negative resistance electronics negative resistance property electrical circuits devices increase voltage device results decrease electric current contrast ordinary increase applied voltage causes proportional increase current law resulting positive resistance positive resistance power current passing negative resistance produces power certain conditions increase power electrical signal negative resistance uncommon property occurs electronic components device types resistance defined static absolute resistance ratio voltage current formula differential resistance ratio change voltage resulting change current formula term negative resistance refers negative differential resistance formula general negative differential resistance terminal component converting power applied output power signal applied electronic particularly microwave frequencies microwave energy produced negative differential resistance devices switching memory circuits examples devices negative differential resistance tunnel gas discharge tubes neon lamps addition circuits containing devices positive feedback negative differential resistance active filters negative resistance devices complicated behavior positive usually encountered electric circuits unlike positive negative resistance varies depending voltage current applied device negative resistance devices negative resistance limited portion voltage current range real negative analogous positive constant negative resistance wide range current negative resistance devices electronic components negative differential resistance include devices tunnel mechanism transferred electron mechanism impact mechanism vacuum tubes operating mode tubes microwave vacuum tubes electric gases exhibit negative differential resistance including devices electric arc tubes neon lamp lamp gas discharge tubes addition active circuits negative differential resistance built devices like feedback number new experimental negative differential resistance materials devices discovered recent years physical processes cause negative resistance diverse type device negative resistance characteristics specified current voltage curve definitions resistance electrical device circuit determined current voltage curve characteristic curve giving current formula given voltage formula materials including ordinary positive encountered electrical circuits obey law current proportional voltage wide range curve resistance straight line origin positive slope resistance ratio voltage current slope line voltage formula independent variable constant negative resistance occurs devices component curve straight line obey law resistance defined resistance constant varies voltage current device resistance device defined ways equal static resistance called resistance absolute resistance resistance common definition resistance voltage divided current formula slope line chord origin point curve power source like battery electric generator positive current flows positive voltage terminal opposite direction current passive sign convention formula formula opposite signs representing points lying 2nd 4th quadrant plane right power sources formally negative static resistance formula term practice term resistance applied passive components static resistance determines power dissipation component passive devices consume electric power positive static resistance active devices produce electric power differential resistance called dynamic resistance derivative voltage respect current ratio small change voltage corresponding change current slope curve point formula differential resistance relevant time varying currents points curve slope negative declining right meaning increase voltage causes decrease current negative differential resistance formula devices type signals usually meant term negative resistance negative resistance like positive resistance measured resistance measured resistance type resistance defined corresponding static formula differential formula seen sign corresponding resistance negative resistance negative positive resistance positive operation way different types resistance distinguished directions current electric power circuit electronic component illustrations representing component attached circuit different types work types terminology electronic device differential resistance formula static resistance formula negative categories devices table called negative term negative resistance means negative differential resistance formula negative differential resistance devices unique capabilities act port increasing power time varying signal applied port tuned circuit possible device negative differential resistance power source devices divided categories depending power internal source port passive negative differential resistance devices known type negative passive terminal components curve downward causing current decrease increasing voltage limited range curve including negative resistance region lies 1st 3rd quadrant plane device positive static resistance examples gas discharge tubes tunnel devices power source general work converting external power port time varying power require bias current applied port addition signal add confusion authors active devices category includes terminal devices covered negative differential resistance section active negative differential resistance devices circuits designed positive voltage applied cause proportional negative current current positive terminal opposite ordinary limited range unlike devices downward sloping region curve passes origin lies 2nd 4th plane meaning device sources power devices like positive feedback type negative resistance feedback active filters circuits produce net power port internal power source separate connection external power supply circuit theory called active type referred linear absolute ideal pure negative resistance distinguish passive negative differential electronics simply called positive feedback regeneration covered active section occasionally ordinary power sources referred negative static absolute resistance formula active devices power sources considered negative negative static resistance section ordinary power sources batteries generators non positive feedback positive differential resistance source resistance devices function port capabilities negative differential negative static absolute resistance point confusion ordinary resistance static absolute resistance formula negative electronics term resistance applied passive materials components wires formula shown law formula passive device electric power passive sign convention formula law formula words material conduct electric current better perfect conductor zero resistance passive device formula violate conservation energy second law authors state static resistance negative easily shown ratio voltage current power source negative electric power potential energy flow device circuit charge flow device direction increasing potential energy conventional current positive charge negative positive terminal direction current positive terminal opposite direction current passive device defined passive sign convention current voltage opposite signs ratio negative formula proved law formula shows power flow device circuit formula formula quantity referred resistance negative matter convention absolute resistance power sources negative regarded resistance sense positive negative static resistance power source abstract useful quantity varies load conservation energy simply equal negative static resistance attached circuit right work charges source energy device positive terminal electric field conservation energy requires negative static source power power come internal source converts form energy electric power battery generator separate connection external power supply circuit device like vacuum tube eventual circuit negative static resistance active infinite voltage current range able produce infinite power active circuit device finite power source eventually passive property means large external voltage current applied static resistance positive formula formula maximum power device produce ends curve eventually turn enter 1st 3rd range curve having negative static resistance limited confined region origin example applying voltage generator battery greater open circuit voltage reverse direction current flow making static resistance positive power similarly applying voltage negative greater power supply voltage cause making resistance positive negative differential resistance device circuit negative differential resistance curve current decreases voltage increases formula curve having peaks regions negative slope representing negative differential resistance passive negative differential positive static resistance consume net power curve confined 1st 3rd passes origin requirement means excluding cases region negative resistance limited surrounded regions positive resistance include origin types negative differential classified types voltage controlled negative resistance short circuit stable type type current single valued continuous function voltage voltage function current common type negative resistance region curve shaped generally like letter voltage increased current increases positive resistance reaches maximum decreases region negative resistance minimum increases devices type negative resistance include tunnel current controlled negative resistance open circuit stable type type dual voltage single valued function current current function voltage common type negative resistance region curve shaped like letter devices type negative resistance include electric arc gas discharge tubes like tubes lamps neon lights devices single negative resistance region devices multiple separate negative resistance regions fabricated stable states interest use digital circuits implement logic compare different devices peak valley current ratio ratio current negative resistance region current formula larger larger potential output given bias current greater efficiency negative differential resistance device signal applied signal biased voltage current lie negative resistance region curve tunnel circuit example tunnel voltage controlled negative differential resistance battery formula adds constant voltage bias operates negative resistance range provides power signal suppose negative resistance bias point formula stability formula formula formula voltage output voltage formula voltage gain formula normal voltage resistance branch resistance output voltage input negative resistance total resistance formula resistance formula output voltage formula greater input formula voltage gain formula greater increases limit formula approaches formula explanation power gain illustrate biased negative differential resistance device increase power signal applied principle voltage current device divided bias component formula component formula formula formula positive change voltage formula causes negative change current formula current voltage device phase means equivalent circuit right current flows device direction increasing potential generator power dissipation negative power produced device flows external circuit formula proper external circuit device increase signal power delivered load serving circuit unlike port device signal leaves device port input signal enters passive device power produced comes input bias current device power converted power device applied signal output power limited bias power formula negative differential resistance region include origin able signal applied bias current producing power power input device power heat equal difference power power device phase difference current voltage differ vary frequency long real component negative phase angle device negative resistance maximum output power limited size negative resistance region formula formula reflection reason output signal leave negative resistance port input signal enters transmission line theory voltage current component divided moving waves incident wave formula travels device reflected wave formula travels away device negative differential resistance circuit magnitude reflection formula ratio reflected wave incident wave greater formula formula reflected output signal larger incident device reflection gain reflection determined negative resistance device formula circuit attached formula formula formula formula device smith chart graphical aide widely design high frequency circuits negative differential resistance corresponds points outside unit circle formula boundary conventional chart special expanded charts stability conditions circuit negative differential resistance multiple points possible operating points lie curve point stable circuit neighborhood point poles left half plane point unstable causing circuit converge point poles axis right half plane respectively points determined bias circuit stability determined formula external circuit different shapes curves condition stability different types negative resistance type negative resistance resistance function formula single valued stability determined poles circuit equation formula circuits formula sufficient condition stability total resistance positive formula stable stable load called open circuit stable type negative resistance function formula single valued stability determined poles equation formula reason referred negative circuits sufficient condition stability total circuit positive formula formula stable stable short output called short circuit stable general negative resistance circuits stability determined standard tests like stability criterion alternatively high frequency circuit design values formula circuit stable determined graphical technique stability circles smith chart operating regions applications simple negative resistance devices formula formula different operating regions device illustrated load lines curve load line straight line determined bias circuit equation formula formula bias supply voltage resistance supply possible operating point points occur load line intersects curve stability require low bias formula voltage source require high bias formula current source voltage source series high resistance load line straight line point slope differential resistance formula facing device increasing formula load line circuit operates possible regions depending formula stable region green illustrated line load line lies region intersects curve point circuits stable poles circuit stable negative resistance operate region energy storage device like circuit unstable stable formula stable formula unstable point line formula load line curve total differential resistance circuit zero poles axis unstable tuned circuit linear operate point practical actually start unstable region poles increases eventual negative resistance decreases increasing stabilize formula region red illustrated line region load line intersect curve points center point point unstable poles outer points stable correct circuit converge points switched input pulse switching circuits like flip operate region formula formula active negative resistance feedback addition passive devices negative differential resistance circuits devices like negative resistance ports input output positive feedback applied negative formula input resistance feedback formula gain formula transfer function feedback path input resistance positive feedback formula loop gain formula greater formula negative circuit acts like negative linear limited range curve having straight line segment origin negative slope negative differential resistance active formula law negative value resistance linear range complicated negative resistance curves pass origin called active applying voltage causes proportional current positive terminal opposite ordinary example connecting battery cause battery charge discharge considered port devices circuits function similarly passive negative differential resistance components like port advantages active devices require external bias provide power coupled negative resistance varied adjusting loop gain linear circuit elements voltage proportional current cause distortion curve voltage controlled type current controlled type negative resistance depending feedback loop connected series negative created feedback circuits create active linear circuit elements negative values widely active filters create transfer functions realized positive circuit elements examples circuits type negative resistance negative frequency dependent negative resistance feedback circuit connected input positive feedback like negative differential input resistance formula cancel positive loss resistance formula inherent tuned circuit formula create effect tuned circuit zero resistance poles axis spontaneous excited tuned circuit frequency sustained power feedback work negative resistance model alternate way analyzing feedback operation linear circuits negative resistance feedback tuned circuit integral feedback network circuit negative resistance frequencies near frequency tuned circuit connected negative resistance parasitic loss resistance formula negative resistance decrease circuit moving poles axis increasing factor narrower called regeneration radio receiver invented later widely active filters example integrated circuits use integrated save space consisting spiral conductor fabricated chip high losses low create high tuned circuits increased applying negative resistance chaotic circuits circuits exhibit chaotic behavior considered quasi periodic like require negative resistance circuit provide power circuit simple circuit widely standard example chaotic system requires active component called usually synthesized negative circuit negative common example active resistance circuit negative shown formula constitute negative feedback non gain output voltage formula voltage formula applied input voltage applied backwards formula causing current flow input current formula input circuit formula circuit converts formula negative formula value formula linear range formula input acts like linear negative value formula input port circuit connected circuit component cancel positive resistance circuit example originally developed cancel resistance telephone cables serving negative replacing formula circuit formula formula negative synthesized negative relation formula formula formula applying positive current negative cause discharge voltage decrease similarly negative characteristic formula formula circuit having negative cancel unwanted positive circuit circuits cancel telephone cables way looking negative current opposite phase current positive instead leading voltage voltage negative acts like reverse dependence frequency decreasing instead increasing like real similarly negative acts like increases frequency negative non foster circuits violate foster application researched create active matching network match antenna transmission line broad range frequencies single frequency current networks allow creation small compact broad exceeding limit negative differential resistance devices widely electronic negative resistance negative differential resistance device microwave vacuum tube connected electrical circuit crystal cavity source bias device negative resistance region provide power circuit store electrical energy internal resistance losses decay zero negative resistance positive resistance creating effect spontaneous continuous occur frequency uses negative resistance mainly high frequencies microwave range feedback function poorly frequencies microwave medium power applications radar speed guns local satellite receivers widely source microwave energy virtually solid state source millimeter wave energy negative resistance microwave vacuum tubes produce higher power applications radar microwave lower frequency gas discharge lamps neon lamps negative resistance model limited port devices like applied feedback circuits port devices tubes addition modern high frequency increasingly port negative resistance devices like microwave frequencies certain loads applied port unstable internal feedback negative resistance port high frequency designed applying load port negative resistance connecting port negative resistance described common circuit illustrates negative resistance work voltage controlled type negative resistance voltage source formula negative resistance region differential resistance formula choke prevents current flowing bias source formula equivalent resistance losses series tuned circuit formula plus load resistance analyzing circuit voltage law gives differential equation formula current formula solving equation gives solution form formula formula shows current circuit formula varies time point formula started initial current formula current frequency tuned circuit constant increasing decreasing depending value circuit sustain steady depends balance formula formula positive negative resistance circuit formula poles left half plane negative resistance positive resistance tuned circuit positive circuit lose energy heat resistance formula die away zero ordinary tuned circuit circuit formula poles axis positive negative equal net resistance zero zero adds energy compensate energy lost tuned circuit load circuit started continue constant condition steady state operation formula poles right half plane negative resistance greater positive resistance negative grow energy condition practical designed region net negative resistance started widely rule thumb formula power turned electrical noise circuit provides signal formula start spontaneous grow grow forever eventually limits large circuit linear analysis strictly apply differential resistance circuit understood considering formula average resistance cycle wave exceeds width negative resistance region voltage swing extends regions curve positive differential resistance average negative differential resistance formula smaller total resistance formula formula negative eventually turns positive stabilize zero formula negative resistance range formula close formula small allow start voltage swing limited linear portion curve output nearly frequency stable circuits formula far formula swing extends curve distortion output wave severe frequency increasingly dependent supply voltage types circuit negative resistance circuits divided types types negative differential resistance voltage controlled current controlled negative resistance voltage controlled type devices require low bias stable load ideal circuit device form shown right voltage source bias device negative resistance region parallel circuit load circuit high frequency circuit unstable frequency negative current controlled type devices contrast require high bias stable load greater ideal circuit like right current source bias consist voltage source series large series circuit series circuit low frequency conditions complicated example active device load resistance modern negative resistance designed frequency domain technique circuit imagined divided reference plane red separates negative resistance active device positive resistance circuit output load right complex negative resistance formula depends frequency general declining current formula linear depending frequency circuit equation formula frequency total formula zero means magnitude negative positive equal formula formula steady state equal sign applies inequality applies circuit excess negative resistance start alternately condition expressed reflection voltage reference plane divided component travelling negative resistance device component travelling opposite direction reflection active device formula greater formula operation waves reflected forth round trip circuit formula equality gives condition steady inequality required provide excess negative resistance conditions analogous criterion feedback necessary sufficient circuits satisfy derived complicated sufficient conditions instead negative differential resistance devices particularly microwave frequencies commonly negative resistance devices port unlike port devices outgoing signal leave device incoming signal enters way separating signals negative resistance directions suffers sensitivity load feedback problems separate input output signals negative resistance use devices directional reflection widely circuit reflection separation accomplished solid state component ports transfers signal applied port direction port port reflection input signal applied port biased negative resistance attached filter port output circuit attached port input signal passed port port outgoing reflected signal routed port little output input characteristic formula input output transmission lines usually matched port purpose filter present correct set gain radio frequencies pure loads second purpose filter cancel prevent standing waves filter components absorb power power passed ports loss input signal power formula output power formula power gain formula square reflection formula formula formula formula negative resistance assuming filter matched formula gain formula reflection stable formula stable formula seen reflection unlimited gain approaching infinity formula approaches point formula characteristic contrasting behavior port generally limited gain stable practice gain limited backward ports extremely low noise implemented reflection applications like radio switching circuits negative differential resistance devices switching circuits device operates changing abruptly state advantage negative resistance device flip flop memory cell built single active device standard logic circuit functions requires active devices switching circuits built negative circuit unstable states output periodically switches forth states time remains state determined time constant circuit produce square waves triangle waves circuit unstable state stable state stable state pulse applied input output switches state remains period time dependent time constant circuit switches stable state delay element flip flop circuit stable states pulse input switches circuit state memory circuits digital applications models instances display regions negative slope voltage clamp experiments negative resistance implied consider typical style circuit model history negative resistance recognized investigations electric arcs lighting 19th century observed voltage arc decreased temporarily arc current increased researchers thought secondary effect temperature term negative resistance applied effect term controversial known resistance passive device negative beginning extending husband william research series meticulous experiments measuring curve arcs established arcs negative resistance controversy support introduced concept differential resistance slowly accepted arcs negative differential resistance recognition research woman voted induction arc realized resistance circuit zero negative produce continuous year built negative resistance connecting circuit arc example electronic student brought arc public attention negative resistance current arc unstable arc lights produce noises investigating effect connected circuit arc negative resistance excited tuned circuit producing musical tone arc demonstrate invention wired tuned circuits arc played tune singing arc limited audio frequencies danish engineers increased frequency radio range operating arc hydrogen atmosphere magnetic field arc radio widely 1920s vacuum tubes early 20th century physical causes negative resistance understood engineers knew generate begun apply showed negative resistance discovered mercury lamps produce build telephone lines discovered vacuum tubes negative resistance parts operating ranges phenomenon called secondary vacuum tube strike plate knock additional surface tube represents current away plate reducing plate current certain conditions increasing plate voltage causes decrease plate current connecting circuit tube hull created negative resistance tube followed invented hull negative originated work report negative decade later vacuum tube developed telephone line telephone service possible pioneered initiated great increase interest new circuits applications developed solid state devices negative differential resistance observed point contact junction called cat researchers noticed junctions biased voltage improve sensitivity radio break spontaneous effect pursued person exploit negative resistance practically russian radio researcher discovered negative differential resistance biased point contact junctions build solid state radio receivers years invention later built receiver achievements overlooked success vacuum tube technology years abandoned research technology dubbed forgotten widely solid state negative resistance device tunnel invented japanese physicist lower parasitic vacuum tubes small junction size function higher frequencies tunnel proved able produce power microwave frequencies range ordinary vacuum tube invention set search negative resistance devices use microwave resulting discovery derived conditions stability negative resistance circuits currently negative differential resistance widely sources microwave energy new negative resistance devices discovered recent decades
Negative resistance