Solving voltage gain in an non-ideal op amp.

[lam58]

Hello I'm a bit stuck on this.

The question states that the non ideal op amp (pictured below) in open loop conditions has an input resistance of 400kΩ, an output resistance of 2kΩ and a voltage gain of 500,000.

I then asks to find the voltage gain, the voltage at the negative input terminal and the input and output resistances when the supply voltage is 50mV. So for the first part finding the gain I assumed V at positive terminal (Vp) = 0.

Thus Vo = A(Vp-Vn) => Vn = Vo/A.

Also [tex]\frac{V_{s}-V_{n}}{R_{s}} = \frac{V_{n}-V{o}}{R_f}[/tex]

Then using Vn = Vo/A

[tex]\frac{R_f}{R_s} (V_s + \frac{V_o}{A}) = V_o (\frac{-1}{A}-1)[/tex]

[tex]\Rightarrow \frac{V_s}{V_o} + A = \frac{(-1/A)-1}{R_f/R_s}[/tex]

[tex]\Rightarrow \frac{V_o}{V_s} = \frac{(R_f/R_s)}{(-1/A)-1} - \frac{1}{A}[/tex]

Putting in the values given:

gain = [tex]\frac{320k/8k}{(1/500k)-1} - \frac{1}{500,000} = -39.999922[/tex]

From this I got [tex]V_o = - 1.9999961[/tex], [tex]V_n = 49.76v[/tex]

However, here I don't know if the above is correct and how to find the input and output resistances. Any help would be much appreciated. :)

EDIT Just realiased how to find input resistance and output resistances using my first equation.

Is the working above correct though?

 

[NascentOxygen]

So for the first part finding the gain I assumed V at positive terminal (Vp) = 0.

Thus Vo = A(Vp-Vn) => Vn = Vo/A.

Check this algebra.

The rest of your analysis ignores the non-idealities of the OP-AMP, apart from its finite gain. You have assumed its input impedance is ∞ and that its output impedance is 0Ω, despite being told the figures to use. You must show these as resistances inside the OP-AMP triangle and incorporate them into your analysis.

 

[lam58]

Check this algebra.

The rest of your analysis ignores the non-idealities of the OP-AMP, apart from its finite gain. You have assumed its input impedance is ∞ and that its output impedance is 0Ω, despite being told the figures to use. You must show these as resistances inside the OP-AMP triangle and incorporate them into your analysis.

Ok I'm lost now. Do I need to add the internal resistances to Rs and Rf?

 

[NascentOxygen]

A google search will tell you everything you need. Search on "non-ideal op-amp analysis"

 

[lam58]

I have been.

 

[lam58]

A google search will tell you everything you need. Search on "non-ideal op-amp analysis"

To find the closed circuit gain would I do A = Aβ/(1+(Rf/Rs)) which would give me roughly 12.2k?

 

[NascentOxygen]

To find the closed circuit gain would I do A = Aβ/(1+(Rf/Rs)) which would give me roughly 12.2k?

Not until you have used the model that shows the OP-AMP itself having those given figures for input impedance and output impedance. A google search will quickly find the non-ideal OP-AMP model.

 

[rude man]

Hello I'm a bit stuck on this.

EDIT Just realiased how to find input resistance and output resistances using my first equation.

Is the working above correct though?

Not likely, since your v_n is way higher than the power supplies and the offset voltage of the op amp woud have to be equal to v_n !

What you want to do is redraw the circuit with an ideal op amp, then add the input and output resistances to the circuit. This will generate new nodes and more simultaneous equations to solve. Be careful how you place those resistances. When you do that you can send us the new schematic. BTW your image is hard to read.