra slope compensation (optional)
Rclass
Resistor setting the classification current level
Rinrush
Resistor setting the inrush current limitation level
Rilim1
Resistor setting the operational current limit level
Cline
Input line capacitor
Zline
Tranzorb (transient voltage suppression diode)
Rdet1
Detection signature and external UVLO programmable resistor 1
where Vuvlo_ref = 1.2 V
Rdet2
Detection signature and external UVLO programmable resistor 2
Classification
Csn1
Snubber capacitor for the switching transistor
Rsn1
Snubber resistor for the switching transistor
Csn2
Snubber capacitor for the power diode
Rsn2
Snubber resistor for the power diode
Rfb1
Resistor for the voltage feedback system
Rfb2
Resistor for the voltage feedback system
Rfb3
Resistor for the voltage feedback system
R det2 +
V uvlo_ref
V uvlo_on
+ 25.5 kW
(eq. 1)
and
R det2 ) R det1 + 25.5 kW
IEEE 802.3af/at specifies five power classes (0 − 4).
During classification the PSE equipment will sense the
current that flows through Rclass to determine what power
consumption class the PD equipment belongs to. Table 2
indicates what resistor value to use for Rclass for the different
classes. Note that a fifth non−standard high−power class is
defined to enable the NCP1081 high power capabilities.
Table 2. IEEE 802.3AF/AT POWER CLASSES
Rclass
(W)
Rbias1
Resistor for extra biasing current in the opto−
coupler (optional)
Rbias2
Resistor for extra biasing current in the TL431
shunt regulator (optional)
10k
Class 0: 15.4 W
130
Class 1: 4 W
Cfb1
Capacitor for the voltage feedback system
69.8
Class 2: 7 W
Cfb2
Capacitor for the voltage feedback system
44.2
Class 3: 15.4 W
Rbw
Current limiting resistor for bias winding usage
30.9
Class 4: IEEE 802.3at device class
Rled
Current limiting resistor for nCLASS_AT LED
22.1
C1..4
Capacitors for noise reduction on the Ethernet
magnetics
Class 5: NCP1081 class, power levels exceeding IEEE 802.3at levels
Cvddl
Decoupling capacitor for VDDL low voltage regulator
Cvddh
Decoupling capacitor for VDDH high voltage
regulator
Rosc
Resistor setting the PWM switching frequency
Power Class
The IEEE 802.3at specification describes a second
classification event to let the application know if higher
power (higher than IEEE 802.3af power levels) can be
switched on. This second classification is either supported
by hardware (NCP1081, not NCP1080) or by software on a
network processor, powered by the NCP1081. The PSE
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AND8332/D
Power Stage Design
decides which classification will be executed. When the
hardware classification is complete the nClassAT pin is low.
When the hardware classification is not executed, meaning
that either the PSE is IEEE 802.3af compliant or that the
high power capabilities will be exchanged by the network
protocols, the nClassAT will remain high. The LED
connected to nClassAT will only light when the second
event hardware classification has completed.
Decide on the System Parameters and Transformer to
Use
Table 5. INPUT PARAMETERS
Programmable Current Limitation
Inrush Current Limit
Table 3 lists the typical values for Rinrush.
Table 3. PROGRAMMABLE INRUSH CURRENT
Rinrush (kW)
Min
Typ
Max
Unit
150
95
125
155
mA
57.6
260
310
360
mA
Table 4. USEFUL VALUES FOR Rilim1
Typ
Max
Unit
84.5
450
510
570
mA
66.5
600
645
690
mA
56.0
720
770
820
mA
36.5
970
1100
1230
mA
Vin
Ethernet input voltage. Take into account the
drop over the diode bridge.
Vout
The desired output voltage
Lprim
The inductance of the primary of the transformer
N
The transformer turns ratio
Pout
The desired output power
Vripple
The desired output ripple
The desired PWM switching frequency
The switching frequency (fs) supported by the NCP108x
ranges up to 500 kHz. Higher frequencies reduce the size of
the transformer but may have adverse effects on other
parameters such as switching loss. The designer will have to
find an optimum between power consumption and material
cost.
Note that this entire design guideline is focused on the
implementation of a current measurement feedback loop on
top of voltage feedback.
Table 4 lists the typical values for Rilim1.
Min
Description
fs
Operational Current Limit
Rilim1 (kW)
Parameter
Configure the Switching Frequency
The PWM switching frequency is configured by an
external resistor Rosc. Rosc is calculated using Equation 2,
below.
Note that non−standard compliant current can be achieved
by lowering Rilim1. Keep in mind that the absolute
maximum rating for the current through the NCP1081 is
1.23 A. Note that the board layout should allow proper
thermal conductivity to avoid exceeding the maximum
junction temperature.
R osc +
38600
fs
kW
(eq. 2)
Where fs (kHz) the desired switching frequency
Continuos Conduction Mode (CCM) or Discontinuos
Conduction Mode (DCM)
Diode Bridge and Cline
Note that the NCP108x is designed to operate in
continuous conduction mode (CCM) and discontinuous
conduction mode (DCM). Pros and cons exist for both
modes of operation. In CCM, the ripple current is smaller
and possibly a smaller output capacitance can be used. In
DCM, the conduction losses are higher (because the currents
are higher) but the switching loss is smaller (due to current
being zero when switch opens). Also in DCM, a smaller
inductor or transformer can be used, leading to lower
leakage inductance. On the other hand, the AC losses in the
DCM transformer may become dominant. Due to the higher
currents in DCM, the DCM converter creates more EMI.
Cline should be a 100nF ceramic with low ESR (< 0.1 W)
and 20% tolerance. The diode bridge should be dimensioned
to allow the maximum current that is chosen for the design.
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AND8332/D
Iprim
Iprim
Iprim
t
t
Also take into account the forward voltage drop of the diode
(typically 0.5 V).
V inT onN 1 + V outT offN 2
D/fs
Critical Conduction Mode
t
å
D/fs
D/fs
Dead time
Discontinuous Conduction Mode Continuous Conduction Mod
N1
N2
+
N
å D max +
Switching frequency, transformer induction and load are
parameters that make the converter run in one or the other
mode. The transition from one to the other mode depends on
these three values. The point where the system transitions
from DCM to CCM is called the critical conduction mode.
Correspondingly, we can define the critical load, frequency
and induction.
2 @ Lc @ fs @ n2
(1 * D )
LC +
2
N
N
1
N
2
)
1
2
V
(eq. 6)
in_min
V
out
Calculate the Various Currents
Ipeak_pri
Iavg_pri
R c @ ǒ1 * D) 2
2 @ fs @ n2
R C(1 * D)
FC +
(eq. 5)
1 * D max V out
Figure 3. CCM/DCM
RC +
V in_min
D max
2
t
(eq. 3)
Ton
2 @ LC @ n
The design procedure described in the following sections
focuses on CCM operation. Equation 3 can be used to find
out how far the design is from running in one or the other
mode.
Ipeak_sec
Toff
t
Figure 5. Primary and Secondary Currents (ccm)
Calculate the Duty Cycle
First calculate the converter duty−cycle D from the
assumption that in one full cycle the secondary voltage
should be zero and thus equal the shaded areas of Figure 4
where T is the period.
Average currents, during Ton:
I avg_pri +
P out
V in @ D @ h transformer
I avg_sec +
V
Vin.n
P out
(eq. 7)
V out @ (1 * D)
Magnetizing currents:
(1-D)T
I mag_pri +
DT
V in @ D
L pri @ f s
(eq. 8)
Vout
I mag_sec +
Figure 4. Determining the Duty−Cycle
V out
V in
D
+n
1*D
ǒVout ) VdiodeǓ @ (1 * D)
L sec @ f s
Peak currents:
(eq. 4)
I peak_pri + I avg_pri )
I mag_pri
or
D+
V out
I peak_sec + I avg_sec )
V out ) nV in
The NCP108x supports duty cycles up to 0.80. Use
Equations 5 and 6 and the data of the chosen transformer to
calculate whether or not the maximum duty cycle can be
met. Note that the duty cycle is at a maximum when the input
voltage is at its lowest (low line), therefore we use Vin_min .
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2
I mag_pri
2
(eq. 9)
AND8332/D
RMS currents:
and
I rms_pri +
P out
Z L + 2pf sL
V in @ ǸD @ h transformer
I avg_sec +
or
(eq. 10)
P out
LC +
V out @ Ǹ(1 * D)
Use the duty−cycle D to obtain a value for Cout.
P out
2D
f sV ripple
V out
(eq. 11)
f LC +
Cout1
s
ǒ1 ) wzesr
Ǔ @ ǒ1 * w s
V ripple_esr
ZC ) ZL
1)
Ǔ
(eq. 16)
s
wp
where
w zesr +
1
R esr @ C out
(eq. 17)
wzesr is a zero originating from the output capacitor and its
equivalent series resistor.
w zrhp +
R load @ (1 * D)
DL prin 2
2
(eq. 18)
wzrhp is a right half plane zero can be explained by the
phenomenon that when there’s a sudden load increase, the
duty cycle will increase instantaneously, building up higher
current but the voltage will drop temporarily until the
required current is present. Since this zero is located in the
(eq. 12)
with
ZC +
zrhp
T power_ccm(s) + K
An additional L−C filter should be added to meet the
ripple specification. A large capacitor should remain at the
side of the load to cope with load changes and to make sure
no stability issues arise from capacitive loading (due to shift
of the filter resonance frequency). Therefore, split the output
capacitance in two, or take an additional one (depending on
the ESR which should not increase) and place an inductor in
between to create an L−C filter.
The damping of the L−C filter is given by Equation 12.
This equation can be rewritten into Equation 13 which gives
the product of L and C.
ZC
(eq. 15)
Equation 16 shows the transfer function of the fly−back
converter in current controlled mode of operation. Note that
adding current measurement in the feedback loop has
advantages on top of implementing only voltage
measurement feedback:
− The feedback is immediate, current can be limited in
the same cycle,
− The order of the transfer function is reduced, leading to
a system that is easier to stabilize,
− The phase margin is better.
Figure 6. Adding an Additional Ripple Filter
+
1
Ǹ
p L2C
Stability Analysis of the Converter in CCM
Lsec
V ripple
(eq. 14)
Choose a value for L and calculate the value for C. Next,
make sure the resonance frequency (Equation 15) is at least
two or three times higher than the cross−over frequency of
the closed loop converter (to make sure the resonant peak
stays well below 0 dB), but still lower than the switching
frequency of the regulator (to make sure switching noise is
filtered).
Cout
Cf1 Cf2
(eq. 13)
2
V ripple + I peak_sec R esr
The parasitic effective series resistance (Resr) of the
capacitor Cout affects the output voltage ripple the most. The
ripple caused by Resr is an order of magnitude larger than the
ripple caused by having a small output capacitance. The
required output ripple specification will not be met by using
an output capacitor only.
Take the closest standard value for the capacitor with the
lowest Resr. It is better to deviate from the calculated
capacitance value when there’s another capacitor value with
lower ESR. Equally important is to measure the chosen
capacitor or parallel capacitors on an impedance analyzer to
make sure the ESR is correct.
Cout1
V ripple(2pf s)
Vripple is the desired output voltage ripple and Vripple_esr
is the voltage ripple that is generated over the ESR of the
output capacitor. The approximate current that flows
through the ESR resistor is the secondary peak current of the
converter, leading to Equation 14.
Output Capacitance and Filter
C out +
V ripple_esr * V ripple
1
2pf sC
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AND8332/D
right half plane, this leads to a gain boost and a phase lag
(which is not desirable and can lead to an unstable system).
wp +
1)D
R loadC out
A bigger phase margin lowers the peaking on transitions
and a higher system bandwidth increases the speed of the
system. The DC error (or static, or steady state error) is
reduced when the low frequency gain is increased.
Use Equation 16 to plot a Bode diagram and inspect where
stability issues may arise.
(eq. 19)
wp , a dominant pole originates from the load and output
capacitor.
K+
R load(1 * D)
(eq. 20)
nR csA V(1 ) D)
where Av = 2 for NCP108x
To investigate and improve the stability of the DC−DC
converter, the technique of frequency response
compensation is used.
This technique is based on the fact that any linear system
in steady state will show at its output a sine wave with
amplitude and phase when it is excited at its input with a sine
wave of given frequency, amplitude and phase. The
amplitude and phase of the output signal may be different
than those of the input signal, however the input and output
frequency will be the same.
This technique uses a Bode plot to assess the stability
criteria. A Bode plot consists of two drawings. One drawing
plots the magnitude of the output signal over the input
signal, using logarithmic scale. The other drawing plots the
phase of the output minus the phase of the input, using
logarithmic scale.
Figure 8. Bode Plot of the Power Sate of a 30 W 3.3 V
Fly−back Converter (note the poor gain at DC)
DC Gain Boosting and Phase Margin Insurance
When we translate the stability requirements to our
fly−back converter design, we should have a system with
high phase margin (around 60°), high bandwidth (unity gain
or cross−over frequency as high as possible but still far
enough from the switching frequency), a high gain at DC,
and a high attenuation at high frequency.
This is achieved by adding a control and compensation
network which uses an opto−coupler for isolation,
introduces an extra zero, two poles (one at DC) and has
following transfer function:
M(dB )
0
Gain margin
Frequency (log )
Phase (degrees )
−180
Phase margin
Frequency (log )
T comp(s) +
Figure 7. Phase and Gain Margin
CTR @ ǒ5KńńR bias1Ǔ
R fb3
(eq. 21)
ǒ1 ) wszǓ
ǒ
A closed loop system is stable if the open loop frequency
response shows a gain of less than 0 dB at the frequency
where the phase shift is 180°. Gain margin is the value by
which the gain of the system can be increased, while keeping
the phase at −180° (Note 1), before the system becomes
unstable. Phase margin is the value by which the phase of the
system can be increased, keeping the gain at 1, before the
system becomes unstable.
R fb1 @ C fb1 @ s @ 1 ) ws
Ǔ
p
The goal of the compensation network is to set the gain
criteria while affecting the phase margin as least as possible.
(Proportional−integral (PI) plus high−frequency pole
compensation)
1. Note that the systems discussed here, all have negative feedback like most feedback systems, hence the −180° of the negative feedback
together with an additional 180° shift would yield 360° overall shift, a positive feedback, unstable system.
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AND8332/D
Step 1: Define the Compensation Circuit Cross−Over
Frequency
plot of the open loop system to find the phase margin at the
cross−over frequency. The pole of the compensation
network needs to be K times larger and its zero needs to be
K times smaller than the cross−over frequency. With K given
by:
Rule of thumb: The converter should have a cross−over
frequency
ǒ
f cross t min
f zrhp f s
, , f zesr, f optocoupler
3 5
Ǔ
ǒboost
) 45Ǔ
2
(eq. 22)
K + tan
where:
− fzrhp is the frequency of the right hand plan zero of the
open loop fly−back converter derived from Equation 18
− fs is the converter’s switching frequency
− fzesr is the frequency of the zero introduced by the
output capacitor’s series resistance, given by
Equation 17
− foptocoupler is the frequency indicating the bandwidth of
the chosen opto−coupler
boost = desired phase margin − actual phase margin + 90
Now, choose a value for Rfb1 and use Equations 24 and 25
to calculate Cfb1 and Cfb2.
fz +
fp +
Step 2: Phase Margin Insurance, Define the Pole and
Zero Frequency of the Compensation Circuit
1
å C fb1 +
2p @ R fb1 @ C fb1
1
2pR fb1 f z
(eq. 24)
1
2p @ ǒ5KńńR bias1Ǔ @ C fb2
å C fb2 +
Instead of using a Type II or Type III compensation
network with operational amplifier, often an equivalent but
cheaper network with TL431 voltage reference is used as an
error amplifier in combination with an opto−coupler for
isolation.
1
(eq. 25)
2pǒ5KńńR bias1Ǔ f p
Step 3: Gain Adjustment
First we need to find out, using the Bode plot, what the
gain (A0) is of the open loop system at fcross . The gain of the
compensation network is given by:
Integrator gain, 1st pole at DC
CTR @
2nd pole where opto−coupler rolls off
Opto−coupler gain
(eq. 23)
5KńńR bias1
R fb3
(eq. 26)
where CTR is equal to the current transfer ratio of the
opto−coupler. The Rbias2 and Rfb3 resistors connected to
the opto−coupler and the TL431 shunt regulator should be
carefully tuned to guarantee a sufficient operating current
for the TL431 (typical TL431 require minimum 1 mA as
bias current). The gain of this network needs to be
sufficiently high to react abruptly on reaching the output
voltage. It is good practice to measure the performance of
this network prior to switching on the NCP1081.
Now equalize the compensation network gain to the
inverse of the open loop gain at cross−over frequency and
calculate Rfb3.
Overall gain(thick line)
0dB
Zero where integrator has unity
gain
Figure 9. Compensation Network Gain
Approximation
At low frequencies Cfb1 and Rfb1 act like an integrator.
The overall gain of the integrator is the product of the
integrator gain and the opto−coupler gain. The
compensation zero is located at the point where the
integrator crosses over.
At mid−range frequencies, the opto−coupler becomes
dominant because the integrator with the TL431 has crossed
unity gain. The gain is determined by the opto−coupler gain,
Rfb3 and the NCP108x 5 kW internal pull−up in parallel with
Rbias1.
At high frequencies the pole of the opto−coupler becomes
dominant. Make sure that the bandwidth of the opto−coupler
is as high as possible. Rbias1 in parallel with the 5 kW internal
resistor should be tuned such that the opto−coupler is
sufficiently biased. We want to configure a known
compensation pole by inserting Cfb2.
We make sure that between the zero and the pole of the
compensation network we have a unity gain of the closed
loop system with the desired phase margin. Use the Bode
CTR @
5 kWńńR bias1
R fb3
+
1
+ A comp
A0
(eq. 27)
Step 4: Set the TL431 DC Regulation Voltage
The shunt regulator compares the output voltage divider
to an internal Vtl431 reference and generates an error voltage
which is applied to the cathode of the opto−coupler. The
output resistor divider made of Rfb1 and Rfb2 should be
calculated to provide exactly Vtl431 to the reference pin of
the TL431 when the power converter output voltage equals
the desired regulated Vout1 voltage. Since Rfb1 was already
chosen before, Rfb2 can be calculated easily.
R fb2 +
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V tl431 @ R fb1
V out * V tl431
(eq. 28)
AND8332/D
Step 5: Check the Compensation Network
Performance
The theoretically derived component values need to be
checked on the real design. Two separate measurement
techniques are proposed to measure the frequency response
of the entire loop and that of the converter without the
compensation network. Most probably, more than one
iteration will be required to get it right.
Figure 10. Bode Plot for a 30 W 3.3 V Converter
Compensation Network
Measure the Full Loop Frequency Response, Including the Compensation Network
Rbw
Dbw
Csn3 Rsn3
VPORTP
Rclass
VDDH
CLASS
Out
Cout3
Dsec
Rinrush
Cline
Cout4
Rled
VDDL
INRUSH
Zline
Frequency response analyser
L2
Cvddh
ChA
ChB
1
2
J3
Cpd
Rdet1
Rilim1
Led
Cvddl
ILIM1
20 … 100
NCP1081
nClassAT
UVLO
Rgate
Rdet2
Cfb2
GATE
TEST2
CS
TEST1
FB
COMP
SS
OSC
VPORTN1
VPORTN2
Rfb3
Csn1
Q1
Rsn1
Rfb1
U2
Cfb1
Rsl
ARTN
RTN
Rcs
TL431
Rfb2
Css
Rosc
Figure 11. Closed Loop Measurement
The proposed technique measures the entire loop
frequency response without breaking the loop. The standard
way of measuring this would be to break the loop and inject
and measure the signal at impedance matched cutting points.
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Measure the Frequency Response of the Power Converter Only, Without the Compensation Network
Rbw
Dbw
Csn3
Rsn3
VPORTP
Rclass
L2
VDDH
CLASS
Cvddh
Dsec
Cline
Zline
Cout3
Cpd
VDDL
INRUSH
Rdet1
1
2
Cout4
Rled
Rinrush
J3
Led
Rilim1
Frequency response analyser
Cvddl
ILIM1
Out
NCP1081
nClassAT
UVLO
Q1
Cfb2
GATE
Cfb1
FB
TEST1
COMP
SS
OSC
VPORTN1
VPORTN2
Rfb1
U2
Rsn1
CS
TEST2
ChB
Rfb3
Rgate
Rdet2
ChA
Csn1
Rsl
ARTN
RTN
Rcs
TL431
Rfb2
Css
Rosc
Figure 12. Open Loop Measurement
This measurement technique measures the loop without
having to break it, but at the same time, the network between
measurement point A and B is eliminated. In this case we
measure the frequency response of the power converter,
without the compensation network.
These possible oscillations are modeled by another
transfer function which will be multiplied with the transfer
function of the power stage, listed in Equation 16.
T h(s) +
Slope Compensation
To overcome sub−harmonic oscillations and instability
problems that exist with constant frequency current mode
control converters running in continuous conduction mode
(CCM) and when the duty cycle is close or above 50%, the
NCP108x integrates a current slope compensation circuit.
This sub−harmonic oscillation phenomenon can be
understood by looking at Figure 13. The current in the
primary transformer is illustrated for two different duty
cycle cases, assuming a current mode PWM controller
without slope compensation. When D > 0.5, a small
disturbance on the primary current causes a duty cycle
asymmetry between consecutive pulse cycles. This error
increases with every cycle (due to the fixed frequency
operation) and will lead to oscillation in the regulation loop
at fs / 2. When D < 0.5 this disturbance diminishes cycle by
cycle.
On
Ts
On
On
1)
)
(eq. 29)
s2
wn 2
where
Qp +
wn + p @ fs
mc + 1 )
se
sn
se +
1
p(m c(1 * D) * 0.5)
V slope*pp
sn +
Ts
V on
L
A sense
Se is the compensation ramp slope, given by the
compensation voltage over the switching period.
Sn is the slope of the sensed current waveform, given by
the voltage over the coil when the switch is on, times the
current measurement gain, divided by the inductance. When
only the current sense resistor is used, Asense = Rcs.
The transfer function shows a peak at fs/2. This peaking
could cause the gain to go above 0 dB again, even after
we’ve done all the compensation (setting the cross−over
frequency and phase margin improvement), rendering the
system unstable once more. The height of the peak is
determined by Qp. The lower Qp, the bigger the damping is
and the lower the peak is.
This damping is achieved by adding a slope to the
comparator trip level. Figure 15 shows that, now even with
D > 0.5, the error reduces every cycle.
The necessary Slope compensation can be calculated
using the following formula:
Fixed fs, Ts constant
On
1
s
w nQ p
Trip level
D>0.5
Trip Level
D<0.5
dV slope + nR cs
Figure 13. Current Control Instability at D > 0.5, for
PWM Controller not using Slope Compensation
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V out
2L prin 2
dt
(eq. 30)
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overall Bode plot needs to be drawn. The closed loop
transfer function is given by Equation 33, product of
Equations 16, 21 and 29.
T closedLoop + T power_ccm(s) @ T comp @ (s)T h(s) (eq. 33)
Stability Analysis in Discontinuous Conduction Mode
(DCM)
We use the values of the components as they were
designed for CCM operation in the equation of the transfer
function of the converter running in DCM mode. We check
by drawing a Bode diagram if the stability requirements are
met for the closed loop system, including the compensation
network and the high frequency effect of the current mode
control.
Note that if one started the design procedure for a power
converter in DCM mode, a similar approach can be used to
check the stability in CCM mode.
Figure 14. Same Converter as in Figure 7, but Now
Including the High Frequency Effect of Current
Control
Step 1: Calculate the Duty Cycle, D, Based on the
Voltage Transformation Ratio
Fixed fs, Ts constant
On
On
On
Ts
V out
On
S1
V in
Slope Trip level
S2
+D
Ǹ
V out
R
åD+
V in
2L prif s
Ǹ
2L prif s
R
(eq. 34)
Step 2: Frequency Response Analysis
The transfer function of the power stage in DCM is given
by Equation 35.
Figure 15. How Slope Compensation Helps
T power_dem(s) + K
1)w
s
zesr
1 ) ws
p
where
dt +
1
fs
where
(eq. 31)
K + nD
and
R cs +
0.36
w zesr +
I PriPeak1.2
where
R sl +
10 mA
2L secf sw
+
V out
V in
(eq. 35)
2
2
å fp +
R loadC out
2pR loadC out
(eq. 37)
Plot the total closed loop frequency response
(Equation 38) and check the stability requirements.
0.36 V Is the threshold voltage of the current comparator,
factor 1.2 adds margin to the measurable current. This
margin is required because there’s an additional voltage
drop over Rsl.
Since the NCP1081 integrated a slope compensation of
110 mV over 1 period, the remaining necessary slope can be
obtained by adding an external Rsl resistor between the CS
pin and Rcs resistor.
dV slope * 110 mV
R load
(eq. 36)
1
1
å f zesr +
R esr @ C out
2pR esr @ C out
wp +
V in D
I PriPeak +
L pri f s
Ǹ
T closedLoop + T power_dcm(s) @ T comp @ (s)T h(s)
(eq. 38)
Switch Drain−Source Voltage Considerations
Special attention to the switch drain−source reverse
voltage is required since in fly−back design, this voltage will
be the sum of the input voltage and the weighted output
voltage, as indicated in Equation 39.
V DS + V in )
(eq. 32)
N1
N2
V out
(eq. 39)
Note the forward diode drop needs to be taken into
account. Also note the leakage inductance will add a voltage
spike. Sufficient margin needs to be built in when choosing
the switch transistor.
(10 mA corresponds to the internal sawtooth current
amplitude)
To make sure the damping of the peak at fs / 2 in the
frequency response is not an issue (gain at fs / 2 < 0), the
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Snubber Design
which increases progressively the duty cycle limit during the
soft start time. This soft start is programmable by Css and
defined by Equation 42.
To avoid destruction of the switching transistor due to the
voltage spikes originating from the leakage inductance,
these transient spikes at the drain of the power switch need
to be reduced. To size the snubber, measure the ringing
frequency and calculate Rsn and Csn.
R sn1 + 2pf ringL leak
C sn1 +
T softstart[ms] + 0.23C ss[nF]
VDDL and VDDH
Cvvdl and Cvddh are noise decoupling capacitors (20%)
with low ESR (< 0.1 W). Cvddl may range from 330 to
470 nF. Cvddh may range from 1 to 2.2 mF. For application
using the auxiliary bias winding to supply the VDDH
regulator, the designer has to make sure that the bias winding
does not force VDDH above 16 V for the maximum load
condition. Use 50 W for Rbw as initial value.
(eq. 40)
1
(eq. 41)
2pf ringR sn1
(eq. 42)
The snubber design for the diode at the secondary side of
the transformer is handled in the same way.
To measure the oscillation frequency in a safe way, use a
low Vin and do not apply any load to the converter to make
sure that the peak voltage is not exceeding the switching
transistor VDS rating.
Converter Efficiency
The overall efficiency of the flyback power converter is
given by Equation 43.
Soft Start
To eliminate possible voltage overshoots on the output
during start up, the NCP1081 provides a soft start function
h+
P out
P out ) P MOSdynamic ) P MOSstatic ) P diode ) P esr ) P MagConductive ) P core ) P NCP108x
Static Power Switch Losses
Each of the power losses in Equation 43 are calculated in
following sections.
Static losses are the conductive losses of the power switch
and calculated using the Rdson resistance coming from the
data sheet and the RMS current.
Dynamic Power Switch Losses
Dynamic switch losses are created during the toggling of
the switch. Parasitic capacitances in the switch are charged
and discharged.
P MOSstatic + ǒR DS(on) ) R CSǓ @ I rms_pri 2 @ D
)
2
(eq. 44)
Secondary Diode Losses
) f s @ Q gtot @ V gatedrive
where
V dsmax + 1.15 @
ǒ
V in )
The secondary diode has a forward voltage drop, affecting
the overall efficiency.
Ǔ
ǒVout ) VdiodeǓ
2
P diode +
(eq. 45)
Q gd @ R gatedrive
V gatedrive @ V GSth
, the switch−on time
P out
V out
@ V diode
(eq. 48)
Capacitor Losses
One of the biggest loss contributors is the parasitic
equivalent series resistor of the output smoothing and the
input bulk capacitors.
the maximum drain−source voltage.
t sw +
(eq. 47)
With RDS(on) the on resistance of the switch, from the data
sheet and Rcs is the calculated current sense resistance.
P MOSdynamic + V dsmax @ I peak_pri @ f s @ t sw
C swout @ V dsmax @ f s
(eq. 43)
(eq. 46)
P esr + R esr_cout @ I 2rms_sec ) R esr_cpd @ I 2
VGSth is the gate to source threshold voltage from the data
sheet
Qgd is the gate to drain Miller charge from the data sheet
Qgtot is the total gate charge from the switch data sheet
Ipeakpri is the peak current at the primary
Vgatedrive is the gate drive voltage of the NCP1081, or 9 V
Vdiode is the forward voltage drop of the diode at secondary
side
Cswout is the switching transistor output capacitance
rms_pri
(eq. 49)
It is important to use low ESR capacitors.
Conductive Losses in Magnetics
Conductive losses are those originating from the DC and
AC resistance of the transformer wire. DC resistance of
primary and secondary windings are listed by the
transformer manufacturer. When the switching frequency
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AND8332/D
increases, additional phenomena such as skin effect and
proximity effect increase the losses even further.
P MagConductive + R dc_pri
@ I2
rms_pri ) R dc_sec
@ I2
With
rms_sec
(eq. 50)
P PortDriver(mW) + I PortDriver(mA)
V portP(V)
P PWM(mW) + I PWM(mA)
(eq. 56)
(eq. 57)
R on_PassSwitch
V portP(V)
(eq. 58)
if the auxiliary winding of transformer is not used, or
P PWM(mW) + I PWM(mA)
V DDH(V)
(eq. 59)
if VDDH is supplied by the auxiliary winding of transformer
NCP1081 Losses
The internal junction temperature can be evaluated.
First calculate the current consumed on the VPORTP pin
in Power Mode:
) I PortDriver (mA) ) I PWM (mA)
V portP(V)
) I PortDriver 2(mA)
To make calculations simpler, we discard the AC
resistance of the copper wire. But note that the AC losses
become substantial with high switching frequencies.
Core losses originate from the energy that is dissipated in
the core of the transformer and can be found from graphs for
the specific core material used and the physical dimensions
of the core.
I VportP (mA) + I Quiescent (mA)
P Quiescent(mW) + I Quiescent(mA)
T J(degC) + T ambient(degC) ) P DissTotal(mW)
R th(Wń deg C)
(eq. 51)
(eq. 60)
1000
With Rth the junction to ambient thermal resistance
With
I Quiescent (mA) + 1.4
(eq. 52)
Secondary Diode Maximum Rating
A rule of thumb for the maximum reverse voltage of the
secondary rectifying diode is
Core Losses
V reverse +
V in_max * N s
Np
(eq. 61)
The maximum current through the diode is given by
Equation 9.
Design Example 1: 30 W Single Output 12 V Supply
A Microsoft Excel® file (NCP108X DESIGN TOOL
FLYBACK CCM.xls) with calculation sheets is provided by
ON Semiconductor, with the presented expressions
incorporated to design a stable and reliable flyback
converter. In Figure 17 all the input data needed for the
design is shown. As a result, the output calculated data is
shown in Figure 18.
The frequency and phase response of the system as well
as the poles and zeroes are calculated by the Excel VBA
macros and shown in logarithmic charts for the power stage,
compensation and close loop networks in Figure 20.
The Excel VBA script calculates also the efficiency for
various output power, gives the final summary of all the
designed components, according to a certain
scematics(shown in Figure 1). In addition there is a
convenient tool to calculate the output divider resistor
values, when the output voltage and the reference voltage of
the shunt feedback regulator are given.
Figure 16. Core Losses
1
1
ƪ385
ƫ
)
2300
I PortDriver(mA) + 0.1 ) I PassSwitch (mA)
(eq. 53)
I PWM(mA) + 1.175 )
ƪ
f s(kHz)
250
0.725 ) 4.35
C gate(nF)
2
ƫ
(eq. 54)
With Cgate the equivalent input capacitance of the external
switching MOSFET
Then calculate the internal power dissipation.
P NCP108x(mW) + P Quiescent(mW) ) P PortDriver(mW)
) P PWM(mW)
(eq. 55)
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AND8332/D
Figure 18. Output Data Calculated by the Flyback
Design Excel Calculation Sheet − Values of the
Detection Signature Resistors and the Maximum
Power Estimated Efficiency
Figure 19. Output Data Calculated by the Flyback
Design Excel Calculation Sheet − Parameter
Extraction of the External Components Values
According to Figure 1
Figure 17. Input Data for the Flyback Design Excel
Calculation Sheet
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AND8332/D
The output of the Scilab script summarizes the design
parameters and the closest standard values of the calculated
component values for the feedback loop.
The Bode plot of the converter without compensator
network and with compensator network is plotted in
Figure 21.
Magnitude vs Frequency, (dB)
60
40
Fp Fcz
Magnitude (dB)
20
0
Fzrhp
Fcross
Fcp
−20
−40
−60
−80
−100
100
1000
10000
100000
1000000
Frequency (Hz)
T_power_stage
T_compensation
T_closed_loop
Phase vs Frequency, (°)
0
−50
−100
Phase (°)
−150
−200
−250
−300
−350
−400
100
1000
T_power_stage
10000
Frequency (Hz)
100000
T_compensation
Figure 21. Gain and Phase Plot of the Compensated
Converter
1000000
T_closed_loop
Figure 20. Output Data Calculated by the Flyback
Design Excel Calculation Sheet − Frequency and
Phase Response of the Designed Flyback Converter
Note: If Scilab or Excel software is not available, using
asymptotic approximation to generate a Bode plot and
computing the values manually will lead to similar results.
Company or Product Inquiries
Design Example 2: 20W Single Output 3.3V Supply
For more information about ON Semiconductor’s Power
over Ethernet products visit our Web site at
http://www.onsemi.com
Scilab scripts are also provided to aid the design
calculation. Scilab is an open−source numeric computation
program that is available free of charge at www.scilab.org.
The input data is shown in Table 6.
Table 6. DESIGN PARAMETERS
Parameter
Value
Vin
36 V (minimal PD input voltage)
Vout
3.3 V
Lprim
42 mH, according to Coilcraft POE300F−33L
data sheet
N
Pout
Vripple
fs
0.09, according to Coilcraft POE300F−33L
data sheet
20W
33 mV
250 kHz
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AND8332/D
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are registered trademarks of Semiconductor Components Industries, LLC (SCILLC). SCILLC reserves the right to make changes without further notice
to any products herein. SCILLC makes no warranty, representation or guarantee regarding the suitability of its products for any particular purpose, nor does SCILLC assume any liability
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operating parameters, including “Typicals” must be validated for each customer application by customer’s technical experts. SCILLC does not convey any license under its patent
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applications intended to support or sustain life, or for any other application in which the failure of the SCILLC product could create a situation where personal injury or death may occur.
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AND8332/D