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T + k RC
(2)
V(t) + V
DD
(1 * e
*tńRC
)
(3)
TMDS442
SLLS757A – AUGUST 2006 – REVISED MARCH 2007
value, and C is the total load capacitance. The parameter, k, can be calculated from equation 3 by solving for
t, the times at which certain voltage thresholds are reached. Different input threshold combinations introduce
different values of t. Table 6 summarizes the possible values of k under different threshold combinations.
Table 6. Value K Upon Different Input Threshold Voltages
V
th-
\V
th+
0.7V
DD
0.65V
DD
0.6V
DD
0.55V
DD
0.5V
DD
0.45V
DD
0.4V
DD
0.35V
DD
0.3V
DD
0.1V
DD
1.0986 0.9445 0.8109 0.6931 0.5878 0.4925 0.4055 0.3254 0.2513
0.15V
DD
1.0415 0.8873 0.7538 0.6360 0.5306 0.4353 0.3483 0.2683 0.1942
0.2V
DD
0.9808 0.8267 0.6931 0.5754 0.4700 0.3747 0.2877 0.2076 0.1335
0.25V
DD
0.9163 0.7621 0.6286 0.5108 0.4055 0.3102 0.2231 0.1431 0.0690
0.3V
DD
0.8473 0.6931 0.5596 0.4418 0.3365 0.2412 0.1542 0.0741 -
From equation 1, R
up(min)
= 5.5V/3mA = 1.83 k Ω to operate the bus under a 5-V pull-up voltage and provide less
than 3 mA when the I
2
C device is driving the bus to a low state. If a higher sink current, for example 4 mA, is
allowed, R
up(min)
can be as low as 1.375 k Ω .
Given a 5-V I
2
C device with input low and high threshold voltages at 0.3 V
dd
and 0.7 V
dd
, the valued of k is
0.8473 from Table 6 . Taking into account the 1.83-k Ω pull-up resistor, the maximum total load capacitance is
C
(total-5V)
= 645 pF. C
cable(max)
should be restricted to be less than 545 pF if C
source
and C
i
can be as heavy as 50
pF. Here the C
i
is treated as C
sink
, the load capacitance of a sink device.
Fixing the maximum transition time from Table 6 , T = 1 μ s, and using the k values from Table 6 , the
recommended maximum total resistance of the pull-up resistors on an I
2
C bus can be calculated for different
system setups.
To support the maximum load capacitance specified in the HDMI spec, C
cable(max)
= 700pF/C
source
= 50pF/C
i
=
50pF, R
(max)
can be calculated as shown in Table 7 .
Table 7. Pull-Up Resistor Upon Different Threshold Voltages and 800-pF Loads
V
th-
\V
th+
0.7V
DD
0.65V
DD
0.6V
DD
0.55V
DD
0.5V
DD
0.45V
DD
0.4V
DD
0.35V
DD
0.3V
DD
UNIT
0.1V
DD
1.14 1.32 1.54 1.80 2.13 2.54 3.08 3.84 4.97 k Ω
0.15V
DD
1.20 1.41 1.66 1.97 2.36 2.87 3.59 4.66 6.44 k Ω
0.2V
DD
1.27 1.51 1.80 2.17 2.66 3.34 4.35 6.02 9.36 k Ω
0.25V
DD
1.36 1.64 1.99 2.45 3.08 4.03 5.60 8.74 18.12 k Ω
0.3V
DD
1.48 1.80 2.23 2.83 3.72 5.18 8.11 16.87 - k Ω
Or, limiting the maximum load capacitance of each cable to be 400 pF to accommodate with I
2
C spec version
2.1. C
cable(max)
= 400pF/C
source
=50pF/C
i
= 50pF, the maximum values of R are calculated as shown in Table 8 .
Table 8. Pull-Up Resistor Upon Different Threshold Voltages and 500-pF Loads
V
th-
\V
th+
0.7V
DD
0.65V
DD
0.6V
DD
0.55V
DD
0.5V
DD
0.45V
DD
0.4V
DD
0.35V
DD
0.3V
DD
UNIT
0.1V
DD
1.82 2.12 2.47 2.89 3.40 4.06 4.93 6.15 7.96 k Ω
0.15V
DD
1.92 2.25 2.65 3.14 3.77 4.59 5.74 7.46 10.30 k Ω
0.2V
DD
2.04 2.42 2.89 3.48 4.26 5.34 6.95 9.63 14.98 k Ω
0.25V
DD
2.18 2.62 3.18 3.92 4.93 6.45 8.96 13.98 28.99 k Ω
0.3V
DD
2.36 2.89 3.57 4.53 5.94 8.29 12.97 26.99 - k Ω
Obviously, to accommodate the 3-mA drive current specification, a narrower threshold voltage range is required
to support a maximum 800-pF load capacitance for a standard-mode I
2
C bus.
When the input low and high level threshold voltages, V
th-
and V
th+
, are 0.7 V and 1.9 V, which is 0.15 V
DD
and
0.4 V
DD
approximately with V
DD
= 5 V, from Table 7 , the maximum pull-up resistor is 3.59 k Ω . The allowable
pull-up resistor is in the range of 1.83 k Ω and 3.59 k Ω .
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