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I am unsure if I am tackling this problem correctly. The input signal is connected to terminal E4 and the output signal is observed at terminal E9

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  1. What is the voltage gain when E1 is connected?

  2. What is the voltage gain when E2 is connected?

  3. Neither E1 or E2 is connected. What is the expected voltage gain?

My solution:

  1. Use the formula: $$A_v = 1 + R_2/R_1$$ which then becomes: $$A_v=1+R_{FB}/R_1$$

  2. Use the same formula, now just substitute R1 with R2.

$$A_v = 1+ R_{FB}/R_2$$

  1. My guess is that there is no there would be no voltage gain, since there are no resistance on the top half of the circuit?

Am I totally wrong here?

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  • \$\begingroup\$ Can you clarify what you mean by connected...? (Connected to what?) \$\endgroup\$ Commented Nov 10, 2019 at 21:07
  • \$\begingroup\$ I have edited the question. The problem specifically says "What is the gain when E1 is connected to E5?" \$\endgroup\$
    – Carl
    Commented Nov 10, 2019 at 21:14
  • \$\begingroup\$ Yes, you are wrong and very confused. \$\endgroup\$ Commented Nov 10, 2019 at 21:30
  • \$\begingroup\$ A complicated scenario with optional sources can be corrected by choosing the same impedance ratio on both Vin+ and Vin- to get a unity gain amplifier. Otherwise it is not. i.e. Rfb/Rin- = Ref/Rin+ \$\endgroup\$ Commented Nov 10, 2019 at 21:38
  • \$\begingroup\$ Your solution is arbitrary. \$\endgroup\$
    – Chu
    Commented Nov 11, 2019 at 0:29

2 Answers 2

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Here is my interpretation of the OP's question and explanations (I have considered the simple case of connecting to ground):

  • "The input signal is connected to terminal E4" means "The input signal is directly connected to terminal E4". So R3, Rref, Vref, E3 and E5 (if only not connected to ground) do not play any role in forming the voltage of the non-inverting input; it is determined only by the input voltage source connected to E4.

  • "What is the voltage gain when E1 is connected?" means "What is the voltage gain when E1 is connected to ground?" So, the circuit is a non-inverting amplifier consisting of R1, RFB and the op-amp... and the OP's formula is correct.

  • "What is the voltage gain when E2 is connected?" means "What is the voltage gain when E2 is connected to ground?" So, again the circuit is a non-inverting amplifier now consisting of R2, RFB and the op-amp... and again the OP's formula is correct.

  • "Neither E1 or E2 is connected." means "Both E1 and E2 are not grounded". Then the circuit is simply a voltage follower where RFB does not play any significant role. So,

  • "My guess is that there is no there would be no voltage gain, since there are no resistance on the top half of the circuit?" means "My guess is that there would be voltage gain of one, since there is no grounded resistance (neither R1 nor R2) on the input of the circuit?"

The purpose of the professor's test is probably to determine whether

  • OP knows what the difference between the op-amp non-inverting amplifier and op-amp follower is;

  • OP understands what is ideal and what real voltage source... and what is the resultant voltage when they are connected in parallel.

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The meaning of "connection" here is that there's a voltage source connected to the named node. I mean an ideal voltage source. Zero impedance and so on. You must also assume that other nodes have no external connections, with exception of E5. And the op amp is ideal: the inputs have infinite impedance (and thus no parasitic capacitance either).

You'll notice that it doesn't matter what is the voltage of that source, as long as the op-amp remains within its input and output voltage range limits based on the 5V power supply. Since no details are given about the op-amp, its assumed ideal and thus the input voltage range is 0-5V, same for output, and the output impedance is zero.

And this assumption must hold since you are not told what voltage is connected into E1 or E2. That's how the language of such problem is meant to be understood. If the author of the problem meant something else, they'd be of line pretty much and purposefully obfuscating.

Neither E1 or E2 is connected. What is the expected voltage gain?

R1 and R2 are not in circuit. RFB configures the op-amp as a voltage follower. The inverting input impedance is infinite in the ideal op-amp, so the resistance of RFB is irrelevant and we replace it with a short. Gain is exactly 1.

What is the voltage gain when E1 is connected? What is the voltage gain when E2 is connected?

You got things right for those cases.

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