# Diode problem

#### unlisted

Joined Jan 20, 2007
11
Hey guys,

I am looking for a point in the right direction for this problem.

The problem asks for the value of R for which the voltage across the resistor is 40mV. I assume I need to workout the current passing through the resistor. Since the resistor is in series with D1, which is in parallel with D2 the current should be divided. Once I have the current I can use Ohm's law to find R.

So I think what I need to find is the current passing through D1 and R.

Thanks

#### Ron H

Joined Apr 14, 2005
7,014
I know how to solve this, and it involves the diode equation. Since it's homework, I won't give you the answer, but I can give you some clues.

But first - have you been exposed to the diode equation? If so, tell us what it is.

#### unlisted

Joined Jan 20, 2007
11
Thanks for the help.

I have been exposed to the diode equation i = Is[exp(v/nVT - 1)]
At room temperature VT = .025V
n is 1, or 2, but we are not given a value for n.

#### Ron H

Joined Apr 14, 2005
7,014
Thanks for the help.

I have been exposed to the diode equation i = Is[exp(v/nVT - 1)]
At room temperature VT = .025V
n is 1, or 2, but we are not given a value for n.
In order to solve this, you first have to solve for n. It is not 1 or 2, but it is somewhere in between. You can solve for n from the information given.
After you solve for n, you can then solve for the current through the two diodes, and then, of course, you can solve for R.
If you get stuck, post your efforts here and I'll give you some more clues. Hint: the "-1" in the equation is insignificant at the current levels you are working with. You may already be aware of this.

#### unlisted

Joined Jan 20, 2007
11
Ok, I solved for n and Is, and got an equation for i.

The V given in the problem statement is the drop across R, right? So
I can't just plug that into my diode equation. Do I need to first solve
for the drops across the diodes?

#### Ron H

Joined Apr 14, 2005
7,014
Ok, I solved for n and Is, and got an equation for i.

The V given in the problem statement is the drop across R, right? So
I can't just plug that into my diode equation. Do I need to first solve
for the drops across the diodes?

I1~Is*e^(v1/nVt)
I2~Is*e^(v2/nVt)
therefore,
(1) I1/I2=e^((v1-v2)/nVt)
Note that Is has fallen out of the equation.
From this relationship, and the information about the diodes given in the problem, you can find n.
Once you find n, remember that you know that in the actual circuit, v1-v2=40mV. From this fact, and using eq. (1), you can find the currents through the two diodes.

Another hint: Naperian logarithims are required to solve for n, and again for I1 and I2.

#### unlisted

Joined Jan 20, 2007
11
I used the natural log to find n. Does v1-v2=40mV come from Kirchoff's voltage law?

#### Ron H

Joined Apr 14, 2005
7,014
I used the natural log to find n. Does v1-v2=40mV come from Kirchoff's voltage law?
It comes from the fact that the anodes are tied together, the cathode of D2 is at zero volts, and the cathode of D1 is at 40mV. Therefore (VD2-VD1)=40mV. I guess that's Kirchhoff's voltage law. When you've been an engineer for 40 years, the names of the laws (in my case, anyway) become irrelevant. Who else had a voltage law? Did you understand the ratio equation, and why Is falls out of the equation? I suppose you could find Is, but you don't need it.

#### unlisted

Joined Jan 20, 2007
11
I understand the ratio equation, that is basically how I solved for n. I just don't get the v1-v2 = 40mV. To me, the two diodes look like they are hooked up in parallel. In which case they should share the same voltage drop, right?

Ok, assuming v1-v2=40 mV I am still unclear on how to find the currents through D1 and D2. I'll look back through the post and see if I can work it out.

Wow, 40 years? Ever think about teaching this stuff?

#### Ron H

Joined Apr 14, 2005
7,014
I understand the ratio equation, that is basically how I solved for n. I just don't get the v1-v2 = 40mV. To me, the two diodes look like they are hooked up in parallel. In which case they should share the same voltage drop, right?

Ok, assuming v1-v2=40 mV I am still unclear on how to find the currents through D1 and D2. I'll look back through the post and see if I can work it out.

Wow, 40 years? Ever think about teaching this stuff?
I work full time as an engineer. I don't have the time or the inclination to teach (except on forums like this).

How can you think the diodes are in parallel when R has 40mV across it? D1 obviously (to me, anyway) has 40mV less across it than D2.
If you accept that, do you understand where this equation comes from?

ln(I2/I1)= (v2-v1)/nVt

You can solve for (I2/I1).
Your other equation is (I2+I1)=10ma (from the schematic).

You now have two simultaneous equations. Solve for I2 and I1.

#### unlisted

Joined Jan 20, 2007
11
I understand where the ratio equation comes from. I guess I am just having trouble with the basics.

Thanks for all the help, and I hope this was useful for others.

#### Ron H

Joined Apr 14, 2005
7,014
I understand where the ratio equation comes from. I guess I am just having trouble with the basics.

Thanks for all the help, and I hope this was useful for others.
I'm still concerned about your statement that the diodes seem to be in parallel. Do you understand that the voltage across the resistor reduces the voltage across D1, and that, since the two diodes are identical, I1 must be less than I2? Have you seen the V-I curve of a diode (basically a plot of the equation), which graphically shows that the current changes as the voltage changes? It is apparent from the equation, but, as they say, a picture is worth ~ e^6.9 equations. #### unlisted

Joined Jan 20, 2007
11
I have seen the curve of a diode, but I don't understand why the voltage across the resistor reduces to D1.

#### Ron H

Joined Apr 14, 2005
7,014
I didn't say it reduces to D1. I said it reduces the voltage across D1.
Does the attached annotated schematic help?

#### unlisted

Joined Jan 20, 2007
11
I see now, I misread your previous post. From the image VD1 must be
the difference in D1 anode and cathode voltages, which is vd - 40mV. Since R decreases the voltage across D1, from the diode graph, I1 must also decrease.That is why I1 must be less than I2.

I think I get it now. I'm going to work through the problem again, and see if I get stuck.

#### unlisted

Joined Jan 20, 2007
11
Ron, thanks for all the help. After reviewing basic circuit analysis, and explaining the solution to someone I now understand the material.

#### Ron H

Joined Apr 14, 2005
7,014
Ron, thanks for all the help. After reviewing basic circuit analysis, and explaining the solution to someone I now understand the material.
That's good. 