Being not too technical I have come across a situation between the WM-DDIII and the DD-100 in the specs on mW headphone power output and load impedance.  What am looking for is way to determine from specs how loud a Walkman may push a certain headphone/earbud knowing that other factors outside just load impedance ( sensitivity , etc.) will affect answers.

From the owner manual of DDIII the headphone amp has excellent power at 20mW + 20mW (at 10% harmonic distortion which is unacceptable but with taking it only to 16mW output is probably less than 1%)  which allows good clean louder listening levels without pushing amp into clipping/higher distortion.   On comparison the DD-100 Boodo Khan from owner manual of one am selling shows 12mW + 12mW headphone output ( CURIOUS its rated WITH the DOL ON ).  Interesting the DD-100 is rated at 63 ohms while the DDIII is at 32 ohms probably due to the full size DR-S100 headphones. The DD-100 also neglects to say at what distortion level 12mW is produced.  

So even though the DDIII is rated higher ( sadly we dont know distortion rating at max power output for DD100) I suspect the actual power output of the DD100 is higher if you can make the statistics/specs equaled out so that we are comparing Apples to Apples information.   I think that power rated at higher impedance if impedance of headphone is lowered then power output number rating would be higher ???

Am a member of www.head-fi.org where I pulled some of the following information which only confuses me more but thought be worthwhile including. 

Ohm is the resistance. the higher the number, the harder to drive. You need an amp once it gets too hard for the source to drive.

• Power Output:
• 187 mW @ 300 ohm
• 250 mW @ 120 ohm
• 500 mW @ 32 ohm

Is there any benefit when amplifying either of the headphones I own? If so, why?

It is variable, and depends on multiple factors. First, headphones have highly variable efficiency. Second, what is "enough power" depends largely on personal preferences and source material (e.g. classical music needs more peak power to sound as loud as pop music because of the lack of aggressive dynamic compression). Finally, the power the "unamplified" source you already have can output may also vary.

Quote:

Yes, see above. Other important factors are efficiency (sensitivity), and the linearity of the impedance curve. To calculate how loud a headphone can get without clipping (high distortion), you need to know the maximum power, and the efficiency (often specified in dB/mW). The power can be calculated from the impedance and either the maximum voltage, or the maximum current, whichever is reached first (V^2/R or I^2*R) - with a high impedance headphone, this is normally the voltage. The maximum voltage is also affected by the output impedance of the source: Vload = Vout * |Zload| / |Zload + Zout|. Note that these impedances can be frequency dependent, and result in a non-linear frequency response. Once you have the power value, you can calculate the sound pressure from it and the sensitivity.

A practical example: assume we have a source that can output 2 Vrms, has an output impedance of 100 Ohm, and feeds a 600 Ohm headphone that has 96 dB/mW efficiency. For simplicity, let's assume that both impedances are purely resistive for now, it is enough for a reasonable power estimate.

  Vload = 2 * 600 / (600 + 100) = 1.714 Vrms

  Pload = 1.714 * 1.714 / 600 = 4.90 mW

  SPL = 10 * log(4.9) / log(10) + 96 = 102.9 dB

Is that enough ? Well, it depends, but here is an article on what maximum levels one should generally aim for when choosing/building an amplifier.

For completeness, let's also calculate how the above example behaves in terms of frequency response. Assume that the minimum impedance of the headphone is 620 Ohm in the audio range, and the maximum is 740 Ohm, and the phase is zero (pure resistance) at both. The difference in the output level will be:

  20 * log((740 / (740 + 100)) / (620 / (620 + 100))) / log(10) = 0.20 dB

This is a minor change, and does not affect the sound much.

You can look for headphone data here. The sensitivities are specified in Vrms/90dB at this page, this changes the calculation as follows (assuming 0.4 Vrms at 90 dB):

  SPL = 20 * log(1.714 / 0.4) / log(10) + 90 = 102.6 dB

There are a number of practical benefits, some are due to historical reasons. Older sources, before iPods and other low voltage portable devices became common, often had high output impedance, but, being AC powered, did not have much difficulty outputting relatively high voltage. There is also an IEC standard from the 1990's that requires headphone outputs to have an impedance of 120 Ohm. This made high impedance headphones preferable, to improve power efficiency and damping factor.
One reason why some higher end headphones have hundreds of Ohms of impedance is using thinner wire in the voice coil (the resistance of a wire is proportional to its length and a material specific factor, and inversely proportional to the area of its cross-section). This makes the coil lighter, and the sound quality is slightly improved, as reduced moving mass allows the driver to respond faster to changes in the audio signal.

Another advantage of high impedance is that it makes the performance of the drivers less dependent on the output impedance of the amplifier. Keeping the ratio of the speaker/headphone impedance and the amplifier output impedance (the damping factor) as high as possible is generally preferred, as it improves the control over the drivers, dampens resonances, reduces frequency response variations that result from the drivers having frequency dependent impedance, and even reduces distortion. Therefore, with a 120 Ohm source, a 600 Ohm headphone (damping factor = 5) is better than a 24 Ohm headphone (damping factor = 0.2).

With a high output impedance source, there is no use making the impedance of the headphone lower than that of the source, since below that level the power output to the headphone will actually decrease. For example, with a source that outputs 2 Vrms through 120 Ohms, here is what the actual useful power output will be on various loads:

  - 16 Ohm: 3.46 mW

  - 32 Ohm: 5.54 mW

  - 64 Ohm: 7.56 mW

  - 120 Ohm: 8.33 mW

  - 250 Ohm: 7.30 mW

  - 600 Ohm: 4.63 mW

Outputs are sometimes AC coupled (i.e. the headphone is fed through a capacitor), this is needed if the output would otherwise have a large DC offset, and affects the bass response. The lower the impedance of the load, the more rolled off the bass will become. For example, the combination of a 100 uF capacitor and 16 Ohm load results in a bass roll-off with the -3 dB point at about 100 Hz. But with a 250 Ohm load the cutoff frequency moves down to about 6 Hz.

Amplifiers generally have worse distortion performace with low impedance loads. Common op-amps are usually not rated for loads below 600 Ohm - this does not mean that anything less will not work, but the distortion will increase. Good amplifiers for low impedance headphones have buffered outputs that can supply the higher required current with low distortion.

Finally, with a high impedance headphone, the signal to noise ratio may be better at the same output power, since doubling the output voltage with the volume control usually results in less than double noise voltage.

But the most important one of the above are probably the compatibility with high output impedance sources, and making the voice coil as light as possible (although there are also low impedance high end headphones now, so it may not actually be that important).

DD-100          DDIII

Is there a way we can sort out a way to generally determine a given Walkman if know specs ( what specs are required to calculate answer as so many Walkman specs give only part of what we seem to need) if it will be able to drive avg. headphones ( under $100 or lets pick a  few examples like Porta Pro, Sony MDR-V6, MDR-E575 (DD9) earbuds ) to what volume.  Know its subjective but say less than avg. loud, avg. loud ( not very loud), Strong loudness without undue audible distortion and Melt headphones my ears cant take it but clean sound ( melt down power like some of the earliest 4 battery players that made 50mW to 500mW output power).

I have done a quick LOUDNESS comparison between 5 players all Sony. 

NOTE need someone to give us the complete specs of the WM-40 as I dont have them all others have taken pics of owners manuals.   ALSO NEED the specs for the 3 headphones I used.

   RULES OF COMPARISON

1.  Vol. set at 9 for MAX

2.  SAME tape used same music TDK-SA dolby OFF (on player also)

3.  New batteries

4.  THREE headphones used

     a.  Koss Porta Pro professional ( new last year)

     b.  Sony MDR-V6 ( Japanese drivers Not later model Chinese)

     c.  Sony MDR-E565  (DD9 orig. earbuds)

Not making distinctions much for depth of bass or high freq. reproduction sticking to volume here although certainly when switching to MDR-V6 the much great high end capable phones and earbuds the vol. is more due to highs.

Porta Pro's

WM-7    CLEARLY the loudest and very clean distortion free sound. ( still amazes me the quality sound this player is capable of even against a DD9).  Porta pros near their max to handle but stayed clean.

WM-40   Weakest performer of the 3 but only slightly less than DD9

DD-100   With NO DOL just slightly louder than DD9 with DOL ON it is ALMOST as loud as the DDIII

WM-DDIII   Noticeably louder than all players other than WM-7.

WM-DD9    Weak performer with less than avg. loudness level achieved even if mega bass set to mid ( high is too heavy handed adds distortion at higher vol). 

SONY MDR-V6

Somewhat less loud than the Porta Pro's but with much better high end and tighter bass although the Porta Pro's bass is impressive still.

Volume levels with each player followed about the same as above.

SONY MDR-E565

WM-7   OMG with the earbuds the WM-7 reaches ear Melt Down volumes !!  About the max my ears can stand and the sound was CLEAN. Simply impressive Kuddos to the 7!

WM-40  Slight louder than DD9 avg. loud level.  This player likes the earbuds to drive

has reasonable loudness level and clear with earbuds.

DD-100   With DOL ON cant go above 7 as distorts the earbuds.  DOL off the loudness is slightly higher than avg. loud but hardly really loud or ear melt down volume.  Clearly the DD-100 is best with headphones that can cope with extended bass and the porta pros shine for this player.  ( note if can will try and do comparison to include the DR-S100 headphones if anyone has detailed specs on these it would help).

WM-DDIII   Reaches above avg. loudness level but not ear melt down cant compare to the WM-7.

WM-DD9   Reaches slightly less than avg. loudness level.  Reasonably loud with earbuds only.  yet far from the DDIII and miles from the WM-7.

There is certainly something to be said having higher power reserve as the WM-7 has to push loud volume levels withOUT distortion.  Loud is beautiful if its CLEAN ( my old Cerwin Vega speakers motto when was in college late 70's .

WM-7

         DD9

Its interesting that the DDIII and the WM-7 BOTH show 20mW X 2 at 10% distortion yet the WM-7 is clearly louder .   WHY IS THIS?  I know in amps there is dynamic headroom or the ability of the amp to push significant more power cleanly for short moments of demand but dont think that is applicable here for steady loud volume.  Both also use 2 batteries so actual power is not issue as it is with the WM-40 and DD9 which are straddled with only 1.5 v.

Lower impedance headphones require more current to be driven properly. Higher impedance headphones require less current to be driven but require a higher voltage output of the amplifier, as proposed by Ohm's law. There is one other thing that has to be taken into account and that is the sensitivity of the headphones.

However, not everything lies in this. Dynamic drivers such as the ones in headphones don't have a constant impedance. It changes with frequency so at lower frequencies it can drop to a lot less than what is specified because the usual consensus is to measure the impedance at 1kHz. This means the amplifier must swing a lot more current at that point. On the other hand, if the impendance drops below the output impedance of the amplifier itself, serious problems can arise.

A good way to tll whether the amplifier is capable of driving headphones is to check the output impedance of the amplifier. It has to be lower than the nominal impedance of the headphones. The factor that defines the relationship is called the damping factor. Some believe it is necessary to achieve a minimum factor of 8times. Not really true because there's a lot more to amplifier design than output impedance. For example, most commercial amplifiers have an unstable output impedance which is caused by insufficient power supply, the main part of any amplifier. This is also the reason why cables in ome cases make a difference that can be heard. Therefore, it's not due to the quality of the cables but due to the comrpomise in the amplifier's design.

At full volume, THD is usually a lot more than 10%. This is a crude generalization of course. The real usable power output is at 0% THD so most specifications are really useless. 

There is one other thing and it is the amplifier's linearity. Frequency response is measured at a given output level. However, amplifiers behave differently at different volume levels and this is due to various factors, the most important being the power supply (again).

The only amplifier in a cassette player that has perfect linearity and zero distortion at full output is Dottor Walkman's DD9.