IR3721 datasheet(6/16 Pages) IRF

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IR3721

DATA SHEET

Page 6 of 16

www.irf.com

09/15/08

THERMAL COMPENSATION FOR INDUCTOR DCR CURRENT

SENSING

The positive temperature coefficient of the inductor

DCR can be compensated if RT varies inversely

proportional to the DCR. DCR of a copper coil, as a

function of temperature, is approximated by

)

⋅

)

(

⋅

)

(

)

(

TCR

DCR

Equation 2

TR is some reference temperature, usually 25 °C, and

TCRCu is the resistive temperature coefficient of

copper, usually assumed to be 0.39 %/°C near room

temperature. Note that equation 2 is linearly

increasing with temperature and has an offset of

DCR(TR) at the reference temperature.

If RT incorporates a negative temperature coefficient

thermistor then temperature effects of DCR can be

minimized. Consider a circuit of two resistors and a

thermistor as shown below.

Rth

Figure 2 RT Network

If Rth is an NTC thermistor then the value of the

network will decrease as temperature increases.

Unfortunately, most thermistors exhibit far more

variation with temperature than copper wire. One

equation used to model thermistors is

⎟

⎠

⎞

⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⋅

)

(

)

(

Equation 3

where Rth(T) is the thermistor resistance at some

temperature T, Rth(T0) is the thermistor resistance at

the reference temperature T0, and β is the material

constant provided by the thermistor manufacturer.

Kelvin degrees are used in the exponential term of

equation 3. If RS is large and RP is small, the

curvature of the equivalent network resistance can be

reduced from the curvature of the thermistor alone.

Although the exponential equation 3 can never

compensate linear equation 2 at all temperatures, a

spreadsheet can be constructed to minimize error

over the temperature interval of interest. The

equivalent resistance RT of the network shown as a

function of temperature is

)

(

)

(

Equation 4

using Rth(T) from equation 3.

Equation 2 may be rewritten as a new function of

temperature using equations 2 and 4 as follows:

()

)

(

⋅

)

(

)

(

DCR

Equation 5

With Rs and Rp as additional free variables, use a

spreadsheet to solve equation 5 for the desired full

scale current while minimizing the IFS(T) variation

over temperature.

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