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Diode detectors for RF measurementPart 1: Rectifier circuits, theory and calculation procedures.

By David W Knight1

Version 0 (provisional) revision 08, 18th Oct. 201.! D. W. Knight, 200"#2008. 201$#201.%lease chec& the a'thors e*site to +a&e s're yo' have the +ost recent version o this doc'+ent and its acco+panyingiles- http-.g$ynh.ino .

/hanges since version 0.0- li+inated perect deco'pling capacitors ro+ e'ivalent circ'its (red'ndant, con'sing).3dded section 4.1 # te+perat're dependence o 5S . 6ection 1.2 # series#parallel to series transor+ation, general or+ith +acros. 6ection 1.$ # sh'nt diode rectiier ith parasitics. 6ection 1" # content added. %ro*le+s ith n'+ericalinsta*ility still 'nresolved.

Abstract7his article addresses the s'*ect o 9: signal detection ro+ the point o vie o those ho designand cali*rate i+pedance +atching *ridges and other +eas'ring instr'+ents operating in the ;: andV;: radio ranges. 7he principal disc'ssion relates to the si+ple diode peadetector< and coversthe dierent possi*le circ'it conig'rations, the associated theory, and the n'+erical +ethodsneeded or data analysis. /irc'it techni'es 'sed to linearise the diode detector o'tp't aredisc'ssed in a separate doc'+ent (Part 2).

3nalysis o the detector transer characteristic or sin'soidal inp't shos that the 3/#ind'cederror ter+ involves the =ero#order +odiied Bessel 'nction o the irst &ind (5 0). 7his res'lt is not

ne, *'t it is oten disregarded. 7he dyna+ic contri*'tion is 'ite 'nli&e the error that occ'rs orD/ inp't, regardless o any co+pensatory +odiication o circ'it para+eters< hich +eans thatlinearity correction sche+es 'sing a reerence diode to prod'ce a D/ a+pliier ith aco+ple+entary gain la can never *e perect. 5t is also shon hoever, that the 3/ error isindependent o re'ency provided that the s+oothing capacitor is large. 7his +eans that thetrac&ing detector syste+, hich involves a'to+atic sel#cali*ration against a lo#re'ency

 precision rectiier, is theoretically so'nd.  By considering the poer dissipated in the detector, it is shon that the inp't i+pedance can *ecalc'lated 'sing irst and =ero#order +odiied Bessel 'nctions o the irst &ind (5 0 and 51). 7hisallos the deter+ination o detector transer#'nctions that ta&e so'rce i+pedance into acco'nt.When this acility is co+*ined ith the a*ility to calc'late the dyna+ic co+ponent o the pea&

detection error, a +eas're+ent o D/ o'tp't ta&en ith a cali*rated volt+eter can *e converted intoa +eas're+ent o 3/ inp't itho't the need or an 3/ reerence. 7he co+p'tation proced'resre'ired are not si+ple, *'t they are descri*ed in detail and given as Basic algorith+s readilyadapta*le to any progra++ing environ+ent.

1 Ottery 6t >ary, Devon, ngland. http-.g$ynh.ino

http://www.g3ynh.info/http://www.g3ynh.info/http://www.g3ynh.info/

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Diode detectors for RF measurementPart 1: Rectifier circuits, theory and calculation procedures.

Table of Contents3*stract.................................................................................................................................................15ntrod'ction..........................................................................................................................................1. ;al#ave rectiier ..........................................................................................................................4

1.1 /irc'it *ehavio'r and *asic design principles .........................................................................41.2 Diode pea& inverse voltage ......................................................................................................81.$ 5np't cho&es .............................................................................................................................81. ?arge signal inp't i+pedance ..................................................................................................@1." 6eparation o port resistance and so'rce i+pedance .............................................................111.4 3ct'al inp't voltage ...............................................................................................................12

1. 5nd'ctively loaded 3> detector.............................................................................................1$2. 6h'nt#diode rectiier .....................................................................................................................12.1 6a+pling loating voltages .....................................................................................................14

$. Voltage#do'*ler rectiier ...............................................................................................................18$.1 Do'*ler inp't i+pedance .......................................................................................................1@

. Bridge rectiier ..............................................................................................................................20". Bi#phase rectiier ..........................................................................................................................24. Diode static voltage vs. c'rrent characteristic ..............................................................................24

4.1 Variation o sat'ra*le lea&age c'rrent ith te+perat're........................................................24.$ Diode +eas're+ents...............................................................................................................2@

. 6ignal diode data ..........................................................................................................................$18. Diode circ'it +odel ......................................................................................................................$$

8.1 Diode stac&ing .......................................................................................................................$$@. Bac& diodes ..................................................................................................................................$10. Vac''+ ther+ionic diodes .........................................................................................................$"11. 3 *rie history o diode detectors ................................................................................................$412. 6i+ple diode volt+eter dyna+ic characteristics ........................................................................1

12.1 3/#D/ 7ranser 'nction .....................................................................................................112.2 %ea& to average c'rrent ratio ..............................................................................................."012.$ Detector poer dissipation and inp't i+pedance ................................................................"212. Diode poer dissipation ......................................................................................................""

12." :ast 'nrestricted co+p'tation o inp't i+pedance .............................................................."812.4 Asing diode dyna+ic resistance to esti+ate inp't i+pedance ............................................"@1$. /alc'lation proced'res or the si+ple diode volt+eter .............................................................41

1$.1 >odiied Bessel 'nction, irst &ind, =ero order ..................................................................411$.2 %olyno+ial 'sed in the asy+ptotic or+, irst &ind, =ero order ..........................................4$1$.$ Deter+ining o'tp't voltage ro+ pea& inp't voltage ..........................................................41$. Deter+ining pea& inp't voltage ro+ o'tp't voltage ..........................................................41$." Derivative o the asy+ptotic or+ polyno+ial, irst &ind, =ero order .................................01$.4 5nverse +odiied Bessel 'nction, irst &ind, =ero order ......................................................11$. >odiied Bessel 'nction, irst &ind, irst order ..................................................................$1$.8 %olyno+ial 'sed in the asy+ptotic or+ , irst &ind, irst order ..........................................

1$.@ 9atio o +odiied Bessel 'nctions, irst order =ero order ................................................"1$.10 Deter+ining o'tp't voltage ro+ so'rce o#load voltage ................................................41$.11 Deter+ining so'rce o#load voltage ro+ o'tp't voltage .................................................@

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1. eneralised hal#ave detector +odel .......................................................................................801.1 6eries diode rectiier ith port resistance and parasitics .....................................................801.2 6eries#parallel to series transor+ation ................................................................................@01.$ 6h'nt diode rectiier ith port i+pedance and parasitics ....................................................@2

1". Detector ith diode series resistance .........................................................................................@"1".1 5nstantaneo's diode c'rrent .................................................................................................@41".2 3verage diode c'rrent *y n'+erical integration ..................................................................@81".$ O'tp't voltage ro+ pea& inp't voltage ............................................................................10"1". /o+parison o n'+erical integration and transor+ation +ethods ..................................101".C %ea& inp't voltage ro+ o'tp't voltage .............................................................................108

@@. Wor& in progress ......................................................................................................................110

Note on detector modelling routines

7he progra+ ro'tines given in the teCt are availa*le ro+ the acco+panying spreadsheet ile-detmodels.ods. 7o access, edit or copy the code, open the ile 'sing 3pache Open Oice2 andselect the top +en' ite+- 7ools >acros Organise >acros OpenOice Basic . 7hen navigate tothe li*rary det+odels.ods 6tandard detector'ncs .

6ee the OO Basic 'ide$ or a description o the progra++ing lang'age. 7he 6tarOice Basic progra++ing g'ide can also provide 'se'l additional detail *eca'se it relates to the lang'age ro+hich OO Basic evolved.

!c"no#ledgements

2 http-.openoice.org$ https-i&i.openoice.orgi&iDoc'+entationB365/'ide http-e*.+it.ed'soicev8.0pddocstaroice#B365/.pd 

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Introduction7he diode detector inds idespread 'se as a high#re'ency volt+eter< its principal advantage,apart ro+ the si+plicity o the circ'it, *eing the a*ility to provide a *andidth o several h'ndred>;= ith +ini+al attention to physical layo't. 7his property +eans that detectors can *e

connected directly to the o'tp't ports o *ridges and other +eas'ring devices, there*y eli+inatingthe need or don conversion or high#speed sa+pling. 7he essential preconditions are that thesignal a+plit'de sho'ld *e tailored to lie so+ehere in the range ro+ a*o't 0.1 V to 10 V 9>6,and that the so'rce netor& sho'ld have a +oderate load#driving capa*ility.

7he diic'lty ith the diode detector hoever, is that there is a *ig dierence *eteen 'sing itto +a&e a cr'de 9: level indicator, and 'sing it to +a&e an acc'rate +eas'ring instr'+ent. 7his is

 pri+arily *eca'se the circ'it *ehaves in an eCtre+ely non#linear +anner or s+all signals and *eco+es only approCi+ately linear as the signal voltage approaches the point at hich the diodeill *e destroyed. /orrection is not straightorard, and idely#'sed linearisation sche+esinvolving a D/ a+pliier ith a co+ple+entary gain la are not co+pletely s'ccess'l *eca'se the

 *ehavio'r 'nder 3/ eCcitation is not the sa+e as 'nder static conditions. 7he +atter o t'rning thediode detector into an acc'rate *road*and volt+eter is nevertheless ell orth p'rs'ing< not least

 *eca'se the perect sol'tion, an active rectiier or s'perdiode circ'it, is typically restricted to an'pper re'ency li+it o a*o't "0 &;=.  5n this article, e ill consider the diode detector on to ays- irstly, as a +eas'ring device inits on right< and secondly, as a circ'it +od'le or incl'sion in +ore ela*orate instr'+ents. 5n thelatter case, e ill ass'+e that the i+ple+entation involves linearisation (or so+e other re#+apping) o the rectiied o'tp't, 'sing either digital or analog'e +ethods. 5t is, o co'rse, o*vio'sthat any correction process is dependent on a detailed &noledge o detector *ehavio'r, and so theirst part o the st'dy is a necessary prec'rsor to the second.  7he archetypical diode detector is a hal#ave rectiier, either driven *y a transor+er, or having

an 9: cho&e as a D/ short#circ'it across its inp't. 7his can *e analysed on the *asis that he cho&eor transor+er is perect, and res'lts in the principal +athe+atical relationship that governs thedetectors dyna+ic *ehavio'r. 7he sol'tion (involving the +odiied Bessel 'nction o the irst &indin =ero order), altho'gh +entioned in the acade+ic literat're, is evidently 'na+iliar to the +aorityo co++entators. 5t is thereore set o't in detail in section 12.1. 7he insight it gives is central tothe +atter o voltage +eas're+ent, *'t it is not s'icient to solve the overall pro*le+.

7he irst iss'e is that the prototype detector to hich the analysis relates is not necessarily the *est circ'it to 'se. 7here are n'+ero's rectiier conig'rations, ith dierent properties andidiosyncrasies, and the variants sho'ld *e considered care'lly *eore +a&ing a choice. 7his is the+aterial covered in sections 1 # $. 3n i+portant s'*teCt to those considerations is that, in+aCi+ising the *andidth o the diode volt+eter, it is a good idea to eli+inate ind'ctive devices.

Doing that introd'ces resistance into the detector D/ ret'rn path, and the res'lting red'ction ineiciency +'st *e ta&en into acco'nt.5n sections % # 11, e ta&e a loo& at the s'*ect o diodes. 7he +ain point is to +a&e the reader

aare o the vario's types and their characteristics< altho'gh a considera*le a+o'nt o *ac&gro'nd+aterial is incl'ded, or conteCt, and to contradict historical +isinor+ation. :ro+ all o that, the

 *est type o diode or a partic'lar signal +eas're+ent applications sho'ld *e clear.  3 co+plete +athe+atical analysis o the prototype detector is given in section 12. 7his is set o'tith all o the logical steps eCplained, so that it sho'ld *e accessi*le to anyone ith so+e&noledge o calc'l's (altho'gh it is possi*le to s&ip to the res'lt in each s'*section). 7he

 principal transer 'nction has already *een +entioned< *'t in addition, it is necessary to deriveeCpressions or the detector inp't i+pedance. Only then does precision +eas're+ent *eco+e

generally possi*le, *eca'se &noledge o the inp't i+pedance allos the o'tp't red'ction d'e toso'rce loading to *e deter+ined.Once e have a co+plete &noledge o the detector transer 'nction, incl'ding loading eects,

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the detector 'aliies as an a*sol'te 3/ voltage +eas'ring instr'+ent< at least in the li+ited sensethat an acc'rate D/ +eas're+ent at the o'tp't can *e converted into the pea& val'e o a sin'soidalinp't, all itho't reco'rse to an 3/ voltage reerence. 7he neCt pro*le+ ith hich e areconronted hoever, is that the co+p'tational proced'res are not p'rely analytical< hich +eans

that there is little to report in the ay o hand*oo& or+'lae. 7he sol'tion is given in section 1&, inthe or+ o a li*rary o n'+erical ro'tines. 7his t'rns o't to *e a si=ea*le collection, +ost ohich is involved ith the calc'lation o +odiied Bessel 'nctions and the circ'+vention o theirarg'+ent#range restrictions. :or the p'rpose o +odelling detectors hoever, or or converting radata into +eas're+ents, e can si+ply pass para+eters to a +ain progra+, hich 'ses the rest othe li*rary as a collection o service ro'tines.  3ter all o that, e still only have an acc'rate &noledge o the *ehavio'r o the si+pledetector. >erci'lly hoever, it transpires that e can ta&e +ore realistic detectors, having so'rceD/ resistance, parasitic reactances, diode lea&age and series resistance< and aggregate the

 para+eters so that they can *e passed to the si+ple detector progra+s. 7he necessarytransor+ations are descri*ed in section 1'.

  3ltho'gh, in section 12, e have descri*ed the detector transer 'nction in ter+s o +odiiedBessel 'nctions, it is also possi*le to solve the integrals or average c'rrent and average poern'+erically. 7his allos analytically intracta*le variants o the o the detector pro*le+, s'ch asinite ti+e constant (ripple), and diode parasitic resistance, to *e incl'ded at the integration stage.5n partic'lar, it transpires that hile diode parallel resistance can *e separated analytically, diodeseries resistance ( 9 ds ) cannot. 7hereore, in section 1$, e set 'p the n'+erical integration +ethodor diodes ith inite oh+ic series resistance and co+pare it ith the transor+ation +ethod osection 1'.

EEEE 5ntrod'ction is still in the process o *eing ritten.

9e+aining topics-

/o+parison o transor+ation and n'+erical integration +ethods.

rror analysis (calc'lation o +eas're+ent standard deviation)

:itting diode data and eCtraction o diode para+eters.

EEEEE

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1. Half-wave rectifier7he si+plest and *est &non 9: detector circ'it is the hal#ave rectiier. Despite its a+iliarityhoever, the eCact details o its operation are oten poorly 'nderstood< not least *eca'se it isre'ently s'*ect to the cas'al pres'+ption that the D/ resistance loo&ing *ac& into driving

netor& is irrelevant. 5t +'st *e 'nderstood that the detector ill not or& i the so'rce is a D/open circ'it (altho'gh there +ay *e a ea& response d'e to diode reverse lea&age c'rrent)< and the3> de+od'lator on hich the teCt#*oo& eCplanation is 's'ally *ased is driven *y an 5:transor+er, hich is eectively a D/ short#circ'it. 5n voltage#sa+pling applications, there is otena signiicant D/ resistance, and this red'ces the +eas'red o'tp't. 7hereore, in the circ'it *elo,the so'rce netor& is depicted in a +anner that gives an analytical separation *eteen the D/resistance (9 port ) and the o'tp't i+pedance ((out ). O co'rse, in practice, the electrical co+ponentsinvolved ill *e co++on to *oth 'antities, *'t separation or the p'rpose o predicting the circ'it

 *ehavio'r is 's'ally trivial. 7he sy+*ol 9 port is 'sed incidentally, *eca'se it is oten the D/resistance o an 9: sa+pling port on an ite+ o test e'ip+ent, s'ch as an i+pedance *ridge.

1.1 Circuit behaviour and basic design principles

7he so'rce prod'ces an on#load voltage Vin) on its side o a hypothetical perect co'pling capacitor,and this has no D/ co+ponent. Vin) is also the voltage that ill *e +eas'red 'sing an 3/#co'pled

 pro*e at the inp't to an act'al detector. 5t ill *e approCi+ately sin'soidal provided that the inp'tresistance o the detector is large relative to the +agnit'de o the o'tp't i+pedance o the generator,F(outF. 3 D/ oset is hoever added to the so'rce voltage on the detector side o the hypotheticalcapacitor, so that the act'al inp't voltage is-

Vin G Vin)  # V*"

here, pres'+ing that the diode polarity is chosen to give a positive o'tp't< V*"  , the backoffvoltage, is negative relative to the gro'nd rail shon. 7he *ac&o voltage arises *eca'se theaverage diode c'rrent (5a+ ) that gives rise to the D/ o'tp't (+eas're+ent) voltage Vm +'st alsolo thro'gh 9 port . 7h's the D/ signal prod'ced *y the rectiication process is shared *eteen theo'tp't load resistance 9 D and the port resistance in proportion to the relative val'es o thoseresistances. 7his +eans that the *ac&o voltage red'ces Vm , or hich reason 9 port is shon

 *elo the gro'nd rail in the diagra+. V*"  can *e +eas'red at the inp't ter+inal *y placing an 9:cho&e in series ith a high#inp't#resistance +'lti+eter (provided that the cho&e has a highi+pedance at the generator re'ency). 5n so+e 3> radio receivers also, an 9:#deco'pledresistance is deli*erately introd'ced in series ith the inal 5: transor+er o'tp't inding, so that

the *ac&o voltage can *e 'sed or a'to+atic gain control (3/).

7o calc'late the detector o'tp't or a sin'soidal inp't, e can deine-

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Vin)  G Vp 6inH

here Vp is the pea& voltage, and H G 2I t is the ti+e#varying phase angle. By this deinition, Vin) 

is the 9>6 o a sin'soidal voltage, so that-

Vp G Vin)  J2

7he o'tp't o the detector is then-

Vm G Vp # Vf   # V*" 

here Vf   is the eective diode orard voltage drop 'nder dyna+ic conditions. :or a se+icond'ctor diode, Vf   variesapproCi+ately logarith+ically ith the average orard

c'rrent, *'t it also has a contri*'tion given *y the logarith+o the the peato#average c'rrent ratio. 7he pro*le+ o calc'lating Vf is investigated in detail in section 12< *'t asa r'le o th'+*, it is orth re+e+*ering that in signal detection circ'its involving average diodec'rrents in the region o 100 L3 to 1 +3 it is a*o't 0.2 V or ger+ani'+ point#contact diodes,a*o't 0.$" V or silicon#+etal 6chott&y diodes, and a*o't 0.4 V or silicon %#M 'nction diodes.

3nother ay o considering the detector is to say that the total detected voltage is the s'+ o theo'tp't and the *ac&o voltage. 7h's-

Vm N V*"  G Vp # Vf   G Vin) 2 # Vf  

When the port resistance is =ero, the inp't voltage no longer has a D/ co+ponent, and this *eco+es-

Vm G Vp # Vf   G Vin 2 # Vf  

hich is the +ore a+iliar eCpression or the o'tp't o a hal#ave detector. Mote that the o'tp't inthis case can approach the pea& val'e o the inp't voltage, provided that Vin  is large relative to Vf  .:or this reason, rectiying detectors are oten reerred to as a pea& detectors, even tho'gh the errorin the +eas're+ent is large in the a*sence o so+e or+ o linearity correction.

5n the circ'it diagra+ given earlier, the o'tp't load resistance 9 D is shon as *eing separate ro+the +eter, and the +eter is ass'+ed to *e a perect volt+eter, i.e., o ininite inp't resistance. 5n

 practice, 9 D is oten the inite inp't resistance o a voltage +eas'ring or sa+pling device, or the parallel co+*ination o an inp't resistance and a load resistor. 5n a passive circ'it, 9 D +ight *e theresistance o a volt+eter constr'cted *y placing a resistor in series ith a +oving#coil+icroa++eter. :or eCa+ple, a 100 L3 +eter padded#'p to 100 & *y +eans o a series resistor+a&es a 10 V :6D ('ll#scale delection) volt+eter.

7he s+oothing capacitor /D sho'ld *e chosen so that the ti+e#constant /D J 9 D is at least 10ti+es the period (1 ) o the loest re'ency at hich +eas're+ents ill *e +ade. 5 the loestre'ency is to *e, say, 1 >;= and 9 D G 10 &, then e ant /D J 9 D to *e greater than 10 Ls, i.e.,

/D E1 n:. 5 a +eter is 'sed as the indicator, it +a&es no practical dierence i the capacitor isso+ehat larger than the +ini+'+ re'ired, and so 0.1 L: (cera+ic dis&) is a typical choice< *'tvery large capacitors ill da+p the +eter response in a +anner that depends on the driving netor&

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o'tp't i+pedance. 3 slo response can *e desira*le i the signal is ittery, *'t in so+e applications,s'ch as inding the n'll point hen ad'sting a +eas'ring *ridge, a ast response is needed. :ast,on a h'+an ti+escale, i+plies a ti+e constant o less than a*o't 10 +s (i.e., P 1 L: or a 10 &load, P 0.1 L: or a 100 & load, etc.).

  Mote incidentally, that i the signal generator is a+plit'de +od'lated (e.g., ith a 1 &;= sineave), and the ti+e#constant /D J 9 D  is chosen to *e shorter than the period o the +od'latingre'ency (e.g., a*o't 100 Ls or 10 & in parallel ith 10 n:), then the indicator can *e a high#i+pedance transd'cer (earphone, etc.), or an a'dio a+pliier and lo'dspea&er. 7his arrange+entcan *e 'se'l hen the detector is attached to an 9: *ridge. Mote that, i a +agnetic transd'cer isconnected directly, a load e'alising netor& is needed (see section 1.)

1.2 Diode peak inverse voltage7he +ini+'+ sae reverse voltage rating or the detector diode (V R- ) is +ost easily deter+ined *ystarting ith 9 port G 0. 5n that case, or large inp'ts, /D is charged to a constant voltage approaching

Vin 2 , hereas the +ost negative instantaneo's voltage appearing at the detector inp't isapproCi+ately #Vin 2 . ;ence the diode +'st have a VR- o at least 22 (i.e., 2.82) ti+es the+aCi+'+ possi*le 9>6 inp't voltage.

alf/#a+e rectifier- Diode VR- E Vin (+aC) J 22

 Mo i e allo 9 port to *e E 0, the o'tp't voltage Vm is red'ced *y an a+o'nt V*"  , *'t then a'antity #V*" is added to the +ost negative eCc'rsion o the inp't aveor+. ;ence the pea&inverse voltage to hich the diode is s'*ected is not aected *y the port resistance.

1. Input chokes7he loss o sensitivity that res'lts ro+ having a inite port resistance can so+eti+es *e a dra*ac&,and the traditional sol'tion to this pro*le+ (ass'+ing that transor+er co'pling is not to *e 'sed) isto place an 9: cho&e across the inp't to the detector. 7he cho&e sho'ld have a reactance that ishigh in co+parison to the detector load resistance at the loest re'ency o operation. $." +; is atypical choice, and has a no+inal reactance o a*o't N0 & at 1.8 >;=. 7his hoever is a largeind'ctance in radio engineering ter+s, and s'ch ind'ctors have s'*stantial sel#capacitance. 7hesel#capacitance ill resonate ith the ind'ctance at so+e re'ency, and the reactance o the cho&eill *eco+e capacitive at re'encies a*ove that". 7his leads so+e co++entators to ass'+e that9: cho&es sho'ld not *e 'sed a*ove the sel#resonance re'ency (69:), *'t this r'le is +isleading.

7he 69: is act'ally the 'nda+ental parallel resonance o the ind'ctor, and corresponds to there'ency at hich the i+pedance *eco+es eCtre+ely large in +agnit'de. ;ence, ro+ an 3/

 point#o#vie, the cho&e disappears at the 69: and so does not sh'nt the netor&. 5t also +atterslittle hether the o#resonance reactance o the cho&e is positive or negative, the necessarycriterion *eing only that it sho'ld have a large i+pedance +agnit'de in co+parison to the otheri+pedances in the netor&. 7hings go horri*ly rong hoever at the irst series#resonantre'ency. 7his occ'rs at approCi+ately tice the 69:, and corresponds to the point at hich thelength o the ire in the cho&e is one electrical avelength. 3t this re'ency, and or a rangeeither side o it depending on the Q, the cho&e acts as a short#circ'it and the o'tp't o the netor&is serio'sly red'ced.  7he potentially idiosyncratic *ehavio'r o the D/ *ypass cho&e is not necessarily an iss'e i theind'ctor is ell designed and the re'ency#range is restricted, *'t sp'rio's resonances cannot

" RF ho"es, their performance a*o+e and *elo# resonance, /o'rtney ;all, ;a+ 9adio, R'ne 1@8, p0#2.

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alays *e r'led#o't itho't practical veriication. 5n general, insoar as the 'se o cho&es cannot *eavoided, an 9: cho&e co+posed o +'ltiple seg+ents (pie#o'nd) gives the highest irst series#resonance and so is to *e preerred. :or a given length o inding ire also, a cho&e ith a erritecore gives +ore ind'ctance than a non#+agnetically#cored coil, and so ill have a higher set o

resonance re'encies. >any designers hoever, preer to eli+inate the cho&e herever possi*le(they are eCpensive, as ell as tro'*leso+e), and accept the loss o sensitivity. 5 the so'rce is aco+plete D/ open#circ'it, the +ost *asic sol'tion is to place a resistor across the port< *'t thissh'nts the 9: signal and it is so+eti+es *etter to place resistance across other ele+ents in thenetor&. 3 good design o'tco+e is that hich gives a port#resistance considera*ly s+aller than thedetector load resistance.

1.! "arge signal input i#pedanceBoth port resistance and diode orard voltage drop are so'rces o error re'iring correction in

 precision +eas'ring applications< *'t there is a third ca'se o error that +'st also *e considered.

7his is the detector inp't i+pedance, hich ill o*vio'sly load the so'rce netor& and ca'se itso'tp't to droop.

3t irst glance, the pro*le+ o calc'lating the inp't i+pedance see+s intracta*le< *eca'se thediode does not o*ey Oh+s la and so the inp't resistance varies d'ring the co'rse o a cycle. :or asingle#re'ency co+ponent o the signal hoever (this *eing hat e +'st consider hendeter+ining i+pedance or the p'rpose o calc'lating the re'ency response), it is s'icient tohave an average pict're o the inp't i+pedance. 7his can *e o*tained *y considering the poerdelivered to the resistive ele+ents in the netor&.  7he 3/ eCcitation ca'ses a direct c'rrent to circ'late, and this ca'ses the voltages Vm , Vf andV*"   to develop. 7hese are related to the pea& voltage *y deinition (*eca'se Vf is act'ally deinedas the voltage error that occ'rs in pea& detection). 7h's-

Vp  G Vin)   2 G Vm N V*"  N Vf

here Vin)  is the 3/ co+ponent o the inp'taveor+ considered in isolation ro+ theD/ oset ca'sed *y V*" . 3lso, in the li&elyevent that there is no physical separation

 *eteen the 3/ so'rce netor& and 9 port , itis the voltage that o'ld *e +eas'red 'singan 3/#co'pled pro*e.

 Mo let 's deine the total resistance aro'nd the loop as 9 tot  , i.e.-

9 tot G 9 D N 9 diode N 9 port

here, to a airly good approCi+ation (hich e ill eCa+ine in detail in section 12.&)-

9 diode S Vf   5a+ 

 Meglecting energy loss d'e to the circ'lating har+onic c'rrents prod'ced *y the rectiication process< the total poer delivered to the detector is-

%in G ( Vm N V*"  N Vf )2  9 tot 

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7h's-

%in G ( Vin) 2 )2  9 tot 

i.e.-

%in G 2 Vin2  9 tot 

 Mo, i the inp't i+pedance is deined as 9 (in , e also have-

%in G Vin2  9 (in 

so that-

9 (in G 9 tot  2

7h's, ass'+ing that har+onic generation is a lesser aspect o the *ehavio'r o the lightly#loaded(voltage sa+pling) 9: detector 4, the inp't resistance or 3/ signals is hal the total D/ resistance.7his res'lt +ight see+ s'rprising, *'t it can *e 'nderstood *y thin&ing o the detector as a &ind ovoltage transor+er. 7he 9>6 average o a D/ signal is the sa+e as its ordinary average, and so inthe process o converting ro+ 3/ to D/, the 9>6 level has *een transor+ed#'p *y a actor o 2.7h's the detector is a 1-2 voltage transor+er, and hence a 1-(2)T (i.e., 1-2) i+pedancetransor+er.

5t sho'ld *e noted hoever that the detector inp't i+pedance is highly varia*le, depending on drivelevel. 7his is +ade o*vio's *y s'*stit'ting or 9 tot  in the eCpression a*ove-

9 (in G ( 9 D N 9 diode N 9 port ) 2

7he varia*le ter+ is 9 diode , hich is not a resistance in the nor+al sense, *'t a 'antity related tothe average poer dissipation in the diode (this is o*tained *y integrating the prod'ct oinstantaneo's diode voltage and c'rrent over a cycle o the inp't aveor+). 5 the detector inp'tvoltage is large in co+parison to Vf hoever, then e have-

9 (in S ( 9 D N 9 port ) 2

7his is the li+iting inp't i+pedance 'nder large signal conditions (neglecting parasitic reactances)<and i 9 port is =ero d'e to the 'se o a cho&e or a co'pling transor+er, it red'ces to-

9 (in S 9 D  2

7he li+iting 3/ inp't resistance is a reasona*le +eas're o the inp't i+pedance hen the detectoris driven hard, or *est linearity. 5t is thereore 'se'l or gaining an idea o the orst#case so'rceloading. 3s the drive level is red'ced hoever, d'e to the non#linear relationship *eteen voltageand c'rrent, 9 diode ill increase and event'ally co+e to do+inate. 7h's the inp't i+pedanceincreases as the drive is red'ced, *eco+ing very large (practically an open#circ'it) hen Vin G 0.5n order to +odel the s+all#signal inp't i+pedance acc'rately, it is irst necessary to develop a

4 7his ass'+ption does not ca'se signiicant discrepancies in data analysis hen +a&ing +eas're+ents 'sing lightly#loaded detectors. 3lso, the 3/ co+ponent o the eective diode orard voltage drop, as derived in section 12,+'st acco'nt or the dissipation o +ost o the har+onic energy.

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theory that descri*es the dyna+ic orard cond'ction characteristic. 7hat +atter is disc'ssed ro+section 12 onards.

7he li+iting 1-2 i+pedance transor+ation r'le applies to all non#voltage#+'ltiplying detectors. 5n

the case o the *ridge rectiier (section '), the li+it is harder to approach *eca'se the detector placesto diode orard voltage drops in series ith the o'tp't. 5n the case o the *i#phase 'll#averectiier (section $) the li+it is slightly easier to approach, *eca'se the average diode c'rrent isshared *eteen to diodes.

 Mote that an idiosyncrasy o hal#ave rectiication is that, since 9 port is part o the so'rce netor&,the rectiication process ca'ses poer to *e dissipated in the so'rce netor&. 7his is 's'ally olittle conse'ence in signal#processing circ'its< *'t it can *e (or sho'ld *e) an i+portantconsideration in the design o poer#s'pplies.

1.$ %eparation of port resistance and source i#pedance7here is no hard and ast r'le or the analytical separation o the generator o'tp't i+pedance andthe port resistance, save to say that is ill 's'ally *e o*vio's. 7a&e, or eCa+ple, the circ'it shon

 *elo, hich is Do'+as *ridge, idely 'sed or +onitoring ;: trans+ission lines and +eas'ringrelection coeicient.

5n the circ'it on the let, the generator is typically a radio trans+itter, and the i+pedance ( is anantenna syste+. 7he *ridge co+*ines a voltage sa+ple, o*tained ro+ the capacitive potentialdivider /1 , /2 , 9  , and the o'tp't o a transor+er in series ith the line, hich prod'ces a voltage

 proportional to the c'rrent. 7he circ'it para+eters are calc'lated so that the *ridge gives no o'tp'then the i+pedance ( is e'al to the design load resistance o the trans+itter. 7his *alancecondition can *e +aintained over a relatively ide re'ency range *y correct choice o theresistance 9 + , hich co+pensates or the alling reactance o the c'rrent#transor+er secondary

inding at lo re'encies. 9 + is typically a e &. 7h's, since the D/ resistance o the c'rrenttransor+er secondary inding ill *e very s+all *y co+parison, it sho'ld *e o*vio's that 9 port ise'al to 9 + .  7he o'tp't i+pedance at the generator re'ency re'ires a little +ore consideration, *'t not+'ch. enerally, the *ridge is designed so that it a*stracts only a very s+all a+o'nt o energyro+ the line. 7h's the generator ill hardly notice its presence, and its o'tp't ill not droopsigniicantly as a res'lt o the additional loading. We can thereore ass'+e that the o'tp'ti+pedance o the generator is eectively =ero. With that ass'+ption< the o'tp't i+pedance o thevoltage sa+pling netor& (*y 7hUvenins theore+) is given *y the parallel co+*ination o itsresistance and reactances. 7he total o'tp't i+pedance is then o*tained *y placing the parallelco+*ination o the c'rrent transor+er load resistance and secondary reactance in series ith theo'tp't i+pedance o the voltage sa+pling netor&. 7h's- Directional apparatus for use #ith high/freuency transmission lines. 7 Do'+a, A6 %at. Mo. 2808"44, 1@"

(iled 1@"$).

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(out G ( 9   3142 ) N ( 9 i  35i )

7his can *e converted to 9N 3 or+ 'sing the standard parallel#to#series transor+ations8.

1.& Actual input voltage:re'ently, the 9: design considerations or an ite+ o test e'ip+ent lead to the relationship

 *eteen so+e 'antity to *e +eas'red and the open circ'it (o#load) voltage o an o'tp't port.6ince the port has a inite o'tp't i+pedance hoever, and the detector has a inite 3/ inp'tresistance< the detector ill not see that voltage. 5nstead, the detector inp't voltage is the o'tp't oa potential divider or+ed *y (o't and 9 (in . 7h's, i S is the open#circ'it so'rce voltage-

in G S 9 (in  ( (out N 9 (in )

7he voltages and i+pedances in this eCpression are,o co'rse, phasors< *'t since the detector does notconserve phase inor+ation, all phasors that appear asactors can *e replaced *y their +agnit'des. 7h's, i e 'se the convention that a voltage not ritten in *old is a +agnit'de ( i.e.- V G FF )-

Vin G VS 9 (in  F (out N 9 (in F

 Mo, i e have co+p'ted (out  in the 9N 3 or+, so that (say)-

(out  G 9 S N 3S

then e can add the inp't resistance to it and or& o't the +agnit'de o the deno+inator in theeCpression or Vin . 7h's-

Vin G VS 9 (in  ( 9 SN 9 (in )2 N S2 X

7his e'ation is pri+arily a state+ent o the o*vio's, in that i e ant to avoid error d'e to so'rceloading, it ill *e necessary to +a&e 9 (in as large as possi*le and F(outF as s+all as possi*le. 6'chchoices are not alays availa*le hoever< there *eing, or eCa+ple, an iss'e hen 'sing a Do'+a

 *ridge to drive a +oving#coil panel +eter, *eca'se the *ridge has a large capacitive reactance

co+ponent in its o'tp't i+pedance at lo re'encies, and the +eter ill typically re'ire 100 L3o drive or 'll#scale delection (:6D). 7he only s+all consolation is that the so'rce loading ill *e red'ced at lo drive levels, *eca'se o the increase in the detector inp't resistance (as disc'ssedearlier). 7his 'nloading eect ill partly oset the inherent non#linearity o the diode detector, it+ight even *e 'sed as the *asis or partial linearity co+pensation i the so'rce i+pedance is +ainlyresistive< *'t in general it ill *e re'ency#dependent and hard to eCploit to any advantage.

We have, in the preceding disc'ssion, 'ncovered a n'+*er o potential so'rces o error aecting the'se o the si+ple hal#ave rectiier or a*sol'te 9: voltage +eas're+ent. 7hey are, so ar,'antiia*le, and largely correcta*le< *'t they de+onstrate that the *ehavio'r o the detector is not'ite as si+ple as +any circ'it designers see+ to ass'+e.

8 6ee or eCa+ple- ! electrical theory. D W Knight.. http-.g$ynh.ino=docs3/theory . 6ection 18. Mote that the parallel i+pedance ( ) operator is deined so that- a  * G a *  (a N *) , here *oth a and * can *ereal, i+aginary, or co+pleC.

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1.' Inductivel( loaded A) detector 3ltho'gh the principal s'*ect o this article is 3/ voltage +eas're+ent< introd'cing therelationship *eteen detector load and inp't i+pedance provides an opport'nity to identiy aidespread design error that occ'rs hen a detector 'sed as an 3> de+od'lator is operated ith an

ind'ctive load. 7his +ista&e typically occ'rs hen a +agnetic transd'cer, s'ch as a telephoneearpiece or a pair o headphones, is driven *y a detector, either directly or thro'gh a step#dontransor+er. 7he iss'e is that the stated i+pedance o the transd'cer is not the sa+e as its D/resistance. 7ypically, the no+inal i+pedance ill *e the i+pedance +agnit'de at so+e +id#*anda'dio re'ency, s'ch as 1 &;=, hereas the D/ resistance is li&ely to *e s+aller *y a actor o

 *eteen a*o't 1" and 120.7h's, or eCa+ple, i e ere to connect a pair o 10 & high#i+pedance headphones to a

detector, it +ight t'rn o't that the D/ resistance o the phones is a*o't 800 < in hich case thelarge signal inp't i+pedance o the detector ill *e a*o't 00 instead o " &. 7he eect,ass'+ing a inite so'rce i+pedance, ill *e to introd'ce eCcessive a'dio distortion *y preventingthe detector ro+ +oving o't o its threshold region< and i the driving netor& is resonant, it ill

radically red'ce the selectivity or strong signals *y red'cing the circ'it Q.  7he deect is present in +ost traditional crystal#set designs@. 5t res'lts in a pec'liar *ehavio'rhere*y there is relative silence *eteen stations, *'t hen a reasona*ly strong distant station ist'ned in, it is heard +iCed ith a strong local station.  7he sol'tion is to place a parallel 9/ netor& in series ith the ind'ctive load, as shon in thediagra+ *elo. 7he netor& is &non a a *enny, ater its inventor Ben 7ong'e10. As'al design

 practice is to 'se the resistor 9 6 to pad the transd'cer resistance to e'al its no+inal i+pedanceval'e, there*y esta*lishing the detector large#signal 9: inp't i+pedance. 7he co'pling capacitor/B is then chosen to have a reactance +agnit'de that is s+all relative to the transd'cer i+pedance(say 110th) at the loest re'ired a'dio re'ency.

 Motice here incidentally, that the transd'cer 7 is shon ith a step#don transor+er, *'t a high#Ytransd'cer co'ld 'st as ell *e 'sed itho't a transor+er. 3lso, the t'ned inp't transor+er is

shon ith separate indings or the resonator and the detector, hereas they can *e co+*ined.7his sidesteps the 'estion o hether or not it is a good idea to tap the detector ta&eo point donthe tan& coil to preserve selectivity. 7he anser is that it is not necessary to trade signal voltage orselectivity i a *enny is 'sed, *eca'se the detector inp't i+pedance, and hence the loaded Q o theilter, can *e controlled *y 9 6 .

@ 6ee, or eCa+ple, 7he *oy8s *oo" of crystal sets, W R >ay, Bernards 9adio >an'als 1@".http-.reCresearch.co+Ctlradio*oys*oo&.pd (accessed 2$rd 3'g. 201)

10 rystal radio set design. Ben 7ong'e. http-*entong'e.co+ (accessed 2$rd 3'g. 201)

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2. %hunt-diode rectifier3n alternative to the standard hal#ave detector conig'ration is the sh'nt diode rectiier, shon

 *elo. 7his is the prototype o the indirectly#gro'nded detector circ'its avo'red *y the /ollins9adio /o+pany in the 1@"0s, and pop'larised in 6W9 and i+pedance#+eas'ring circ'it

constr'ction articles *y /ollins design engineer Warren Br'ene11 and others12.

 Mote that a voltage placed in s'are *rac&ets reers to the D/ co+ponent o a aveor+. 3s in the previo's section, Vin) represents the 3/ co+ponent o the inp't voltage, hereas the act'al inp't,Vin , ac'ires a D/ oset d'e to the rectiying action o the diode. 3s *eore also, e ill deine-

Vin) G Vp 6inH

here Vp is the pea& voltage, and H G 2I t , so that-

Vp G Vin)  2

7he circ'it appears, at irst glance, to place a diode across

the detector port< *'t it does no s'ch thing *eca'se o theaction o the co'pling capacitor / . When Vin) irst goesnegative (relative to the polarities shon on the circ'itdiagra+), D1 cond'cts and cla+ps one end o / nearly to=ero, eCcept or a shortall d'e to the diode orard voltageVf  . 7his +eans that the +ost negative eCc'rsion o Vin  iscla+ped to #Vf  . 7hen, since the charge in / re+ainss'*stantially constant on the ti+escale o the 3/ signal, thenear#sin'soidal voltage at the cathode o D1 averages a*o'tNVp # Vf . 7he ilter co+prising the 9: cho&e, 9 port and /Dre+oves the 3/ co+ponent to give a +eas'red voltage o

Vp # V*"  # Vf , hich is the sa+e as or the ordinary hal#ave detector. Overall, the +ain theoretical dierence *eteen the ordinary detector and the sh'ntdiode detector is the order in hich Vp , V*"  and Vf are added together.  Mote that, as ar as is possi*le, the no+enclat're has *een +ade consistent ith that 'sed or theordinary detector. 7h's 9 port , altho'gh it is no longer part o the so'rce netor&, has eCactly thesa+e eect on the D/ o'tp't as does the D/ resistance o the so'rce netor& in the precedingsection.

:or the ilter that re+oves the 3/ co+ponent, e have the choice o 'sing a cho&e, a resistance,or a co+*ination o the to (s'ch as a realistic cho&e). 3s *eore, the 'se o a cho&e +ini+ises V*"

 *'t introd'ces the possi*ility o parasitic resonances, and so i so+e red'ction in sensitivity istolera*le, the tro'*leso+e cho&e can *e eli+inated.

11 !n 9nside Picture of Directional attmeters, Warren B Br'ene, Q67, 3pril 1@"@, p2#2812 9n/5ine RF Po#er -etering, Do'g De>a, Q67, Dec. 1@4@, p11#14.

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9nput impedance 7he 3/ inp't resistance o the sh'nt detector o*eys the sa+e 1-2 i+pedance transor+ation r'le asthe si+ple detector, i.e.<

9 (in G ( 9 D N 9 diode N 9 port ) 2

7he ilter co+ponents hoever are eectively in parallel ith that, and the reactance o theco'pling capacitor is eectively in series< so that the total (neglecting parasitics) is-

(in  G 3 N ( 9 port N 3RF ) Z ( 9 D N 9 diode N 9 port ) 2 [

5 the co'pling capacitor is very large, and the cho&e (as is oten the case) is o+itted, this red'cesto-

Yin  G 9 port Z ( 9 D N 9 diode N 9 port ) 2 [

7he co'pling capacitor can also *e physically o+itted i the driving netor& is open#circ'it to D/.5 there is any D/ path across the detector port hoever, / is essential< and i needed it sho'ld *echosen to have a reactance that is alays s+all in co+parison to 9 (in . 5 the loest re'ency ooperation is say 1 >;=, and 9 Yin  is a*o't 100 & or large inp'ts, then the voltage drop across thecapacitor +ight *e considered to *e negligi*le i its reactance +agnit'de is (say) alays less than1\ o 9 (in , i.e., less than 1 & at 1 >;=. 6ince / G 12I FcF, e can then calc'late that /sho'ld *e at least 1"@ p:. 5t +a&es no practical dierence i the capacitor is so+ehat larger thanthe +ini+'+ re'ired, and so 1 n: or greater o'ld *e a sensi*le choice. Mote hoever, that thedetector response ill *eco+e sl'ggish i the capacitor is very large and the ret'rn path has arelatively high resistance, *eca'se it ill ta&e ti+e or the circ'it to reach e'ili*ri'+.

Diode P9 6ince the voltage at the cathode o the diode averages at ro'ghly NVinX 2 (ass'+ing that the diode

 polarity is chosen to give a positive o'tp't), the instantaneo's pea& inverse voltage s'stained *y thediode ill *e  VinX22 . ;ence, as in the case o the si+ple hal#ave rectiier, the VR- or thediode +'st *e at least 22 ti+es the +aCi+'+ possi*le 9>6 inp't voltage.

Shunt diode rectifier- Diode VR- E Vin (+aC) J22

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2.1 %a#pling floating voltagesOne o the great advantages o the sh'nt#diode detector is its s'ita*ility or sa+pling voltagesacross netor& co+ponents that are loating ith respect to gro'nd. 3 practical eCa+ple is given inthe diagra+ *elo, hich depicts a circ'it or deter+ining co+pleC i+pedance ( ( G 9N 3 ) 'sing

only scalar voltage +eas're+ents. 7his techni'e as originally descri*ed *y Doyle 6trandl'nd1$, *'t the i+ple+entation shon *elo is d'e to > r'challa1.

7his circ'it prod'ces ive D/ voltages, hich (ass'+ing perect linear rectiication) are proportional to the +agnit'des o the 3/ voltages across the so'rce, the reerence resistor 9 ref , thereerence reactance ref , the load (, and the 'nction *eteen the to reerence ele+ents andgro'nd (the o'tp't voltages are all reerred to gro'nd). 7he 'll set o voltages is s'ch that, eventho'gh the individ'al +eas're+ents contain no phase inor+ation, they can *e co+*ined in vario'says to deter+ine any o the i+pedance or ad+ittance#related attri*'tes o the load, ( (incl'dingthe sign o the reactance or s'sceptance)1".  7he diodes D1 , D$ and D" all have their anodes connected to gro'nd, and so the correspondingdetectors conor+ to the prototype circ'it given earlier, eCcept that they are intended to eedoperational a+pliiers having high inp't resistance and so 'se resistive ilters and dispense ith thecho&es. 3lso notice that there is a 1 > resistor across each o the diodes, the reasons or its

 presence in each case *eing irstly< that the detector +'st have a load i it is not to have an ininiteti+e constant (and connecting it across the diode avoids loading the o'tp't)< and secondly< that theop. a+p. ill re'ire a e n3 o inp't *ias c'rrent, and it is a very *ad idea to get that via thediode. Mote that the voltages prod'ced *y these three detectors ill *e positive ith respect togro'nd.  7he detectors 'sing the diodes D2 and D have the sa+e design considerations as the others,eCcept that they +eas're 3/ voltages that loat relative to gro'nd. 7his is possi*le *eca'se the

1$ !mateur measurement of R43;, Doyle 6trandl'nd, Q67, R'ne 1@4", p2#2. Z3n ingeneo's graphical +ethod or +eas'ring co+pleC i+pedance 'sing only scalar +eas're+ents[.

1 omple< 9mpedance -easurement =sing only Scalar oltage -easurements, > r'challa, /o++'nicationsQ'arterly, Oct. 1@@8, p$$#$. Z3nalytical approach to 6trandl'nds +ethod and other i+prove+ents [.

1" :or a co+plete analysis, see- 9mpedance and admittance measurement using scalar +oltage samples .D W Knight. http-.g$ynh.ino=docs*ridges

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+eas'ring circ'it is isolated ro+ the o'tside orld *y co'pling capacitors, hich +eans that the3/ signals are g'aranteed to have no D/ co+ponent. 7his allos the D2 detector to get its gro'ndreerence via the " inp't sh'nt resistor, hile D gets its reerence via the " resistor and the"1 reerence resistor in series. 6ince the detector c'rrents are only o the order o a e L3, the

anodes o D2 and D are eectively gro'nded ro+ the D/ point#o#vie, and so the detectors give positive o'tp'ts reerenced to gro'nd.

3nother eCa+ple o the 'se o sh'nt#diode detectors is given in the circ'it *elo. 7his shos thedetector arrange+ent 'sed in the >:R24@ antenna analyser 14. 3 greatly si+pliied version o thedriving arrange+ent is also incl'ded to sho that the circ'it has co+plete D/ isolation ro+ the 9:so'rce (and also, that it or&s at A;:).

7he >:R engineers chose to 'se conventionalhal#ave detectors or 3/ voltagesreerenced to gro'nd, and sh'nt detectors or the loating voltages. 5n this case, the ilter resistor is &, a*o't 1000J the resistanceneeded to *alance the *ridge, *'t also s+alleno'gh to +ini+ise the voltage drop ca'sed

 *y the 1 > load resistors. 7he D/ signalsare applied to />O6 op. a+ps., hich havean inp't lea&age c'rrent o aro'nd 1 p3(so+ehat less than +ight *e ca'sed *y aingerprint on the circ'it *oard), and so thereis no signiicant loading apart ro+ theresistor. 7he >:24@ 'ses diode linearityco+pensation (hich ill *e disc'ssed in alater section), and 12#*it 3#D conversion< andthe res'lt is a re+ar&a*ly acc'rate instr'+ent,a*le to +eas're i+pedance#related 'antitiesithin an order#o#+agnit'de o "0 to *etter 

than ]2\.

14 http-.+enterprises.co+

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. *oltage-doubler rectifier7he circ'it shon *elo is o*tained *y the si+ple eCpedient o replacing the ilter co+ponents othe sh'nt#diode detector ith a second diode. 7he eect, at least no+inally, is to do'*le the voltageo'tp't in co+parison to a hal#ave rectiier, to eli+inate the port resistance and hence the *ac&o

voltage, and to re+ove the need or an 9: cho&e. 7he circ'it can also *e 'sed or the detection oloating 3/ voltages provided that the conditions o'tlined in section 2.1 are +et.. 6'ch are itsadvantages that e +ight onder hy it is not 'niversally adopted< *'t it t'rns o't that its principalstrength is also its principal dra*ac& in voltage#sa+pling applications. 7he iss'e is that itseectiveness at converting 3/ inp't into D/ o'tp't +eans that it has a s'rprisingly lo inp'ti+pedance.

3s *eore, e ill deine Vp G Vin) 2 , here Vin) is the 3/ co+ponent o the inp't voltage. 7heoperation o the circ'it is then as ollos-

When Vin  irst goes negative, D1 cond'cts and cla+ps oneend o the co'pling capacitor / to #Vf  . 7his ca'ses thecapacitor to *e charged to Vp / Vf  . 7he charge in / thenre+ains s'*stantially constant on the ti+escale o the 3/

signal, and so the voltage across /

is placed in series ithVin , 'lti+ately ca'sing the s+oothing capacitor /D to *echarged, via D2 , to tice the pea& 3/ inp't +in's todiode orard voltages. Mote that since the diodes operatealternately, this detector cond'cts on *oth positive andnegative hal#cycles o Vin , hich +eans that it is act'ally atype o 'll#ave rectiier. 3lso notice that the detector hasan o'tp't shortall o to diode orard voltages< *'t since it also give tice the o'tp't o a hal#ave detector, the overall degree o non#linearity is (at least no+inally) the sa+e as or the hal#ave detector .

Diode P9 D'e to the cla+ping action o D1 , the voltage at the anode o D2 cannot all s'*stantially *elo=ero. ;ence, since the voltage across the s+oothing capacitor /D is very nearly NVin 22 , VR- orD2 +'st *e at least 22 ti+es the +aCi+'+ possi*le 9>6 val'e o Vin . 5n the case o D1 , since itseect is to cla+p the +ost negative eCc'rsion o the inp't voltage approCi+ately to gro'nd,there*y charging / to Vin 2 , the voltage across / ill *e placed in series ith Vin)  hen it+a&es its positive eCc'rsion. ;ence VR- or D1 +'st also *e at least 22 ti+es the +aCi+'+

 possi*le 9>6 val'e o Vin .

oltage dou*ler- Both diodes, VR- E Vin (+aC) J 22

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.1 Doubler input i#pedance5n order to deter+ine the inp't i+pedance o the voltage do'*ler, e can 'se an arg'+ent si+ilar tothat given in section 1.'.

%rovided that the loading on the so'rce is not so great as to ca'se s'*stantial har+onic

distortion, +ost o the har+onic energy generated *y the rectiication process ill *e dissipated inthe dyna+ic co+ponent o the diode orard voltage (section 12). 5n that case, the D/ poerdissipated in the netor& ill *e the sa+e as the 3/ inp't poer. 7he total D/ voltage prod'cedis-

2Vp G 2 Vin) 2

and the total D/ resistance is-

9 tot G 9 D N 29 diode 

;ence-

%in G ( Vin)  22 )2  9 tot  G 8 Vin) 2  9 tot 

 *'t, *y deinition-

%in G Vin) 2  9 (in 

;ence-

9 (in G 9 tot  8

and or large signals, hen 9 D EE 9 diode ,

9 (in S 9 D  8

7h's, hereas the hal#ave detector is a 1-2 i+pedance transor+er, the voltage do'*ler is a 1-8i+pedance transor+er.

7he disadvantage o the voltage do'*ler 1 or non#invasive voltage#+eas're+ent p'rposes can no *e de+onstrated *y a si+ple eCa+ple. 6'ppose e decide to 'se a voltage do'*ler to drive a

100 L3 +oving#coil +eter padded to 100 & to give 10V :6D. Meglecting diode resistance and parasitics, the detector inp't i+pedance ill correspond to a resistance o a*o't 12." &. 5 eere to 'se a hal#ave detector hoever, e o'ld get hal the o'tp't voltage, *'t e co'ld easilyred'ce the +eter padding resistance to "0 & (incl'ding 9 port) and there*y increase the sensitivity to" V :6D. 7his alternative hal#ave detector ill no give eCactly the sa+e +eter readings as thedo'*ler, eCcept that its large#signal inp't i+pedance ill *e a*o't 2" &. We have not,incidentally, o'nd a so'rce o ree energy *y 'sing a non#+'ltiplying detector. We have +erelyavoided p'+ping the s+oothing capacitor 'p to a high voltage, only to drop the voltage *ac& donagain 'sing a resistor.

1 6ee also- rystal radio set design technical help, Ben 7ong'e,http-*entong'e.co+Ctalset0deeCp0deeCp.ht+l

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!. +ridge rectifier3 non#+'ltiplying detector that re'ires no 9: cho&es, does not have a *ac&o voltage, and doesnot care hether or not there is a D/ path thro'gh the so'rce netor&, is the 'll#ave *ridge,shon *elo-

7his circ'it is nearly 'niversal in +odern poer s'pplies, *'t it has to disadvantages in signal

detection applications< one *eing that it has to diode orard#voltages in the path to the load, andthe other *eing that either the o'tp't or the inp't ter+inals +'st *e alloed to loat ith respect tothe syste+ gro'nd.  Despite the caveats, one advantage o the *ridge rectiier is that the +aCi+'+ inverse voltageor any o the diodes is only 2 ti+es the 9>6 inp't voltage. 7he +agnit'de o the inverse voltageacross D2 is is prevented ro+ rising a*ove Vin 2 *y the cla+ping action o D1 and vice versa. 7hesa+e arg'+ent applies or D$ and D .

6ridge rectifier- 3ll diodes, VR- E Vin(+aC) J 2

Principle of operation 3ltho'gh the *ridge rectiier is very a+iliar, its +ode o operation is s'rprisingly diic'lt to'nderstand. 7his can *e +ade apparent *y as&ing the 'estion- 5 the circ'it a*ove is gro'nded asshon, hat voltage aveor+s, +eas'red relative to gro'nd, ill appear at points V1 and V2  ^ 5yo' have not previo'sly needed to solve this pro*le+, it ill pro*a*ly ta&e yo' a hile to or& o'tthe anser.  3 si+ple ay to ind the sol'tion is to i+agine adding centre taps to *oth the inp't netor& andthe load netor&, as shon in the diagra+ *elo.

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5t is not really necessary to tap into the s+oothing capacitor as ell as the load resistor, *'t i e doso the circ'it *eco+es re+iniscent o the a+iliar d'al#rail poer s'pply18. 3ll e have to do tot'rn it into the d'al#rail s'pply is +ove the earth to the centre tap and eed it ith a centre#tappedtransor+er instead o a resistive potential divider. 7h's it sho'ld *e o*vio's that i the to hal#

o'tp'ts are e'ally loaded (hich they are), there ill *e no c'rrent loing along the connection *eteen the inp't and o'tp't centre taps. 7his +eans that, ith the negative ter+inal o the o'tp'tgro'nded, the alternating voltages V1 and V2 +'st *e sy++etric a*o't a D/ oset at hal theo'tp't voltage. 6o no, i e let-

Vin G Vp 6inH

7hen-

V1 G ( Vm N Vp 6inH ) 2

and

V2 G ( Vm # Vp 6inH ) 2

 Mote that these to voltages are identical apart ro+ a 180_ phase dierence. 3lso, the 3/ co+ponent in each case is hal the inp't voltage.

 Mo co+pare the graph o the operation cycle given a*ove ith the corresponding graph or thevoltage do'*ler in section &. 5t appears that the *ridge circ'it splits the inp't voltage into tohalves in antiphase. 7hese to hal#voltages are then applied si+'ltaneo'sly to a pair o voltagedo'*lers. 6ince there is no overall voltage +'ltiplication hoever, the inp't i+pedance is-

9 (in G ( 9 D N 29 diode ) 2

Ripple freuency

7he rectiiers descri*ed in sections 1 # & all top#'p the s+oothing capacitor once per cycle. 7he *ridge rectiier hoever, tops 'p the capacitor tice per cycle, hich +eans that it do'*les theripple re'ency. 3lso, i the circ'it is 'sed itho't s+oothing, it *eco+es a highly eicient

re'ency do'*ler, re+oving the 'nda+ental re'ency#co+ponent co+pletely (ass'+ing perectsy++etry). 7he re'ency#do'*led o'tp't is not sin'soidal, o co'rse, *'t it can *e iltered.  7he re'ency do'*ling eect is 'se'l in +ains#re'ency poer#s'pply applications *eca'se itred'ces the re'ired s+oothing capacitance or a given level o ripple. 5t is hoever, 's'ally olittle i+portance in radio#re'ency applications *eca'se s+oothing capacitors are, in any case,s+all.

7he *i#phase (hal#*ridge) rectiier circ'it disc'ssed in section $ also do'*les the ripplere'ency< *'t note that the voltage do'*ler (section &) does not, even tho'gh it is a type o 'll#ave rectiier.

18 5t t'rns into a pair o *i#phase rectiier poer s'pplies o opposite polarity. 6ee section $.

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Freuency sampling

7he act that the inp't ter+inals o a *ridge rectiier, hen +eas'red relative to gro'nd, carry an3/ signal o hal the loating inp't voltage can *e eCploited or the p'rpose o sa+pling the inp'tre'ency. 7his is the traditional +ethod or eCtracting the poer#line re'ency ro+ +ains

transor+ers itho't 'sing a separate inding, and is 'sed to provide a si+ple and acc'rate ti+ingreerence in devices s'ch as electronic cloc&s.

3 poer#line sa+pling circ'it is shon on theright. 7he orard voltage or silicon %#M

 poer diodes is a*o't 0. V, so the poer#s'pply prod'ces a ra D/ o'tp't o ."2 # 2J0. G @.2 V, hich is intended or reg'lation to " V or poering logic circ'itry.7h's the voltage to gro'nd on either side o the3/ inp't to the rectiier is $." V 9>6, ith a

D/ oset o N.4 V. 7his corresponds to a peato#pea& eCc'rsion o $." J 22 G 10.4 V, *'t it is ed thro'gh a resistor and a co'plingcapacitor to a pea& clipper co+prising to1M18 silicon %#M signal diodes. 7hese havea orard voltage o a*o't 0.4 V, and so theres'lting aveor+ is li+ited to lie *eteen0.4 V a*ove the N" V rail and 0.4 V *elogro'nd, i.e., it is clipped to 4.2 V %#%. 7his isconverted into a clean " V %#% s'are ave *y+eans o a />O6 6ch+idt trigger.  5t sho'ld *e 'nderstood, o co'rse, that any s'*stantial loading o the voltage at the 3/ inp'tside o a *ridge ill 'pset the sy++etry. :or a circ'it designed to prod'ce h'ndreds o +illi#a+ps,or even a+ps, o o'tp't c'rrent hoever, a sa+pling netor& s'ch as this ill +a&e no +eas'ra*ledierence. Mote that the 100 n: capacitor has a reactance o #$2 & at "0 ;= (#2 & at 40 ;=),and altho'gh there ill *e har+onics present, it constit'tes a very ea& co'pling. 7he 1 & resistor gives the diodes and the 6ch+idt trigger so+e protection ro+ any ast transients that +ight appearon the poer#line.

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2$

oupling capacitor

Beca'se the *ridge rectiier introd'ces no net D/ co+ponent into the c'rrent loing in the so'rcenetor&, it can *e ed via a co'pling capacitor (or capacitors) i so desired. 5n poer s'pplieshoever, the 'se o a co'pling capacitor can *e dangero's 'nless the i+plications o so doing are

considered in advance.  5n the thoro'ghly nasty circ'it shon onthe right, a *ridge is ed via a co'plingcapacitor, and o'r sitches are provided or the p'rpose o si+'lating a short#circ'it(hich is the 's'al ail're +ode) in any oneo the o'r diodes.

?et 's irst consider hat happens hendiode D$ is shorted. 5n that case, V2 is p'lledto gro'nd, D1 and D2 *egin to act as a voltagedo'*ler, and D is har+lessly reverse#*iased

(it is ass'+ed, incidentally, that none o thediodes have their VR- ratings eCceeded hen the event occ'rs). :ro+ an eCternal point o vie, theeect is approCi+ately to divide the inp't i+pedance *y a actor o (ass'+ing a p'rely resistiveload), and to do'*le the o'tp't voltage. 6horting#o't D1 ill, o co'rse, have a si+ilar eect.  Mo consider the eect o shorting#o't D2. 5n that case, V1 is tied to the positive o'tp'tter+inal, D$ and D act as a voltage do'*ler prod'cing an o'tp't that is negative relative to the

 positive ter+inal, and D1 is per+anently reverse *iased. 6horting o't D ill have a si+ilar eect.  7h's, hen the *ridge is capacitively co'pled, there are o'r ays in hich the +ost co++ontype o diode ail're can do'*le the o'tp't voltage and 'arter the inp't i+pedance. 3 'se isgenerally too cr'de a saety device to detect s'ch an i+pedance change, and circ'itry s'*ected totice its intended operating voltage can +al'nction in n'+ero's 'npleasant ays. 6'ch +ight *ethe conse'ence o ailing to consider this idiosyncrasy. On the other hand, a voltage do'*lercirc'it can *e provided ith a hal#o'tp't (J`) acility *y the addition o to +ore diodes an asingle#pole sitch.

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$. +i-phase rectifier7he *i#phase (or hal#*ridge) rectiier as once idely 'sed in the poer s'pplies o valve (t'*e)e'ip+ent. 3s a poer rectiier, it is a poor choice in co+parison to a 'll *ridge< and aterseleni'+ ;V rectiiers1@ *eca+e availa*le in 1@$$, its chie design +erit see+s to have *een that it

+aCi+ised the proits or oners o light#*'l* actories hile increasing the si=e and co+pleCity othe +ains transor+er at the c'sto+ers eCpense20 21. 7he circ'it creates a serio's ire ha=ard in theevent that one o the rectiiers sho'ld ail open circ'it 22, *eca'se a D/ co+ponent ill then *e

 present in the transor+er secondary c'rrent, ca'sing core sat'ration and overheating.  5n signal detection applications hoever, the circ'it has the advantage o *eing a 'll#averectiier ith only a single diode orard#voltage drop in the path to the load. By cond'cting on

 *oth hal#cycles o Vin , the circ'it also halves the average diode c'rrent or a given o'tp't voltage,and so red'ces the diode orard voltage drop co+pared to that o a hal#ave rectiier. Beca'se o the logarith+ic diode V#5 characteristic hoever, the Vf red'ction is only a e \.

3 disadvantage o the circ'it that it 's'ally re'ires a centre#tapped co'pling transor+er (altho'ghit can *e constr'cted as a pair o hal#ave rectiiers driven *y a d'al#ended (*alanced o'tp't)a+pliier). 7he o'tp't voltage o the transor+er#co'pled version is given approCi+ately *y theolloing eCpression (hich neglects transor+er losses and diode orard voltage drop)-

Vm G Vin (2) Ms Mp  # Vf  

Where Ms Mp  is the t'rns ratio. /orrect operation re'ires that the transor+er has s'icient pri+ary ind'ctance not to load the driving netor& signiicantly at the loest re'ency ooperation, and that the transor+er is otherise or&ing ithin its pass#*and. :or ;: radiore'ency applications, the transor+er can *e o'nd on a s+all errite toroid or to#hole(*inoc'lar) core. Mote incidentally, that i a transor+er is 'sed or the ratio ar+s (i.e., the voltage#dividing netor&) o a +eas'ring *ridge, it is possi*le to co+*ine this transor+er ith the *i#

 phase detector transor+er *y 'sing the act that the *ridge is a linear reciprocal netor& (i.e.,generator and detector ports are interchangea*le). 7he res'lting conig'ration, a type o

1@ 6eleni'+ high#voltage rectiiers (see- http-en.i&ipedia.orgi&i6eleni'+rectiier) ere considera*ly +oreeicient than valves and re'ire no heater s'pply, *'t e'ip+ent +an'act'rers associated ith the valve cartels didnot 'se the+. 7he slo adoption o se+icond'ctors in so+e 'arters is 'rther disc'ssed in section 11.

20 3s pointed o't *y Bo* Weaver (private e#+ail, 1th 3'g 201), the eight o copper re'ired is not greatlyincreased hen a *i#phase is 'sed instead o a *ridge, *eca'se the to secondary indings provide hal the c'rrenteach. 7he +an'act'ring ti+e and the a+o'nt o ins'lating +aterial hoever, ill *e increased, and the valverectiier (in sae design practice at least) re'ires an additional loating heater inding.

21 7he +ar&eting o radio receivers in the 1@$0s, partic'larly in the A63, led to t'*e ars. Asing +ore t'*es ass'pposed to +a&e a *etter radio set. 7her+ionic rectiiers ere co'nted as t'*es, even tho'gh they ere nothing todo ith the signal chain, *'t the se+icond'ctor rectiier as not so easily t'rned into a +ar&eta*le concept.

22 6ilicon rectiiers 's'ally ail short#circ'it, hich is sae ith an ade'ately speciied transor+er *eca'se it ill *lo the pri+ary#side 'se. Valve rectiiers co+e in to types< single cathode d'al anode, hich cannot ail ithone diode open circ'it< and the +ore 's'al d'al diode ith d'al ila+ents in parallel, hich is a ire ha=ard andsho'ld *e replaced *y a solid#state rectiier and a sot#start circ'it i the e'ip+ent is to *e re#certiied or 'se. 5t isa good idea to replace or re#or+ the s+oothing capacitors hen changing to solid state rectiication (an increase ino'tp't voltage occ'rs).

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2"

transor+er ratio#ar+ *ridge (793B) is shon *elo-

7his circ'it allos the 'n&non and reerence i+pedances, the generator, and the o'tp't netor&,all to have one ter+inal connected to gro'nd. 7he transor+er ill introd'ce so+e +inor voltageshortall, d'e to losses and lea&age ind'ctance< *'t it ill not introd'ce non#linearity 'nless it isoperated close to core sat'ration, hich is highly 'nli&ely given the trivial poer re'ire+ent o asignal detection circ'it. 3 partic'lar disadvantage o the conig'ration hoever, is that it involves

st'ing the ratio#ar+ transor+er ith a relatively large a+o'nt o ire, hich +ight +a&e itdiic'lt to +ini+ise stray capacitance *eteen the pri+ary and secondary indings. 7he ratio#ar+transor+er +'st *e designed ith *alance as the principal criterion, and it is not necessarily a goodidea to try to +a&e it peror+ additional 'nctions.

With regard to diode VR- , note that the *i#phase rectiier is si+ply to hal#ave rectiiers eedingthe sa+e s+oothing capacitor. ;ence the inverse voltage rating or a diode +'st *e at least 22ti+es the 9>6 voltage at the transor+er o'tp't.

 Mote that the *i#phase circ'it is a re'ency#do'*ling rectiier, hich can *e either an advantage ora disadvantage in 9: applications.

3s +entioned *eore, the *i#phase rectiier gives an i+prove+ent in linearity over the hal#averectiier *y dividing the rectiier c'rrent *eteen to diodes< *'t as ill *e disc'ssed in the neCtand later sections, the diode orard voltage drop varies logarith+ically ith c'rrent in s'ch a aythat the i+prove+ent ill not *e partic'larly large, and so the additional co+pleCity +ight not *earranted.

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&. Diode static voltage vs. current characteristic3ll o the diode detectors descri*ed in the preceding sections have at least one diode orard#voltage drop in the path to the +eas'ring device. Ander static conditions (i.e., hen a D/ *ias isapplied) the voltage across the diode ( Vd ) varies approCi+ately in proportion to the logarith+ o

the c'rrent ( 5d ) passing thro'gh it. 7he c'rrent also depends on the te+perat're o the diode 'nction. :or +any types o diode, this *ehavio'r is descri*ed to a good approCi+ation *y a+odiied or+ o the 6hoc&ley diode e'ation2$ 2 2" 24.

Vd G 5d 9 ds N + ( &6 7e ) lnZ ( 5d 5S ) N1 [

here-

5d is the static or instantaneo's orard c'rrent.

9 ds is the ordinary oh+ic series resistance o the diode.

5S is the 'nction reverse sat'ration lea&age c'rrent (see section %.1). Mote that this 'antityvaries ith te+perat're independently o the ther+al voltage, V7 (disc'ssed *elo).

+ is a di+ensionless correction actor *eteen 1 and 2 (&non as the ideality actor ore+ission coeicient )2.

ln is the nat'ral logarith+ operator (?oge ).

&6 is Bolt=+anns constant ( &6 G 1.$80442J10#2$ o'les&elvin).

e  is the charge o an electron ( e G 1.40218@2J10#1@ co'lo+*).

7 is the te+perat're in Kelvin, K, i.e., the a*sol'te te+perat're (/ N2$.14).

7he actor &6 7e  has di+ensions o volts and is oten given the sy+*ol V7 (the ther+al voltage).

V7 G &6 7e G 2".$ +V at 20/.

7he +odiied 6hoc&ley e'ation is then +ore conveniently ritten-

Vd G 5d 9 ds N + V7 lnZ ( 5d 5S ) N1 [ %.1

When + G 1 and 9 ds G 0 , the diode orard characteristic red'ces to the 6hoc&ley ideal diodee'ation-

2$ 7he theory of p/n 3unctions in semiconductors and p/n 3unction transistors. W 6hoc&ley. Bell 6yste+ 7ech.Ro'rnal 28($), 1@@, p$"#8@. 6ee p", e'ation $.1$ Z5deal diode e'ation ith oh+ic resistance[.

2 arrier generation and recom*ination in P/N 3unctions and P/N 3unction characteristics, / 7 6ah, 9 M Moyce,W 6hoc&ley, %roc. 59, 6ept. 1@", p1228 # 12$. ZDeviation ro+ ideality[.

2" Physics of semiconductor de+ices. 6 > 6=e. Wiley, 1@4@. 6BM 1 82@0 Z2nd edition 1@81 and $rd edition 2004also eCist[. /hapter $, part (p@4#102). /'rrent#voltage characteristics o %M 'nction diodes.

24 7he art of electronics, % ;oroit= and W ;ill. 2nd edition 1@8@, /a+*ridge Aniv. %ress. 56BM 0#"21#$0@"#.*ers#>oll +odel or transistors. p@#80.

2 >ost o the original articles 'se n or the e+ission coeicient, *'t here e ill reserve n or other p'rposes.

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Vd G ( &6 7e ) lnZ ( 5d 5S ) N1 [

hich, 'sing the notation eCp(C) G e

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2@$.14 K (i.e., 20_/), and e call 5S at this te+perat're 5S2>& , then e can rite-

ln( 5S  5S2>& ) G a7 N * . . . . . . . (%.2)

here 7 is the te+perat're, a is the gradient o the line, and * sets the point at hich the line crossesthe aCis. Mo note that hen 5S G 5S2>& , ln(5S 5S2>&) G 0 . 7h's-

0 G 2@$a N *

i.e.-

 * G #2@$a

3lso note that i the sat'ration lea&age c'rrent do'*les or a 20 K rise in te+perat're, then-

ln(2) G $1$a N * G $1$a # 2@$a G 20a

i.e.-

a G ln(2) 20

:eeding the eCpressions or a and * *ac& into e'ation (%.2) gives-

ln( 5S  5S2>& ) G 7 Zln(2) 20 [ # 2@$ Zln(2) 20 [

i.e.-

ln( 5S  5S2>& ) G ln(2) ( 7 # 2@$ ) 20

Cponentiating *oth sides and rearranging then gives-

5S G 5S2>& eCp ln(2) ( 7 # 2@$ ) 20 X %.&

 Mote that this eCpression contains the ass'+ption that 5S do'*les or a 20 K te+perat're rise. 5till s'ice i no other inor+ation is availa*le< *'t i to +eas're+ents o 5S are +ade at dierentte+perat'res ( 70 and 71 say), then a +ore acc'rate or+ can *e ritten-

5S G 5S70 eCp ln( 5S71  5S70 ) ( 7 # 70 ) ( 71 # 70 ) X %.'

7he large te+perat're variation o the diode characteristic, altho'gh 'antiia*le, s'ggests thatdetector diodes 'sed or precision voltage +eas're+ent applications sho'ld ideally *e operated in ate+perat're controlled environ+ent. 7he detector, or eCa+ple, +ight *e placed inside a s+allte+perat're reg'lated cha+*er, si+ilar to (or act'ally) a crystal oven.

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2@

&. Diode #easure#ents7he graph *elo shos the +eas'red orard voltage vs. c'rrent characteristics o a variety os+all signal diodes.

7he 1M18 is a silicon %#M 'nction diode. 7he 1M"11 (3gilent "082#2800) is a silicon 6chott&ydiode (i.e., silicon#+etal 'nction diode). 7he O3 is an archaic ger+ani'+ gold#*onded diode,and the rest are ger+ani'+ point#contact diodes. 7o 1M18 diodes ro+ dierent +an'act'rersere +eas'red +erely to ill'strate the point that silicon %#M diodes have the highest orardvoltage and are thereore a poor choice or lo voltage detectors. 7he 1M"11 c'rve is the averageo res'lts ro+ o'r diodes, all ro+ the sa+e *atch, hich had practically identical characteristics.

7he O3 c'rve is the average or o'r diodes ro+ to +an'act'rers, all having si+ilarcharacteristics. 7he O3@0, O3@1, and 1M40 c'rves are ro+ single eCa+ples, and are thereore notnecessarily representative o the type. 3ll data ere recorded at an a+*ient te+perat're o 21/.

7he data indicate that the 5M18, the 1M"11, and the O3, all o*ey a logarith+ic V5relationship reasona*ly ell, hereas the ger+ani'+ point#contact characteristics shoconsidera*le c'rvat're d'e to high oh+ic resistance. With regard to the orard voltage drophoever, the ger+ani'+ diodes are all s'perior to the 5M"11 in the 1 to 100 L3 range, and the

 preerence or the latter +ay +erely relect the act that +any se+icond'ctor +an'act'rers nolonger a*ricate ger+ani'+. 6ilicon 6chott&y diodes, s'ch as the 1M"11 and 1M424$ have *etterhigh#re'ency peror+ance than ger+ani'+ diodes, *'t ger+ani'+ diodes or& ell at V;: andare thereore oten ade'ate or ;: applications. 3+ong the ger+ani'+ diodes, there is little

dierence *eteen the gold#*onded and standard varieties in the 1 L3 to 100 L3 range, *'t theO3 is the *est choice or c'rrents 'p to 1 +3. We sho'ld o*serve hoever, that detector diodesonly cond'ct signiicantly on the pea& o the applied aveor+, and so the instantaneo's c'rrent is

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+'ch higher than the average c'rrent, the dierence *eing a*o't an order o +agnit'de$1 (seesection 12). 7hereore, in selecting diodes or average c'rrents in the region o 1 L3 to 100 L3, esho'ld consider the steady#state voltage drop in the region 10 L3 to 1 +3< in hich case theger+ani'+ gold#*onded diode oers the loest orard#drop itho't contest. Mote hoever, that

one o the conse'ences o the diode e'ation is that lo orard voltage#drop is associated ithhigh reverse sat'ration lea&age c'rrent. 3lso, there ill *e a non#sat'ra*le reverse lea&age c'rrent,ro'ghly e'ivalent to a resistance in parallel ith the diode, and ger+ani'+ diodes are orse than+odern silicon diodes in that respect. ;ence, i reverse lea&age is an iss'e, silicon 6chott&y diodesare to *e preerred. 7o p't this +atter in perspective hoever, the reverse lea&age c'rrent o anO3 diode as +eas'red as ollos-

Vr   Volts 1.0 2.0 $.0 ".0 10.0 1".0 20.05r   L3 1.1 1.$ 1. 2.1 .1 4.$ 8.8

7 G 21/

7he lea&age c'rrent is approCi+ately linear in the " V # 20 V range and can *e +odelled *yass'+ing a parallel resistance o a*o't 2 >. 6'ch a deect has little eect on the operation o adetector loaded ith a 10 & # 100 & resistance, *'t ill *e deleterio's in the high#i+pedancedetector circ'its disc'ssed earlier. 6o+e 'sers o e diodes in high#i+pedance detectors act'ally'se the+ itho't a D/ ret'rn path ('sing the diode lea&age or that p'rpose)< *'t s'ch circ'its are'npredicta*ly dependent on the characteristics o the partic'lar diode 'sed.

6o+e inal points in avo'r o the silicon 6chott&y diodes are that ger+ani'+ diodes sho a iderspread o characteristics, and that the O3 and the later 33#series e#3' diodes are o*solete.;ence the 6i 6chott&y diodes are deinitely preera*le in applications re'iring diode +atching,

 precise cali*ration, or availa*ility thro'gh nor+al co++ercial channels. 7he 1M"11 in partic'laralso, has a high reverse *rea&don voltage or a silicon device o its class, its V R-  o 0 V +a&ingit s'ita*le or hal#ave detectors o 'p to 2. V D/ o'tp't. 3n O3 hal#ave detector has a+aCi+'+ D/ o'tp't o 10.4 V i VR- is not to *e eCceeded.

$1 ali*rating diode detectors. R re*en&e+per. Q, 3'g. 1@@0, p$#8.

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'. %ignal diode data7he ta*le *elo shos so+e collected diode data. 7he inor+ation is +ostly historical, *'t the

 point is to *e aare o the typical orard voltages, reverse *rea&don voltages and reverse lea&agec'rrents associated ith the vario's types. 3lso note that e diodes are noadays 's'ally MO6 or

salvaged, and so old spec. sheets are not necessarily red'ndant.:or s+all#signal 9: rectiier volt+eters, diodes sho'ld *e chosen or lo orard voltage drop

and lo 'nction capacitance (hich is given in *rac&ets here &non). 3n eCa+ple %ico#a+pdiode (%3D) is also incl'ded. 7hese are not 'sed as detectors, *'t are connected anode to cathodeacross diodes placed in op#a+p eed*ac& loops, to prevent ild eCc'rsions in the rong o'tp't

 polarity range.

7ype Description Vr ma

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e) ?inear syste+s datasheet. .linearsyste+s.co+) 67 >icroelectronics datasheet .st.co+

7ypical reverse lea&age c'rrent at a given voltage gives a ay o esti+ating the eective parallelresistance. %rovided that the reverse sat'ration lea&age c'rrent is +'ch s+aller than the totalreverse lea&age c'rrent-

9 dp G Vr  5r 

5 the sat'ration lea&age c'rrent is high, it sho'ld *e s'*tracted ro+ the total to ind the oh+iccontri*'tion, i.e.<

9 dp G Vr  (5r # 5S )

Point contact 3unctions

 Mote that point#contact diodes are so+eti+es 6chott&y diodes and so+eti+es not. 5 the point#contact res'lts in a se+icond'ctor#+etal 'nction, then the diode +ight *e reasona*ly classiied as a6chott&y type. Oten hoever, there is an initial *'rn#in step in +an'act're, hich ca'ses so+e o the +etal to di'se into the se+icond'ctor crystal and or+ a %#M 'nction $$. iven this a+*ig'ity,the ter+ 6chott&y diode is 's'ally reserved to +ean diodes having a se+icond'ctor#+etal 'nctionor+ed *y evaporation o +etal on to the crystal s'race.

$$ Schott"y *arrier de+ices. R / 5rvin and M / Vanderal, in -icro#a+e semiconductor de+ices and their circuitapplications, ; 3 Watson (d.), >cra#;ill 1@4@, ?//M 48#11@. p$0#$4@, see p$1.

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$$

,. Diode circuit #odel3 s'ita*le +odel or in#circ'it diode si+'lation is shon on theright. 7he non#linear *ehavio'r is descri*ed *y the three

 para+eters o the +odiied 6hoc&ley ideal diode e'ation

(5s , +, V7  in e'ation %.1), and all o the other para+eters can *erepresented as conventional circ'it ele+ents.

?ds is the series partial ind'ctance associated ith every circ'itco+ponent, and / 3 is the 'nction capacitance. ?ds is a e n;or ire#ended diodes (the old 20 n; per inch r'le provides aro'gh g'ide), *'t is very s+all or s'race#+o'nt devices (neglecting %/ trac&s). / 3 is as per the+an'act'rers literat're (2 p: or the 1M"11) 'nless 'antiied eCperi+entally. Mote that a hal#ave diode detector 's'ally eeds into a s+oothing capacitor. 7he s+oothing capacitorintentionally has nearly =ero reactance at the generator re'ency. 7he capacitance sh'nting thediode also +a&es =ero contri*'tion to the D/ o'tp't. ;ence, at the driving re'ency, / 3 iseectively connected *eteen the inp't#side netor& and gro'nd. 7his can help to si+pliy the 9:+odelling pro*le+ at higher radio re'encies. 9eactances, o co'rse, can *e neglected at loerre'encies.

3 si+'lation o the D/ or instantaneo's characteristic o a1M"11 6chott&y diode (neglectingreactance) is shon on the right(see open doc'+ent spreadsheetile detmodels.ods, sheet 1).Voltage and c'rrent are deined as

 positive hen the anode is positiveith respect to the cathode. 7oc'rves are shon< one ith 9 dsta&en into acco'nt, and the other ith 9 ds G 0 (i.e., ignored). 7hetypical 9 ds o 2" i+plies as'*stantial contri*'tion to theorard voltage at 5d G 10 +3, *'tit is not so i+portant ith c'rrentso a e +icroa+ps. 5 9 dp is letopen circ'it (i.e., ignored) the diode

reaches its reverse sat'rationlea&age c'rrent hen the negative *ias eCceeds +ore than a*o't 0.1V. 5 9 dp is incl'ded, the total c'rrent 'nder negative *ias is#5s N Vd  9 dp  (here Vd is negative). 7he +odel ass'+es that the reverse *rea&don voltage isnever approached.

,.1 Diode stacking7he diode static c'rrent vs. voltage characteristic (neglecting parallel resistance) is given *y the+odiied 6hoc&ley e'ation (%.1).

Vd G 5d 9 ds N + V7 lnZ ( 5d 5S ) N1 [

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5 e p't several identical diodes in series, then the orard voltage drop or a given c'rrent is+'ltiplied *y the n'+*er o diodes (nd  say). 7h's

Vnd G nd 5d 9 ds N nd + V7 lnZ ( 5d 5S ) N1 [

7h's the eect is to +'ltiply the ther+al voltage (V7 ) and the series resistance *y the n'+*er odiodes. 7he parallel resistance is, o co'rse, si+ilarly +'ltiplied, as is the series partial ind'ctance.7he capacitance hoever is halved.

. +ack diodesOne 'rther rectiying device that e sho'ld +ention in passing is the backward diode or *acdiode $ $". 7his is a type o t'nnel diode or sa&i diode. D'e to heavy doping o these+icond'cting +aterial (oten ger+ani'+), the t'nnel diode has a negative resistance region in itsV5 characteristic, hich +a&es it 'se'l as an a+pliier, oscillator or trigger device. 7he *ac&diode is a less#heavily doped version, hich +eans that the negative resistance characteristic largelys'ppressed. 7his gives it a characteristic +ore li&e that o a nor+al diode, eCcept that it has aneCtre+ely lo orard voltage drop, so+ehere in the region o @0 +V or 10 +3 orard c'rrent.  Anort'nately hoever, there is no general or&aro'nd as ar as the diode e'ation is concerned.7he *ac& diode has an eCtre+ely lo reverse *rea&don voltage, and a lea&age c'rrent o aro'nd1 +3 or only "00 +V o reverse *ias$4. 7he reason is that, relative to the nor+al electrode na+ingor a given +aterial type, the *ac& diode is 'sed *ac&ards< i.e., it cond'cts +ore in the reverse

direction than in the orard direction. 7his is d'e to the 'ant'+#+echanical t'nnelling eectater hich this class o devices is na+ed.7he diode can thereore only *e 'sed in eCtre+ely lo#i+pedance lo#voltage circ'its, hich

+a&es it 'ns'ita*le or the constr'ction o conventional pea& detectors. 5t does hoever +a&e agood s'are#la detector, and can thereore *e 'sed or direct conversion o voltage readings into

 poer readings$.  5t also has lo capacitance, and is ree ro+ charge storage eects, +a&ing so+etypes 'se'l 'p to a*o't 0 ;=.  Bac& diodes are still a c'rrent +icroave technology$8, *'t they are eCpensive. When a s'are#la detector is re'ired or +ore general 9: applications, and pres'+ing that active circ'itry can *e'sed, a +ore cost eective sol'tion is to 'se a linear detector olloed *y an anti#logarith+ica+pliier or an analog'e +'ltiplier. 3nother sol'tion is to digitise the o'tp't o a linear detector

and peror+ the arith+etic 'sing a co+p'ter or a +icrocontroller. Detector linearisation ill *edisc'ssed in part 2.

$ 7he art of electronics. 2nd ed. ;oroit= b ;ill (previo'sly cited). Bac& diode as a s'are#la detector, p8@1#8@2.7'nnel diode p1#1", p1040.

$" !mplifier and*oo" . d. 9 : 6hea. >c ra ;ill 1@44. 56BM 0#0#0"4"0$#1. /h. 12. 7unnel diodes and*ac"#ard diodes. / 6 Ki+ and R R 7ie+ann. 7heory, characteristics and applications.

$4 @ffecti+e noise reducer and hearing protector. 9 ? 9od, Q67, 3pril 1@8, p0. 6i+ple a'dio clipper circ'it'sing *ac& diodes. ives V5 characteristic or eneral lectric BD1.

$ Ne# approach to measuring SR at high freuencies. A ? 9ohde. ;a+ 9adio. >ay 1@@, p$#$".7he 9ohde b 6char= M3A6 80 9: poer +eter 'ses *ac& diodes as s'are#la detectors.

$8 http-.aeroleC.co+a+s+etelics+icro#+etelics#prods#7D#>7D.c+

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1. *acuu# ther#ionic diodesiven that se+icond'ctor diodes are not ideal rectiiers, so+e readers +ight onder i ther+ionicdiodes (valves) are capa*le o *etter peror+ance. 7he anser hoever is a +ost e+phatic no7he orard voltage o an indirectly heated valve diode in the lo#c'rrent (space#charge li+ited)

regi+e$@ is given *y the eCpression-

Vf  G ( 5f K )$2 # Vc

here K is a constant deter+ined *y the geo+etry o the diode and Vc is called the contact potential , *y analogy ith the potential developed *y a ther+oco'ple. 7he diode contact potentialarises *eca'se so+e o the electrons eected ro+ the cathode arrive at the anode even hen there isno *ias, and so the anode *eco+es negatively charged. 7his +eans that the diode +'st *e reverse

 *iased in order to prevent it ro+ cond'cting, and the a+o'nt o *ias re'ired varies ith the heater te+perat're and the age o the valve.

5n precision +eas're+ent ter+s, the contact potential is enor+o's. 3sa+ple o eight do'*le#diode valves o type B@1 (43?") shoedcontact potentials ranging ro+ 0.8 V to 0.@4 V (ith a +ean o 0.$ V) hen +eas'red 'sing a volt+eter ith 10 > inp't resistanceand a sta*ilised 4.$0 V D/ heater s'pply (d'e to drit, sensi*le+eas're+ent as i+possi*le 'sing a ila+ent transor+er connected tothe 3/ +ains s'pply). 3 100 L3 +oving coil +eter ith an internalresistance o @80 as connected across a diode having an open#circ'it contact potential o 0. V, and registered a =ero#*ias c'rrent o 0 L3, i.e., the diode gave a D/ o'tp't o .8 LW d'e to the ther+al

c'rrent. When the +eter as padded to 10 &, to si+'late the diodeloading in a reasona*ly realistic detector circ'it, the =ero#*ias c'rrentas 22 L3, i.e., 22\ o 'll#scale delection.

Witho't even considering the other (+aniold) shortco+ings o thedevice, e +ay saely concl'de that, in co+parison to se+icond'ctor diodes, ther+ionic diodes have no +erit in s+all