# Determining Vo in a diode circuit using iterative analysis

simulate this circuit – Schematic created using CircuitLab

Say we have this circuit. Then we were asked to find Vo using iterative analysis. We were told to stop when the estimate is accurate to within 15mV. I just want to confirm my understanding of the question.

• Is the 15mV the Vo that we should be aiming to get?
• And so, if it is, we should be looking for the values of Id or Vd, right?
• What will be the right approach here? Could I first assume Vd to be 1/2Vout (Since I could find Id when I know Vd) and then just adjust it till I get to 15mV?

My KVL equation is: (Id is based from the exponential model of the diode) $$Vout = V1 - iD(R1) - 2Vd$$

The following are given: Is (reverse sat. current) = 1fA Ideality factor = 1 Operating temp = 27 C

• Take a look at this and then share your approach with us? The question is asking you to calculate Vout +/- 15mV, 15mV is NOT the answer. You haven't stated what the diode model (I assume it's been provided) is so the information in the question is incomplete. Oct 5, 2020 at 6:02
• The diode model has not been stated explicitly. But since saturation current, ideality factor and operating temp is given, I think its natural to assume that its the exponential model?
– user263783
Oct 5, 2020 at 6:07
• Great. So since your working are going to rely upon that formula you'll need to show it here...I don't see an operating temp or saturation current provided either. Oct 5, 2020 at 6:08
• Vout will be 1V theoretically, but not in real life. The diodes require 0.5V to 0.7V in order to be on, if they are on, they will maintain the voltage at their own voltage, if they are not on, then the voltage will equal the source, which is 1 V. Diodes start conducting at 0.3V approximately, so some current will flow even then. The resistor will limit the current. You have to know what will the voltage be over the diodes, for a specific current. They must be described in the datasheet. Oct 5, 2020 at 6:13
• @mhaselup Ill edit the question! Thank you!
– user263783
Oct 5, 2020 at 6:19

To give you an idea of the iterative method let's assume a value of 4K ohms for R1

1. And let's make an initial guess of 0.3V across each diode totalling 0.6V

2. Given 1V - 0.6V = 0.4V drop across 4K ohms will provide a current of 0.1mA check using the Diode model the corresponding forward voltage (x2 for two diodes) and get a new estimate for the voltage across them.

3. Plug the model calculated forward voltage into your original equation and recalculate the current i.e. (1V - 2*Vd)/4K and repeat step 2.

Stop when Vout changes between steps by <=15mV

• I can't quite get the last statement. For ex, if for the first iteration to 6th iteration, i get a diff of +-1mV, and then for thet next, I get 15mV difference from the last iteration, I should stop?
– user263783
Oct 5, 2020 at 6:53
• You will get a series of values for Vout e.g. 0.6, 0.5, 0.45, 0.435, .. for example. Since the last two values differ by 0.15 (15 mV) you can stop at this point. Oct 5, 2020 at 6:54
• Got it! Thank you for the clear explanation!
– user263783
Oct 5, 2020 at 6:58
• Work out the voltage Vd for the given current using the model. Then double it as you have two (presumably identical) diodes. Oct 5, 2020 at 11:05
• I=(1 - 2*Vd)/2000 Oct 5, 2020 at 12:12
1. No, you're asked to find the output voltage within a tolerance of 15mV.

2. See above.

3. Initial assumption doesn't matter too much, it saves iterations if you are closer. If you assume a current (it will be fairly low in this case, maybe uA for a silicon diode), then calculate Vo, then you'll have a new current based on (1V-Vo)/R1. Calculate Vo again, repeat until it converges well enough.