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Can we solve this circuit without using virtual ground or not?

I attempted to calculate the feedback voltage by division of voltage in \$R_f\$ and \$R_{\text{in}}\$ but is \$V_f\$ equal to:

$$(V_o - V_{\text{in}})\frac{R_\text{in}}{R_{\text{in}} + R_f}$$

or:

$$-(V_o - V_{\text{in}})\frac{R_f}{R_{\text{in}} + R_f}$$

Depending on the direction of current inside the feedback circuit the sign changes, which affects \$\beta\$ (feedback factor).

Note I am studying about feedback and I don't want to learn the virtual ground for now at least.

Null
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Cartoon Ryan
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2 Answers2

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Assume the OpAmp has an open loop gain A and the inverting node is Vx.

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Now you can write one KCL equation for the node Vx and one equation for the relationship of the OpAmp as follows:

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Next solve the system of these two equations:

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Finally taking the limit of these ratios as A approaches infinity.

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emnha
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  • You are effectively invoking the virtual ground principle with your next-to-last equation, saying that Vx/Vin goes to 0 as A goes to infinity. Since Vin is finite this can only be true if Vx goes to 0, which is just restating the virtual ground principle. – Elliot Alderson Oct 11 '21 at 21:46
  • @ElliotAlderson I know that but from the question I understood that the OP does not want to use virtual ground directly, just use something basic that he/she has learned. Using virtual ground gives you the result directly but the OP does not want that. Also I solved it for any gain `A`, the last step is just for the special case where A is inifnity and thus the virtual ground. – emnha Oct 11 '21 at 22:35
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The feedback voltage Vf at the inverting input is just:

Vf = \$(\frac{V_{IN}}{R_{IN}}+\frac{V_{OUT}}{R_{F}})\cdot(R_{IN}||R_F) \$ where \$R_{IN}||R_F \$= \$ \frac{R_{IN}\cdot R_F}{R_{IN}+R_F}\$

So neither is the answer to 'which is correct'.

When you add the equation Vout as a function of Vf you can determine the response to Vin. The negative sign arises in that equation.

Spehro Pefhany
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  • I dont understand how you ended up with this formula – Cartoon Ryan Oct 08 '21 at 21:04
  • It's a formula that works for any multi-resistor divider and allows you to immediately write down the solution. Vout = (V1/R1 +.. + Vn/Rn)* R1||..||Rn). I thought I invented it ;-) , but someone else had a person's name associated with it, one that escapes me at the moment. R1||...||Rn = 1/(1/R1+..+ 1/Rn), of course. – Spehro Pefhany Oct 08 '21 at 21:32
  • Ah ok because in this case(https://www.youtube.com/watch?v=Ff_Top73fH0 at 8:28) the solution is more intuitive so I though it was as easy as in the video for my case. – Cartoon Ryan Oct 08 '21 at 21:37
  • The talking in the video from India is in a foreign language. Why are most electronics You Tube videos from India? – Audioguru Oct 11 '21 at 16:43
  • Because it has 1.3 billion people and a lot of the educated class is English speaking. – Shredder Oct 11 '21 at 18:34
  • @Audioguru One reason is that Youtube videos pay a relatively small amount unless the creator has a huge subscribership, but even that amount is significant in a place that is very low income (India has about 1/5 of China GDP per capita and 1/30 of USA GDP per capita at nominal exchange rates). There are lots of Indians who are knowledgeable in STEM fields. I've watched some cryogenics courses, for example, not bad but the teaching style is not everyone's cup of tea. – Spehro Pefhany Oct 11 '21 at 18:51