# Small signal diode model question

#### sexymonkeys

Joined Apr 15, 2010
5
I'm stuck on a question that I have no understanding of and I was wondering if someone could help.

When vin(t)=2.5+cos(2*pi*100*t) for 0<t<30

Use the small signal model of the diode to predict the output voltage of the circuit. Assume the opamp is ideal and R = 2000ohms, Is = 10^-16 A, Vt = 0.0252 V. The diode current is given by the equation iD = Is(e^(vd/Vt) - 1).

How would I go about doing this? I don't understand how I can use the small signal model to do this, because I can't seem to understand what exactly the small signal model is trying to achieve and what equations are relevant because my textbook is a little too flaky about it (at least for me) and I also tried Wikipedia in the hopes that it would have something that might help, but no luck there. Since the small signal model involves a current - voltage graph, I don't get what part of it would give me the answer I need to get the sinusoidal output voltage for the answer. I also don't know how to use the small signal model.

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#### retched

Joined Dec 5, 2009
5,208
I am missing the circuit.. If you are having trouble attaching it, click on 'Go Advanced' when posting or editing and scroll below the text box until you see 'Manage Attachments'. A pop up will arrive that will direct you to your attachment. This will allow us to host your image so if a year in the future, someone else would like to learn from this info, the image will still be available.

#### sexymonkeys

Joined Apr 15, 2010
5

#### t_n_k

Joined Mar 6, 2009
5,447
Resistor R sets the input current, since i(t)=Vin(t)/R.

This same current i(t) flows in the diode.

You then solve the ideal diode equation for the unknown value of Vd(t) given the known value of i(t). You'll need to re-arrange the diode equation to obtain Vd(t) as the subject of the equation. You'll have a logarithmic function.

#### sexymonkeys

Joined Apr 15, 2010
5
Yep, I already have the equation Vout = -Vt ln (vin/(Is R)) that I derived in that way, but I'm stuck on how to figure out the output voltage for an input voltage of 2.5+cos(2*pi*100*t) using the small signal diode model. I assume that the small signal diode approximation results in a different output voltage than just substituting values into the Vout equation because of the way the question is asked though.

#### t_n_k

Joined Mar 6, 2009
5,447
The simplest [approximate] approach is to calculate the mean [DC] diode drop first - ignoring the AC component.

Then use the dynamic diode resistance r=Vt/Idc[mA] to find the superimposed AC component of the total diode voltage. The total diode voltage will then be the sum of the DC and dynamic resistance AC voltage drops - use only the AC signal current to determine the AC component drop.

An more accurate solution would require calculation of several diode drops over the full range of the current swing - rather more a graphical solution than a single valued solution.

My guess is that you can probably ignore the small signal non-linearities that might be more representative of the true output.

#### sexymonkeys

Joined Apr 15, 2010
5
Thanks a lot. That helped. I think I can figure it out now.

#### t_n_k

Joined Mar 6, 2009
5,447
I noticed a small error in my last post ....

r=Vt/Idc or r=Vt[mV]/Idc[mA] whichever you prefer.