MATH’S NOTES
BY IRWIN MATH,* WA2NDM
I
QRXU0DUFKFROXPQZHGLVFXVVHG
WKHGHWDLOVRIWKHW\SLFDOFLUFXLWU\FRP
PRQO\XVHGWRGHOLYHU$&SRZHUWR
RXUKRPHV7KLVPRQWKZHZRXOGOLNH
WR IROORZ XS E\ GLVFXVVLQJ ZD\V WR
DVVXUHWKDWWKLVSRZHULVFRQQHFWHGWR
RXURXWOHWVSURSHUO\DQGVDIHO\
7REHJLQZLWKZHDOOSOXJRXUDSSOL
DQFHV DQG DPDWHXU JHDU LQWR WR WKH
QHDUHVWKDQG\$&OLQHRXWOHWDWRQHWLPH
RUDQRWKHU:HDOVRXVHDOOW\SHVRIOLQH
FRUGV H[WHQVLRQV DQG KRPHPDGH
MXPSHUFDEOHVDVZHOO RUDWOHDVWVRPH
RIXVGR 6RZHWKRXJKWWKLVZRXOGEH
DJRRGWLPHWRRIIHUDFRXSOHRILGHDV
WKDWPD\FRPHLQKDQG\
$V\RXPRVWOLNHO\NQRZPRVW³SURS
HU ́OLQHFRUGVQRZDGD\VFRQWDLQWKUHH
ZLUHV2QHLVFRQQHFWHGWRWKHKLJKVLGH
RIWKH$&OLQHWKHVRFDOOHG³KRW ́VLGH
WKHVHFRQGLVFRQQHFWHGWRWKHQHXWUDO
RU³$&ORZ ́VLGHDQGWKHUHPDLQLQJ
ZLUHLVDJURXQGFRQQHFWLRQWKDWLVQRW
LQWHQGHGWRFRQGXFWDQ\SRZHUEXWLV
WKHUHIRUVDIHW\UHDVRQV)RUWKHEHVW
DQGVDIHVW FRQQHFWLRQVDOORIWKHVH
PXVWJRWRWKHSURSHUSRLQWV)LJXUH
VKRZV D FRPPRQ 1RUWK $PHULFDQ
86$ $&RXWOHWZLWKWKHSURSHUFRQ
QHFWLRQSRLQWVODEHOHG<RXZLOOQRWH
WKDWWKH³KRW³RSHQLQJLQWKHFRQQHFWRU
LVVPDOOHUWKDQWKHQHXWUDORSHQLQJDQG
LVFRPSOHWHO\GLIIHUHQWIURPWKHJURXQG
FRQQHFWLRQ)RUPRVWDSSOLDQFHVDPD
WHXU UDGLR HTXLSPHQW LQFOXGHG LW LV
LPSRUWDQWWKDWWKHSURSHUOHDGJRWRWKH
SURSHUSODFHVLQWKHHTXLSPHQW7KH
JURXQGZLUHLVXVHGWRDVVXUHWKDWLIDQ\
SUREOHPRFFXUVZLWKLQWKHHTXLSPHQW
VXFKDVWKHKRWOHDGDFFLGHQWDOO\FRP
LQJLQFRQWDFWZLWKDQ\PHWDOSRUWLRQRI
WKHHTXLSPHQWVXFKDVDIURQWSDQHOWKH
XVHU ZLOO QRW JHW D VHULRXV HOHFWULFDO
VKRFN 8QIRUWXQDWHO\ PDQ\ RXWOHWV
DQG RFFDVLRQDOO\ SRZHU FRUGV DUH
ZLUHGEDFNZDUGVZLWKWKHKRWDQGQHX
WUDOOHDGVUHYHUVHGDQGLQVRPHFDVHV
ZLWKQRVDIHW\JURXQGFRQQHFWLRQDWDOO
7KLVLVLQYLWLQJDSUREOHPDQGWKHVLP
SOHGHYLFHVKRZQLQ)LJXUHFDQGHWHFW
DQ\SUREOHPZLWKWKLVZLULQJ
$VLPLODUGHYLFHZDVDQGSUREDEO\
VWLOOLVDYDLODEOHFRPPHUFLDOO\EXWDOVR
TXLWHHDV\WRFRQVWUXFW1RWHWKDWWKLV
YHUVLRQLVEDVHGRQD GHVLJQDQG
FDQEHHDVLO\EXLOWE\DQ\RQHZLWKD
IHZ1(QHRQODPSVDQGDVOLJKWELW
RI LQFHQWLYH <RX PLJKW FRQVLGHU
PRXQWLQJDOOFRPSRQHQWVLQDVPDOO
SODVWLFER[FHPHQWHGWRDSLQSOXJWR
PDNH D QHDW SRUWDEOH RXWOHW WHVWHU
.HHSLQPLQGWKDWLQWKH³ROGGD\V ́
PRVWKDPVEXLOWWKLQJVIDUPRUHFRP
SOH[WKDQWKLVVRZK\VXSSRUWVRPH
IRUHLJQFRPSDQ\ZLWKDFKHDSNQRFN
RIIZKHQ\RXFDQGRWKHVDPHDQG
KDYHWKHSOHDVXUHRINQRZLQJWKDW\RX
³GLGLW\RXUVHOI" ́,WZLOOFRQQHFWZLWKD
OLYH$&OLQHVREHYHU\FDUHIXOEXLOGLQJ
LW0DNHFHUWDLQ\RXFDQQRWFRPHLQ
FRQWDFWZLWKDQ\SRLQWWKDWFRXOGFRPH
LQFRQWDFWZLWKWKH$&OLQH
,I\RXORRNDW)LJXUH\RXZLOODOVR
VHHDFKDUWWKDWVKRZVZKDWODPSOLJKWV
LQYDULRXVFRQGLWLRQV7KHROGYHUVLRQ
XVHGQHRQODPSVWKDWFRQWDLQHGLQWHU
QDOUHVLVWRUVEXWWKLVYHUVLRQXVHVXOWUD
AC Line Detection
FR&4PDJD]LQH
)LJXUH6WDQGDUG86 $& /LQH2XWOHW
$& /RZ
2U
1HXWUDO
$& +LJK
2U
³+RW ́
3URWHFWLYH
*URXQG
)LJXUH6FKHPDWLF'LDJUDPRIDQ³2OG)DVKLRQHG ́2XWOHW7HVWHU
$V\RXPRVWOLNHO\NQRZPRVW
³SURSHU ́OLQHFRUGVQRZDGD\V
FRQWDLQWKUHHZLUHV
&4$XJXVW 9LVLW2XU:HE6LWH