VHF COMMUNICATIONS 2/2000

Dipl.-Ing. Jv.Parpart

THE I/Q MODULATORDESCRIBED

Oigitalised image and sound signalshave become an everyday eccu rencein the last decade. Polished algnrithmsfor data reduction make it possible totransfer more and more informationin a rest ricted frequency band, withor without a wir e. Many digitalmodulatinn processes require a so~

called I/Q modulator as kl'y clement.What this clement docs is to control acarrier frequenc y as regards phaseami, if necessary, amplitude, withea ch carrier condlucn or each condi­tion change rep resented by a bitsequence.

1.I'RELIMINARY REMARKS

In principle. tile I/Q modu lator is fullydigitalisab lc. Its output signal can bepredicted, depending on the data to betransferred, and can be gene ratedthrough IliA conversion, lt s all a ques­tion oftechno logy.

However. the I/Q modulator presented

106

here stems from a time in whichcomponents were still wired. It operatesas an analogue or a linear unit. Th ecircuit, laid out using purely passivetechniques, allows for an insight intowhat is go ing on. Var ious application sare d iscussed, start ing from a basiccircu it (F ig. I), which can be eas ily builton the board shown in Figs. :2 and 3.

2.FROM IlSIl MODULATORTO I/Q MOIlULATOR

By multiplying an oscillator signal (frc ­qucncy: fa ) ",... ith a modulation signal(frequ ency: .lin), we obtain two newsignals with the Frequencies f o - fin andfo + fin . If a comp lete base band signalis multiplied by an oscillator signal - themodu lation process two side bands areobtained (hence DSB, for dou ble sideband). If a DC vo ltage is applied to themultiplier, th is means that the carrier(othe rwise suppressed) appcars in thespectrum .

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VHF COMMUN ICATIONS 212000(~--- - - - - - - - - ---"-"-"'= = = = = =In practise. multiplication is often car­tied out with the help of an e lectron iccommutator switch (e.g. a d iode ringmixer). The po lar ity of the modulationsignal thus changes within the osc illatorfreq uency cycle . Add itio nal products arcgenerated by means of this pn)Cl...ss. aswell as the modulation produ cts referred10 above. Th ey are grouped around theodd-numbered harm onics of the oscilla ­lor frequency and must be el iminatedthrough filt ration

In compariso n to rbe base hmll!. tileUSH signal takes up double the bandwidth. But since frequencies an: alwaysscarce, 11 would be nice if we coulddouble the usc of the doubled handwidth. lt is actually possihle to separatetwo DSU signals again on the receptionside, insofar as they have been gener­ated with the same oscillato r frequencyand with a dc fin...d oscillator phase. Inthe idcal case. this gives us two trans­mission channels independent o f eachother.

f rom the mathema tical point Ill' view.the l/O modulator consists of twomultipliers which conta in the modulationsignals (/(1) and (J( t)). There is 90"difference between the oscillator signals.By convention the lead ing oscillatorsignal is applied 10 the multiplier in theQ path. If we look at the I oscillatorsignal as a reference. then the Qosci llator signal is displaced by a quar­tor-period to the left on the time axis. Inthe vector representation. is rotat ed 90"anti-clockwise

The output signals from the multipliersarc added and then transmitted. r ig. 4shows the interaction of modu lator anddemodulator. on the assumption that the

multiplie rs have orthogo na l phases inthe I and Q channels. and that thetransmiss ion signa l causes no signa ldelay (d irect connection). It can be seenfrom the draw ing that if the receivero scillator is running synchronously withthe transmitter esciflator ( ~ = 0). we getback Itt) and (Xt) through synchronousrt..-ctificarion and subsequen t low· pa<;sfiltration (provided w ith a system-de­pend ent proportionality factor).

there arc four condit ions altogether fro:from cross-talk. namely ~ = OC, 9OC.1110" and 270" . So at the demodulatoroutputs there is either the original, atransposition with I inversion. a two­sided inversion. or a tmnspo-citinn withQ inve rsion. Mind you. the phase posi­t ion must be kept 10 vel')' precisely withrespect to channel se p aration (c.g. - I "already causes a 35 dD cross-talk ).Moreover. any deviation from the re­quired orthogonalit y brings problem swith it. Modulator errors and dcmod ula­tor errors can com pensate for each otheror be cumulat iv'c. which makes th is area\'Cry undefined . If we assume that wehave an orthogonal demod ulator, a I :>modulator error causes a channel cross­talk of 35 to 41 d H.

3.COMI'LEX MOll llLAnON

We arc now making the assumpt ion thatthe two modulation signals, l(t) andQ(t), receive d iscrete amplitudes ( n

d iffe rent values. multi- valent data trans­fer). and that the change from one valueto the other takes p lace at fixed times. Itis best if we represent this in vector

108

VHF COMMUNICATIONS 2/2000=~~~~~~'--------------\l'

Fig. 2: 1.11)outof I/Qmodulatorevpc r tmenta tprinted ci rc ui tboard

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VHF COMMUNICATIONS 2/2000(tc ----'-=--'===e=~""'"

cos ( wtl COS(w t ...1)

k I( t ) cos (t) ...

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IIQ·[lemroJator

Fig. 4: tntcractton of I /Q modulato r and IIQ demodula tor

terms. The f signal is plotted on the x:axis and the Q signal on the y axis. EachI-Q combination corresponds to a read­ing with a defined amplitude and phase(an oscilloscope can make thai veryclear in x-y representation) .

One knov...n repres entat ive of the com­plex modulat ion procedures is, for ex­ample, QAM (quadrature amplitudemodulation). QAM is distinguished byequidistant amplitude values in the f andQ channe ls. All possible pairings arca lso allowed. With four different valuesper channel (e.g. I Y, - 0.33 Y, + 0.33V, r 1 V). we have 16-QAM. for therearc 16 diffe rent combinations.

Also frequen tly encountered is PSK(phase shift key ing). PSK sets theamplitude values in the I and Q channelsin such a way that the total vectorsalways lie on a circle . With fivedifferent values per channel (e.g . IV, -

0 .7 1 V, 0 V. -f 0.71 V, -+- I V). we arcdealing with S-PSK, for we can thenreprese nt eight phase-diffe rent iated read­ings with the same length (only spec i­fied l-Q combinat ions are perm ittedhe re).

If any reading (Zs = l(t) + KXt)) is sentover the transm ission system, in accord­ance with Fig. 4, the correspondingcombinat ion o f the demod ulator outputsgIves

In plain English, the read ing rece ivedcorresponds to the reading transmitted,but its phase ang le is rotated through ~

in a clock wise direc tion. If ~ is suffi­ciently stable, the informa tion transmis­sion could take place in such a form thatreadings following each other in a

110

VHF COMMUNICATIONS 2/2000

temporal sequence were compared withone another. It is advantageous if thecarrier recovery c ircuit provides lor 4' '"'­0". 90", 180" or 270" (a Costas loop cando this), for then the amplitudes at thedemodulato r outputs take on only thepre-speci fied discrete va lues (no channelcross-talk). and can cons eque nt ly berecognised using window comparatorc ircuits without interference . It would heeven better if there were only onescanning point. bUI the Costas loop doesnot cater for th is. The uncertaintyremains as to which quadra nt we are in.Ccdewords can be agreed. or the d iffer­ence can be evaluated for phase anglesfollowing one another.

Understandably. peop le II) to transmitas much information as poss ible per unito f time. The liner the I-Q amplitudesub-division is. the more data can betransmitted fo r a given bandwidt h. Butthen a good signal/noise ratio is re­qu ired. with linear behav iour frum thecomponents taking. part in the transmis­sion. \Ve can allow ourselves 6-I-QAMin the cable television systems. Insatellite technology, we do not wish todifferentiate amplitudes from one an­other. We rely on robust 4-QAM =

4-I'SK. through which we can obtain ahigh degree o f efficiency for the trans­mitte r high- level stage (constant levelcontrol).

4.A:"O IIQ ~lOlllILATOR 1"1 APRACfI CAL FOIUIAT

Fo llowing this theo retica l introduction.let us now conside r an I/Q modu lator in

practise . The circu it can easily be fittedonto half a European standard size pcboa rd. This is cert ainly very large bytodays industrial standards. but aga instthis we can get by with standardcommerc ia l components. Fig. 2 showsthe layout (solder side) and f ig. J thecomponents plan for the I/Q modulatorexper imental printed circuit hoard. Thetop face of the I.S-mm. epoxy printedcircuit hoard is not etched so tha t alleart h connectio ns can be through-ho leplated . The rema ining bores arc counter­sunk. ANC angle sockets form theinter face s to the outs ide world.

The heart o f the circu it co nsists o f two7·dBm Schottky d iode ring mixers( /(U I , R.\I2 ). It is impo rtant that allmixe r co nnections are accessible and notconnected to ea rth at the man ufactur ingstage . Each mixer port is separated fromthe external inputs and outputs by meanso f add itional attenuat ion. The syste mcharacteristic impedance is 75 Ohms.

T he osc illator frequency shou ld lie inthe range between 35 and 40 Mil l . Anex ternal generator supp lies the osc illatorsignal ( IJ dBm). A 3-d B attcnuaror (R7.R8, R9) is fo llowed by a 3-dB 90"d istributor. de-coupled at the outputs. ina bridge circuit (RIO, z.t, C l ). One ofthe distr ibutor outputs must be lappedoff potential- free, which is provided furby the transformer integrated in RM2.The ring mixers thus each have allosci llato r leve l of 7 dBm (R.lf1 receivesa signa l running 90 0 ahead o f RM I) , sothat they sec a broad-band matchin g,and are de-coupled from one another.

The reactive impedances o f L I and C I.together with the resistance RIO. mustcorrespond to the system chara cter istic

111

VHF COMMUNICATIONS 212000(f<------------...::.~~!.!!.!:!!.'~~~

Fig. 5: Reflection att en ua tion at in pu tof 3-dB 90° d istributor

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appears at the rota! output at approx i­mately 60 d fjm, condit ioned by thecoup lings and asymmetries of the mixerand the per ipheral circuit. ln accordancewith the laws or vector addit ion. we canmake the vector 10 disappear com­pletely. by a suitable adjustment of PIand IYJ. (more and more fascinating").

The mod ulation signals. I( t) and Q(I).

(up to approximately 10 MHz ) find theirway to the rntxcr inputs through 18-dBeue nuarors (R·t R5. R6 or R1 4. R15.16). They arc AC coupled through C3,C4 or C6. C7. the lower limitingfreq uency is approximately ~O kHz. Ifwe now apply 2 Vss (sinuso idal) eitherto the J input or the Q input. we obtaintwo sidebands at the tota l output . eac hwith approx imately 20 d Rm.

If we feed the modulat ion signal 10 bothinputs simultaneously. and if we use

A Stabilised DC circ uit of approximately6 V is obta ined from the voltage led infrom outside, using mo, fJI and CR. AIX' voltage adjustable within a range o fo mV to , 20 mV is applied at themixer inputs through the netwo rk con­sisting of RI, R2, R3 and 1'1 (or HI I,H12, HIJ and 1'2) . 1'1 and 1'2 take theform or l fl -Ium helical potentiometers.We can thus generate components of thecar rier frequency orthogonal 10 oneanother at the total output each with up10 approximately 30 dll m. Without IX:voltage compensation (0 mV at themixer inputs), the carrier frequency

impedance. Moreo ver, the source toscil­lator] must be broa d-band matched. L1lakes the form of a balancahlc induct­ance ( 11 turns of enamelled copper wireon a 4-1111ll. rod , ferrite core). n shouldlikewise he balancable, if applicable(tr irnntcr). T he cr iterion for the correctvalues or 1,1 and Cl is a sharp form ofreflection attenuation at the distributorinput at the desired oscillator frequency(Fig. 5) . with the minimum being o f nointeres t as an ac tual reading (because o fthe final d irectivity of the measurementsystem) but being of interest only forreasons of rcproducibility.

lhc mixers output signals an: combinedby a bridge circuit (R I 7, NJR. /( 19). Inthis connection, an attenuation of 6 1marises ill each cas e. One of the couplerinputs must be switched potent ial- free,

which is provided for by the transformerintegrated into RMI. The cond ition forthe de-coupling is that R17. R18 andRI9 correspond to the system character­istic impedance, and in addition the sink(total output) must be broad-handmarched .

112

VHF COMMUNICATIONS 2/2000

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orthogonal signals tor this. then onesideband can be strongly attenuated(theoretica lly obliterated ), The remain­in!! sideban d is increased by 6 dl3. Sincet h~ circuit is passive. the process cana lso be reversed, A signa l (j~) led intothe total output generates two orth ogo ­nal signals with fo - Is at the I and Qinputs tatter subsequent low-pas-, filtra ­tion). If fil > ft. then the Q signal willtak e precedence. 'ffs »fo, it is the otherwav round. Single-sideband technologyha; been llI<lki;;g, use of the optionsarising from this (including the com bi-

nation poss ibilitie s) for decades .

As rcaards da ta transmiss ion, since themodulator ope rates in a very linearmanner . the I and Q modulation signalscan he re fiabiv divided into ten or moreequal stages in the range between I Vand + I V (whether \H' can also actua llymake use o f this rela tively fine quantisa ­tion depends on other conditions secabove). Tilt' filtrat ion of the modulat ionsi!!na ls required for hand limitation cantake place in the basis band. on the basisof the given linearity. Initially, no stat icvo ltages are transmitted (no DC cou -

113

VHF COMMUNICATIONS 2/2000

C3 and C4 remain short-circu ited, HI IS

removed.

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piing). We shall come back to this.

Parts list:

1 x 27 Ohms, 1%. R8

4 x 75 Ohms, 1%, R IO. R17, R18, R l9

4 x 100 Ohms. 1'%, R4, e« R14, RI6

2 x 27() Ohms. Jl%, R5. RI5

I x 330 Ohms. 5%, 1/3 W, R20

2 x 390 Ohms, 1%,,1<7, R9

4 x 1.8 kOhms, 5~"u , RI, R'2 . Rl l. R l2

2 x 7.5 Whms, 5%" 1<3, HIJ

'2 x 2 kOhms, sp indle tr immer, f' l , 1'2

2 x HPF 505 (min i-circuits), RA11 , RAt:..

Or similar. VIl F mixe r

1 x 56 pF (if applicable, trim mer). C l

fi x 100 nft, ce ramic , C2 [0 C7

I x 47 IlF, electrolytic capacitor, C8

I x 0.3 1l1I, I I winding on a-mm. core.Ll

v cgr kit with balancing core

1 x Z PD 6V2, Zener diode. 0 1

The 90° coupler (L1, Cl) is tun ed to38.9 1\1Hz. The video signal must beaquired at the black level (0 V). andcomes to the ! input. With PI. theres idual carrier can be set as desired.With a 10% residual carrier. the syn­chronuus level at the total output isappro ximately 14 d Rm.

What are the Q channel and 1'2 for'?Well. because of inter-carr ier sou nddemodulation , the modu lator may giveoff only a Fl awless I signal. Any Qremains (and there arc always some)cause a pha se modu lation of the imagecarrier The 1.,Q modulator com pensatesfor this, by generating an invers e Qcarr ier (DC voltage at Rl(2 ).

Profession al television test demodulatorscan measure the image carrier phasemodification (IeI'M). Fig. 6 shows theprecision or measureme nt to be de­scribed as perfect II shou ld be pointedout that the tuning of the QO~ cou pler isnot crit ica l in this application case , Thecompensation is out standingly tem pera­ture-stable . We j ust have to pay ca re fulattention to the DC voltages.

5.AN EXCURSION 1:"1'0VIJ)F:O TF:CII:"OLOGY

I.,SIMU LATIO,\ OF AIVIULTl-VALE'lT DATATllAI\S~IISSIO'\

Video signals can be converted into theintermediate-frequency plane with theI/Q modu lator shown here. The follow­ing circui t change is requ ired for nega­tive modulation (e .g. standard BiG). R3changes [Tom 7.5 kOhms to 15 kOhms,

114

In this experiment. the rand Q channe lsare to be loaded with data. for simula­tion purposes . non-synchronous. ste ppedvideo signa ls arc fed into the mo dulator

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inputs (DC coupling). The stages corre­spond to the voltage values 0.3 V, 0 V,+ 0.14 V. -'- 0 .28 V. +- 0.42 V. +- 0.56 Vand + 0.7 V. Considered vectorially. thisgives at least 49 poss ible combinations,of which only the first quadrant iscompletely occupied.

The I'Q mod ulator is driven by DCcoupling i.c. C3, C4, C6 and (7 areshort-circuited . An external vol tagesource is dispense d with (if the positionof the zero point in the receiver werecritical, a bipolar adjustable DC voltagewould have to be fed to the mixersthrough R3 and RI3),

An advantageous ly priced residual side­band filter, with pre-amplification andpost-amplificatio n. forms the transm is­sion channel. lts transmiss ion curve(approximately 0.7 dBpp) and groupdelay (approximately 50 nspp) arelogged in Fig. 7. So that the modulatorsignal match es into the ti ller, the oscilla­tor frequency is pushed into the centreof the band (here: 36.3 Ml-lz]. t,1 andCI are carefully balanced.

Now we still need a suitable demodula­tor. The author used a circuit with thesame structure as that in the modulator(Fig. 4 suggests this) . The osci llator

115

VHF COMMUNICATIONS 2/2000(~ -----------=~~~~~~

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signals (or the modulator and dcmodula­lor came from the same source. One ofthe branches was phase-adj ustable. usinga variable-length line (a so-called trom­hone).

The ampl itude cycle of the total systemconsisting of the modulator, the filterand the demodulator was tested first(F ig. 8). The transmission curves IS .....IE and QS --). QE are quasi-identical thetransmission range goes up to approxi­mately 3.5 MHz. The cross-talk attenua­tion levels. IS - ) QE and QS --). IE arcext remely similar [more than 25 dB toapproximately 3 M!h ).

116

The demodulated signals can be lookedat with the oscilloscope a fter low-passfiltration with )g ,. 20 ~ I HL Fig. 9shews both channels (the pho to qualityis unfortunately not optimal). The DCvoltage values are correct ly transmitted.i.e. the black value remai ns <I t 0 V.However, the channel cross-talk expandsthe original d ear contours. An :\-yrepresentat ion is very informative . Sincethe mod ulation signals. in terms o f lime.move over each other. new I-Q cornbi­nat ions are arising all the time. Some ofthese random constellations are shownin Fig. 10. From the purely qualitative

VHF COMMUNICATIONS 2/2000

Fi~, 'J; Oscilloscope trac e ofd emodulated sig na l<.

poin t of view, it can be staled that thereshould be 111.1 great difficult y in findin g areliable answer to the question of ex­actly what complex numerica1 value IS

being transmitted at any mom ent.

7.COI\CLlJSIO:-;

T he trans mission o f digita l data in thehigh-frequency plane is a new challengefor high-freque ncy technology. The I'Qmod ulator often for ms the interfa cebe tween d igital and analog ue technol­ogy. This article is intended to awake anunderstanding of the problems involvedand to provide stimul atio n for furtherobservations and experim en ts.

8.LIT ERAH iRE IlH EREI\CES

f l] Glasmac hers. G .

Fig, Ill: \ -y representation ofd emodu lat ed sh: na ls

Digital phase modu lation

Vl lf Report s, no. 2, 1999

[21 :YUillSl. R.

Digital modulat ion procedu res

IWillig. 1989

[JJ Dambachcr. 1'.

Digital technology for tele vis ion broadcasting

Springer. 1997

[4] Parpart. J.V.

Broadband high-frequen cy tra nsformerscircuits and system s

l liithig. 1997

[5J Mini-Ci rcuits: KF/I I-" DesignersGuid e 1999

[61 Hewlett Packard

Digital rad io link system theo ry andprac tise

Seminar Docu ments, 199 1

117