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Using TLC5940 With Higher LED Supply Voltages and Series LEDs

Hello i am trying to understand the application report slva280, but since my knowlegde about electronics are limited i need some kind of help mostly on my calculations.

I am unable to calculate VOUTx correctly,
Lets say i use LEDs with Vf = 3 Volt @20mA,

Question 1: When LED is on the equivalent circuit is a voltage source (Vf) 3V with a series resistor(Rled),right;

Question 2: When LED is off the equivalnet circuit is a resistor (Rled), right;

With that in mind lets do some calculations

Figure 1

Case when LED is on: Vcc  = Vf + VOUTx (we ignore Rled to keep things simple), so VOUTx = 5 - 3 = 2 V, -0,3 <VOUTx < 18 we are in the safe area.

Case when LED is off: I assume Id = 0 A, so VOUTx = 5 Volts.


Figure 2


Three LEDS in series, lets calculate the same thing.

Case when leds are off: Vout = 5 Volt

Case when LEDS on: VOUTx = Vcc - 3*Vf = 5 - 9 = -4 Volts, so VOUTx is now negative exceeds the limits.

In order to correct this problem we have to use a bigger value for Vcc lets say 20Volts.

Lets do the calculation oncemore

Case Leds on: VOUTx = 20 - 9 = 11Volts. OKEY

Case Leds off: VOUTx =  20Volts. PROBLEM!

Figure 3

Figure 3 shows a typical solution if you want to connect many Leds in series, using a Mosfet
.I assume we use the mosfet in two regions, cutoff region, and triode region (Ron).

Lets do some calculations again

Case 1 when led is ON:

We must ensure Vgs > Vth and Vds < Vgs - Vth, if those conditions are true VOUTx must be

VOUTx = Vcc - id*Ron - Vf = 5 - 0,02*10 - 3 = 1,8 Volt.

Case 2 when led is OFF :

we must ensure Vgs < Vth , since MOSFET is an open circuit

VOUTx = high Impedance ???

Okey guys thats what i have done so far,please if you find some errors in my logic correct me.

lets get back to the application report

Page 3, says

Even though the driver is off,the LEDs have a forward voltage drop due to leakage currents that flow through them.

When the driver is off and no current is flowing, the voltage across the LEDs is 29V.
I cant understand why the voltage across the LEDs is 29V.

 

The voltage on the OUTx pin is 2V,which is greater than VCC– VGS(th),or greater than 3.3V–1.5V = 1.8V.

I cant understand why VOUTx is 2V

 

THANKS