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13th January 2020, 13:07 #1
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Finding the input impedance of CCCS
Good day everyone! I need your help on this one. I'd like to derive the equation for the closedloop input impedance of the circuit attached. The final form of the equation is also shown below.
Here's what I have tried
I was stuck. Can you tell what other route I can take to go about this derivation? Thanks!

13th January 2020, 15:21 #2
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Re: Finding the input impedance of CCCS
Zin(CL) formula is not correct, instead of R2, an effective resistance of R2 + RLR1 must be put in.

13th January 2020, 15:44 #3
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13th January 2020, 19:24 #4
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Re: Finding the input impedance of CCCS
It's the impedance seen with Av = 0 and Rout = 0.

13th January 2020, 22:45 #5
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14th January 2020, 04:52 #6
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14th January 2020, 07:57 #7
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Re: Finding the input impedance of CCCS
R1 is the resistor that complicates a bit the derivation of the input resistance. So, if it were not there, results will be easier. Assuming R1 infinite, I find those 3 things Rio, Rn and Rd. Then I combine them and reintroduce R1 back to get the final result.

14th January 2020, 10:25 #8
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14th January 2020, 10:42 #9
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Re: Finding the input impedance of CCCS
You can easily find the input impedance using the superposition.
if Vo is the output of the opamp, V+ its noninverting input and V its inverting input and Iin the stimulus:
1) exclude Iin, then (Va) = Vo*RL/(R1+RL)
2) short Vo, then (Vb) = Iin*[R1*RL/(R1+RL)+R2]
Applying superposition (V)=(Va) + (Vb) = Vo*RL/(R1+RL)+Iin*[R1*RL/(R1+RL)+R2]
We know that Vo = A*[(V+)  (V)], but (V+)=0 thus Vo=A*(V)
Substituting Vo:
V = A*(V)*RL/(R1+RL) + Iin*[R1*RL/(R1+RL)+R2]
Zin = (V)/Iin = [R1*RL/(R1+RL) + R2]/[1 + A*RL/(R1+RL)]
If we call, nw, B=RL/(R1+RL) we will have:
Zin = (R1*B+R2)/(1+A*B)
in case R2 >> R1*B then we can approximate Zin = R2/(1+A*B)
Sorry, in my derivation I exchanged the label R1 with RL (R1 is the output series and RL is to ground)
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14th January 2020, 14:36 #10
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Re: Finding the input impedance of CCCS

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14th January 2020, 16:18 #11
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Re: Finding the input impedance of CCCS
Negative feedback always decreases the output impedance. If something external tries to change the output voltage then the negative feedback sends the change to the inverting input to cancel the change.

14th January 2020, 16:52 #12
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14th January 2020, 18:51 #13
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Re: Finding the input impedance of CCCS
Positive feedback (bootstrapping) increases the output impedance.

14th January 2020, 18:56 #14
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14th January 2020, 19:10 #15
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14th January 2020, 20:13 #16
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14th January 2020, 21:22 #17
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Re: Finding the input impedance of CCCS
Yes, you can choose another element as the extra element, of course. The formulation of the result will be different, because you will have to find Rn and Rd from the point of view of the new extra element. But you can always manipulate algebraically the results for different extra elements to look the same at the end. And of course, when you substitute the numerical values, you must get the same result.

14th January 2020, 22:22 #18
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Re: Finding the input impedance of CCCS
I presume you have to calculate the output impedance seen by the load, that is by RL. To do this you have to substitute the load with a generator and calculate the current flowing through the generator and the voltage across it, then apply Z=V/I.
I used a current generator and I did the following derivation (neglecting input and output impedance of opamp, I considered it as ideal, but the finite OL gain):
In this case we have a current generator so we need a very high impedance, ideally infinite. The feedback regardless to its value (the opamp is ideal here) allows to greatly increase the impedance since the voltage is boosted by the OL gain of the amplifier.Last edited by albbg; 14th January 2020 at 22:31.

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14th January 2020, 22:55 #19
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Re: Finding the input impedance of CCCS
Applying Blackman's impedance formula gives the output impedance in 1 line. And yes, it is R1*(1+A)
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14th January 2020, 23:28 #20
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