Resistance offered by the photo diode

To calculate the resistance offered by the photo diode, we need to understand the relationship between the current flowing through the diode and the voltage across it. The current-voltage characteristic of a photo diode can be approximated by the equation:

I = Is * (e^(V/Vt) - 1)

Where:
- I is the current flowing through the diode
- Is is the reverse saturation current
- V is the voltage across the diode
- Vt is the thermal voltage (approximately 26 mV at room temperature)

Given:
- Illumination intensity: 100 lumen/cm²
- Current flowing through the diode: 1.8 mA

Step 1: Calculate the reverse saturation current (Is)

The reverse saturation current (Is) can be calculated using the equation:

Is = I / (e^(V/Vt) - 1)

Since we don't have the voltage across the diode (V), we need to make an assumption to proceed with the calculation. Let's assume a typical value for the voltage drop across a silicon photo diode, which is around 0.7 V.

Is = 1.8 mA / (e^(0.7/0.026) - 1)
= 1.8 mA / (e^(26.92) - 1)
= 1.8 mA / (3.1264e+11 - 1)
≈ 1.8 mA / 3.1264e+11
≈ 5.76e-12 A

Step 2: Calculate the resistance (R)

The resistance offered by the photo diode can be calculated using Ohm's Law:

R = V / I

Since we don't have the voltage across the diode (V), we can rearrange the equation to solve for it:

V = I * R

Substituting the given values, we have:

V = 1.8 mA * R

Step 3: Calculate the resistance offered by the photo diode

To calculate the resistance offered by the photo diode, we need to determine the voltage drop across the diode. This can be done by assuming a typical value for the forward voltage drop of a silicon photo diode, which is around 0.7 V.

V = 0.7 V

Substituting the values into the equation found in Step 2, we have:

0.7 V = 1.8 mA * R

Solving for R:

R = 0.7 V / 1.8 mA
= 0.7 V / 0.0018 A
= 388.89 Ω

Therefore, the resistance offered by the photo diode when illuminated by 100 lumen/cm² and carrying a current of 1.8 mA is approximately 388.89 Ω.