Finding & Sketching Transfer Function of Diode Circuit + Sinusoidal Vg

[petrides]

Hello all, long time reader, first time poster. Just in need of some help on finding the transfer function of the following diode circuit, and sketching the graph of this transfer function.


R1=1k, R2 = 4k and R3 = 7k, we want Vo vs Vg.

The follow on question also invloves finding and sketching the transfer function assuming that Vg is a sinusoidal function, Vg = 10sin(0.1t)

Thanks for any help

Andrew Petrides

 

[berkeman]

Hello all, long time reader, first time poster. Just in need of some help on finding the transfer function of the following diode circuit, and sketching the graph of this transfer function.


R1=1k, R2 = 4k and R3 = 7k, we want Vo vs Vg.

The follow on question also invloves finding and sketching the transfer function assuming that Vg is a sinusoidal function, Vg = 10sin(0.1t)

Thanks for any help

Andrew Petrides

Welcome to the PF.

Talk it out. At what positive value of Vo will you start to get some conduction through a diode? What value of source voltage does that correspond to? You need to do the work on this problem...

 

[Mene]

Hello Andrew,

Thank you for reaching out for help on finding the transfer function of your diode circuit. I would be happy to assist you with this task.

The transfer function of a circuit is defined as the ratio of the output voltage to the input voltage, assuming all other inputs are held constant. In your case, the output voltage (Vo) is dependent on the input voltage (Vg) and the values of the resistors (R1, R2, and R3).

To find the transfer function, we can use Kirchhoff's laws and Ohm's law to analyze the circuit. First, we can apply Kirchhoff's voltage law (KVL) to the loop containing the diode and resistors R2 and R3. This gives us the equation:

-Vg + Vo + Vd = 0

Where Vd is the voltage across the diode. We can then apply Ohm's law to the resistors to get:

-Vg + Vo + Vd = 0
-Vg + Vo + Vd = 0
-Vg + Vo + Vd = 0
-Vg + Vo + Vd = 0

Next, we can use the diode equation to relate the voltage across the diode (Vd) to the current through the diode (Id). The diode equation is given by:

Id = Is(e^(Vd/Vt) - 1)

Where Is is the reverse saturation current of the diode and Vt is the thermal voltage (kT/q).

Substituting this into our equation, we get:

-Vg + Vo + Is(e^(Vd/Vt) - 1) = 0

We can then solve for Vd by rearranging the equation:

Vd = Vt*ln((Vg - Vo)/Is + 1)

Finally, we can substitute this back into our original KVL equation to get the transfer function:

Vo = Vg - Vt*ln((Vg - Vo)/Is + 1)

To sketch the graph of this transfer function, we can plot Vo on the y-axis and Vg on the x-axis. We can also choose different values for Is and Vt to see how they affect the shape of the curve.

For the follow-on question, we can use the same process to find the transfer function assuming Vg is a sinusoidal function. We would substitute Vg = 10