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Operational Amplifier + Diode

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gianx80

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Hi, I have to do this exercise in preparation for my first and only exam about electronics. This is the scan of the exercise (the first one):

**broken link removed**

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and this is the scan of the proposed solution:

**broken link removed**

Uploaded with ImageShack.us

I have to find the "transfer function" Vo/Vi (is this the correct English name?), Bode plot. For point 2, I can't translate it into English, sorry.

I'm a total newbie, so I can't understand the proposed solution. Why, for example, Vx/Vi = 1+sRC1? Can you explain me the solution step by step?

Thanks in advance!

EDIT

I added the scans as an attachment to this post. Added complete traduction.

TRADUCTION INTO ENGLISH

Exercize 1
In this circuit we have a real diode and a real operation amplifier.
Io = 1 microAmpere, C1 = C2 = 10 picoFarad, R = 10 kilo Ohm.

1) Find the transfer function Vo/Vi and draw the related Bode plot.
2) I can't translate this point, so I'm not searching any kind of advise about this point

SOLUTION

In the small-signal model the diode acts like a resistor with this value:
rd = Vt/Id = 26mV/1microAmprere = 26 kilo Ohm.
In order do find the tansfer function we use this equivalent circuit:

[DRAWING]

We find that:

Vx/Vi = 1 + R/(1/sC1) = 1+ sRC1

Vo/Vx = (1/sC2)/(rd + (1/sC2)) = 1/(1 + srdC2)

From this we obtain:

Vo/Vi = Vo/Vx*Vx/Vi = (1 + sRC1)/(1 + srdC2)

[The final part of the solution is about point 2].

Now you have all the exercise in English. Could you help me?
 

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Hi,

In non-inverting amplifier Gain (A) = 1 + R1/R2

The impedance of capacitor at given frequency (fr) is Xc = 1/(2*pi*fr*C)

In your case R1 = R (in drawing) and R2 = Xc1 = 1/(2*pi*fr*C1)

If we write 2.pi.fr = s then R2 = Xc1 = 1/(s*C1)

opamp output is at Vx so Vx= Gain * Vi

Vx/Vi = Gain (A) = 1 + R/Xc1

or Vx/Vi = 1 + R/{1/(s*C1)}

So Vx/Vi = 1 + R * (s*C1) ----------- 1

rd and C2 forms voltage divider

voltage divider formula: Vout = R4/(R4 +R3) * Vin or Vout/Vin = R4/(R3+R4)

In your case R3 = rd (in drawing) and R4 = Xc2 = 1/(2*pi*fr*C2) or 1/(s*C2)

or Vo/Vx = [1/(s*C2)] / [rd + 1/(s*C2)]

So Vo/Vx = 1 / [1+ s*rd*C2] ------------------2

Now the total Gain = Vo/Vi

Vo/Vi = Vo/Vx * Vx/Vi (multiply and divide by same Vx)

Vo/Vi = [1 + R*s*C1] / [1 + rd*s*C2]

I hope this will make you understand.
 

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