Calculating Hybrid Parameters for an Inverting Op Amp

[Kerren]

Hi guys This question has been bugging me for a REALLY long time so thanks in advance for the help !

Homework Statement

Calculate the Hybrid Parameters for an inverting op amp shown below:


https://www.dropbox.com/s/45mjldud2ar5pwg/invOpAmp.jpg


And I need to get it into the form of:

https://www.dropbox.com/s/5vto0ipwtbre7qk/hequiv.jpg

Homework Equations

$V_1 = aI_1 + bV_2$

and

$I_2 = cI_1 + dV_2$

The Attempt at a Solution

I tried doing it like this:
https://www.dropbox.com/s/9gnpycdi3p6g1ys/p1.jpg

https://www.dropbox.com/s/5u7f3109u1i8zoa/p2.jpg


But I got stuck trying to get $I_2$, $I_1$ and $V_2$ all in the same equation.

So I redrew the equivalent model to see if maybe there was another loop I could use:
https://www.dropbox.com/s/p23mwsbjdmmpbex/p3.jpg

Which lead to the exact same result


So at the moment I'm thinking maybe it isn't possible to get the second equation?


Here the calculations are if they don't load:

 

[The Electrician]

It's conventional to designate the h-parameters as h11, h12, h21 and h22. Using the letters a, b, c and d invites confusion with the ABCD parameters:

http://en.wikipedia.org/wiki/Two-port_network

Is this an actual homework problem?

The h21 parameter is the ratio of the output current (with the output shorted to ground) to the input current. If the opamp is taken to be ideal with zero output impedance, then the output current into a short will be infinite for any non-zero input current, and hence, h21 would be "∞".

The parameter h11 is the input impedance with the output shorted. We can see by inspection that it would be R1+R2.

The h12 parameter is the reverse voltage transfer ratio with the input open circuited. To determine this, we apply a voltage to the output and take the ratio of that voltage to the voltage that would appear at the input; it would be "1". The opamp would fight the application of a test voltage to its output, but that's the definition of h12.

Finally, the h22 parameter is the output conductance with the input open circuited. Since an ideal opamp has zero output impedance, h22 will be "∞".

Using h parameters with this circuit wouldn't be appropriate if the opamp is ideal. I would assume a small output impedance (call it Ro); then h21 and h22 wouldn't be "∞", and you wouldn't have the fighting voltage source problem when applying the test voltage to the output to determine h12.

 

[Kerren]

Thank you!

Awesome! Thanks so much for the response !

I originally had $R_o$ in my calculations but since the op amp is ideal I had to make it equal to zero With $R_o$ in the mix I did have another loop but my problem there was that I was introducing a variable that was not given in the question so I'd have to try to get it in terms of $I_1$, $V_1$, $I_2$ or $V_2$ which also didn't seem practical. Since having an $R_o$ that isn't zero implies that the op amp isn't ideal I decided I'd have to try another route!

It was never stated in the question that it was possible to get a working solution, so I can argue that it is, in fact, impossible using an ideal op amp

Your explanation makes perfect sense, thank you very much for your time and effort !

 

[The Electrician]

I'm interested to know a few things about this. Is this a problem given to you in a college level course? What college?

Did this problem come from a text, or did the Prof make it up? If from a text, what text?

 

[Kerren]

I've PMed you all the details :)!

Our Professor made this one up :D!