5 October 2015 Stereo Cross-feed Network for Headphones 1 of 12 Copyright 2015 Peter H. Lehmann. All Rights Reserved.

Transcription

1 5 Octoer 05 Stereo Cross-feed Network for Hedphones of Copyrght 05 Peter H. ehmnn. All ghts eserved. The Dlemm The vst mjorty of stereo recordngs re engneered for reproducton wth pr of left nd rght chnnel loudspeker systems. Thus tht engneerng tkes nto ccount tht sound emntng from ech speker system s herd t oth of the lstener's ers. Wth the pr of speker systems conventonlly postoned on opposte sdes of the lstener ech t n equl ngle n the rnge of 0º to 45º, there re two frequency-dependent fctors ffectng ntensty of the sound emntng from ech speker s herd t one er reltve to tht t the opposte er. Frstly, there s ntensty gn effected y ntomcl prts of the humn outer er tht s t mxmum when the speker system s to one sde (reltve to drectly n front) of the lstener t 45º ngle. Ths gn cn occur only t the er tht s on the sme sde of the hed s the to the left or to the rght -poston of the speker system, ths er eng desgnted the ner er. The humn hed s n ostcle to the sound rechng the fr er on the opposte sde of the hed, defetng the posslty of ny gn y tht er. Secondly, s result of dffrcton y the humn hed, the ntensty of sound emntng for exmple from the left speker system s reduced t the rght or fr er, reltve to the ntensty herd t the ner er. The extent of tht reducton ncreses s the frequency of the sound ncreses from hundreds to thousnds of Hertz. When lstenng to stereo recordng wth hedphones, reproducton y the left nd rght hedphones occurs exclusvely for respectvely the left nd rght ers. Ths stuton s not wht the recordng engneer n most cses hd ntended! The plcng of speker trnsducers drectly gnst the ers elmntes lrge prt of outer er gn, nd coustc cross-feed from the left trnsducer to the rght er nd vce vers does not occur. The soluton to ths prolem s to electronclly restore wht s elmnted coustclly s result of lstenng wth hedphones or er nserts. Ths s wht my cross-feed network does, tht s, to lrge extent t mmcs ntensty t the fr er reltve to tht t the ner er s functon of frequency correspondng to lstenng wth pr of stereo loudspeker systems. Network Overvew Ths network s pssve crcut connected n cscde etween power mplfer nd hedphones. Wth the network so connected, the lod seen y the output stge of the mplfer t mnmum s equl to the rted mpednce of the hedphones. The network conssts of only ten prts. The vlues of the components of the network correspond to rted mpednce of the hedphones. The cross-feedng of the network cuses loclzton of the nstruments of recordng to e herd s orgntng n front of the lstener wthout degrdng chnnel seprton, nd does not produce udle dstorton. As the network s connected etween power mplfer nd hedphones, t cn e used wth udo source plyers. No power supply s requred, nd the network s smple to construct. A power mplfer tht s sutle for drectly drvng your hedphones s lso sutle to drve the network n cscde wth your hedphones. For sgnls of frequency greter thn 8 khz nd ncresng, the level of the cross-feed sgnl reltve to tht of the drect sgnl of my network ncresngly lcks correspondence to the theoretcl dfference of sound ntensty t the fr er wth respect to tht t the ner er (of lstenng to reproducton y one of pr of stereo spekers). Ths defect s to some extent

2 5 Octoer 05 Stereo Cross-feed Network for Hedphones of Copyrght 05 Peter H. ehmnn. All ghts eserved. mtgted y the fct tht very lttle of muscl sound producton occurs ove 0 khz. Insertng the cross-feedng network etween power mplfer nd hedphones does result n lowerng of volume, however not to sustntl degree. The network cn only e properly used wth hedphones of rted mpednce tht the network hs een desgned to. If the ctul mpednce of the hedphones sustntlly devtes from rted mpednce t some frequency, ths my result n mproper cross-feed y the network. If source mpednce of the power mplfer tht the network s connected to s comprle to rted mpednce of the hedphones, ths my lso result n n ncorrect cross-feed chrcterstc. Acoustcs Where sound source s locted few meters wy nd t 45º ngle reltve to drectly n front of lstener, there s frequency-dependent outer er gn of the ner er only. Sound cn only rech the opposte or fr er y dffrcton whch defets sound pprochng the fr er t 45º ngle. The three structurl fetures of the outer er tht effect gn re the conch, flnge nd metus. Werng hedphones, the phone rdtes drectly or strght nto the er cnl wth the result tht the conch nd flnge do not provde ny gn. It s ssumed tht the metus, whch provdes gn y resonnce, s not defeted y the werng of hedphones nd s eqully opertve t oth ers. Column of Tle lsts the comned frequency-dependent ntensty gn of the conch nd flnge only, tht s, omttng tht of the metus. Dffrcton of sound emntng from source to one sde of the lstener, commonly referred to s the sound shdow, cuses the dfference of ntensty t the fr er wth respect to tht t the ner er to stedly ncrese wth ncresng frequency of the sound. Column of Tle lsts the frequency-dependent dfference of ntensty t the fr er reltve to tht t the ner er for sdengle or zmuth equl to 45º. Column of Tle lsts the frequency-dependent ntensty dfference resultng from oth outer er gn t the ner er only nd the sound shdow. Tht s, the entres of Col. re the ntensty levels n db of Col. sutrcted from those of Col.. Wth the excepton of devton n the low frequency rnge tht s to e explned elow, the cross-feedng network mmcs ntensty dfference of Col. nd the mxmum ntensty gn of Col. tht occurs t 5 khz. Descrpton The network s shown t Fg. connected etween n nput phone jck J nd n output phone jck J. The network components n the drect sgnl pth from the left chnnel mplfer output (tp contct of J) to the left hedphone re resstor n prllel crcut wth the n-seres connecton of cpctor C, nductor nd resstor. In the sme mnner resstor n prllel crcut wth the n-seres connecton of cpctor C, nductor nd resstor connects the rng contct (rght chnnel nput) of J to the rght hedphone. To effect left to rght chnnel cross-feed, resstor s connected from the tp contct of nput jck J to the rng contct of output Jck J. esstor connected from the rng contct of nput Jck J to the tp contct of output Jck J effects cross-feed of the rght chnnel mplfer output to the left hedphone.

3 5 Octoer 05 Stereo Cross-feed Network for Hedphones of Copyrght 05 Peter H. ehmnn. All ghts eserved. esstor tos Superposton ppled to the network of Fg., s shown t Fg., s used to fnd the requred resstor rtos. Fg. s equvlent to Fg. ncludng shortng the rng contct of nput jck J to ground or the shell. Fg. dffers from Fg. n tht resstors nd of Fg. hve een susttuted for respectvely the left nd rght hedphones of Fg.. These resstors hve resstnce equl to rted mpednce of the hedphones. For the moment dsregrd the component vlues shown t Fg.. At Fg., CH (chnnel)-a voltge source produces sne wve nd the CH-B source s shorted. Ths results n the voltge drops cross resstors nd equl to respectvely the drect nd cross-feed outputs. Ths fgure wll e used to derve the resstor rtos resultng n () s functon of frequency ove the low frequency rnge, electrcl power dsspted y wth respect to tht of correspondng s closely s possle to decels of Col. of Tle, nd () for frequency ntlly very much less thn the seres resonnt frequency Fs (5 khz), nd ncresng to equl to Fs, then correspondng ttenuton of the voltge drop cross decreses y 9 db. Where frequency s sustntlly less thn the resonnt frequency Fs, nd decresng, stndng for voltge drop, then the rto / should fltten to equl to 0.7. Ths s done to compenste for the fct tht t frequences less thn khz, loclzton of sound sources t dstnce depends more on reltve phse t the ers thn ntensty (ccordng to the dulty hypothess of sound loclzton). Wth ths smple network, I mde no ttempt t mmckng the correct phse reltonshp t low frequences. The cross-feed sgnl t - db reltve to the drect sgnl n the low frequency rnge susttutes. To solve for the requred rto of resstor vlues to produce ths low-frequency shelf, smplfyng ssumpton s tht the mpednce of resstor n prllel crcut wth the n-seres connecton of cpctor C, nductor, nd resstor equls the resstnce of. Solvng for / s result of voltge dvson gven ths ssumpton, t s found tht tht rto equls /. Thus must equl.4 tmes to produce the - db shelf. Wth respect to frequency equl to 5 khz, or seres resonnt frequency Fs of C n-seres wth of Fg., the level of the cross-feed sgnl wth respect to tht of the drect sgnl should e equl to the -8 db of Col. of Tle. Tht s, / should equl 0.. At frequency equl to Fs, the ssumpton s mde tht mpednce of resstor n prllel crcut wth the n-seres connecton of cpctor C, nductor nd resstor equls the resstnce of. Mkng ths ssumpton, y voltge dvson, / s equl to /. Thus settng equl to 0. tmes results n the desred ttenuton of the cross-feed sgnl reltve to tht of the drect sgnl. In Col. of Tle, for frequency ncresng from hundreds to thousnds of Hertz, coustc gn of the outer er s ntlly zero nd reches mxmum t 5 khz equl to 9 db. To mmc ths wth the network, ttenuton of the voltge drop cross, wth respect to the ppled voltge of source CH-A, should decrese y 9 db for tht ncrese of frequency.

4 5 Octoer 05 Stereo Cross-feed Network for Hedphones 4 of Copyrght 05 Peter H. ehmnn. All ghts eserved. In the low frequency rnge t Fg., mpednce n-seres wth equls the resstnce of. At 5 khz or Fs, mpednce n-seres wth equls the resstnce of. Gven these two smplfyng ssumptons, n equton s derved for the ncrese of voltge drop cross tht occurs correspondng to the ncrese of frequency. Tht equton s set equl to.8, s 0 tmes log 0 of.8 equls 9 db. We know tht equls.4 tmes nd equls 0. tmes ; thus equls 0.8 tmes. Susttutng.4 nd 0.8 for respectvely nd n the equton solve for s fctor tmes. The soluton s equls.9 tmes. The proper vlues of cpctor C nd nductor were determned wth computer smulton progrm comprng the voltge drop to voltge drop n the network of Fg. s functon of frequency. Where the vlues of resstnce of the resstors of the network re ccordng to the ove equtons, t ws found y trl nd error tht rectnce of nd C should equl or rted hedphone mpednce t the resonnt frequency Fs (5 khz). When the network s confgured n ths wy, wth the excepton of the low frequency rnge, reltve ttenuton compred to (coustc) ntensty dfference of Col. of Tle s functon of frequency on verge closely corresponds. Decels of Col. 4 of Tle re the result of computer smulton of the network of Fg. where component vlues of the network re those shown t Fg.. Construct the Network Where rted mpednce nd senstvty of the hedphones to e connected to the network equl out 50 Ω or less nd 00 db/ mw, wttge of the resstors of the network could most lkely e /4 Wtt. To e on the sfe sde, recommended wttge n ll cses s / Wtt. If DC of nductor s sgnfcnt, then tht DC should e sutrcted from the clculted vlue of resstor. The pr of nductors should e mounted t rght ngle nd t lest 8 cm prt. Here re the equtons n order for solvng vlues of the components of the network of Fg.. In the equtons stnds for rted hedphone mpednce =. 4 mh C = μf Mnmum lod to mplfer Mnmum lod of the network connected n cscde etween mplfer nd hedphones occurs t the seres resonnt frequency of C n-seres wth. Fg. s used to nlyze mnmum lod presented to ech chnnel mplfer. Adoptng the smplfyng ssumpton tht resstnce of n prllel crcut wth equls the resstnce of, nd notng tht nd equl respectvely 4. nd 0.5, t s clculted tht lod seen y the mplfer equls.0. The comned

5 5 Octoer 05 Stereo Cross-feed Network for Hedphones 5 of Copyrght 05 Peter H. ehmnn. All ghts eserved. mpednce of the network nd hedphones s greter thn t frequences other thn resonnt frequency Fs. In other words, the properly constructed network nserted etween your mplfer nd hedphones won't drw more current thn your mplfer cn supply. Freq. khz Col. coustc gn t ner er db Col. coustc ntensty dfference db Col. db of Col. mnus Col. Col. 4 0 tmes log 0 ( / ) db TAB : Comprng cross-feed reltve level of the network of Fg. n Col. 4 to reltve coustc level of Col.. Columns & re tken from respectvely Fg. 4. on p.76, nd Fg..5 on p. 4 (zmuth = 45º), of Herng y Gulck, Gescheder nd Frsn, Oxford Unversty Press, 989.

6 5 Octoer 05 Stereo Cross-feed Network for Hedphones 6 of Copyrght 05 Peter H. ehmnn. All ghts eserved. FIGU : Cross-feed Network for Hedphones

7 5 Octoer 05 Stereo Cross-feed Network for Hedphones 7 of Copyrght 05 Peter H. ehmnn. All ghts eserved. FIGU : Applcton of superposton to the network of Fg..

8 5 Octoer 05 Stereo Cross-feed Network for Hedphones 8 of Copyrght 05 Peter H. ehmnn. All ghts eserved. APPNDIX- FO FNC ONY, NOT FO PUBICATION A. Dervton of =.4 eferrng to Fgure, gven tht frequency << the resonnt frequency Fs equl to 5 khz, then X X C where stnds for "n prllel crcut wth". The voltges nd stnd for respectvely the CHA nput voltge nd the voltge drop cross the "" lod resstor (stndng for lod of hedphone ""). Drect ttenuton s the rto of wth respect to ccordng to the equton, Cross-feed ttenuton s the rto of wth respect to ccordng to the equton, Solvng for cross-feed wth respect to drect ttenuton, l

9 5 Octoer 05 Stereo Cross-feed Network for Hedphones 9 of Copyrght 05 Peter H. ehmnn. All ghts eserved. Solvng for / y susttutng for the two multpled terms to the rght of the equl sgn, Accordng to the plnned reltve ttenuton chrcterstc of the network, 0.7 0log 0 db Fnlly, 4. B. Dervton of = 0. Attenuton of wth respect to tht of s t mxmum t the seres resonnt frequency F S of C n-seres wth. Wth respect to frequency equl to F S, solve for ttenuton of the drect nd cross-feed voltge drops cross the lods t Fgure, then solve for /. Assume tht <<. Then,

10 5 Octoer 05 Stereo Cross-feed Network for Hedphones 0 of Copyrght 05 Peter H. ehmnn. All ghts eserved. Solvng for cross-feed ttenuton gn s occurs t resonnt frequency F S nd referrng to Fg., Gven the erler ssumpton tht <<, Fnlly solvng for cross-feed ttenuton wth respect to drect ttenuton, db og C. Dervton of =.9 For frequency ntlly << the resonnt freq. Fs, nd ncresng to Fs, to mmc gn of the outer er, ttenuton of the drect sgnl voltge should decrese y out 9 db. Note tht 0 tmes log 0 of.8 equls 9 db.

11 5 Octoer 05 Stereo Cross-feed Network for Hedphones of Copyrght 05 Peter H. ehmnn. All ghts eserved. The drect sgnl voltge t Fg. s. Where equls "n prllel crcut wth", two smplfyng ssumptons re the followng. freq. << Fs (C--) n seres freq. = Fs (C--) n seres At Fg., solvng for t freq. = Fs wth respect to tht sme voltge t freq. << Fs,.8 Thus B.8 =.4 =0. =0.8 + ( )= ( +. 4 ) ( )= ( 0.8 ) ( +.4 ) ( +.4 )+.4 (0.8 ) ( +.4 )+. 4 = = = = =.04 =.9

12 5 Octoer 05 Stereo Cross-feed Network for Hedphones of Copyrght 05 Peter H. ehmnn. All ghts eserved. D. Mnmum Network Impednce Mnmum lod to the mplfer occurs t resonnce, so the relevnt components determnng the lod seen y the mp re, nd (stndng for hedphone mpednce). As hs een prevously clculted, =.4 & =.9 = 4. = 0. = 0.5 eferrng to Fg., the drect sgnl leg hs n-seres wth the prllel comnton of nd. Cll the drect sgnl leg T nd equls "n prllel crcut wth". = =0.8 T = + T = =. Contnung t Fg., the cross-feed sgnl leg conssts of n-seres wth ( ). = =0.5 Cll the cross-feed sgnl leg T. T = +0.5 T = =4.45 Fnlly, the (mnmum) lod s seen y the mplfer t resonnce of the network s equl to T T. T T = (. ) (4. 45 ) T T = =.0