all about gain

8/19/2019 All About Gain

1/11

INTRO: For those interested in headphone amps, gain is an important

topic. Here are the essentials about gain with lots of links to more

information. In addition to this introduction explaining gain, there are

later sections on:

• Excess Gain

• Gain Calculations

• Gain etails

RELATED ARTICLES: !he following ma" be useful understanding

how gain fits into the bigger picture:

• Headphone #mps Explained

• #mplifier $ower %e&uirements

• 'oise #nd "namic %ange

WHAT IS GAIN? $ut simpl", gain is the maximum amount an

amplifier can increase a signal. In the world of headphones, it(s usuall")oltage gain. !he diagram abo)e shows a source with a weak output

made * times stronger b" an amplifier. #ppl"ing gain to a signal doesn+t

normall" change the d"namic range, it ust makes e)er"thing louder.

-ther wa"s to specif" gain, such as power and current, are rarel" used

for headphone gear.

YACA (Yet Another Car Analogy): !he relationship between gain,

)olume, and maximum power can be confusing to some. sing caranalogies might help:

• Gain I Li!e The Gear Sele"tion / 0hen a car is in its lowest

gear its top speed is limited to a fairl" low )alue but it can climb

steep hills. It(s somewhat the same with a headphone amp set to

http://nwavguy.blogspot.com/2011/09/all-about-gain.html#excessgainhttp://nwavguy.blogspot.com/2011/09/all-about-gain.html#gaincalculationshttp://nwavguy.blogspot.com/2011/09/all-about-gain.html#gaindetailshttp://nwavguy.blogspot.com/2011/02/gain-and-headphone-ampsdacs.htmlhttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://nwavguy.blogspot.com/2011/09/noise-dynamic-range.htmlhttp://en.wikipedia.org/wiki/Gainhttp://en.wikipedia.org/wiki/Amplifierhttp://en.wikipedia.org/wiki/Voltage_gain#Voltage_gainhttp://nwavguy.blogspot.com/2011/09/all-about-gain.html#gaincalculationshttp://nwavguy.blogspot.com/2011/09/all-about-gain.html#gaindetailshttp://nwavguy.blogspot.com/2011/02/gain-and-headphone-ampsdacs.htmlhttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://nwavguy.blogspot.com/2011/09/noise-dynamic-range.htmlhttp://en.wikipedia.org/wiki/Gainhttp://en.wikipedia.org/wiki/Amplifierhttp://en.wikipedia.org/wiki/Voltage_gain#Voltage_gainhttp://nwavguy.blogspot.com/2011/09/all-about-gain.html#excessgain


2/11

low gain. !hink of a gain switch as 1st, 2nd, and *rd gear on a car(s

transmission. ifferent gears are used for different dri)ing

conditions.

• #ol$%e i li!e the Throttle (A""elerator) / !he )olume controladusts the o)erall power to the headphones much like the throttle

in a car adusts the power to the wheels.

• &a'i%$% oer i li!e To* S*ee+ / 3ost cars are capable of

going faster than most people need. 0hile a car might ha)e a top

speed of 144 3$H, in first gear, it might onl" do 54 3$H. 6o gain

can be used as a wa" to limit maximum output and better match

the output to a gi)en pair of headphones. !he difference betweenthe top speed and the highest speed limit is somewhat analogous to

excess gain.

WHY DOES GAIN &ATTER? If "ou don(t ha)e enough gain, "our

headphones probabl" won+t get loud enough. If "ou ha)e too much gain,

"ou will be forced to use onl" a small portion of the )olume control(s

range, there ma" be increased channel balance problems, more noise,

more distortion, and "ou could e)en damage "our headphones more

easil". 3ost an" amp will perform worse at higher gain settings so youwant to use the least amount of gain that gets the job done.

GAIN AND #OL,&E ARE I&LE&ENTED DI--ERENTLY:

!urning down the )olume is not the same as lowering the maximum gain

7with a few rare exceptions8. # race car doesn(t turn into a famil" car if

"ou ne)er use more than half throttle. Certain compromises were made

in the race car that make it less suitable for famil" car dut" e)en if "ou

tr" to dri)e it slowl". !he same is true with a high gain amp. It(simportant to not ha)e much more gain than "ou reall" need.

GAIN CAN .E ,SED TO LI&IT &A/I&,& OWER: If "ou

ha)e some fairl" efficient headphones that are as loud as "ou would e)er

want with onl" 4.9 )olts of audio. ut "ou ha)e a high/end desktop

headphone amp that can put out 14 times as much 79 )olts8. " reducing

http://nwavguy.blogspot.com/2011/09/all-about-gain.html#excessgainhttp://nwavguy.blogspot.com/2011/09/all-about-gain.html#excessgain


3/11

the gain, e)en if "ou accidentall" turn the )olume all the wa" up, "ou

can limit the maximum power to "our headphones. !his can help pre)ent

hearing damage and e)en headphone damage. It also also allows using

much more of the )olume control(s range making )olume adustments

easier and more accurate.

GAIN CAN CHANGE WITH DI--ERENT HEADHONE

LOADS: If an amp doesn+t ha)e an output impedance below 2 ohms the

gain will change with different loads. !he higher the output impedance,

the more dramatic the change. For example, an amp with a 124 ohm

output impedance with ;< gain at no load, will ha)e onl" *.;< gain with

*44 ohm headphones and onl" 4.=< gain with 1= ohm headphones. !his

is another reason it+s important to know the output impedance.

GAIN CANNOT CORRECT -OR A LAC0 O- &A/I&,&

OWER: If "our headphones need ; )olts but "our amp is onl" good

for 2 )olts cranking up the gain won(t help an" and will ust make the

amp clip sooner. Clipping is what happens when an amp runs out of

power. !he rest of this article assumes "our amp is capable of enough

power for "our headphones. For more on this topic see: 3ore $ower>

GAIN DETAILS

HOW IS GAIN E/RESSED? Gain is usuall" expressed as a factor

7ratio8, such as 5


4/11

WHAT ARE TYICAL GAINS? Headphone amps that ha)e ust a

single fixed gain t"picall" range from 2< 7= d8 to ;< 715 d8. For

amps with two gain settings, low gain might be 2< to *< and high gain

;< to ?


5/11

from a lower output impedance. 6ome amps, like the -2, can be easil"

configured for 1< gain and impro)e the sound of higher impedance

sources. For more on headphone amps in general, see: Headphone #mps

Explained

E/CESS GAIN

E/CESS GAIN: If "our amp has ust enough gain for "our headphones

to hit the desired le)el at full )olume with a 4 dF6 signal it(s sort oflike ha)ing a car with a top speed e&ual to the highest speed limit in "our

area. !here might be times when "ou want to go e)en faster. ut how

much extra do "ou need> !he amount of )olume control range abo)e

where a 4 dF6 signal clips is considered @excess gainA. Here are some

points to consider:

• E'"e Gain I A Tra+eo11 / #s described abo)e in Why Does

Gain Matter , too much gain has negati)e side effects. 6o it(s atradeoff between those side effects and how much excess gain "ou

want.

• E'"e Gain I Only ,e1$l -or 2$iet Tra"! / 3ost properl"

recorded digital music is designed to hit, or get within 1 d of, 4

dF6. If "our amp has excess gain, using full )olume with normal

tracks will cause the amp to clip 7badl" distort8 and ma" e)en

damage "our headphones. ut, without excess gain, rare &uiet

tracks ma" not be loud enough e)en with the )olume at 144B. -ne

solution is ha)ing a reasonable amount of excess gain. #nother

solution is to normalie &uiet tracks to 4 dF6 using #udacit" or

other software. !his simpl" raises the le)els so the loudest portion

of the track is at 4 dF6. Det another solution is to use %epla"Gain

http://nwavguy.blogspot.com/2011/08/o2-summary.htmlhttp://nwavguy.blogspot.com/2011/02/gain-and-headphone-ampsdacs.htmlhttp://nwavguy.blogspot.com/2011/02/gain-and-headphone-ampsdacs.htmlhttp://nwavguy.blogspot.com/2011/08/o2-summary.htmlhttp://nwavguy.blogspot.com/2011/02/gain-and-headphone-ampsdacs.htmlhttp://nwavguy.blogspot.com/2011/02/gain-and-headphone-ampsdacs.html


6/11

which helps e&ualie all tracks to roughl" the same percei)ed

)olume.

• Re*layGain (3ol$%e le3eling) / If "ou use something like

%epla"Gain nearl" all of "our music should pla" at a consistentsubecti)e le)el. %epla"Gain is essentiall" like ha)ing someone

automaticall" adust the )olume for each track 7or C8. !he default

target loudness of ? d lea)es 15 d of headroom between the

a)erage )olume and 4 dF6. For the most compressed pop music

this means the peak le)els will be as much as = d below 4 dF6,

while d"namic music will get much closer to, or e)en hit, 4 dF6.

If "ou use %epla"Gain, or something similar, for )olume le)eling,

"ou ma" want up to = d of excess gain to allow for the o)erall)olume reduction %epla"Gain applies to some tracks. For more on

a)erage )olume see: 3ore $ower>

• Dyna%i" Range It+s important to note that neither the gain of an

amplifier, nor %epla"Gain, normall" changes the d"namic range of

music. Gain changes normall" appl" e&uall" to the softest and

loudest portions of the signal 7music8. !o change the d"namic

range "ou ha)e to appl" compression, limiting, 7or d"namic range

expansion8.

• Cli**ing 3 &a'i%$% SL 6ome amps ha)e plent" of power

and "our headphones, or ears, will gi)e up before the amp does

when dialing up excess gain on a recording that alread" hits 4

dF6. ut, in some circumstances 7especiall" with low sensiti)it"

headphones8, the amp might run out of power first. If "ou want to

be assured "our amp will ne)er clip, ust work backwards from the

amp+s maximum output into "our headphone impedance todetermine the gain. If "our amp maxes out at 9 )olts, and "our

source is 2 )olts, set the gain to *.;< and the amp will ne)er clip

e)en at full )olume with a worst case recording. 6ee: 3ore

$ower>

http://en.wikipedia.org/wiki/ReplayGainhttp://en.wikipedia.org/wiki/ReplayGain#Target_loudnesshttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://en.wikipedia.org/wiki/Dynamic_rangehttp://en.wikipedia.org/wiki/Dynamic_range_compressionhttp://en.wikipedia.org/wiki/Compandinghttp://en.wikipedia.org/wiki/Compandinghttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://en.wikipedia.org/wiki/ReplayGainhttp://en.wikipedia.org/wiki/ReplayGain#Target_loudnesshttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://en.wikipedia.org/wiki/Dynamic_rangehttp://en.wikipedia.org/wiki/Dynamic_range_compressionhttp://en.wikipedia.org/wiki/Compandinghttp://en.wikipedia.org/wiki/Compandinghttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://nwavguy.blogspot.com/2011/09/more-power.html


7/11

• 4 +. E'"e Gain I A Reaona5le &a'i%$% / I would aim for

at least * d of extra gain but somewhere around d the negati)e

side effects alread" mentioned start to outweigh the ad)antages. #

few might want to go as high as 12 d but onl" if the"()e used

something like %epla"Gain to normalie their music librar" to alower than normal a)erage )olume or ha)e other unusual

re&uirements.

• The &ath * d of extra gain means multipl"ing the minimum

gain b" 1.5 and for = d multipl" b" 2, and for d multipl" b"

2.?.

THE CHANNEL .ALANCE RO.LE&: e)ices with con)entional)olume controls ma" ha)e audible channel imbalance at )er" low

)olumes. It(s extremel" difficult to manufacture )olume control

potentiometers that maintain tight channel balance below about /54 d

7referenced to full )olume8. Ha)ing too much excess gain forces using

onl" the lower portion of the )olume control(s range with normal

recordings. If "our amp has 14 d of excess gain, for example, /54 d

below 4 dF6 on the )olume control is /;4 d below full )olume. !he

channel balance error will likel" be much greater and more audible.

6ome products get around this problem b" using digitall" controlled

electronic )olume controls that can maintain better channel balance at

low settings but these can add distortion and often controlled b"

updown buttons rather than a simple knob. 6tepped precision

attenuators are another solution but are expensi)e and sometimes their

step sie is too great.

GAIN CALC,LATIONS


8/11

HOW DO YO, CON#ERT -RO& Gain Ratio / TO +.? !he math

re&uires using a function known as base 14 logarithm 7-G on a

calculator8. ut "ou can also ust use an online d calculator:

• -nline d Calculator

• Gain in d 24 J -G14 7 Gain Factor 8 Ki.e. 20 * !G"0 # $ % &

"2 d'(

• Gain Factor #'!I-G14 7 Gain in d 24 8 Ki.e. )+,!G"0

# "2 - 20 % & $ L

HOW &,CH GAIN DO I NEED? !his comes down to onl" three

things:

• How much )oltage "our headphones need

• How much output "our source has

• How much excess gain "ou want.

HEADHONE RE2,IRE&ENTS: For a gi)en pair of headphones,

the 3ore $ower> article helps determine what "our headphones need.

!his is related to the sensiti)it" and impedance of "our headphones

which )ar" widel". !he most efficient IE3s onl" need about 4.1 )olts to

pla" loudl", 6ennheiser H=44s need about 2.* )olts and e"er !??4/

=44s need about = )olts or =4 times more than the IE3s.

SO,RCE O,T,T LE#EL: 6ources ha)e a maximum output le)el.

It(s the output )oltage at 4 dF6 7the loudest digital music can get8 and

at full )olume 7if the source has a )olume control8. 6ources can beroughl" di)ided into the follow categories 7all )oltages are Mrms8:

• orta5le layer / 3ost of these ha)e a maximum output of 4.; /

1.4 )olts from either their headphone acks or - 7ine -utput

ock8 connectors. !he i$od !ouch is 4.; )olts from the -.

http://www.learningmeasure.com/cgi-bin/calculators/dB.plhttp://nwavguy.blogspot.com/2011/09/more-power.htmlhttp://www.learningmeasure.com/cgi-bin/calculators/dB.plhttp://nwavguy.blogspot.com/2011/09/more-power.html


9/11

• ,S. oere+ DAC / 3ost of these ha)e a maximum output of

1.; )olts or less.

• Nor%al Ho%e A$+io Gear / !he %edbook standard for an" home

e&uipment that pla"s digital audio is 2 )olts. 6ome go slightl"higher up to 2.; )olts. !here are also a few 6 powered #Cs

that can manage similar )oltages 7such as the H%! 3usic 6treamer

II8.

• ,n$$al (rare) Ho%e So$r"e / # few companies, arguabl"

unwisel", ha)e decided to go well abo)e the established standard

and output more than 2.; )olts. ut I(m not aware of an" that go

abo)e *.* )olts unless the" ha)e a )olume control.

• .alan"e+ O$t*$t / !hese can be misleading because balanced

outputs normall" ha)e twice the output of unbalanced outputs. # 5

)olt balanced output, used with an unbalanced adapter or cable, is

reall" onl" 2 )olts.

• ,n!non So$r"e 6ee ID Gain 3easurements below.

CALC,LATING THE RE2,IRED GAIN: -nce "ou()e figured outthe abo)e three re&uirements, it(s fairl" eas" to calculate the gain "ou

need. Nust follow these steps 7examples are gi)en for the H=44(s dri)en

from an i$od - with * d excess gain8:

• Calculate 3inimum Gain: Gain Factor Mout Min Ki.e. 2./out

with 0.1 in & 2./-0.1 & $. L

• Con)ert !o d: 3inimum Gain in d 24J-G7 Gain Factor 8

Ki.e. 20*!G#$.% & "/.2 d'L

• #dd Excess Gain: Final Gain in d 3inimum Gain O Excess

Gain Ki.e. 1*.2 O * 1=.2 dL

• !he result is 1=.2 d 7=.;


10/11

• Dou can also multipl" 5.=< b" 1.5 to get =.;< 71.5 is * d excess

gain as a ratio8

• If "ou know the output impedance multipl" b" 7Pload O Pout8

Pload

IN,T O#ERLOAD: #lso be aware that man" de)ices, especiall"

portable ones, ha)e inputs that can be o)erloaded b" certain sources.

ecause the %edbook standard is 2 )olts, a lot of de)ices are designed to

onl" handle about 2.1 )olts such as the Fii- E desktop amp. #nd the

portable Fii- E9 o)erloads at about 1.2 )olts on the input because it was

designed for use with portable pla"ers which are generall" under 1 )olt.

6ometimes the input o)erload point ma" depend on the gain settings. 6ocheck the documentation for a gi)en amp//especiall" if "ou plan to use

home sources with a portable amp, or sources with more than 2 )olts of

output.

RESISTOR #AL,ES: 6ome amplifiers let "ou set the gain b"

changing resistor )alues. !he diagram to the right shows a t"pical non/

in)erting amplifier stage. !he gain is gi)en b" 1 O 1444;44 *. For all

the math, see 0ikipedia Gain and 0ikipedia #mplifiers. 6ome

amplifiers ma" ha)e multiple gain stages, in which case "ou ha)e tomultipl" the gain of each stage together. 6o an amp with a 2< and *<

stage has a total gain of =


11/11

7carefull" so not to cause short circuits8 measure the output of "our

amplifier. on+t connect "our headphone as the" could be damaged. #nd

don+t tr" higher fre&uencies as most meters are not accurate much abo)e

=4 h. MoutMin Gain

.OTTO& LINE: Gain is important. !here(s a definite sweet spot for

most headphones and sources. !he closer an amp comes to ha)ing the

ideal gain, the better o)erall performance "ou will get.

all about gain

Documents