{"text_format":"3","workbook":"xls","n_sheets":1,"sheets":["Complex Functions Method"],"not_rendered":{"external_links":2,"defined_names":1},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"Complex Functions Method","index":0,"n_rows":44,"n_cols":24,"rows_kept":44,"merged":[[1,1,1,10]],"flags":["formulas_cached_only"]}
[]
[null,"FEEDER PARAMETERS AND REMOTE ANTENNA IMPEDANCE MEASUREMENT",{"$nulls":11},"Antenna details.",null,"Dummy load - 100 ohm resistor in parallel with 150 pF capacitor in a PL259 plug. "]
[{"$nulls":13},"Feeder details.",null,"37.0 metres RG213 mil. spec. accurately measured."]
[null,"1. Terminate the feeder with a resistive load of 1/3 to "]
[null,"    1/2 of the specified Zo and measure R+/-jX at the ",{"$nulls":4},"Enter value of load resistance.",null,null,{"v":20,"d":"20.0"},"ohms",null,"Enter frequency",null,null,{"v":1,"d":"1.000"},{"v":3,"d":"3.000"},{"v":5,"d":"5.000"},{"v":7,"d":"7.000"},{"v":9,"d":"9.000"},{"v":11,"d":"11.000"},{"v":13,"d":"13.000"},{"v":15,"d":"15.000"},"MHz"]
[null,"    near end at the frequency of interest. ",{"$nulls":4},"Enter measured impedance.*",null,null,"72.0-43.7j","ohms",null,"Enter value of load resistance.",null,null,{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},{"v":20,"d":"20.0"},"ohms"]
[{"$nulls":12},"Enter measured impedance.",null,null,"78.9+48.6j","26.1+16.2j","25.3-16.7j","72.0-43.7j","66.4+43.0j","26.7+13.0j","28.0-21.4j","83.3-39.9j","ohms"]
[null,"2. Change the termination to a resistive load of 2 to 3 "]
[null,"    times the specified feeder Zo and measure R+/-jX  ",{"$nulls":4},"Enter value of load resistance.",null,null,{"v":120,"d":"120.0"},"ohms",null,"Enter value of load resistance.",null,null,{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},{"v":120,"d":"120.0"},"ohms"]
[null,"    at the near end at the same chosen frequency.",{"$nulls":4},"Enter measured impedance.*",null,null,"26.8+13.2j","ohms",null,"Enter measured impedance.",null,null,"25.7-18.6j","70.0-45.9j","68.3+39.5j","26.8+13.2j","28.6-17.1j","78.7-35.2j","59.7+35.9j","25.7+6.7j","ohms"]
[]
[null,"3. Connect the antenna and measure R+/-jX at the ",{"$nulls":10},"Enter  impedance measured"]
[null,"    near end at the same chosen frequency.",{"$nulls":4},"Enter measured impedance.*",null,null,"39.6+28.0j","ohms",null,"with antenna connected.",null,null,"28.9-15.6j","53.6-35.8j","93.9+13.3j","39.6+28.0j","24.6+2.4j","32.9-28.8j","109.7-33.2j","46.8+43.6j","ohms"]
[]
[null,"    For this spreadsheet to operate the ",{"$nulls":4},"Feeder complex impedance ",null,null,"50.2-1.1j","ohms",null,"Feeder complex impedance",null,null,"51.4-2.4j","49.8-2j","50.1-1.4j","50.2-1.1j","50.7","51.5-0.8j","51.3-2j","49.9-2.7j","ohms"]
[null,"    Analysis Toolpak must be enabled by ",{"$nulls":4},"Matched feeder loss",null,null,{"v":0.6753803334394681,"d":"0.675"},"dB",null,"Matched feeder loss",null,null,{"v":0.22220011585885063,"d":"0.22"},{"v":0.4326731179492047,"d":"0.43"},{"v":0.5795086666962755,"d":"0.58"},{"v":0.6753803334394681,"d":"0.68"},{"v":0.7226351951557113,"d":"0.72"},{"v":0.897721371088585,"d":"0.90"},{"v":0.7890591135580255,"d":"0.79"},{"v":0.7997561521313141,"d":"0.80"},"dB"]
[null,"    clicking on tools and then on Add-Ins.",{"$nulls":4},"Feeder effective length",null,null,{"v":0.3077791499895147,"d":"0.3078"},"l",null,"Feeder effective length",null,null,{"v":0.18803069326243022,"d":"0.188"},{"v":0.06369849022044237,"d":"0.064"},{"v":0.4352443938600159,"d":"0.435"},{"v":0.3077791499895147,"d":"0.308"},{"v":0.18078356938884013,"d":"0.181"},{"v":0.05159355754663509,"d":"0.052"},{"v":0.41912722435646865,"d":"0.419"},{"v":0.2880433096229598,"d":"0.288"},"l"]
[null,"    Then tick the Analysis Toolpak box in "]
[null,"    the Add-Ins list and click OK.",{"$nulls":4},"Antenna impedance",null,null,"69.7-46.8j","ohms",null,"Antenna resistance ",null,null,{"v":102.783068045062,"d":"102.8"},{"v":93.4697832545961,"d":"93.5"},{"v":82.560452931279,"d":"82.6"},{"v":69.6688881564534,"d":"69.7"},{"v":58.3711159876576,"d":"58.4"},{"v":46.6280640837782,"d":"46.6"},{"v":38.865153090068,"d":"38.9"},{"v":29.2221521307828,"d":"29.2"},"ohms"]
[{"$nulls":6},"True SWR at antenna ",null,null,{"v":2.2547291938145184,"d":"2.25"},null,null,"Antenna reactance",null,null,{"v":-6.99515865360381,"d":"-7.0"},{"v":-25.9665864517549,"d":"-26.0"},{"v":-40.4199553564197,"d":"-40.4"},{"v":-46.8320745826687,"d":"-46.8"},{"v":-48.4556825081543,"d":"-48.5"},{"v":-52.0937066648796,"d":"-52.1"},{"v":-50.746165133459,"d":"-50.7"},{"v":-48.2665158525356,"d":"-48.3"},"ohms"]
[null,"* Impedances must be entered as R+/-Xj.",{"$nulls":4},"True SWR at transmitter",null,null,{"v":1.9850176535130228,"d":"1.99"},null,null,"True SWR at antenna ",null,null,{"v":2.001949130816346,"d":"2.00"},{"v":2.0339978173917697,"d":"2.03"},{"v":2.1486832714772155,"d":"2.15"},{"v":2.2547291938145184,"d":"2.25"},{"v":2.3938930912075636,"d":"2.39"},{"v":2.7212870928165693,"d":"2.72"},{"v":2.8576178606888827,"d":"2.86"},{"v":3.2684563695870326,"d":"3.27"}]
[null,"  Excel does not recognise impedances",{"$nulls":4},"SWR at tx. ref. to 50 ohms",null,null,{"v":1.9333485503957102,"d":"1.93"},null,null,"True SWR at transmitter",null,null,{"v":1.9287681868050628,"d":"1.93"},{"v":1.892209355425003,"d":"1.89"},{"v":1.9379029384619124,"d":"1.94"},{"v":1.9850176535130228,"d":"1.99"},{"v":2.066311375826766,"d":"2.07"},{"v":2.2060187346902485,"d":"2.21"},{"v":2.3419235451689504,"d":"2.34"},{"v":2.5846328139771875,"d":"2.58"}]
[null,"  entered as R+/-jX.",{"$nulls":4},"Feeder loss at actual SWR",null,null,{"v":0.8734392977457812,"d":"0.87"},"dB",null,"SWR at tx. ref. to 50 ohms",null,null,{"v":1.9685242811881483,"d":"1.97"},{"v":1.977326269801194,"d":"1.98"},{"v":1.9300313030503349,"d":"1.93"},{"v":1.9333485503957102,"d":"1.93"},{"v":2.038692881956391,"d":"2.04"},{"v":2.234435317874949,"d":"2.23"},{"v":2.4410909397383853,"d":"2.44"},{"v":2.400103425049481,"d":"2.40"}]
[{"$nulls":10},"compiled by g4jnh",null,"Feeder loss at actual SWR",null,null,{"v":0.27483668256372634,"d":"0.27"},{"v":0.5345708948019989,"d":"0.53"},{"v":0.7329355167679287,"d":"0.73"},{"v":0.8734392977457812,"d":"0.87"},{"v":0.9651834192586259,"d":"0.97"},{"v":1.2806121318223849,"d":"1.28"},{"v":1.1711986004755643,"d":"1.17"},{"v":1.296841181122228,"d":"1.30"},"dB"]
[]
["EQUATION 3 - NUMERATOR",{"$nulls":8},"359124-158636j",{"$nulls":5},"420849+139428j","151698+142641j","135564-149006j","359124-158636j","354154+153676j","131089+124006j","167906-164758j","379054-158572j"]
["FEEDER COMPLEX CHARACTERISTIC IMPEDANCE",{"$nulls":8},"50.163043410683-1.06549026305713j","ohms",{"$nulls":4},"51.4233953244667-2.40445223557255j","49.8399979717805-2.03157630198529j","50.147352650031-1.36103521580754j","50.163043410683-1.06549026305713j","50.6751830309839-4.71939192196676E-002j","51.4989420798713-0.768369550249206j","51.3285191852668-2.00010339225645j","49.9275314273647-2.71671623104353j","ohms"]
[]
["ANGLE OF REFLECTION COEFFICIENT AT LOW RESISTANCE TERMINATION",{"$nulls":8},{"v":3.1214677247174816,"d":"3.1215"},"radians",{"$nulls":4},{"v":3.098875629705447,"d":"3.0989"},{"v":3.102696041418498,"d":"3.1027"},{"v":3.115877276963675,"d":"3.1159"},{"v":3.1214677247174816,"d":"3.1215"},{"v":3.140721907815291,"d":"3.1407"},{"v":3.1279501594803385,"d":"3.1280"},{"v":3.1058696646639326,"d":"3.1059"},{"v":3.0898952065200476,"d":"3.0899"},"radians"]
["ANGLE OF REFLECTION COEFFICIENT AT TX. WITH LOW RESISTANCE TERMINATION ",{"$nulls":8},{"v":-0.7461991414232005,"d":"-0.7462"},"radians",{"$nulls":4},{"v":0.7360122512948604,"d":"0.7360"},{"v":2.302237205733286,"d":"2.3022"},{"v":-2.3535650841033986,"d":"-2.3536"},{"v":-0.7461991414232005,"d":"-0.7462"},{"v":0.8689285738884078,"d":"0.8689"},{"v":2.4796063940360544,"d":"2.4796"},{"v":-2.1610383711671193,"d":"-2.1610"},{"v":-0.5297637751886752,"d":"-0.5298"},"radians"]
["FEEDER EFFECTIVE ELECTRICAL LENGTH - POLAR",{"$nulls":8},{"v":1.933833433070341,"d":"1.9338"},"radians",{"$nulls":4},{"v":1.1814316892052932,"d":"1.1814"},{"v":0.400229417842606,"d":"0.4002"},{"v":2.734721180533537,"d":"2.7347"},{"v":1.933833433070341,"d":"1.9338"},{"v":1.1358966669634416,"d":"1.1359"},{"v":0.32417188272214204,"d":"0.3242"},{"v":2.633454017915526,"d":"2.6335"},{"v":1.8098294908543613,"d":"1.8098"},"radians"]
[]
["MAGNITUDE OF REFLECTION COEFFICIENT AT LOW RESISTANCE TERMINATION",{"$nulls":8},{"v":0.43011784280477855,"d":"0.4301"},{"$nulls":5},{"v":0.4409956922680666,"d":"0.4410"},{"v":0.4280703040905594,"d":"0.4281"},{"v":0.43012857657060505,"d":"0.4301"},{"v":0.43011784280477855,"d":"0.4301"},{"v":0.43403088864308764,"d":"0.4340"},{"v":0.44065677206208115,"d":"0.4407"},{"v":0.43993575757933634,"d":"0.4399"},{"v":0.4294150231293649,"d":"0.4294"}]
["MAGNITUDE OF REFLECTION COEFFICIENT AT TX. WITH LOW RESISTANCE TERMINATION",{"$nulls":8},{"v":0.3681708715944631,"d":"0.3682"},{"$nulls":5},{"v":0.41900030165227187,"d":"0.4190"},{"v":0.3874786602030434,"d":"0.3875"},{"v":0.3763981066529637,"d":"0.3764"},{"v":0.3681708715944631,"d":"0.3682"},{"v":0.3674998096717076,"d":"0.3675"},{"v":0.3583672480376317,"d":"0.3584"},{"v":0.36684563097237216,"d":"0.3668"},{"v":0.3571919140714758,"d":"0.3572"}]
[]
["TANH (GAMMA - L) ",{"$nulls":8},"0.590700233929659-2.51178351985523j",{"$nulls":5},"0.17680604696001+2.42614651910643j","5.86545322804706E-002+0.42182859555292j","7.89250758219396E-002-0.428650983218893j","0.590700233929659-2.51178351985523j","0.453141456573003+2.07158892568169j","0.114479119142754+0.332064157135123j","0.118391927458275-0.55094418223036j","1.43429988059536-3.56313529706729j"]
["COMPLEX ANTENNA IMPEDANCE",{"$nulls":8},"69.6688881564534-46.8320745826687j","ohms",{"$nulls":4},"102.783068045062-6.99515865360381j","93.4697832545961-25.9665864517549j","82.560452931279-40.4199553564197j","69.6688881564534-46.8320745826687j","58.3711159876576-48.4556825081543j","46.6280640837782-52.0937066648796j","38.865153090068-50.746165133459j","29.2221521307828-48.2665158525356j","ohms"]
[]
["MAGNITUDE OF REFLECTION COEFFICIENT AT ANTENNA",{"$nulls":8},{"v":0.38550955213081345,"d":"0.3855"},{"$nulls":5},{"v":0.33376619228183835,"d":"0.3338"},{"v":0.34080374463837426,"d":"0.3408"},{"v":0.36481385151778284,"d":"0.3648"},{"v":0.38550955213081345,"d":"0.3855"},{"v":0.41070624611561046,"d":"0.4107"},{"v":0.4625515446360687,"d":"0.4626"},{"v":0.48154532869078803,"d":"0.4815"},{"v":0.5314465401942254,"d":"0.5314"}]
["MAGNITUDE OF REFLECTION COEFFICIENT AT TX. WITH ANTENNA CONNECTED",{"$nulls":8},{"v":0.3299872120869269,"d":"0.3300"},{"$nulls":5},{"v":0.31711905059247397,"d":"0.3171"},{"v":0.3084871272376806,"d":"0.3085"},{"v":0.3192423160694801,"d":"0.3192"},{"v":0.3299872120869269,"d":"0.3300"},{"v":0.34775052013080615,"d":"0.3478"},{"v":0.37617332726122343,"d":"0.3762"},{"v":0.4015422636190529,"d":"0.4015"},{"v":0.4420627986772852,"d":"0.4421"}]
["DITTO BUT REFERENCED TO 50 OHMS",{"$nulls":8},{"v":0.3181853551872658,"d":"0.3182"},{"$nulls":5},{"v":0.3262645642906777,"d":"0.3263"},{"v":0.32825635527894403,"d":"0.3283"},{"v":0.3174134358503671,"d":"0.3174"},{"v":0.3181853551872658,"d":"0.3182"},{"v":0.3418222644756561,"d":"0.3418"},{"v":0.3816540436140128,"d":"0.3817"},{"v":0.4187889727343116,"d":"0.4188"},{"v":0.41178259894523817,"d":"0.4118"}]
[]
[{"$nulls":9},{"v":0.675434628161514,"d":"0.675"},{"v":0,"d":"0.000"},{"$nulls":4},{"v":0.22221797882128694,"d":"0.222"},{"v":0.4327079011158387,"d":"0.433"},{"v":0.5795552541676989,"d":"0.580"},{"v":0.675434628161514,"d":"0.675"},{"v":0.7226932887588473,"d":"0.723"},{"v":0.8977935401019415,"d":"0.898"},{"v":0.7891225470682245,"d":"0.789"},{"v":0.7998204455906271,"d":"0.800"}]
[{"$nulls":9},{"v":0.3077791499895145,"d":"0.308"},{"v":0.4999999999999997,"d":"0.500"},{"$nulls":4},{"v":0.18803069326243044,"d":"0.188"},{"v":0.06369849022044244,"d":"0.064"},{"v":0.43524439386001584,"d":"0.435"},{"v":0.3077791499895145,"d":"0.308"},{"v":0.1807835693888403,"d":"0.181"},{"v":0.05159355754663579,"d":"0.052"},{"v":0.4191272243564687,"d":"0.419"},{"v":0.2880433096229597,"d":"0.288"}]