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So I took the time to measure the current dependency on voltage of a diode I have. I applied an exponential fit to it, and have a pretty reliable equation (within 1%).

I'm interested in how a diode-resistor-capacitor series circuit response to different signals. Naturally, I'm starting with just DC voltage.

The equation that I have for the voltage/current dependency for the diode is of the form

$ I=ae^{bV_D} $ (1)

where $V_D$ is the voltage across the diode.

Using Kirchhoff's law, I get the following differential equation with an initial condition:

$ V = RQ' + \frac{1}c Q + \frac{1}b ln(\frac{Q'}a)$

$Q(0)=0$

where R is the resistance of the resistor, c is the capacitance of the capacitor, a and b are the exponential regression constants from equation 1, and V is the applied DC voltage.

Any one know if it's possible to analytically solve this equation?

So I took the time to measure the current dependency on voltage of a diode I have. I applied an exponential fit to it, and have a pretty reliable equation (within 1%).

I'm interested in how a diode-resistor-capacitor series circuit response to different signals. Naturally, I'm starting with just DC voltage.

The equation that I have for the voltage/current dependency for the diode is of the form

$$ I=ae^{bV_D} \tag{1}$$

where $V_D$ is the voltage across the diode.

Using Kirchhoff's law, I get the following differential equation with an initial condition:

$$V = RQ' + \frac{1}c Q + \frac{1}b \ln\left(\frac{Q'}a\right)$$

$$Q(0)=0$$

where $R$ is the resistance of the resistor, $c$ is the capacitance of the capacitor, $a$ and $b$ are the exponential regression constants from equation (1), and $V$ is the applied DC voltage.

Does anyone know if it's possible to analytically solve this equation?