{"text_format":"3","workbook":"xls","n_sheets":2,"sheets":["data","max 10 stages cascade"],"not_rendered":{"external_links":1,"defined_names":2},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"data","index":0,"n_rows":29,"n_cols":10,"rows_kept":29,"merged":[[11,0,11,10]],"flags":["formulas_cached_only"]}
["Low Jitter Hard Limiter"]
[]
[{"v":1,"d":"1.000E+00"}," ρin - input slope (slew rate) [V/s]"]
[{"v":1,"d":"1.00"}," V - input voltage swing [Vpp]"]
[{"v":1000000,"d":"1000000.0"}," g - required slope gain"]
[]
[]
[{"v":1,"d":"1.000"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":3},{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.20319"}]
[]
["when k is in [½, 1] guarantees that the output crosses the half way point at time th and gives the stage its correct slope gain g"]
[]
["k=1 minimizes jitter --- it increases only gradually when k is reduced from 1 to 0,6. There may be advantages to operating in this region if long term stability is important, since the capacitor in the filter may be subject to drift with temp. Reducing k also gives the stage a well defined bandwidth, since it will behave like an RC filter."]
[]
[{"v":20.25925762900039,"d":"20"}," number of stages of the optimun cascade structure",{"$nulls":3}," assuming equal noise contribution of the stages and equal range of the limiters"]
[]
[]
[]
["UTILITIES"]
[{"v":1,"d":"1.000E+00"}," Fsine - sine frequency [Hz]"]
[1," Vsine - peak to peak voltage [V]",null,null,{"v":3.1415,"d":"3.142E+00"}," ρ - max slope (slew rate) [V/s]"]
[]
[1," V - voltage swing [V]"]
[{"v":1,"d":"1.000E+00"}," Τ - risetime [s]",null,null,{"v":1,"d":"1.000E+00"}," ρ - slope (slew rate) [V/s]"]
[]
[1," V - voltage swing [V]"]
[{"v":3.1832e-07,"d":"3.183E-07"}," ρ - slope (slew rate) [V/s]",null,null,{"v":3141492.8373963307,"d":"3.141E+06"}," Τ - risetime [s]"]
[]
[{"v":1,"d":"1.000E+00"}," ρin - max input slope (slew rate) [V/s]"]
[{"v":1000000,"d":"1.000E+06"}," ρout - required output slope [V/s]",null,null,{"v":1000000,"d":"1000000.0"}," g - required slope gain"]

{"sheet":"max 10 stages cascade","index":1,"n_rows":163,"n_cols":12,"rows_kept":163,"merged":[[14,10,15,10],[17,8,18,8],[29,10,30,10],[32,8,33,8],[44,10,45,10],[47,8,48,8],[59,10,60,10],[62,8,63,8],[74,10,75,10],[89,10,90,10],[104,10,105,10],[119,10,120,10],[134,10,135,10],[149,10,150,10]],"flags":["formulas_cached_only"]}
[6,"Slope amplification stages"]
["          ▲▲▲"]
[]
[{"v":7.446090611745038e-09,"d":"7.45E-09"}," J - total jitter of the squaring stages [s]"]
[]
["1st stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier + source noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":2.9257864933423687,"d":"2.93"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":2.9257864933423687,"d":"2.93"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":2.996079311618622,"d":"3.00"},"GBW",null,"[Hz]"]
[]
[{"v":2.3313021677439383,"d":"2.33"}," g1 - slope gain",null,1]
[{"v":2.9257864933423687,"d":"2.93"}," G - amplifier voltage gain",null,null,{"v":9.324852613869025,"d":"9.3"}," dB"]
[{"$nulls":5},"Hz",null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"v":0.2144724124217081,"d":"2.145E-01"}," τ - RC time constant [s]",null,null," Fc = ",{"v":0.7420747923809328,"d":"0.742"},null,10,null,{"v":10,"d":"10.0"},null,{"v":21447.219794951012,"d":"21447.2"}]
[]
[{"v":2.3313021677439383,"d":"2.3"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":2.81621665515264e-17,"d":"2.82E-17"}," J² - jitter contribution [s²]",null,null,{"v":5.3068037980997936e-09,"d":"5.31E-09"}," J - jitter [s]",null,{"v":1000,"d":"1000.0"},null,214,472,412]
[]
["2nd stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":3.4104461971425,"d":"3.41"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":7.950780612372381,"d":"7.95"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":9.490498326322895,"d":"9.49"},"GBW",null,"[Hz]"]
[]
[{"v":2.717484898663793,"d":"2.72"}," g2 - slope gain"]
[{"v":3.4104461971425,"d":"3.41"}," G - amplifier voltage gain",null,null,{"v":10.656224050699537,"d":"10.7"}," dB"]
[{"$nulls":5},"Hz",null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"v":0.07892312944486489,"d":"7.892E-02"}," τ - RC time constant [s]",null,null," Fc = ",{"v":2.016577041974254,"d":"2.017"},null,10,null,{"v":10,"d":"10.0"},null,{"v":7892.305052181436,"d":"7892.3"}]
[]
[{"v":6.335278435066317,"d":"6.3"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":1.40810832757632e-17,"d":"1.41E-17"}," J² - jitter contribution [s²]",null,null,{"v":3.75247695206289e-09,"d":"3.75E-09"}," J - jitter [s]",null,{"v":1000,"d":"1000.0"},null,78,923,129]
[]
["3rd stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":4.633918019220052,"d":"4.63"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":29.357160897030017,"d":"29.36"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":47.61353690586139,"d":"47.61"},"GBW",null,"[Hz]"]
[]
[{"v":3.6923620872328824,"d":"3.69"}," g3 - slope gain"]
[{"v":4.633918019220052,"d":"4.63"}," G - amplifier voltage gain",null,null,{"v":13.31896692436056,"d":"13.3"}," dB"]
[{"$nulls":5},"Hz",null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"v":0.02137469933345871,"d":"2.137E-02"}," τ - RC time constant [s]",null,null," Fc = ",{"v":7.4459326157699675,"d":"7.446"},null,10,null,{"v":10,"d":"10.0"},null,{"v":2137.467795878075,"d":"2137.5"}]
[]
[{"v":23.392141905702935,"d":"23.4"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":7.0405416378816e-18,"d":"7.04E-18"}," J² - jitter contribution [s²]",null,null,{"v":2.6534018990498968e-09,"d":"2.65E-09"}," J - jitter [s]",null,{"v":1000,"d":"1000.0"},null,21,374,699]
[]
["4th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":8.555051604756708,"d":"8.56"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":200.12098114908054,"d":"200.12"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":599.2158623237248,"d":"599.22"},"GBW",null,"[Hz]"]
[]
[{"v":6.816768891617384,"d":"6.82"}," g4 - slope gain"]
[{"v":8.555051604756708,"d":"8.56"}," G - amplifier voltage gain",null,null,{"v":18.64445267168261,"d":"18.6"}," dB"]
[{"$nulls":5},"Hz",null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"v":0.003135605691391898,"d":"3.136E-03"}," τ - RC time constant [s]",null,null," Fc = ",{"v":50.75720182425997,"d":"50.757"},null,10,null,{"v":10,"d":"10.0"},null,{"v":313.5602555789342,"d":"313.6"}]
[]
[{"v":159.45882525109516,"d":"159.5"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":3.5202708189408e-18,"d":"3.52E-18"}," J² - jitter contribution [s²]",null,null,{"v":1.876238476031445e-09,"d":"1.88E-09"}," J - jitter [s]",null,{"v":1000,"d":"1000.0"},null,3,135,606]
[]
["5th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":29.15890482274345,"d":"29.16"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":4649.644708643164,"d":"4649.64"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":47.45249163161455,"d":"47.45"},"GBW",null,"[kHz]"]
[]
[{"v":23.234169060861248,"d":"23.23"}," g5 - slope gain"]
[{"v":29.15890482274345,"d":"29.16"}," G - amplifier voltage gain",null,null,{"v":29.295424166326708,"d":"29.3"}," dB"]
[{"$nulls":5},"kHz",null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"v":0.00013495665298717018,"d":"1.350E-04"}," τ - RC time constant [s]",null,null," Fc = ",{"v":1.1793014082411117,"d":"1.179"},null,10,null,{"v":10,"d":"10.0"},null,{"v":13.495651803065213,"d":"13.5"}]
[]
[{"v":3704.8933041302757,"d":"3704.9"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":1.7601354094704e-18,"d":"1.76E-18"}," J² - jitter contribution [s²]",null,null,{"v":1.3267009495249484e-09,"d":"1.33E-09"}," J - jitter [s]",null,{"v":500,"d":"500.0"},null,0,269,913]
[]
["6th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":338.74146214059186,"d":"338.74"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":1.255000974915978,"d":"1.26"},"output slew rate",null,"[V/μs]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":148.7923028308173,"d":"148.79"},"GBW",null,"[MHz]"]
[]
[{"v":269.91330597434103,"d":"269.91"}," g6 - slope gain"]
[{"v":338.74146214059186,"d":"338.74"}," G - amplifier voltage gain",null,null,{"v":50.597367155614904,"d":"50.6"}," dB"]
[{"$nulls":5},"kHz",null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"v":4.999999999999988e-07,"d":"5.000E-07"}," τ - RC time constant [s]",null,null," Fc = ",{"v":318.30914183855435,"d":"318.309"},null,10,null,{"v":10,"d":"10.0"},null,{"v":0.04999995000004987,"d":"0.0"}]
[]
[{"v":1000000.0000000024,"d":"1000000.0"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":8.800677047351998e-19,"d":"8.80E-19"}," J² - jitter contribution [s²]",null,null,{"v":9.381192380157225e-10,"d":"9.38E-10"}," J - jitter [s]",null,{"v":100,"d":"100.0"},null,0,5,0]
[]
["7th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":0,"d":"0.00"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":0,"d":"0.00"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":0,"d":"0.00"},"GBW",null,"[Hz]"]
[]
[{"v":0,"d":"0.00"}," g7 - slope gain"]
[{"v":0,"d":"0.00"}," G - amplifier voltage gain",null,null,{"$error":"#VALUE!"}," dB"]
[{"$nulls":5},{"$error":"#DIV/0!"},null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"$error":"#DIV/0!"}," τ - RC time constant [s]",null,null," Fc = ",{"$error":"#DIV/0!"},null,10,null,{"v":10,"d":"10.0"},null,{"$error":"#DIV/0!"}]
[]
[{"v":0,"d":"0.0"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":0,"d":"0.00E+00"}," J² - jitter contribution [s²]",null,null,{"v":0,"d":"0.00E+00"}," J - jitter [s]",null,{"v":100,"d":"100.0"},null,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
["8th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":0,"d":"0.00"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":0,"d":"0.00"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":0,"d":"0.00"},"GBW",null,"[Hz]"]
[]
[{"v":0,"d":"0.00"}," g8 - slope gain"]
[{"v":0,"d":"0.00"}," G - amplifier voltage gain",null,null,{"$error":"#VALUE!"}," dB"]
[{"$nulls":5},{"$error":"#DIV/0!"},null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"$error":"#DIV/0!"}," τ - RC time constant [s]",null,null," Fc = ",{"$error":"#DIV/0!"},null,1,null,{"v":10,"d":"10.0"},null,{"$error":"#DIV/0!"}]
[]
[{"v":0,"d":"0.0"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":0,"d":"0.00E+00"}," J² - jitter contribution [s²]",null,null,{"v":0,"d":"0.00E+00"}," J - jitter [s]",null,{"v":100,"d":"100.0"},null,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
["9th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":0,"d":"0.00"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":0,"d":"0.00"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":0,"d":"0.00"},"GBW",null,"[Hz]"]
[]
[{"v":0,"d":"0.00"}," g9 - slope gain"]
[{"v":0,"d":"0.00"}," G - amplifier voltage gain",null,null,{"$error":"#VALUE!"}," dB"]
[{"$nulls":5},{"$error":"#DIV/0!"},null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"$error":"#DIV/0!"}," τ - RC time constant [s]",null,null," Fc = ",{"$error":"#DIV/0!"},null,null,100,{"v":10,"d":"10.0"},null,{"$error":"#DIV/0!"}]
[]
[{"v":0,"d":"0.0"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":0,"d":"0.00E+00"}," J² - jitter contribution [s²]",null,null,{"v":0,"d":"0.00E+00"}," J - jitter [s]",null,{"v":100,"d":"100.0"},null,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
["10th stage"]
[]
[{"v":4e-09,"d":"4.00E-09"}," √N0 - amplifier noise [V/√Hz]",{"$nulls":5},"Amplifier"]
[{"v":1,"d":"1.00"}," V - range of the clipper [Vpp]",{"$nulls":5},{"v":0,"d":"0.00"},"output swing",null,"[V]"]
[{"v":1,"d":"1.00"}," k - normalized half-level crossing time [½, 1] ",{"$nulls":5},{"v":0,"d":"0.00"},"output slew rate",null,"[V/s]"]
[{"v":0.7968121300200202,"d":"0.7968"}," g/G - slope-gain / voltage-gain ratio",null,null,{"v":0.2031878699799799,"d":"0.203188"},null,null,{"v":0,"d":"0.00"},"GBW",null,"[Hz]"]
[]
[{"v":0,"d":"0.00"}," g10 - slope gain"]
[{"v":0,"d":"0.00"}," G - amplifier voltage gain",null,null,{"$error":"#VALUE!"}," dB"]
[{"$nulls":5},{"$error":"#DIV/0!"},null,"uF","nF","pF"," RC Filter"," R [ohm]"]
[{"$error":"#DIV/0!"}," τ - RC time constant [s]",null,null," Fc = ",{"$error":"#DIV/0!"},null,null,1,{"v":10,"d":"10.0"},null,{"$error":"#DIV/0!"}]
[]
[{"v":0,"d":"0.0"}," ρout - slope (slew rate) of the output [V/s]",{"$nulls":5}," R [ohm]"," RC Filter","uF","nF","pF"]
[{"v":0,"d":"0.00E+00"}," J² - jitter contribution [s²]",null,null,{"v":0,"d":"0.00E+00"}," J - jitter [s]",null,{"v":100,"d":"100.0"},null,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
[]
["Time Interval Counter / Comparator Contribution"]
[]
[{"v":0.00015,"d":"1.50E-04"}," √N0 - input noise [V/√Hz]"]
[{"v":1000000.0000000024,"d":"1000000"}," Input Slew rate [V/s]"]
[{"v":1.499999999999996e-10,"d":"1.50E-010"}," Trigger jitter [s]"]
[]
[{"v":7.447601318432506e-09,"d":"7.45E-009"}," J - total jitter [s]"]