# Finding Vout from circuit contain diodes.

1. Jun 16, 2013

### dla

1. The problem statement, all variables and given/known data
I am suppose to find an R value so that Vo=80mV given that both diodes are identical, conducting 10mA at 0.7 V and 100 mA at 0.8 V

2. Relevant equations

$I = I_{s} e^{v/{V_{t}n}}$

3. The attempt at a solution

I get that if the diodes are the same n, V_t and I_s are the same. So first I need to solve for n by using the equation and information above to create 2 equations assuming room temperature. Then I can make two equations from D1 and D2 and combine them to solve for V.

My main question is how did they know that Vo=V_2-V_1, voltage drop of diode 2 - voltage drop of diode 1. Why not the other way around? It might be simple but I am having a hard time seeing it any help will be much appreciated.

The circuit is attached. Thanks.

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2. Jun 16, 2013

### marcusl

No, n is the ideality factor of the diode. It is a "fudge factor" that accounts for some real-life departures from the ideal Schockley equation, and is usually set to one in the absence of specific information about the device being used.

The voltage at the common anode connection is pinned by the voltage drop of diode 1--there is no choice, because its drop sits between the source and ground--so it is V1. The drop V2 is determined by the current through the right branch, which depends partly on R, so Vo=V1-V2. The trick is to find how the current splits. You'll use Kirchoff's laws, Ohm's law and the Schockley equation to solve your problem.

3. Jun 16, 2013

### CWatters

By applying KVL around the loop.... Earth -> resistor -> D1 -> D2 -> Earth

+Vo + V_1 + (-V_2) = 0

Rearrange to give

Vo = V_2 - V_1

4. Jun 16, 2013

### rude man

This is exctly the right approach. Use the given diode voltages at 10 mA and 100 mA to solve for n.

Then the rest is just summing currents to zero at the anodes node.

5. Jun 16, 2013

### marcusl

Sorry, looks like I misread the problem. I took it as D1 operated at 10 mA and .7V, D2 at 100 mA and .8V. Apologies to the dla and rude man. Those two sets of values are sufficient to solve for Is and n, after which the problem can be solved as the other respondents said.

6. Jun 17, 2013

### dla

Thanks for the replies everyone. And I see it now CWatters thank you.

Actually marcusl your reply made me wonder how did we know that n is not 1?

When I made the two equations, I thought I had three unknowns at first: n, V_T and I_s. I didn't know if I should have assumed n=1 or assumed V_T was at room temperature and use V_T=25 mV. I ended up doing the latter because the solution showed it.

But if anyone can explain that would be great.

7. Jun 17, 2013

### Staff: Mentor

n and VT are both constants for a diode that is operating at a fixed temperature. That means that $nV_T$ is also a constant. So even if you assumed the wrong value for VT, the "variable" n that pops out of your solving for n from the given potential and current values would compensate. No problem!

I find it convenient to replace n and VT with a single variable, Vx, when the particulars of n and VT separately are not relevant.

8. Jun 17, 2013

### dla

Oh that makes a lot more sense! Very much appreciated, thanks gneill!

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