AN892: Design Guide for Isolated DC/DC Using the Si882xx/883xx

AN892
D E S I G N G U ID E F O R I S O L A T E D D C / D C U S I N G
S I 882 X X / 8 8 3 X X
THE
1. Introduction
The Si882xx/Si883xx products have integrated digital isolator channels with an isolated dc-dc controller. This
application note provides guidance for selecting external components necessary for the operation of the dc-dc
controller.
Digital isolation applications with primary side supply voltage 3.0 V  VIN  5.5 V and load power requirements of
≤ 2 W can use Si882xx/Si883xx products. These products’ dc-dc controller uses the asymmetric half bridge
flyback circuit topology.
Figure 1 shows the minimum external components required for the asymmetric half bridge flyback. They are a
blocking capacitor C1, input capacitor C2, flyback transformer T1, diode D1, output capacitor C10, voltage sense
resistors R5 and R6, and compensation network components R7 and C11.
Figure 1. Minimum Required External Components
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Copyright © 2015 by Silicon Laboratories
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2. Simplified DC Steady State Analysis
Analyzing the asymmetric half bridge behavior in DC steady state provides formulas to assist with selecting values
for the components used in Figure 1. For this analysis, it is assumed that components are ideal, 100% efficiency
(PIN=POUT), and the circuit has reached equilibrium.
Figure 2 shows the critical components of the asymmetric half bridge flyback. The transformer model includes
magnetizing inductance Lm and inductance leakage Llkg. RLOAD does not necessarily represent a physical resistor,
rather it is an expression of VOUT/IOUT.
Figure 2. Asymmetric Half Bridge Flyback Converter
To analyze this architecture, a cycle can be divided into eight distinct operating modes. However, for DC steady
state analysis, the two modes where the system operates the majority of the cycle are only required: when S1 is
closed and S2 is open, and when S1 is open and S2 is closed. Figure 3 depicts the simplified magnetizing and
leakage inductance current waveforms.
Figure 3. Inductor Currents
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2.1. S1 Closed, S2 Open
VIN is applied to the series combination of C1 and inductance Lm + Llkg. As a result, current flows through
inductance Lm + Llkg in a linear fashion.
l m RIPPLE
V IN – V C1 =  L m + L lkg   -------------------------t S1
Equation 1.
Where Im,RIPPLEis the magnetizing current ramp during tS1 and tS1 is the time that S1 is closed.
2.2. S1 Open, S2 Closed
In this mode, a resonant tank circuit formed by C1, Lm, and Llkg, and -VC1 is applied across Lm + Llkg. The resonant
tank causes the current through leakage inductance to rise as a sinusoid while the voltage at the secondary
impressed on the primary causes the current through the primary to reduce in a linear fashion. When llkg  lm, the
difference current (Im-Ilkg) flows out of the dot on the primary side of the ideal transformer. Therefore current must
flow into the dot on the secondary side and through the diode. Governing current equations are
– V OUT
l m RIPPLE
-------------------------- = ----------------t S2
Lm N
Equation 2.
I Llkg  t  = I m  sin   r t 
Equation 3.
1
 r = ---------------------------L lkg  C1
Equation 4.
where N and tS2 are primary to secondary turns ratio and time that S2 is closed respectively. r is the resonance
tank frequency in rads/s.
The current through the diode in the secondary can be written as the difference of llkg and lm scaled by the
transformer turns ratio.
l lm – I lkg
I D1 = --------------------N
Equation 5.
As the sinusoidal current returns to match the magnetizing current, the resonance ceases and consequently no
current will flow from the dot on the primary or through the secondary into the diode.
2.3. Voltage Transfer
Let duty cycle D be defined as the ratio of time S1 is closed over the complete switching period TSW:
t S1
D = ---------------------t S1 + t S2
Equation 6.
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Now tS1 and tS2 can be expressed in terms of D and switching period as:
t S1 = DT SW
Equation 7.
t S2 =  1 – D T SW
Equation 8.
and assume diode D1 has no voltage drop when conducting, the volt-second balance equation for Llkg can be
written as:
L lkg
V OUT
-----------------------  V IN – V C1 DT SW +  -------------– V C1  1 – D T SW = 0

L lkg + L m
N
Equation 9.
With the condition that Llkg << Lm, Equation 9 simplifies to:
V OUT
V C1  -------------N
Equation 10.
The volt-second balance equation for Lm is:
V OUT
Lm
– --------------  1 – D T SW + ------------------------  V IN – V C1 DT SW = 0
N
L lkg + L m
Equation 11.
With the condition that Llkg<<Lm, Equation 11 simplifies to:
V OUT
------------- 1 – D    V IN – V C1 D
N
Equation 12.
Substituting Equation 10 into Equation 12 yields the following relationships:
V OUT
--------------  V IN D
N
Equation 13.
V C1  V IN D
Equation 14.
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2.4. Magnetizing Current
If during the tS1 portion of the cycle (S1 closed, S2 open), VIN charges C1 in a linear fashion. Rearranging Equation
1 and substituting Equation 7 and Equation 14, ripple magnetizing current is:
V IN D  1 – D T SW
 V IN – V C1 t S1
 V IN – V IN D t S1
I m RIPPLE = --------------------------------------- = ------------------------------------------ = -------------------------------------------L m + L lkg
L m + L lkg
L m + L lkg
Equation 15.
The average magnetizing current is related to the output current as
l m AVE = I LOAD N
Equation 16.
The peak magnetizing current is given by:
V IN D  1 – D T SW
l m PK = l m AVE + -------------------------------------------2  L m + L lkg 
Equation 17.
Si882xx/Si883xx controller limited the peak magnetizing current to approximately 3A. If more current than 3A is
sensed during S1 on and S2 off mode, the controller immediately switches to the S1 off and S2 on mode. The
controller maintains the same switching period, but reduces the duty cycle D to limit peak current.
2.5. Input Capacitor
The purpose of C2 input capacitor is to provide current during switching cycles. During S1 closed, S2 open, C2
provides current to C1 in series with Lm + Llkg.
l IN = I m AVE D = I LOAD DN
Equation 18.
During the tS1 portion of the cycle (S1 closed, S2 open), VIN recharges C2. The voltage ripple on C2 can be written
as:
I C2  1 – D T SW
V IN RIPPLE = --------------------------------------C2
Equation 19.
Substituting Equation 18 into 19:
I LOAD D  1 – D T SW N
V IN RIPPLE = -------------------------------------------------------C2
Equation 20.
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2.6. Diode and Output Capacitor
Current flows through D1 only during the (1–D)TSW portion of the steady state cycle. During the DTSW portion of
the cycle, lLOAD is sourced solely by the output capacitor C10. Output voltage ripple on C10 can be calculated by
I LOAD DT SW
V OUT RIPPLE = -------------------------------C10
Equation 21.
Applying the charge balance of C10,
– I LOAD DT SW +  1 – D T SW = 0
Equation 22.
1
I D1  AVE  1 – D  = I LOAD -----------------1 – D
Equation 23.
When D1 is reversed biased, it must withstand
V D1 REV  D  = V IN  1 – D N + V OUT
Equation 24.
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2.7. VSNS Voltage Divider
For the purpose of selecting sense resistors (R5/R6), the entire dc-dc converter can be modelled as a noninverting amplifier as shown in Figure 4. Notice that the non-inverting input, supply voltage (V+), and output voltage
of the amplifier correspond to the internal 1.05V reference, VIN, and VOUT of the dc-dc converter.
VIN
+
-
I VSNS
1.05V
VREF
V+ POWER STAGE
VOUT
VC10
VSNS
RLOAD
R5
R6
Figure 4. Simplified VOUT Gain Model
Assuming infinite DC gain and applying KCL at the inverting input of the amplifier, VOUT can be expressed as:
R5
V OUT = 1.05  -------- + 1 + R5  I VSNS
 R6

Equation 25.
where IVSNS represents the input offset current at VSNS pin. From Equation 25, it can be observed that a very
large R5 could reduce the output voltage accuracy.
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3. Dynamic Response
The Si8822xx start-up response consists of three regions of operation: Soft-Start (SS), Proportional-Mode (PMode), and Proportional Integral Mode (PI-mode). Figure 5 shows a typical VOUT response during startup.
Figure 5. VOUT during Start Up
3.1. Soft Start
In soft start mode, the dc-dc peak current limit is gradually increased to limit the sudden demand of current needed
from the primary supply. This mode of operation guarantees that VOUT monotonically increases and minimizes the
probability of a voltage overshoot. Once, 90% of the final VOUT is reached, soft start mode ends, and Proportional
(P) Mode starts. The total duration of soft start is load dependent as it affects how many switching cycles are
required for VOUT to reach 90% of final value. In this mode of operation, the voltage feedback loop is inactive and
hence loop stability is not a concern.
3.2. Proportional Mode
Once the secondary side senses 90% of VOUT, the control loop begins its P-mode operation. During this mode of
operation the dc-dc converter closes the loop (dc-dc converter secondary side communicates with the primary
side) and therefore, analyzing the loop stability is required.
Figure 6 shows a simplified block diagram of voltage sensed feedback control. gmp represents the equivalent
modulator and power stage transconductance of the dc-dc converter and resistors R5 and R6 are the feedback
resistors used to sense VOUT. C10 is the output capacitor, and RLOAD represents output load. Parameter gmfb and
Ro,gmfb are the effective error amplifier transconductance and the error amplifier output resistance, respectively.
During the P-Mode, an integrated resistor RINT is connected to the COMP pin. R7 and C11 are external
components connected to the COMP pin used in P-I mode.
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Figure 6. Simplified Voltage Sense Feedback Loop
For stability analysis, the loop at the input of the error amplifier is broken to obtain the small-signal transfer function
from Vfb,in to Vfb,out:
V fb out
1
H p  s  = ------------------ = A DC P ---------------------V fb in
s
 1 + -----
 p
Equation 26.
1
 pd  -------------------------R Load C 10
Equation 27.
R6
A DC P = – ---------------------- gm fb  R INT ||R o gmfb   gm p  R LOAD ||R5 + R6  
R5 + R6
Equation 28.
gm ea
gm fb = -------------------------------------------------gm ea  R5  R6  + 1
Equation 29.
gmea is the error amplifier transconductance. For the Si882xx/883xx, gmea  1x10-3, RINT  50k and
Ro,gmfb>>RINT. If R5 and R6 are chosen such that their parallel resistance is sufficiently larger than 1/gmea,
Equation 29 simplifies to:
1
gm fb  ------------------------- R5  R6 
Equation 30.
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Typically, RLOAD << (R5 + R6) and gmp is approximately 3/N. The DC gain in P-mode simplifies to:
3
A
50x10  3R LOAD
 – -----------------------------------------------·
DC P
R5  N
Equation 31.
Notice that the DC gain of P mode is proportional to RLOAD and inversely proportional to R5. At heavy loads (small
RLOAD), a very large R5 could significantly increase the output voltage error as the DC gain reduces. Conversely, a
very small R5 increases power consumption and gmfb variability due to higher dependency on gmea, which can
significantly vary more than 1/(R5||R6) over temperature or from part to part. The total duration of this mode is
approximately 7ms.
3.3. Proportional Integral Mode
After P-mode, the controller switches to PI-mode, the steady state and final operation mode. During this mode of
operation, the error amplifier drives an impedance that consists of the series combination of resistor R7 and
capacitor C11. To achieve a smooth transition between P and PI modes, it is recommended to set R7 to match
RINT R7 and C11 are connected to the COMP pin.
.
R7 = R INT  50x10
3
Equation 32.
In PI-mode, the loop transfer is given by:
s -
 1 + -------
 z1
H PI  s  = A DC PI -------------------------------------------------------s  
s
 1 + -------- 1 + ---------

 p1 
 p2
Equation 33.
where
1
 p1  -------------------------------R o gmfb C11
Equation 34.
1
 z1  ------------------R7C11
Equation 35.
1
 p2  -----------------------------R LOAD C10
Equation 36.
R o gmfb gm p R LOAD
A DC PI = – --------------------------------------------------R5
Equation 37.
Notice that the loop transfer function in PI-Mode has an additional pole-zero pair when compared with P-Mode. In
addition, the loop DC-gain is much higher in PI-Mode than in P-Mode due to Ro,gmfb>>RINT.
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Figure 7 shows the magnitude Bode plot of the loop in PI mode.
Figure 7. Simplified Transfer Function PI Mode
4. Design Example
Consider the desired requirements listed in Table 1.
Table 1. Design Requirements
Parameter
Value
Input Voltage
5.0 V  10%
Output Voltage
5.0 V
Input Voltage
Ripple
 150 mV
Output Voltage
Ripple
 50 mV
Maximum Output
Current
400 mA
4.1. Transformer Design
The design of a transformer for the asymmetric half bridge flyback is very similar to the design of a flyback
transformer operating in continuous current mode. This section provides a starting point for the transformer design
which is often an interative process.
Equation 13 establishes the relationship between turns ratio n and duty cycle D. For this design, D=0.25 was
chosen. The formulas derived in the DC steady state section are based on ideal elements. In practice, a larger duty
cycle is expected due to losses in the parasitics. Accounting for forward voltage drop across D1 of 0.5V and solving
Equation 13 for turns ratio:
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V OUT + Vf D1 5 + 0.5
N  ---------------------------------  ---------------------  4.4
5  0.25
V IN D
Equation 38.
A 1:4 turns ratio was chosen.
The next parameter to choose is the primary inductance. Equation 16 gives the average magnetizing current.
Im AVE = NI LOAD = 4  0.4  = 1.6A
Equation 39.
Equation 15 shows that magnetizing current ripple is inversely proportional to primary inductance. There are
considerations for choosing the magnitude of the magnetizing current ripple. Choosing a very small primary
inductance leads to a large current ripple. Care must be taken not to approach the cycle-by-cycle current limit of
approximately 3A. For this design, peak current was chosen not to exceed 2.5A at specified maximum ILOAD. A
ripple current of 1.8A was targeted. Rearranging Equation 15,
–6
V IN D  1 – D Tsw
5  0.25  0.75 4x10
L m + L lkg = -------------------------------------------- = --------------------------------------------------------- = 2.08H
I m RIPPLE
1.8
Equation 40.
The result of Equation 40 suggests the combination of magnetizing current and leakage inductance should be
2.08 H. Leakage inductance is unavoidable in transformer design and it should be minimized for the best energy
transfer in an asymmetric half bridge flyback converter. A transformer was designed with primary inductance of
2 H and leakage inductance 100 nH. Figure 8 shows the expected magnetizing current during the portion of the
cycle that S1 is closed and S2 is open.
Figure 8. Magnetizing Current
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4.2. C1 Selection
When S2 is closed, a resonant current in the primary is developed with frequency given by Equation 4. To ensure
zero current switching of the diode by the time S1 closed, S2 open mode begins, C1 should be chosen so that at
least half of the resonant period is completed in (1–D)Tsw time.

 r  --------------------------- 1 – D T sw
Equation 41.
Combining Equation 4 and Equation 41 and solving for C1:
1  1 – D T sw 2
C1  ----------  ----------------------------  9.1uF

L lkg 

Equation 42.
The next standard size capacitor 10 F was chosen.
4.3. D1 Selection
Equations 23 and 24 define the requirements for selecting D1. Substituting into Equation 23,
1
1
I D1  AVE  1 – D  = I LOAD  ------------- = 0.4  ----------- = 0.533A
 0.75
 1 – D
Equation 43.
Diode current capacities are usually specified in rms. Assuming a half wave sinusoid current through D1, consider
the translation of average to rms:

l D1 RMS  1 – D  = I D1 AVE  1 – D   ----------- = 0.592A
 2 2
Equation 44.
Substituting into Equation 24, consider using the maximum expected VIN as the worst case requirement for reverse
biasing:
V D1 REV  D  = V IN MAX  1 – D  N + V OUT = 5.5  0.75 4 + 5 = 21.5v
Equation 45.
Equations 24 and 45 do not include the voltage spike due to the interaction of the diode capacitance and leakage
inductance and as a result, a diode with a larger withstanding voltage is required in practice. When selecting D1,
Schottky diodes are the preferred choice due to their low forward voltage as it minimizes the associated power
loss.
A 1A, 40V Schottky diode was selected.
4.4. C10 Selection
C10 is inversely proportional to output voltage ripple and sets the crossover frequency of control loop gain. It is
suggested to use the minimum size capacitor to meet output voltage ripple requirements. Rearranging Equation
21,
I LOAD DT sw 0.4  0.25  4x10 – 6
C10 = -----------------------------------  ---------------------------------------------------  8F
V OUT RIPPLE
0.05
Equation 46.
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A 10uF capacitor was chosen.
4.5. C2 Selection
In most applications, VIN also supplies the VDDA pin that powers the dc—dc controller and left side digital isolator
circuitry. It is recommended to minimize voltage ripple at VDDA. Solving Equation 20:
I LOAD D  1 – D T SW N 0.4  0.25  0.75  4x10  4
C2  --------------------------------------------------------  -------------------------------------------------------------------------------  8F
V IN RIPPLE
0.15
–6
Equation 47.
A 10F capacitor was chosen.
4.6. R5 and R6
The ratio of R5 and R6 is determined by the 5 V output voltage requirement. To reduce the dependence of
feedback gain on the internal error amplifier transconductance, it is recommended to have the parallel combination
resistance to be  10 k. Higher values of R5 + R6 reduce power loss through the divider, but at the expense of
increasing output voltage error due to lVSNS which varies part to part. So R5 and R6 are chosen to target 10k
parallel resistance.
3
R5  R6
10x10 = ---------------------R5 + R6
Equation 48.
R5
5 = 1.05  -------- + 1
R6
Equation 49.
Substituting Equation 48 into Equation 49 and solving for R6,
3
3.76R6
3
3
10x10 = -------------------- R6 = 12.66x10  R5 = 48.1x10
4.76
Equation 50.
The nearest 1% resistor to 12.66 k is 12.7 k. However, setting R5 to either 47.5k or 48.7k does not target
exactly 5V as well as other 1% resistor pairs. A better match was found with R6=13.3 k and R5=49.9 k.
4.7. Compensation Network
The compensation network is comprised of R7 and C11. R7 is fixed to match RINT and 49.9 k is the nearest 1%
resistor value. The C11 places the compensation zero in relationship to the crossover frequency. The equation for
crossover frequency can be had by multiplying the P-mode gain (Equation 31) by the frequency of the pole created
by RLOAD and C10 (Equation 36):
3
50x10  3R LOAD
1
f c  ------------------------------------------------  -------------------------------------  12.1kHZ
R5  N
2R LOAD C10
Equation 51.
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To achieve good phase margin, it is suggested to place the zero between 1/4th to 1/10th of the estimated
crossover frequency. The zero placement was chosen to lead the crossover frequency by a factor of 6.
6
6
- = 1.58nF
C11 = ------------------------- = -------------------------------------------------------------------3
3
2f c  R7
2  12.1x10  49.9x10
Equation 52.
A 1.5 nF capacitor was chosen.
4.8. Design Summary
Table 2 shows the component selection that meet the design requirements.
Table 2. Design Summary
Part Reference
Description
Manufacturer
Manufacturer Part
Number
C1 C2 C10
CAP, 10uF, 10V, ±10%, X7R, 1206
Venkel
C1206X7R100-106K
C11
CAP, 1.5nF, 16V, ±10%, X7R, 0603
Venkel
C0603X7R160-152K
D1
DIO, FAST, 40V, 1.0A, SOD-128
Panasonic
DB2440100L
R5 R7
RES, 49.9K, 1/10W, ±1%, ThickFilm, 0603 Venkel
CR0603-10W-4992F
R6
RES, 13.3K, 1/16W, ±1%, ThickFilm, 0603 Venkel
CR0603-16W-1332F
T1
TRANSFORMER, POWER, FLYBACK,
2.0uH PRIMARY, 100nH LEAKAGE, 1:4,
1 TAP, SMT
UTB02185S
Rev. 0.1
UMEC
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