1. 我们都知道, 在场地受限的条件下架设天线最方便的方法之一是从窗口拉一根长线出来, 拴到对面的树上, 然后在地面上或者外墙上拉若干条工作频率四分之一波长长度的地网, 和良好的地线拧在一起, 用长线天线调谐器调谐. 下面我们将计算这种型式的长线天线的优选长度.

2. 首先给出结果: 长线天线的优选长度为43.6±0.5m(用于工作在最低到1.8MHz)和22.6±1m(用于工作在最低到3.5MHz).

3. 网上广泛流传的一个数据是工作在最低到3.5MHz的长线天线的优选长度为22.55m. 使用该结果转换成英制(74英尺)搜索, 搜得如下网站: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX/technote/XXXXXXXXXXXm

4. 从上述网站知, 长线天线的优化原则有二:
4.1 整条线的长度长于要工作的最低频率的四分之一波长(否则工作效率低);
4.2 线长尽可能避开业余频段的二分之一波长及其整数倍(在二分之一波长及其整数倍时天线阻抗高, 天线调谐器不好匹配).

5. 上述网站给出了优化所用程序, 但优化所用业余频段为第二区的频率规划, 给出的最终结果为英制, 并且没有给出公差. 将程序修改为第三区的频率规划(1.8-2, 3.5-3.9, 7-7.2, 10.1-10.15, 14-14.35, 18.068-18.168, 21-21.45, 24.89-24.99, 28-29.7MHz)、使用公制并输出长度和频率极值, 两优选长度的计算结果如下:

Gap = 58 kHz at 1.72083497047424 MHz (43.5533420656143 meters)
    minf= 1.69166994094849 , maxf= 1.75
    maxmeters= 44.3042173671469 , minmeters= 42.8274945105608

Gap = 376 kHz at 3.31187510490417 MHz (22.6301159897283 meters)
    minf= 3.12374997138977 , maxf= 3.5
    maxmeters= 23.9929941235635 , minmeters= 21.4137472552804

留出一定安全系数, 不妨定两优选长度为43.6±0.5m和22.6±1m.

6. 这一长度指的是从天线调谐器的接线端子到天线另一端的理想长度, 使用时应根据实际情况调整(在实际的架设和接地条件下让天线的四分之一波长自然谐振频率尽可能接近1.72或3.31MHz).

附修改过的程序如下:
'[s:9]rogram XXXXXXXXXXXS calculates the quarter-wave lengths for random wire antennas
'avoid even multiples of half wavelength in any of the HF amateur radio bands
'(c) J. C. Sprott (XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX/)
'Compile with the PowerBASIC console compiler 6.03

#COMPILE EXE

DEFEXT a-z

FUNCTION PBMAIN () AS LONG
    CLS
    fmax=30                         'Maximum frequency to consider (MHz)
    xmax&=1e5*fmax                  'Number of frequencies to consider (every 10 Hz)
    FOR i&=1 TO xmax&
        f=i&*fmax/xmax&             'This is the quarter wavelength frequency
        hmax&=fmax/f                'This is the highest harmonic allowed
        bad&=0
        FOR h&=2 TO hmax& STEP 2    'Consider only even harmonics of a quarter wave
            fh=h&*f                 'This is the harmonic fequency of a quarter wave
            IF fh>=1.8 AND fh<=2 THEN bad&=1
            IF fh>=3.5 AND fh<=3.9 THEN bad&=1
            IF fh>=7 AND fh<=7.2 THEN bad&=1
            IF fh>=10.1 AND fh<=10.15 THEN bad&=1
            IF fh>=14 AND fh<=14.35 THEN bad&=1
            IF fh>=18.068 AND fh<=18.168 THEN bad&=1
            IF fh>=21 AND fh<=21.45 THEN bad&=1
            IF fh>=24.89 AND fh<=24.99 THEN bad&=1
            IF fh>=28 AND fh<=29.7 THEN bad&=1
        NEXT h&
        IF bad&=0 THEN INCR gap&    'This frequency is in an acceptable gap
        IF bad&=1 AND gap&>0 THEN   'This is the end of that gap
            fm=f-0.5##*gap&*fmax/xmax& 'This is the midpoint of the gap
            khz&=2000*(f-fm)        'This is the width of the gap
            feet=0.25*983.571056/fm
            meters=feet*0.3048
            maxmeters=0.3048*0.25*983.571056/(fm-(f-fm))
            minmeters=0.3048*0.25*983.571056/(f)
            PRINT"Gap =";khz&;"kHz at";CSNG(fm);"MHz (";LTRIM$(STR$(meters));" meters)"
            PRINT "    minf="; CSNG(fm-(f-fm));", maxf="; CSNG(f)
            PRINT "    maxmeters="; maxmeters; ", minmeters=" ; minmeters
            gap&=0                  'Start looking for a new gap
        END IF
    NEXT i&
    WAITKEY$
END FUNCTION

计算结果如下:
Gap = 1 kHz at .874265015125275 MHz (85.7269997008703 meters)
    minf= .873529970645904 , maxf= .875
    maxmeters= 85.799131562146 , minmeters= 85.6549890211216
Gap = 4 kHz at 1.07472002506256 MHz (69.7373412549142 meters)
    minf= 1.07251000404358 , maxf= 1.07693004608154
    maxmeters= 69.8810411030959 , minmeters= 69.5942311881751
Gap = 24 kHz at 1.15448999404907 MHz (64.9188086457928 meters)
    minf= 1.1423100233078 , maxf= 1.16666996479034
    maxmeters= 65.6110122414068 , minmeters= 64.2410582199605
Gap = 7 kHz at 1.24100494384766 MHz (60.3930809251223 meters)
    minf= 1.23750996589661 , maxf= 1.244500041008
    maxmeters= 60.5636442481122 , minmeters= 60.2234756074579
Gap = 13 kHz at 1.25600504875183 MHz (59.6718288489945 meters)
    minf= 1.24950003623962 , maxf= 1.26250994205475
    maxmeters= 59.9824853089087 , minmeters= 59.3643736631642
Gap = 4 kHz at 1.27074003219604 MHz (58.9798978496635 meters)
    minf= 1.26874995231628 , maxf= 1.27272999286652
    maxmeters= 59.0724062214632 , minmeters= 58.887678764138
Gap = 33 kHz at 1.36639499664307 MHz (54.8509877403543 meters)
    minf= 1.35001003742218 , maxf= 1.38277995586395
    maxmeters= 55.5167112787915 , minmeters= 54.2010409417849
Gap = 12 kHz at 1.39417004585266 MHz (53.7582327789878 meters)
    minf= 1.38833999633789 , maxf= 1.39999997615814
    maxmeters= 53.9839775512348 , minmeters= 53.534368138201
Gap = 15 kHz at 1.49250495433807 MHz (50.2163244970579 meters)
    minf= 1.48501002788544 , maxf= 1.5
    maxmeters= 50.4697715123005 , minmeters= 49.9654102623209
Gap = 23 kHz at 1.54385495185852 MHz (48.5460845697824 meters)
    minf= 1.53215003013611 , maxf= 1.55555999279022
    maxmeters= 48.9169568211215 , minmeters= 48.1807936649704
Gap = 33 kHz at 1.6666749715805 MHz (44.9686443928668 meters)
    minf= 1.65000998973846 , maxf= 1.68333995342255
    maxmeters= 45.4228249486254 , minmeters= 44.5234565764975
Gap = 58 kHz at 1.72083497047424 MHz (43.5533420656143 meters)
    minf= 1.69166994094849 , maxf= 1.75
    maxmeters= 44.3042173671469 , minmeters= 42.8274945105608
Gap = 50 kHz at 1.97500503063202 MHz (37.9483167857708 meters)
    minf= 1.95000994205475 , maxf= 2
    maxmeters= 38.4347338698168 , minmeters= 37.4740576967407
Gap = 114 kHz at 2.20176005363464 MHz (34.0400931043717 meters)
    minf= 2.14500999450684 , maxf= 2.25851011276245
    maxmeters= 34.9406834436582 , minmeters= 33.184761366335
Gap = 62 kHz at 2.30217003822327 MHz (32.5554217948637 meters)
    minf= 2.27099990844726 , maxf= 2.33333992958069
    maxmeters= 33.0022524850204 , minmeters= 32.1205291099803
Gap = 14 kHz at 2.48200488090515 MHz (30.1966012935032 meters)
    minf= 2.47500991821289 , maxf= 2.48900008201599
    maxmeters= 30.2819444743582 , minmeters= 30.111737803729
Gap = 26 kHz at 2.5120050907135 MHz (29.8359738111514 meters)
    minf= 2.49900007247925 , maxf= 2.52501010894775
    maxmeters= 29.9912426544543 , minmeters= 29.6823043843317
Gap = 88 kHz at 2.58124995231628 MHz (29.0355894986853 meters)
    minf= 2.53749990463257 , maxf= 2.625
    maxmeters= 29.5362031107316 , minmeters= 28.5516630070405
Gap = 119 kHz at 2.74062991142273 MHz (27.3470389631148 meters)
    minf= 2.68126010894775 , maxf= 2.79999995231628
    maxmeters= 27.95257281781 , minmeters= 26.7671840691005
Gap = 41 kHz at 2.99067497253418 MHz (25.0606018351982 meters)
    minf= 2.97001004219055 , maxf= 3.01133990287781
    maxmeters= 25.2349707218095 , minmeters= 24.8886261244102
Gap = 83 kHz at 3.06962490081787 MHz (24.416049319862 meters)
    minf= 3.02800011634827 , maxf= 3.11124992370605
    maxmeters= 24.7516893637653 , minmeters= 24.0893902429832
Gap = 376 kHz at 3.31187510490417 MHz (22.6301159897283 meters)
    minf= 3.12374997138977 , maxf= 3.5
    maxmeters= 23.9929941235635 , minmeters= 21.4137472552804
Gap = 436 kHz at 3.93042492866516 MHz (19.0687051383709 meters)
    minf= 3.71251010894775 , maxf= 4.14834022521973
    maxmeters= 20.187990172008 , minmeters= 18.0670136472616
Gap = 352 kHz at 4.34100484848022 MHz (17.2651529757467 meters)
    minf= 4.16499996185303 , maxf= 4.51701021194458
    maxmeters= 17.9947455926726 , minmeters= 16.5924174162734
Gap = 125 kHz at 4.60433483123779 MHz (16.2777285739377 meters)
    minf= 4.54199981689453 , maxf= 4.66666984558105
    maxmeters= 16.5011262425102 , minmeters= 16.0602989698182
Gap = 100 kHz at 5.00001001358032 MHz (14.9895930995101 meters)
    minf= 4.95000982284546 , maxf= 5.05001020431518
    maxmeters= 15.14100282494 , minmeters= 14.8411815805278
Gap = 175 kHz at 5.16249990463257 MHz (14.5177947493426 meters)
    minf= 5.07499980926514 , maxf= 5.25
    maxmeters= 14.7681015553658 , minmeters= 14.2758315035203
Gap = 860 kHz at 5.79250478744507 MHz (12.9388089252372 meters)
    minf= 5.36251020431518 , maxf= 6.22249984741211
    maxmeters= 13.9763124718614 , minmeters= 12.0446951214916
Gap = 752 kHz at 6.62375020980835 MHz (11.3150579948641 meters)
    minf= 6.24749994277954 , maxf= 7
    maxmeters= 11.9964970617817 , minmeters= 10.7068736276402
Gap = 1609 kHz at 8.22951030731201 MHz (9.10723911794036 meters)
    minf= 7.42501020431518 , maxf= 9.03400993347168
    maxmeters= 10.0940086805919 , minmeters= 8.29621789144371
Gap = 1416 kHz at 9.79199981689453 MHz (7.65401505243886 meters)
    minf= 9.08399963378906 , maxf= 10.5
    maxmeters= 8.2505631212551 , minmeters= 7.13791575176013
Gap = 1720 kHz at 11.5850048065186 MHz (6.46940725476436 meters)
    minf= 10.7250099182129 , maxf= 12.4449996948242
    maxmeters= 6.988162751688 , minmeters= 6.02234756074579
Gap = 1505 kHz at 13.2475004196167 MHz (5.65752899743207 meters)
    minf= 12.4949998855591 , maxf= 14
    maxmeters= 5.99824853089087 , minmeters= 5.3534368138201