# Fairchild SEMICONDUCTOR RC5051 User Manual

## Page 12

**AN50**

**APPLICATION NOTE**

**12**

** **

**Embedded Sense Resistor (PC Trace Resistor)**

Embedded PC trace resistors have the advantage of near zero

cost implementation. However, the value of the PC trace

resistor has 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 variation of

the resistor. All three error sources must be considered for

laying out embedded sense resistors.

**• Sheet resistivity.**

For 1 ounce copper, the thickness variation is typically

1.15 mil to 1.35 mil. Therefore error due to sheet resistiv-

ity is (1.35 - 1.15)/1.25 = 16%

**• Mismatch due to L/W. **

Percent error in L/W is dictated by 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 which is calculated as

follows.

where: W = minimum width required for proper power

dissipation (mils) and I

L

= Load Current in Amps.

For 15A of load current, minimum width required is

300mils, which reflects a 1% L/W error.

**• Thermal Consideration. **

Due to I

2

R power losses the surface temperature of the

resistor will increase leading to a higher value. In addition,

ambient temperature

variation will add the change in resistor value:

where: R

20

is the resistance at 20

°

C,

α

20

= 0.00393/

°

C, T

is the operating temperature, and R is the desired value.

For temperature T = 50

°

C, the %R change = 12%.

Table 9 is the summary of the tolerance for the Embedded

PC Trace Resistor.

**Table 9. Summary PC Trace Resistor Tolerance**

**Design Rules for Using an Embedded Resistor**

The basic equation for laying an embedded resistor is:

where:

ρ

= Resistivity(

µΩ

-mil),

L = Length(mils),

W = Width(mils), and

t = Thickness(mils).

For 1oz copper, t = 1.35 mils,

ρ

= 717.86

µΩ

-mil,

1 L/1 W = 1 Square (

■

).

For example, you can layout a 5.30m

Ω

embedded sense

resistor using the equations above:

L/W = 10

■

Therefore, to model 5.30m

Ω

embedded sense resistor, you

need W = 200 mils and L = 2000 mils. Refer to Figure 9.

**Figure 9. 5.30m**

Ω

** Sense Resistor (10 **

■

**)**

You can also implement the sense resistor in the following

manner. Each corner square is counted as 0.6 square since

current flowing through the corner square does not flow

uniformly and it is concentrated towards the inside edge, as

shown in Figure 10.

**Figure 10. 5.30m**

Ω

** Sense Resistor (10 **

■

**)**

**A Design Example Combining an Embedded Resistor and a Discrete Resistor**

For low cost implementation, the embedded PC trace resistor

is most desirable. However, its wide tolerance (29%) pre-

sents a challenge. In addition, requirements for the CPU

change frequently, and, thus, the maximum load current may

be subject to change. Combining embedded resistors with

discrete resistors may be a desirable option. Figure 11 shows

a design that provides flexibility with a solution to address

wide tolerances.

In this design, you have the option to choose an embedded

or a discrete MnCu sense resistor. To use the discrete sense

resistor, populate R21 with a shorting bar (zero Ohm resis-

tor) for proper Kelvin connection and add the MnCu sense

resistor. To use the embedded sense resistor, on the other

hand, populate R22 with a shorting bar for Kelvin connec-

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%

W

I

L

0.05

----------

=

R

R

20

1

α

20

T

20

–

(

)

]

+

[

=

R

ρ

L

W

t

Ч

-------------

Ч

=

W

I

L

0.05

----------

10

0.05

----------

200mils

=

=

=

L

R

W

×

t

×

ρ

------------------------

0.00530

200

Ч

1.35

Ч

717.86

---------------------------------------------------

2000mils

=

=

=

1

1

1

1

1

1

1

1

1

1

W = 200 mils

L = 2000

.6

.6

.8

1

1

1

1

1

1

1

1

W

L

t