CS5165A
http://onsemi.com
15
Droop Resistor Tolerance
Tolerance due to sheet resistivity variation 16%
Tolerance due to L/W error 1.0%
Tolerance due to temperature variation 12%
Total tolerance for droop resistor 29%
In order to determine the droop resistor value the nominal
voltage drop across it at full load has to be calculated. This
voltage drop has to be such that the output voltage full load
is above the minimum DC tolerance spec.
V
DROOP(TYP)
+
[V
DAC(MIN)
* V
DC(MIN)
]
1 ) R
DROOP(TOLERANCE
)
Example: for a 300 MHz PentiumII, the DC accuracy spec
is 2.74 < V
CC(CORE)
< 2.9 V, and the AC accuracy spec is
2.67 V < V
CC(CORE)
< 2.9 3V. The CS5165A DAC output
voltage is +2.812 V < V
DAC
< +2.868 V. In order not to
exceed the DC accuracy spec, the voltage drop developed
across the resistor must be calculated as follows:
V
DROOP(TYP)
+
[V
DAC(MIN)
* V
DC
PENTIUMII(MIN)]
1 ) R
DROOP(TOLERANCE
)
+
2.812 V * 2.74 V
1.3
+ 56 mV
With the CS5165A DAC accuracy being 1.0%, the internal
error amplifier’s reference voltage is trimmed so that the
output voltage will be 40 mV high at no load. With no load,
there is no DC drop across the resistor, producing an output
voltage tracking the error amplifier output voltage, including
the offset. When the full load current is delivered, a drop of
−56 mV is developed across the resistor. Therefore, the
regulator output is pre−positioned at 40 mV above the
nominal output voltage before a load turn−on. The total
voltage drop due to a load step is DV−40 mV and the
deviation from the nominal output voltage is 40 mV smaller
than it would be if there was no droop resistor. Similarly at full
load the regulator output is pre−positioned at 16 mV below
the nominal voltage before a load turn−off. The total voltage
increase due to a load turn−off is DV−16 mV and the
deviation from the nominal output voltage is 16 mV smaller
than it would be if there was no droop resistor. This is because
the output capacitors are pre−charged to value that is either
40 mV above the nominal output voltage before a load
turn−on or, 16 mV below the nominal output voltage before
a load turn−off (see Figure 15).
Obviously, the larger the voltage drop across the droop
resistor ( the larger the resistance), the worse the DC and
load regulation, but the better the AC transient response.
Design Rules for Using a Droop Resistor
The basic equation for laying an embedded resistor is:
R
AR
+ ò
L
A
or R + ò
L
(W t)
where:
A = W × t = cross−sectional area
ρ = the copper resistivity (mW − mil)
L = length (mils)
W = width (mils)
t = thickness (mils)
For most PCBs the copper thickness, t, is 35 mm (1.37
mils) for one ounce copper. ρ = 717.86 mW−mil
For a Pentium II load of 14.2 A the resistance needed to
create a 56 mV drop at full load is:
Response Droop +
56 mV
I
OUT
+
56 mV
14.2 A
+ 3.9 mW
The resistivity of the copper will drift with the
temperature according to the following guidelines:
DR + 12% @ T
A
+)50°C
DR + 34% @ T
A
+)100°C
Droop Resistor Width Calculations
The droop resistor must have the ability to handle the load
current and therefore requires a minimum width which is
calculated as follows (assume one ounce copper thickness):
W +
I
LOAD
0.05
where:
W = minimum width (in mils) required for proper power
dissipation, and I
LOAD
Load Current Amps.
The Pentium
®
II maximum load current is 14.2 A.
Therefore:
W +
14.2 A
0.05
+ 284 mils + 0.7213 cm
Droop Resistor Length Calculation
L +
R
DROOP
W t
ò
+
0.0039 284 1.37
717.86
+ 2113 mil + 5.36 cm
Output Inductor
The inductor should be selected based on its inductance,
current capability, and DC resistance. Increasing the
inductor value will decrease output voltage ripple, but
degrade transient response.
Inductor Ripple Current
Ripple Current +
[(V
IN
* V
OUT
) V
OUT
]
(Switching Frequency L V
IN
)
Example: V
IN
= +5.0 V, V
OUT
= +2.8 V, I
LOAD
= 14.2 A,
L = 1.2 mH, Freq = 200 kHz
Ripple Current +
[(5.0 V * 2.8 V) 2.8 V]
[200 kHz 1.2 mH 5.0 V]
+ 5.1 A
Output Ripple Voltage
V
RIPPLE
+ Inductor Ripple Current Output Capacitor ESR
Example:
V
IN
= +5.0 V, V
OUT
= +2.8 V, I
LOAD
= 14.2 A, L = 1.2 mH,
Switching Frequency = 200 kHz
Output Ripple Voltage = 5.1 A × Output Capacitor ESR
(from manufacturer’s specs)
ESR of Output Capacitors to limit Output Voltage Spikes
ESR +
DV
OUT
DI
OUT
