Hi, I am asked to find a method to find i vs v characteristics, using a digital oscilloscope. As a hint, it is said that I should connect a resistor of 1kohm between the signal generator and the terminal a to observe i in mA.

I think that I should connect a floating signal generator and a 1kohm resistor in series between the terminals a and b. Then I can connect Channel1 to b, Channel2 to positive terminal of the signal generator and Ground Probe of DSO to terminal a. Then inverting both channels in XY mode should give me i vs v characteristics. But I couldn't find the an expression of voltage V'(t) that the signal generator must give to circuit as a function of V(t), in order to obtain V(t) between the terminals a and b.

 

I have solved that finally. I think I will directly obtain the i vs v charactestics on the screen, then I don't have to find a mathematical equation between V' and V.

But in the second part, a capacitor of 1microFarad is connected between a and b terminals. It is asked to find Vc(t). But I am confused about it, since there is notsignal generator in the circuit, which element affect the frequency of oscillation?

 

The frequency of oscillation is determined by Rf, the connected capacitor and the values of R1 and R2. The capacitor is charged/discharged via Rf and the two thresholds at which the output changes are set by R1-R2 (schmitt trigger).

 

Thank you for your help, but even I couldn't solve it.
When capacitor is connected between terminals a and b, I am trying to do the same analysis as it is not a capacitor but only V(t), and as an additional equation I am trying to use i(t)=C(dVc(t)/dt). Is there something missing, or is it enough to solve it?

 

This is not a linear circuit, thus you can't solve it with one equation.
Split the solution into two parts. One when the output is saturated positive and one when it is saturated negative. Since you know Vo(t) you can determine v(t) by using the exponential equation of an RC circuit (assuming no current flows into the inverting input). Thus, you will be able to determine at what time the output will change state by finding the voltage at the non-inverting input (voltage divider).

 

Thanks for your help. I was trying to solve it, as opamp is in linear region. Why it is enough to analyse the + saturation and - saturation?

 

Oh I get it. Because that region is unsteady. I tried to do that in saturation regions. I have attached them. Is it what you mean? Or is it still wrong?

 

Thanks for your help. I was trying to solve it, as opamp is in linear region. Why it is enough to analyse the + saturation and - saturation?

Because the circuit has positive feedback which causes the output to saturate. Look for schmitt trigger.

 

I have solved it. Thank you

 

What is the formula you derived for the frequency of oscillation?

 

I have found like that,

T=2*Rf*C*ln{[1+R2/(R1+R2)]/[1-R2/(R1+R2)]}

 

I have found like that,

T=2*Rf*C*ln{[1+R2/(R1+R2)]/[1-R2/(R1+R2)]}

Here is a link which verifies your answer:

http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/square.html