I have the following problem.

"An amplifier stage with \$A_{voc}=100\frac{V}{V}\$, \$R_i=100k\Omega\$, \$R_o=10k\Omega\$ is connected to another amplifier with \$A_{voc}=10\frac{V}{V}\$, \$R_i=10k\Omega\$, \$R_o=100\Omega\$. They are in cascade, so to speak.

What is the open-circuit voltage gain for this cascade?"

My initial thought was that you just multiplied the two \$A_{voc}\$'s together and there you had it.

That would make the total oc-voltage-gain 1000.

But it turns out the answer to this question is \$500 \frac{V}{V}\$. Can anyone explain why this is?

There were no schematic included for this problem, but I would assume it looks something like this.

enter image description here

  • 1
    \$\begingroup\$ Where are the resistors placed in the circuit? Where is the circuit of the amplifier stage with the resistors? \$\endgroup\$ – Andy aka Dec 12 '19 at 11:34
  • \$\begingroup\$ I have added a schematic. \$\endgroup\$ – Carl Dec 12 '19 at 11:42

The question is poorly worded, and of the two possible ways to connect the amplifiers I think you picked the one that is different from what the instructor assumed.

I think the question intends that the output of the amplifier with \$R_O = 10\,\text{k}\Omega\$ is connected to the input of the amplifier with \$R_i = 10\,\text{k}\Omega\$. And that's a big hint right there...

  • \$\begingroup\$ If I understand you correctly, you are suggesting that \$R_o\$ and \$R_i\$ in both amplifiers switch places? If so, I am not sure how to continue from there either... \$\endgroup\$ – Carl Dec 12 '19 at 13:35
  • \$\begingroup\$ Not quite...the second amplifier does not have a load resistor, it is open circuit. Remember that the quoted values of gain relate the output voltage to the input voltage when there is no load, so when the input resistance of one amplifier acts as a load for the second amplifier the actual gain of the first amplifier will be something less than its open-circuit gain. \$\endgroup\$ – Elliot Alderson Dec 12 '19 at 13:42
  • \$\begingroup\$ Okay, I think I can see where you are going, though I have some trouble of understanding. Anywho, so the actual way I was supposed to solve was like this: Av1 = Avoc* (Ro/Ro+Ri) = 100 * (10/10+10) = 100*1/2=50. Avoc,total = Av1*Avoc,2 = 50*10 = 500? \$\endgroup\$ – Carl Dec 12 '19 at 13:54

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