{"text_format":"3","workbook":"xls","n_sheets":12,"sheets":["1 - Buffer Stage","2 - 12dB LR Xover","3 - 24dB LR Xover","4 - Delay Correction","5 - Shelving Lowpass","6 - Shelving Highpass","7 - Notch Filter","8 - 6dB per Octave Dipole Equal","9 - Linkwitz Transform","10 - Variable Gain","Pluto Equaliser","Closed Box Design"],"not_rendered":{"charts":2,"images":18,"external_links":2,"defined_names":32},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"1 - Buffer Stage","index":0,"n_rows":34,"n_cols":9,"rows_kept":34,"flags":["formulas_cached_only"]}
["1 -  Buffer stage"]
{"$rows_empty":7}
[{"$nulls":8},"Capacitance:"]
[]
[{"$nulls":8},"For \"X\" microfarads type XE-6"]
[{"$nulls":8},"For \"X\" nanofarads type XE-9"]
[{"$nulls":8},"For \"X\" picofarads type XE-12"]
{"$rows_empty":9}
["6dB/Octave Highpass Buffer:"]
["Ro:",21500,"Ohms","F =",7.402555492646296,"Hz"]
["Co:",{"v":1e-06,"d":"1.00E-06"},"Farads"]
[]
["12dB/Octave XO-Lowpass:"]
["C:",{"v":1e-07,"d":"1.00E-07"},"Farads","F=",100.09744848546876,"Hz"]
["R:",15900,"Ohms"]
[]
["Dipole EQ and 6dB/Octave Lowpass filter"]
["R2:",11000,"Ohms","F=",3.078432168121767]
["C:",{"v":4.7e-06,"d":"4.70E-06"},"Farads","Gain=",4.21455938697318,"Times","Gain=",12.495043556398882,"dB"]
["R1:",2610,"Ohms"]

{"sheet":"2 - 12dB LR Xover","index":1,"n_rows":26,"n_cols":8,"rows_kept":26,"flags":["formulas_cached_only"]}
["2 -  12 dB/oct Linkwitz-Riley crossover"]
[]
[]
[]
[]
[]
[{"$nulls":7},"Capacitance:"]
[]
[{"$nulls":7},"For \"X\" microfarads type XE-6"]
[{"$nulls":7},"For \"X\" nanofarads type XE-9"]
[{"$nulls":7},"For \"X\" picofarads type XE-12"]
{"$rows_empty":11}
["All the Rs have to be the same and all the Cs have to be the same"]
[]
["R:",{"v":23700,"d":"2.37E+04"},"Ohms","Fp=",98.75585945141187,"Hz"]
["C:",{"v":6.8e-08,"d":"6.80E-08"},"Farads"]

{"sheet":"3 - 24dB LR Xover","index":2,"n_rows":27,"n_cols":9,"rows_kept":27,"merged":[[4,0,21,0]],"flags":["formulas_cached_only"]}
[]
[]
["3 -  24 dB/oct Linkwitz-Riley crossover"]
[]
[]
[]
[]
[{"$nulls":8},"Capacitance:"]
[]
[{"$nulls":8},"For \"X\" microfarads type XE-6"]
[{"$nulls":8},"For \"X\" nanofarads type XE-9"]
[{"$nulls":8},"For \"X\" picofarads type XE-12"]
{"$rows_empty":11}
["Again, all the Rs have to be the same and all the Cs have to be the same"]
[]
["R:",{"v":2370,"d":"2.37E+03"},"Ohms","Fp=",2157.211192642469,"Hz"]
["C:",{"v":2.2e-08,"d":"2.20E-08"},"Farads"]

{"sheet":"4 - Delay Correction","index":3,"n_rows":25,"n_cols":10,"rows_kept":25,"merged":[[2,0,13,0]],"flags":["formulas_cached_only"]}
["4 -  Delay correction"]
[]
[]
[]
[]
[]
[{"$nulls":9},"Capacitance:"]
[]
[{"$nulls":9},"For \"X\" microfarads type XE-6"]
[{"$nulls":9},"For \"X\" nanofarads type XE-9"]
[{"$nulls":9},"For \"X\" picofarads type XE-12"]
{"$rows_empty":7}
["R:",{"v":2370,"d":"2.37E+03"},"Ohms","To=",{"v":0.00012798,"d":"1.28E-04"},"Seconds",null,"To=",127.98,"microseconds"]
["C:",{"v":2.7e-08,"d":"2.70E-08"},"Farads","Fp=",2487.184608405928]
["Clp",{"v":2.2e-10,"d":"2.20E-10"},"Farads","This is the 220pF capacitor shown above"]
[]
[]
["Note - this also has a 6db/octave lowpass ( using the 200pF capacitor ) to roll off the gain at HF."]
["Calculate this as:",null,{"v":305245.38375890936,"d":"305245.38"},"Hz"]

{"sheet":"5 - Shelving Lowpass","index":4,"n_rows":29,"n_cols":9,"rows_kept":29,"merged":[[2,0,12,0]],"flags":["formulas_cached_only"]}
["5 -  Shelving lowpass"]
[]
[]
[]
[]
[{"$nulls":8},"Capacitance:"]
[]
[{"$nulls":8},"For \"X\" microfarads type XE-6"]
[{"$nulls":8},"For \"X\" nanofarads type XE-9"]
[{"$nulls":8},"For \"X\" picofarads type XE-12"]
[]
[]
[]
[]
[]
["Non-Inverting Configuration:",null,null,"Inf Gain",0,"dB"]
["R1:",2370,null,"DC Gain",9.98306503708715,"dB"]
["R2:",5110,null,"F1=",31.14578142698539,"Hz"]
["C:",{"v":1e-06,"d":"1.00E-06"},null,"F2=",98.29976585394547,"Hz"]
[]
["Inverting Configuration:",null,null,"Inf Gain",0.025796424282078914,"dB"]
["R1:",2370,null,"DC Gain",10.006258347631924,"dB"]
["R2:",7500,null,"F1=",30.840395126902944,"Hz"]
["R3:",3480,null,"F2=",97.30676393488343,"Hz"]
["C:",{"v":4.7e-07,"d":"4.70E-07"}]
[]
["The inverting configuration contains a capacitor which rolls off the gain at HF. The -3db frequency is set by the size of the cap in relation to the paralell resistance of the two resistors."]
["Capacitor",{"v":2.2e-10,"d":"2.20E-10"},"Farads ( this is shown as the 220pF capacitor above )"]
["Flp:",304340.17331052094,"Hz"]

{"sheet":"6 - Shelving Highpass","index":5,"n_rows":35,"n_cols":9,"rows_kept":35,"merged":[[2,0,9,0]],"flags":["formulas_cached_only"]}
["6 -  Shelving highpass"]
[]
[]
[]
[]
[{"$nulls":8},"Capacitance:"]
[]
[{"$nulls":8},"For \"X\" microfarads type XE-6"]
[{"$nulls":8},"For \"X\" nanofarads type XE-9"]
[{"$nulls":8},"For \"X\" picofarads type XE-12"]
[]
[]
["Non-Inverting Configuration:"]
["R1:",5110,"Ohms","DC Gain",0,"dB"]
["R2:",5110,"Ohms","Inf. Gain",6.020599913279624,"dB"]
["C:",{"v":1.5e-08,"d":"1.50E-08"},"Farads","F1:",1038.1927142328464,"Hz"]
[{"$nulls":3},"F2:",2076.3854284656927,"Hz"]
[]
[]
[]
["Inverting Configuration:"]
["R1:",5110,"Ohms","DC Gain",0,"dB"]
["R2:",5110,"Ohms","Inf. Gain",6.020599913279624,"dB"]
["R3:",5110,"Ohms","F1:",1038.1927142328464,"Hz"]
["C:",{"v":1.5e-08,"d":"1.50E-08"},"Farads","F2:",2076.3854284656927,"Hz"]
[]
[]
["Again, the capacitor in paralell with the feedback resistor ( shown as 100pF in the above drawings ) rolls off the gain at HF:"]
["For the non-inverting case:"]
["Cap:",{"v":1e-10,"d":"1.00E-10"},"Farads"]
["Flp",{"v":311457.8142698539,"d":"311457.81"},"Hz"]
[]
["For the inverting case:"]
["Cap:",{"v":1e-10,"d":"1.00E-10"}]
["Flp",{"v":311457.8142698539,"d":"311457.81"},"Hz"]

{"sheet":"7 - Notch Filter","index":6,"n_rows":35,"n_cols":10,"rows_kept":35,"merged":[[2,0,14,0],[39,0,78,0]],"flags":["formulas_cached_only"]}
["7 -  Notch filter",{"$nulls":7},"This is used in Circuit C"]
{"$rows_empty":15}
["Synthesis:"]
["First, choose the following:",null,null,"Then in Circuit A:"]
["R1 ( in a) above ):",5110,"Ohms","R3:",1518.5021061217333,"Ohms"]
["a ( notch depth )",-12.8,"dB","L:",2.4915166627291514,"Henries"]
["Fo",291,"Hz","C:",1.200578299847915e-07,"Farads"]
["Q",3]
[]
["For circuit B:"]
["Choose Rt",1000,null,"Top resistor in the chain - Between the output terminal and 120nF"]
["Choose R2:",147000,null,"This needs to be high - to maximise Rp, which should be >> ZL in the operating range"]
[null,"R1:",518.5021061217333,{"$nulls":6},"c=L/(R1*R2)"]
[null,"R2:",147000,{"$nulls":6},"Rs=R1+R2"]
[null,"C:",3.280427914627313e-08]
["For Circuit C:"]
["Choose Rt",511,"Ohms","This is the top resistor in the chain in circuit C, between the 120nF capacitor and the output terminal"]
["Choose R2",511,"Ohms","The bottom resistor in the chain in circuit C."]
["For Circuit C:","R1:",496.5021061217333]
[null,"R2:",511,{"$nulls":5},"This is used in Circuit B"]
[null,"C:",9.820233193675501e-06]

{"sheet":"8 - 6dB per Octave Dipole Equal","index":7,"n_rows":24,"n_cols":9,"rows_kept":24,"merged":[[2,0,19,0],[2,8,14,8]],"flags":["formulas_cached_only"]}
["8 -  6 dB/oct dipole equalization"]
{"$rows_empty":16}
[{"$nulls":8},"A) The shelving lowpass filter cannot correct for a peak. "]
[{"$nulls":8},"B) The bridged-T based circuit is limited in the shape of curves that can be realized. It has also higher gain for opamp noise than signal at high frequencies. "]
[{"$nulls":8},"C) The shelving lowpass with added notch filter is the most flexible circuit. (models.htm#D)   Top"]
[]
[]
["No need to have any calculations here - The circuit to use is C. It can be calculated by calculating the two parts independently"]
["Using the calcs in 5 - Shelving Lowpass and 7 - Notch filter"]

{"sheet":"9 - Linkwitz Transform","index":8,"n_rows":75,"n_cols":15,"rows_kept":75,"flags":["formulas_cached_only"]}
{"$rows_empty":16}
["The worksheet below is lifted directly from SL's website"]
[]
[]
[null,"Equalizer with complex poles and zeros",{"$nulls":8},"© LINKWITZ LAB - 26 October 2000"]
[null,"Enter your own values for the numbers in bold typeface"]
[null,"Values are in Hz, kOhm and nF"]
[]
[null,"Measure f0, Q0 using < f0Q0.gif > ",{"$nulls":3},"1) Specify:",null,null,"3b) Calculated poles & zeros",{"$nulls":3},"4b) Calculated poles & zeros"]
[null,"Choose target for  fp, Qp",{"$nulls":3},"f0 =",72," ","f0",{"v":73.41270095716735,"d":"73"},null,null,"f0",{"v":73.32987841370137,"d":"73"}]
[{"$nulls":5},"Q0 =",2.1,null,"Q0",{"v":1.8720194968118609,"d":"1.87"},null,null,"Q0",{"v":2.1397134406994103,"d":"2.14"}]
[null,"Component layout",{"$nulls":3},"fp =",20," ","fp",{"v":21.187460513536355,"d":"21"},null,null,"fp",{"v":21.163442076594798,"d":"21"}]
[null,"R2 ----- C2",null,"R2 ----- C2",null,"Qp =",0.7,null,"Qp",{"v":0.648007236532329,"d":"0.65"},null,null,"Qp",{"v":0.7281515922899118,"d":"0.73"}]
[null,"R1 ----- R1",null,"R3 ----- R3",null,"C2 =",{"v":100,"d":"100.0"}," ","fp1",{"v":31.83098861837907,"d":"32"},null,null,"fp1",{"v":28.3143467518049,"d":"28"}]
[null,"        C1",null,"        C3",{"$nulls":4},"fz1",{"v":32.0812221511581,"d":"32"},"= fp1 ??",null,"fz1",{"v":28.568469411576974,"d":"29"},"= fp1 ??"]
[{"$nulls":8},"Adc [dB]",{"v":21.58769186033234,"d":"21.6"},null,null,"Adc [dB]",{"v":21.587786441038208,"d":"21.6"}]
[null,"For realizability with the given"]
[null,"circuit k must be positive.",{"$nulls":3},"2b) Multiply calculated",{"$nulls":3},"Find the optimum standard value combination "]
[{"$nulls":5},"values by M to change",{"$nulls":3},"that approximates the specified poles and zeros"]
[null,"2a) Calculated values",{"$nulls":3},"impedance level"]
[null,null,"k > 0  ??",{"v":0.22040816326530593,"d":"0.22"},null,"Select M =",2.32,null,"3a) Select standard values",{"$nulls":3},"4a) Select standard values"]
[null,null,"R1",{"v":4.312541038195481,"d":"4.31"},null,"R1",{"v":10.005095208613515,"d":"10.01"},null,"R1 =",{"v":10,"d":"10.00"},"kOhm",null,"R1 =",5.11,"kOhm"]
[null,null,"R2",{"v":1.901038498469843,"d":"1.90"},null,"R2",{"v":4.4104093164500355,"d":"4.41"},null,"R2 =",4.64,"kOhm",null,"R2 =",2.15,"kOhm"]
[null,null,"R3",{"v":55.890531855013435,"d":"55.89"},null,"R3",{"v":129.66603390363116,"d":"129.67"},null,"R3 =",{"v":121,"d":"121.00"},"kOhm",null,"R3 =",{"v":61.9,"d":"61.90"},"kOhm"]
[null,null,"C1",{"v":2627.29469387755,"d":"2627.3"},null,"C1",{"v":1132.4546094299785,"d":"1132.5"},null,"C1 =",{"v":1000,"d":"1000.0"},"nF",null,"C1 =",{"v":2200,"d":"2200.0"},"nF"]
[null,null,"C3",{"v":202.72335600907024,"d":"202.7"},null,"C3",{"v":87.38075690046132,"d":"87.4"},null,"C3 =",{"v":82,"d":"82.0"},"nF",null,"C3 =",{"v":180,"d":"180.0"},"nF"]
[null,null,"C2",{"v":100,"d":"100.0"},null,"C2",{"v":43.10344827586207,"d":"43.1"},null,"C2 =",{"v":47,"d":"47.0"},"nF",null,"C2 =",{"v":82,"d":"82.0"},"nF"]
[null,null,"Adc [dB]",{"v":22.25210003069149,"d":"22.3"}]
[]
[null,"Formulas used are those from < f0Q0fpQp.gif >. "]
[]
[]
[null,"The equalizer cancels the original complex poles with zeros"]
[null," (f0, Q0) and adds a new pair of complex poles (fp, Qp) to"]
[null," obtain a targeted 2nd order highpass filter response."]
[]
[{"$nulls":3},"f0, Q0",null,"fp, Qp"]
[null,"Frequency",null,"Original",null,"Target",null,"Equalizer"]
[null,"Hz",null,"dB",null,"dB","dB"]
[null,10,null,{"v":-34.14381753845776,"d":"-34.1"},null,{"v":-12.345999157693985,"d":"-12.3"},{"v":21.797818380763776,"d":"21.8"}]
[null,{"v":12.599210498948732,"d":"13"},null,{"v":-30.0414100743838,"d":"-30.0"},null,{"v":-8.722993568333079,"d":"-8.7"},{"v":21.318416506050724,"d":"21.3"}]
[null,{"v":15.874010519681995,"d":"16"},null,{"v":-25.885588524685584,"d":"-25.9"},null,{"v":-5.544448172380526,"d":"-5.5"},{"v":20.341140352305057,"d":"20.3"}]
[null,20,null,{"v":-21.64294476466125,"d":"-21.6"},null,{"v":-3.0980391997148637,"d":"-3.1"},{"v":18.544905564946387,"d":"18.5"}]
[null,{"v":25.198420997897465,"d":"25"},null,{"v":-17.25734783654154,"d":"-17.3"},null,{"v":-1.5307148968607773,"d":"-1.5"},{"v":15.726632939680764,"d":"15.7"}]
[null,{"v":31.74802103936399,"d":"32"},null,{"v":-12.632143365774008,"d":"-12.6"},null,{"v":-0.6955270172935819,"d":"-0.7"},{"v":11.936616348480426,"d":"11.9"}]
[null,40,null,{"v":-7.598410655073876,"d":"-7.6"},null,{"v":-0.30479933113473656,"d":"-0.3"},{"v":7.29361132393914,"d":"7.3"}]
[null,{"v":50.39684199579493,"d":"50"},null,{"v":-1.8939464605676752,"d":"-1.9"},null,{"v":-0.13356090516202457,"d":"-0.1"},{"v":1.7603855554056507,"d":"1.8"}]
[null,{"v":63.49604207872798,"d":"63"},null,{"v":4.280093105636595,"d":"4.3"},null,{"v":-0.059919643237098086,"d":"-0.1"},{"v":-4.3400127488736935,"d":"-4.3"}]
[null,80,null,{"v":6.580247359067675,"d":"6.6"},null,{"v":-0.027953414503357976,"d":"-0.0"},{"v":-6.608200773571033,"d":"-6.6"}]
[null,{"v":100.79368399158986,"d":"101"},null,{"v":4.491061056184483,"d":"4.5"},null,{"v":-0.013690112444745495,"d":"-0.0"},{"v":-4.5047511686292285,"d":"-4.5"}]
[null,{"v":126.99208415745596,"d":"127"},null,{"v":2.730099197494302,"d":"2.7"},null,{"v":-0.007062696162741133,"d":"-0.0"},{"v":-2.737161893657043,"d":"-2.7"}]
[null,160,null,{"v":1.6626363132548292,"d":"1.7"},null,{"v":-0.003828336629837281,"d":"-0.0"},{"v":-1.6664646498846665,"d":"-1.7"}]
[null,{"v":201.58736798317972,"d":"202"},null,{"v":1.0233657941123084,"d":"1.0"},null,{"v":-0.0021650601670302194,"d":"-0.0"},{"v":-1.0255308542793387,"d":"-1.0"}]
[null,{"v":253.98416831491193,"d":"254"},null,{"v":0.6350815408495265,"d":"0.6"},null,{"v":-0.0012659707105768803,"d":"-0.0"},{"v":-0.6363475115601034,"d":"-0.6"}]
[null,320,null,{"v":0.39627945319497826,"d":"0.4"},null,{"v":-0.0007586356189861476,"d":"-0.0"},{"v":-0.3970380888139644,"d":"-0.4"}]
[null,{"v":403.17473596635944,"d":"403"},null,{"v":0.24814007212935607,"d":"0.2"},null,{"v":-0.0004624798416372755,"d":"-0.0"},{"v":-0.24860255197099335,"d":"-0.2"}]
[null,{"v":507.96833662982385,"d":"508"},null,{"v":0.15572509398910483,"d":"0.2"},null,{"v":-0.0002852197396876477,"d":"-0.0"},{"v":-0.15601031372879248,"d":"-0.2"}]
[null,640,null,{"v":0.09786576458390783,"d":"0.1"},null,{"v":-0.00017724658895446055,"d":"-0.0"},{"v":-0.0980430111728623,"d":"-0.1"}]
[null,{"v":806.3494719327189,"d":"806"},null,{"v":0.06155850256304518,"d":"0.1"},null,{"v":-0.00011069373650229863,"d":"-0.0"},{"v":-0.06166919629954748,"d":"-0.1"}]
[null,{"v":1015.9366732596477,"d":"1,016"},null,{"v":0.038742533060244,"d":"0.0"},null,{"v":-6.934986613771343e-05,"d":"-0.0"},{"v":-0.03881188292638171,"d":"-0.0"}]

{"sheet":"10 - Variable Gain","index":9,"n_rows":22,"n_cols":1,"rows_kept":22,"merged":[[2,0,8,0]],"flags":["formulas_cached_only"]}
["10 -  Variable gain"]
{"$rows_empty":19}
["Not really any calculations here - just choose suitable values for R1,R2 and R3."]
["Probably seldom any reason to change the 5k values SL has chosen above."]

{"sheet":"Pluto Equaliser","index":10,"n_rows":57,"n_cols":20,"rows_kept":57,"flags":["formulas_cached_only"]}
[{"$nulls":19},"F0Q0.gif from SL's website"]
[null,"Equalizer with complex poles and zeros",{"$nulls":8},"© LINKWITZ LAB - 27 July 2006"]
[null,"Enter your own values for the numbers in bold typeface"]
[null,"Values are in Hz, kOhm and nF"]
[]
[null,"Measure f0, Q0 using < f0Q0.gif > ",{"$nulls":3},"1) Specify:",null,null,"3b) Calculated poles & zeros",{"$nulls":3},"4b) Calculated poles & zeros"]
[null,"Choose target for  fp, Qp",{"$nulls":3},"f0 =",60," ","f0",{"v":59.60399460264797,"d":"60"},null,null,"f0",{"v":59.313545284764764,"d":"59"}]
[{"$nulls":5},"Q0 =",0.75,null,"Q0",{"v":0.7376259625866679,"d":"0.74"},null,null,"Q0",{"v":0.7412380035910905,"d":"0.74"}]
[null,"Component layout",{"$nulls":3},"fp =",100," ","fp",{"v":102.26473324959441,"d":"102"},null,null,"fp",{"v":102.26473324959441,"d":"102"}]
[null,"R2 ----- C2",null,"R2 ----- C2",null,"Qp =",0.7,null,"Qp",{"v":0.6719789776942373,"d":"0.67"},null,null,"Qp",{"v":0.6719789776942373,"d":"0.67"}]
[null,"R1 ----- R1",null,"R3 ----- R3",null,"C2 =",{"v":100,"d":"100.0"}," ","fp1",{"v":44.64374280277569,"d":"45"},null,null,"fp1",{"v":44.20970641441537,"d":"44"}]
[null,"        C1",null,"        C3",{"$nulls":4},"fz1",{"v":45.73417904939522,"d":"46"},"= fp1 ??",null,"fz1",{"v":45.73417904939522,"d":"46"},"= fp1 ??"]
[{"$nulls":8},"Adc [dB]",{"v":-9.378020925894454,"d":"-9.4"},null,null,"Adc [dB]",{"v":-9.462880257482507,"d":"-9.5"}]
[null,"For realizability with the given"]
[null,"circuit k must be positive.",{"$nulls":3},"2b) Multiply calculated",{"$nulls":3},"Find the optimum standard value combination "]
[{"$nulls":5},"values by M to change",{"$nulls":3},"that approximates the specified poles and zeros"]
[null,"2a) Calculated values",{"$nulls":3},"impedance level"]
[null,null,"k > 0  ??",{"v":0.7919999999999998,"d":"0.79"},null,"Select M =",1.01,null,"3a) Select standard values",{"$nulls":3},"4a) Select standard values"]
[null,null,"R1",{"v":9.868238038932004,"d":"9.87"},null,"R1",{"v":9.966920419321324,"d":"9.97"},null,"R1 =",{"v":10,"d":"10.00"},"kOhm",null,"R1 =",{"v":10,"d":"10.00"},"kOhm"]
[null,null,"R2",{"v":15.63128905366829,"d":"15.63"},null,"R2",{"v":15.787601944204972,"d":"15.79"},null,"R2 =",{"v":16.2,"d":"16.20"},"kOhm",null,"R2 =",{"v":16.2,"d":"16.20"},"kOhm"]
[null,null,"R3",{"v":3.5525656940155215,"d":"3.55"},null,"R3",{"v":3.588091350955677,"d":"3.59"},null,"R3 =",3.48,"kOhm",null,"R3 =",3.48,"kOhm"]
[null,null,"C1",{"v":722.5343999999999,"d":"722.5"},null,"C1",{"v":715.3805940594058,"d":"715.4"},null,"C1 =",{"v":713,"d":"713.0"},"nF",null,"C1 =",{"v":720,"d":"720.0"},"nF"]
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