So I use http:// www. digizoid. com/ power .php to calculate the mW needed to power headphones.
My HiFiMan HE400i impedance is 35ohms and my bayerdynamics custom studios are 80ohms.
Most manufacturer specs state for 16/32/300 ohms like for example:
- My fiio k3 specs on unbalanced output 220mW(16Ω); 120mW(32Ω).
- On the Fiio Q5S I plan to buy, specs on unbalanced are 280 mW (16Ω), 210 mW (32Ω); 30 mW（300Ω)
How do you get to the middle ground for 35ohm or 80ohms based on the manufacturer specs? I'm not worried the Q5S or the K3 can push the custom studios, but wanted to know if for example I buy a 150ohm or 600 ohm can in the future.
Thanks
The issue here is that almost all headphone amps have a current limit AND a voltage limit.
A way to figure out how much output power will be available is by first looking at available power at the lowest impedance.
If that is not very high you can be pretty sure the output current is limited.
When powers are specified at 16 Ohm or 32 Ohm you can make some calculations for output
current limits.
When also output power is given at 300 Ohm or 600 Ohm you can easily calculate the maximum output
voltage.
We can assume that manufacturers supply actual maximum output numbers but some of them simply supply incorrect numbers.
To calculate
current limit: convert mW to W by dividing the mW rating by 1000.
Then
divide output power (in W) by the given lowest impedance (Ohm) and then take the SQRT (square-root) of the outcome: I=√(P/R).
This will give you the
max. output current the amp can deliver in
Amp. When the output power is not extremely high you can assume this current is the actual limit.
Now we need the max. output voltage. As most amplifiers/sources can easily provide enough current to for headphones above 120 Ohm one can safely assume that output powers given at 300 or 600 Ohm are caused by output voltage limiting.
To calculate
voltage limit:
multiply output power (in W) by the given highest impedance (Ohm) and then take the SQRT (square-root) of the outcome: V=√(PxR) . This will give you the
max. output voltage the amp can deliver in
Volt.
With these numbers you can calculate the output power in various impedances but is not really as straight forward as it seems.
One needs to make 3 calculations based on the current and voltage and then see what the power will be for a specific impedance.
First you calculate the maximum power which is max. current x max. output voltage. The outcome is max power in mW.
This value is only valid for a specific impedance though. This differs from amp to amp and can only exist at the point where the maximum voltage is available at the point where the impedance is a certain value where it draws the maximum current AND still reaches the maximum output voltage.
This is easy to calculate:
Divide the max. output voltage (V) by the current (in A) and you get the impedance in Ohms: R=(V/I).
Let's call this the
optimal power impedance for now.
Note you need to convert mA to A for this. 1000mA = 1A, 100mA = 0.1A.
Once you have this
optimal power impedance you can determine if you need the maximum
Voltage or maximum
Current to calculate output power in a certain impedance.
For impedances
below the determined
optimal power impedance you must use the
Current limit formula below.
For impedances
above the determined
optimal power impedance you must use the
Voltage limit formula below.
Current limit formula: Headphone impedance (Ohm) x max output current (mA) x max output current (mA) (
I² x R) = power in
mW in that impedance.
Voltage limit formula: first (max output Voltage (V) x max output voltage (V) ) and divide that outcome with the impedance (
V²/R) = power in
W in that impedance. Convert to mW by multiplying W x 1000.
Now the example above:
Q5:
max. current = 132mA (0.132A)
max. voltage = 3V
optimal power impedance = 22 Ohm
max. output power in 22 Ohm = 3V x 0.132A = 0.396W (396mW) in 22 Ohm.
Below and above 22 Ohm the output power will thus always be less than the max. output power.
This means for both 35 Ohm and 80 Ohm you need the voltage limit formula as the impedance is above 22 Ohm
35 Ohm = 0.257W (257mW)
80 Ohm = 0.113W (113mW)
For the K3 you don't know the max. voltage but given the fact that they do not give this and it is a portable device the optimal impedance most likely is between 16 and 32 Ohm.
So you can calculate the max. output voltage based on the 32 Ohm power
V=√(PxR) = 1.96V
35 Ohm = 0.109W (109mW)
80 Ohm = 0.048W (48mW)
