Originally Posted by Navyblue
How are the Zout, Vout and R1 power on the table calculated?
Zout is calculated by: Zout = R3 + ( R1 || R2)
Which is R1 and R2 in parallel, and R3 is in series with that combination. This is the impedance seen looking towards the amplifier from the headphone output. You can think of it as setting the output of the voltage source (in this case, the amplifier, to 0, or ground) and then connecting an ohm-meter to the output.
Vout is calculated by first determining the output voltage of the amplifier, and then calculating the voltage at the node common to all 3 of the resistors.
So for the 20W example:
P = I(rms)*V(rms) = 1/2 (V(peak) * I(peak))
V(rms) = I(rms)*R & V(peak) = I(peak)*R
20 = V(rms)^2 / R
V(rms)^2 = 20*R = 20*8 = 160 Vrms^2
V(rms) = sqrt(Vrms^2) = sqrt(160) = 12.65
Which is the RMS output voltage of the amplifier -- the input to R1.
Now calculate the voltage at the node:
1) Calculate equivalent resistance of R2, R3, and Rload
Req = (47+120)||120 = 20040 / 287 = 69.82
2) Calculate voltage of the node using voltage-divider equation
Vout(rms) = (12.65*69.82)/(180+69.82) = 883.22 / 249.82 = 3.54 Vrms
3) Figure out why author of the page is wrong...
Vout(peak) = 3.54Vrms * sqrt(2) = 5.006 Vpeak
So that's how you can calculate the voltage.
For the power dissipated in R1:
Power = V(rms)^2 / R = (12.65-3.54)^2/180 = 0.46W
I think the reason the author gives a range is due to his/her uncertainty (rms vs. peak)
Power calculated using a mix of peak/rms values = (12.65-5)^2 / 180 = 0.33 W (which is incorrect)
and if you round up the 0.46W value you get 0.5W... And in practice you would definitely round up to find a suitable sized resistor... in this case you might even want to go with a 1W resistor or parallel two 0.5W resistors to make sure it doesn't burn up.
Originally Posted by Navyblue
My speaker output is 50w x 2 @ 8 ohms and my headphone is DT880 600 ohms. Basically I am trying to determine what would be the optimal resistor to use.
Thanks.
Uh, it's gonna be a couple minutes... workin on it.