# Power dissipation in a Darlington built with an optocoupler and NPN

Joined Feb 28, 2017
12
--SOLVED--
I have implemented a PWM control over a relay from an Arduino. To isolate both circuits I have used an optocoupler 4N35 from Vishay. Since it cannot provide enough current flow to drive the relay, I have used a BC548B transistor creating a Darlington structure with the internal output transistor of the 4N35.

The problem is that I have simulated the circuit but then, when I try to calculate the currents in the circuit I am unable to achieve the simulated values. I don't know how to achieve the $$V_CE(OK3)$$ neither $$I_F$$.

$$I_{K1} = \frac{+12V_{PS2}-V_{CE(Q4)}}{K1}$$

$$I_{K1}=\frac{I_{C(Q4)}}{\beta _{Q4}}\frac{\beta _{OK3}}{(\beta _{OK3}+1)}+I_{C(Q4)}$$

$$V_{CE(Q4)}=V_{CE(OK3)}+V_{BE(Q4)}$$

$$P_{OK3}=I_FV_D+I_{C(OK3)}V_{CE(OK3)}$$

$$P_{Q4}=I_{C(Q4)}V_{CE(Q4)}$$

Even if I've checked the 4N35 datasheet, I am unable to calculate the values for my circuit. The $$V_F$$ for the input diode is only expressed by a fixed current of 10 mA. Then, I am unable to know what will be the $$V_CE(OK3)$$ and therefore I cannot achieve the $$V_CE(Q4)$$. Summarizing, I have nothing.

I hope you can guide me.

Salus

Moderators note: removed the plains from the post

Last edited:

#### AlbertHall

Joined Jun 4, 2014
11,401
Connect the collector of the opto to the positive rail by a 3k3 resistor instead of to the NPN collector.

Joined Feb 28, 2017
12
Connect the collector of the opto to the positive rail by a 3k3 resistor instead of to the NPN collector.
Thanks for the suggestion but it is not possible. The circuit is like the picture and I should calculate the power dissipation in this case. Unfortunately I'm not able to modify it.

#### crutschow

Joined Mar 14, 2008
27,459
Do you need an exact expression for the power dissipated, or just an engineering approximation?

Joined Feb 28, 2017
12
Do you need an exact expression for the power dissipated, or just an engineering approximation?
It depends on how approximated would be the expression ;-) The problem is for example, that I cannot determine the I_F because it depends on the R7 and also on the V_D. Well, I know the value of the R7 but how can I know the current through it? In the same way, I don't know how to determine the V_CE(OK3), if I achieve these parameters, then the power dissipation will be easy to calculate.

#### dl324

Joined Mar 30, 2015
12,929
Reformatted tex commands so they can be read...
The problem is that I have simulated the circuit but then, when I try to calculate the currents in the circuit I am unable to achieve the simulated values. I don't know how to achieve the $$\small V_CE(OK3)$$
neither
$$\small I_F$$.

$$\small I_{K1} = \frac{+12V_{PS2}-V_{CE(Q4)}}{K1} I_{K1}=\frac{I_{C(Q4)}}{\beta _{Q4}}\frac{\beta _{OK3}}{(\beta _{OK3}+1)}+I_{C(Q4)} V_{CE(Q4)}=V_{CE(OK3)}+V_{BE(Q4)} P_{OK3}=I_FV_D+I_{C(OK3)}V_{CE(OK3)} P_{Q4}=I_{C(Q4)}V_{CE(Q4)}$$

Even if I've checked the 4N35 datasheet, I am unable to calculate the values for my circuit. The $$\small V_F$$ for the input diode is only expressed by a fixed current of 10 mA. Then, I am unable to know what will be the $$\small V_CE(OK3)$$ and therefore I cannot achieve the $$\small V_CE(Q4)$$. Summarizing, I have nothing.

Last edited:

#### dl324

Joined Mar 30, 2015
12,929
The problem is for example, that I cannot determine the I_F because it depends on the R7 and also on the V_D.
Why do you care? You just want to drive the optical emitter in the optocoupler hard enough to saturate the transistor switch.

Joined Feb 28, 2017
12
Reformatted tex commands so they can be read...
I've tried but i don't know the reason why it doesn't read the Tex labels.

Joined Feb 28, 2017
12
Why do you care? You just want to drive the optical emitter in the optocoupler hard enough to saturate the transistor switch.
Because I have to justify the power dissipated by this circuit. It works perfectly but I have to calculate the theoretical part of the design.

#### dl324

Joined Mar 30, 2015
12,929
I've tried but i don't know the reason why it doesn't read the Tex labels.
You used [plain] in all of your tex commands.

Joined Feb 28, 2017
12
You used [plain] in all of your tex commands.
I should use only the ?
Now, I think I cannot modify the first post but I'll check it ;-)

#### dl324

Joined Mar 30, 2015
12,929
Because I have to justify the power dissipated by this circuit.
Given the voltage driving the opto emitter, you can calculate dissipation in the current limit resistor and the emitter. Knowing the CTR of the optocoupler, you can estimate collector currents in the transistors.

You can decrease dissipation in the external transistor if you connect the optocoupler transistor as a split darlington instead of darlington.

Joined Feb 28, 2017
12
Given the voltage driving the opto emitter, you can calculate dissipation in the current limit resistor and the emitter. Knowing the CTR of the optocoupler, you can estimate collector currents in the transistors.

You can decrease dissipation in the external transistor if you connect the optocoupler transistor as a split darlington instead of darlington.
But the voltage on the Diode depends on the current and vice versa. How can I determine both?
By the way, is it normal that the page doesn't allow me to edit the first post?

#### bertus

Joined Apr 5, 2008
21,453
Hello,

By using the [plain] the [tex] command is not parsed.

Bertus

Joined Feb 28, 2017
12
Hello,

By using the [plain] the [tex] command is not parsed.

Bertus
Yes, I have understood it, the thing is that now is too late to edit de main post.

#### bertus

Joined Apr 5, 2008
21,453
Hello,

I have removed the plains from your opening post.

Bertus

#### dl324

Joined Mar 30, 2015
12,929
But the voltage on the Diode depends on the current and vice versa. How can I determine both?
Iterative calculations, and associated circuit changes, are sometimes required. When you're designing the circuit, you use an approximate voltage for the LED and select a resistor. If you require a more precise current, you modify the current limit resistor value.
By the way, is it normal that the page doesn't allow me to edit the first post?
I don't know. I've only started a few posts and didn't need to make changes.

Joined Feb 28, 2017
12

Joined Feb 28, 2017
12
Iterative calculations, and associated circuit changes, are sometimes required. When you're designing the circuit, you use an approximate voltage for the LED and select a resistor. If you require a more precise current, you modify the current limit resistor value.
I don't know. I've only started a few posts and didn't need to make changes.
Thanks a milion!

#### dl324

Joined Mar 30, 2015
12,929
Forward voltage and current transfer characteristics for 4N35:

The second graph is not aplicable in my case, I think. There is no 10V as $$V_{CE}$$.