basic feedback analysis question

[asafdav2]

basic feedback analysis

let's say i have this circuit
**broken link removed**

the feedback consists R3, R2, Rs, and is PISO. the problem is, how do i calculate the feedback factor β? the answer is -0.83, but no matter what i do, i cant seem to derive it myself. can anyone help me with the calculation?

thanks

 

[seadolphine2000]

First, you have to decompose R2 by Miller's theorem, where C1 will be open circuit in DC and short circuit for approximate all frequencies.

Second, you can remove R3 since it's connected to ground from both terminals.

Finally, try to solve for mid-band frequency and you will get the feedback factor.

Hope this helps,... Please correct me if I'm wrong.

 

[wicked]

sorry i am not sure, how is r3 grounded at both terminals, i thought that a current source is replaced by open? or did i miss somthing

Added after 1 minutes:

sorry, the op-amp?

 

[pixel]

you should not remove r3
I have roughly calculated for beta 0.47

 

[seadolphine2000]

As I thought, ZT is an OpAmp, since the +ve terminal is grounded physically, then the -ve terminal will be virtually grounded(from OpAmp charactaristics).

 

[eecs4ever]

I agree with seadolphine.

By definition:

shunt feedback ---> short the other side... (virtual ground at the + node)


C∞ does not attenuate any AC signal. (a cap of inifinte capacitance has impedance 1/jwC , where C is infinite) .

By definition β = ifeedback / iout

we can solve for β since this is simply a resistor divide between the 1k Resistor and the 5k resistor. The impedance of the cap is 0 at any AC frequency.

KCL: Current divider
ifeedback = ( 5k / (1k+5k) ) * iout
ifeedback = 5/ 6 * iout

so β = ifeedback / iout = 5/6 = 0.83

 

[asafdav2]

thanks all for the answers

eecs4ever, i have a question about your answer - i'm not sure about this part:

By definition:

shunt feedback ---> short the other side... (virtual ground at the + node)

i drawed the way i usually use to determine parallel input feedback circuits beta (which i guess is flawed)

does it mean that the returned current is totaly independent to changes in R3? because it seems a bit counter intuitive to me...

edit:
i just realized you take into account the fact that Zt is ideal op-amp ... well 1) that's not the case, forgot to mention it (it's actually a non-ideal trans impedance amp), and 2) i'm more interested about the beta calculation in the general case, i.e without op-amp.

thanks

 

[seadolphine2000]

I think this topology is (Shunt mixing - series sampling)

so to get the feedback factor, you have to short the (If). This result in shorting R3.

Check this picture, I scanned it from my lectures. As you see, you shunt mixing, so to take the effect of the feedback at input, you need to short the input of the feedback network.

At the output, you have series sampling, so to take the feedback effect at the output of the amplifier, you need to open circuit the output of the feedback network.