Exercises with voltage and power

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Joined Jan 28, 2021
Can you tell me if my result results are correct, and if there are errors where are they?
I used the symbol rms to indicate the root-mean-square, Avo is open-circuit voltage gain, Ap is the power gain, Rl is the load resistance. i stands for input, s for source and o per output.

> 1) A sensor producing a voltage of 1 V rms with a source resistance of 1 MΩ is available to drive a 10-Ω load. If connected directly, what voltage and power levels result at the load? If a unity-gain (i.e., A vo = 1) buffer amplifier with 1- MΩ input resistance and 10-Ω output resistance is interposed between source and load, what do the output voltage and power levels become? For the new arrangement, find the voltage gain from source to load, and the power gain (both expressed in decibels).

I calculated the output power when the source is directly connect to the load in this way:

I used voltage divider formula for Vorms.

Vorms = Vsrms * (Rl/(RL+Rs)) = 10uV

Iorms = Vorms/Rl = 1uA

Porms = Vorms*Iorms = 10fW

Then I consider the case when the opamp is between source and load:

This is my input rms voltage, I used the voltage divider formula.
Virms = Vsrms*(Ri/(Rs+Ri)) = 1/2V

This is my output rms voltage, I used the voltage divider formula.
Vorms = Virms*(Rl/(Rl+Ro)) = 1/4V

This is the voltage gain.
Av = Vorms/Virms = 1/2 -> -6dB

I calculated the output power.
Po = Vorms^2 / Rl = 6,25mW

I calculated the source power.
Ps = Vs^2 / (Rs + Ri) = 0,5uW

Then I calculated the power gain (this result seems strange, too high. What do you think?)
Ap = Po/Ps = 12500 -> 40,9dB

> 2) The output voltage of a voltage amplifier has been found to decrease by 20% when a load resistance of 1 kΩ is connected. What is the value of the amplifier output resistance?

I made some initial assumptions for the 20 per cent decrement. I assumed unit gain and Virms = 1V.
Assuming Virms = 1 V then 1 - 0,20*1 = 0,80 = Vorms

Then I considered the voltage divider formula.
Vorms = Virms*(Rl/(Ro + Rl)) = 0,80 -> Ro = Rl*(1-0,80)/0,80 = 250 Ohm

> 3) An amplifier with an open-circuit voltage gain of +40 dB, an input resistance of 10 kΩ, and an output resistance of 1 kΩ is used to drive a 1- kΩ load. What is the value of A vo ? Find the value of the power gain in decibels.

I calculated the linear value for the open-circuit voltage gain.
Avo = 10^(40/10) = 10000

I calculated the power gain as a product of voltage gain and current gain using voltage divider formula for the first part (I semplified Virms), while the second part is the current gain ((Avo*Virms*(1/(Ro + Rl)))/(Virms/Ri)).

Ap = Avo*(Rl/(Rl+Ro))*Avo*(Ri/(Ro+Rl)) = 25*10^7 -> 84dB