Solving Basic Diode Circuit: Voltage Across Diodes @ 1mA

[sisyphus0321]

Homework Statement

Given a basic circuit of a voltage source and two diodes in series:
D1 is .7v @ 10mA
D2 is .6v @ .1mA
If I is 1mA, What is the voltage across the two diodes?

Homework Equations

VT~.026
Vt= 60log (I(t)/Is
I1 produces V1
I2 produces V2
so V2 = V1 + 60(mV)[log (I2/I1)]

The Attempt at a Solution

Just plain lost on how to start. I get that this needs to be turned into a ratio between the two votage/current values across the diodes, but where do I start?

 

[CEL]

Homework Statement

Given a basic circuit of a voltage source and two diodes in series:
D1 is .7v @ 10mA
D2 is .6v @ .1mA
If I is 1mA, What is the voltage across the two diodes?

Homework Equations

VT~.026
Vt= 60log (I(t)/Is
I1 produces V1
I2 produces V2
so V2 = V1 + 60(mV)[log (I2/I1)]

The Attempt at a Solution

Just plain lost on how to start. I get that this needs to be turned into a ratio between the two votage/current values across the diodes, but where do I start?

The inverse saturation current Is is different in each diode. Determine Is from the data you have at the currents 10mA and .1 mA and use it to find the voltages at 1mA.

 

[sisyphus0321]

So solving for V2=V1 + 60mV[log(I2/I1)] I get D1=.64V and D2=.66v than using Kirchoff I can assume that the solution would be 1.3V? I know the whole thing is theoretical anyway because of the lack of resistance but is this the solution?

 

[CEL]

So solving for V2=V1 + 60mV[log(I2/I1)] I get D1=.64V and D2=.66v than using Kirchoff I can assume that the solution would be 1.3V? I know the whole thing is theoretical anyway because of the lack of resistance but is this the solution?

I would use the expression $$I=I_se^{\frac{V}{V_T}}$$, using I =10mA and V=.7V, to obtain Is for D1. Then use I = .1mA and V = .6V, to obtain Is for D2.
In reality, there should be a resistance limiting the current, but it is irrelevant, since we don't know the voltage of the source.

 

[Redbelly98]

I don't think we can obtain I_s1 or I_s2 without knowing V_T. But I agree, the diode equation is probably the key here.

Note, they seem to be asking for the sum V1+V2. If so, it's not necessary to find V1 and V2 separately, we just need the sum.

 

[CEL]

I don't think we can obtain I_s1 or I_s2 without knowing V_T. But I agree, the diode equation is probably the key here.

Note, they seem to be asking for the sum V1+V2. If so, it's not necessary to find V1 and V2 separately, we just need the sum.

The OP already gave the value of V_T: 26mV at 300K.
I don't see how we can find the sum without knowing the indi8vidual values of V1 and V2. Remember that the two diodes have different characteristics.

 

[Redbelly98]

The OP already gave the value of V_T: 26mV at 300K.

Aha, I missed that. Thanks.

I don't see how we can find the sum without knowing the indi8vidual values of V1 and V2. Remember that the two diodes have different characteristics.

Guess it's a moot point, because knowing V_T we can find I_S1 and I_S2, as you said earlier, and then both V1 and V2 at 1 mA.

So the key is using the 10 mA and 0.1 mA info to find I_S1 and I_S2, using the diode equation in post #4.

p.s.
Alternative, less straightforward method: one could also write out an expression for V1+V2, and find that it depends on the product i1·i2.