Fairchild RC5042, RC5040 specifications Resistor mΩ, = 2000mi

AN42 APPLICATION NOTE

Table 8. Rsense for various load currents

ILoad,max	RSENSE	RSENSE
	PC Trace	Discrete
(A)	Resistor (mΩ)	Resistor (mΩ)
10.0	6.5	8.6
11.2	5.8	7.8
12.4	5.3	7.1
13.9	4.8	6.4
14.0	4.7	6.3
14.5	4.6	6.1

Discrete Sense Resistor

Discrete iron alloy resistors come in a variety of tolerances and power ratings, and are ideal for precision implementa- tions. Either an MnCu alloy wire resistor or an CuNi alloy wire resistor is ideal for a low cost implementation.

Embedded Sense Resistor (PC Trace Resistor)

Embedded PC trace resistors have the advantage of almost zero cost implementation. However, the value of the PC trace resistors have large variations. Embedded resistors have 3 major error sources: the sheet resistivity of the inner layer, the mismatch due to L/W, and the temperature varia- tion of the resistor. When laying out embedded sense resis- tors, consider all error sources described as follows:

•Sheet resistivity.

For 1 ounce copper, the thickness variation is typically between 1.15 mil and 1.35 mil. Therefore, the error due to sheet resistivity is (1.35 – 1.15)/1.25 = 16%.

•Mismatch due to L/W.

The error in L/W is dictated by the geometry and the power dissipation capability of the sense resistor. The sense resistor must be able to handle the load current and, therefore, requires a minimum width, calculated as follows:

IL

W = ---------

0.05

where W is the minimum width required for proper power dissipation (mils), and IL is the load current in Amps.

For a load current of 15A, the minimum width required is 300mils, which reflects a 1% L/W error.

•Thermal Considerations.

The I2R power losses cause the surface temperature of the resistor to increase along with its resistance value. In addition, ambient temperature variations add the change in resistor value:

R = R20[1 + α20(T – 20)]

where R20 is the resistance at 20°C, α20 = 0.00393/ °C,T is the operating temperature, andR is the desired value.

For temperature T = 50°C, the %R change = 12%.

Table 9 is a summary of tolerances for the Embedded PC Trace Resistor.

Table 9. Summary PC Trace Resistor Tolerance

Tolerance due to sheet resistivity variation	16%
Tolerance due to L/W error	1%
Tolerance due to temperature variation	12%
Total Tolerance for PC Trace Resistor	29%

Design rules for using an embedded resistor

The basic equation for laying an embedded resistor is:

L		L
R = ρ ⋅ W------------⋅t	W		t

where ρ is the Resistivity (W-mil), L is the Length (mils), W is the Width (mils), and t is the Thickness (mils).

For 1oz copper, t = 1.35 mils, ρ = 717.86 ∝Ω-mil, 1 L/1 W = 1 Square ( ■ ).

For example, you can layout a 5.30mΩ embedded sense resistor. From Equations above,

	IL		10
W = 0.05---------		= 0.05---------		= 200mil
L =	R-----------------------⋅W ⋅ t		=	--------------------------------------------------0.00530⋅ 200 ⋅ 1.35	= 2000mi
	ρ			717.86

L/W = 10 ■.

Therefore, to model 5.30mΩ enbedded resistor, you need W = 200 mils, and L = 2000 mils. See Figure 10.

1 1 1 1 1 1 1 1 1 1

W = 200 mils

L = 2000

Figure 10. 5.30mΩ Sense Resistor (10 ■)

You can also implement the sense resistor in the following manner. Each corner square is counted as 0.6 square since the current flowing through the corner square does not flow uniformly, concentrated towards the inside edge. This is shown in Figure 11.

1	1	1	1	1	1
.6					.6
1					1
.8

Figure 11. 5.30mΩ Sense Resistor (10 ■)

A Resign Example Combining an Embedded Resistor with a Discrete Resistor

For low cost implementation, the embedded PC trace resistor is the most desirable alternative, but, as discussed earlier, the wide tolerance (±29%) presents a challenge. In addition, changing CPU requirements may force the maximum load

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