Circuit description

AN2983

16/32

Doc ID 15679 Rev 1

The drawback of this configuration is that since the circuit is now more sensitive to input

voltage variations, Vin has to be more tightly regulated.

The following equations demonstrate what has been previously asserted.

Equation 33

Equation 34

Where: I_Led_avg is the LEDs’ average current, I_Led_pk is the LEDs’ peak current and

Va = (Vin - VLed) is the LEDs’ cathode voltage.

Equation 35

Equation 36

To make I_Led_avg independent of VLed, the VLed coefficient has to be reduced to zero.

Equation 37

That is to say, setting:

Equation 38

reduces Equation 36 to:

Equation 39

In other words, connecting Ra to the cathode of the LEDs’ string, the average LED current

depends only on Vth and Vin.

VLed

*

L

toff

2

1

pk

_

Led

_

I

avg

_

Led

_

I

⎟

⎠

⎞

⎜

⎝

⎛

−

=

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

+

⎟

⎠

⎞

⎜

⎝

⎛

=

Ra

Rb

*

Va

Ra

Rb

Ra

*

Vth

*

Rs

1

pk

_

Led

_

I

()

VLed

*

L

toff

2

1

Ra

Rb

*

VLed

Vin

Ra

Rb

Ra

*

Vth

*

Rs

1

avg

_

Led

_

I

⎟

⎠

⎞

⎜

⎝

⎛

−

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

−

⎟

⎠

⎞

⎜

⎝

⎛

+

⎟

⎠

⎞

⎜

⎝

⎛

=

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

+

+

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

+

⎟

⎠

⎞

⎜

⎝

⎛

=

L

toff

2

1

Ra

Rb

*

Rs

1

*

VLed

Ra

Rb

*

Vin

Ra

Rb

Ra

*

Vth

*

Rs

1

avg

_

Led

_

I

0

L

toff

2

1

Ra

Rb

*

Rs

1

=

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

0

Rs

/

L

toff

2

1

Ra

Rb

=

⎟

⎠

⎞

⎜

⎝

⎛

=

⎟

⎠

⎞

⎜

⎝

⎛

()

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

+

⎟

⎠

⎞

⎜

⎝

⎛

=

Ra

Rb

*

Vin

Ra

Rb

Ra

*

Vth

*

Rs

1

avg

_

Led

_

I