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The diode in the circuit of Fig. E4.9 is a large high-current device whose reverse leakage is reasonably independent of voltage. If V = 1 V at 20C, find the value of V at 40C and at?
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The diode in the circuit of Fig. E4.9 is a large high-current device w...
Solution:

Given parameters:

- V1 = 1 V at 20°C
- T1 = 20°C
- T2 = 40°C

To find:

- V2 at 40°C
- V3 at ?

Assuming the diode is ideal, we can use the Shockley equation to find the voltage drop across it:

V = Vt*ln(I/Is)

Where,

- V = voltage
- Vt = thermal voltage (kT/q), where k is Boltzmann's constant, T is temperature in Kelvin, and q is the charge of an electron
- I = current through the diode
- Is = reverse saturation current

We can assume that the forward voltage drop of the diode is negligible compared to the reverse leakage current, so we can use the reverse saturation current as the current through the diode.

At 20°C:

V1 = Vt*ln(Is)

Is = exp(V1/Vt)

At 40°C:

Is2 = exp(V2/Vt)

Since the reverse leakage is reasonably independent of voltage, we can assume that Is2 is equal to Is, so we can set the two equations equal to each other:

exp(V1/Vt) = exp(V2/Vt)

Taking the natural logarithm of both sides:

V2/Vt = V1/Vt

V2 = V1 * (T2/T1)

V2 = 1 V * (313 K/293 K) = 1.07 V

To find V3, we need to know the temperature. Assuming we know the temperature, we can use the same equation:

V3 = V1 * (T3/T1)

Where T3 is the temperature in Kelvin.
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The diode in the circuit of Fig. E4.9 is a large high-current device whose reverse leakage is reasonably independent of voltage. If V = 1 V at 20C, find the value of V at 40C and at?
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