VHF COMMUNICATIONS 2/95
Detlef Burchard, Dipl.-1ng., Box 14426, Nairobi, Kenya
Frequency Doubling using Semi-Conductor Diodes
At low input voltages. every rectirier circuit has an area where there is a quadratic relationship between the output quantity and the input quantity. One use for this ratio is the measurement of the power or the root mean square value as carried out, for example. in (2). Another application is frequency doubling, which is the suhject of this article.
1. FUNDAMENTAL PRINCIPLES Semi-conductor diodes have in general exponential voltage-current characteristics. This can he used directly to derive a quadratic relationship for the rectified current at input voltages of below 2 UT (Ur temperature voltage 25 to 5OmV). The relationships are explained in more detail in (1). The following formula is also obtained from the same literature:
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For a sinusoidal diode with the amplitl"!': tr, the standardised diode current Us has essentially three terms: the first, with the input frequency, which increases linearly with the input voltage; the second, which corresponds to the rectified current and increases quadrati cally with the input voltage; and the third, which is an alternating current with a doubled frequency (2 n) and with an amplitude equal to the rectified current. Tt is this third term which is of interest to us here. It also increases quadratically with the input voltage. The first term, the input frequency fraction, can theoretically he made to vanish by means of It push-pull arrangement using two diodes. In practise, of course, this is not completely successful. However, it is relatively easy to ensure that the doubled input frequency emerges from the output at least ten times stronger than any other fraction . 91
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According to ( I), the e.m.f o f the doub led freq uency generated is independent of the type of diode and the point of operation. By contrast. the infernal resistance at which this c.m.f is availa ble chan ges very considerably with the type of diode and the semi , conductor materi al. Without a bia. cu rrent. the internal resistance o f ~ ; d iodes wi ll be a few hu ndred megOhms, a few megohms for Scho ttky di odes, and a few len s of kiioO hms for Gc diodes . The figures apply to small -signal d iodes. In highfrequen cy circuits we would (ike lower Ohm values, right down to Son. in order to match 10 a system impe dan ce. Thi s is possible if a suitab le bias c urrent is selected . In general, the AC resistanc e in the area of expo nential voltage-current ratio is expre ssed by:
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that such bias currents arc possib le only using Schottky diode s. Gc d iodes leave the exponential area abo ve about l 00 lJA. The border between Sc hottky diodes and Si diodes even earlier, at 1Oj.U\ (IN4 148). Other univ ersal Si diodes go some what furth e r: I N41 51 to 30 j.lA and I N4448 to \( )(Ij.lJ\ . The border between Schottky diodes and Si diodes lies at the po int where 50n. technology begins. i.c . per hap s between I M Hz and to MHz. Gc d iodes are not required, unless we w arn to mange witho ut a bia s current.
2_ CIRCUITS Th e freq uency doubling circuit using semi-co nductor diodes is in no way di fferent from a rectifier circuit. Instead o f the OC the AC is now coupled out. Fig.! shows a circuit suitable from audio 10 radio frequencie s, in whic h t he inp ut-side phase reversal and isolation of the source is carried out by opera tional amplifiers. The offset vo ltages o f
VHF CO MMUNICATIONS 2/95
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Burchard the amplifiers and the variations in the diodes are balan ced out by the zero preset. The resistances R2 prevent protect against lo w loads for the ampli liers. Th ey would he selected to be between a few hundred Ohms and a few kiloOluns . If the load resistance Rl. = R 2, the best power matching is obta ined using the bias curre nt marked up Iv. Per idle operation, we naturall y obt ain double the output volt age. and then the bias current is not at all critical. Nor is any speci al current source required for the bias current. A resistor to the negat ive ope rating voltage o f the operat ional amplifier is fully sufficient.
rig. 2 shows how we ll this doubler operates and how litt le distortion it prod uces. I Icrc fast type LM3 6 1
94
opamps were used, so that eve n a signal of 1 MHz is still satisfactorily squared (Fig.3). Thus we have here a wide-hand circuit. which functions from low frequencies right up to a higher limit determin ed by the opa mp. For low d istorti on the input vo ltage of 200mVss shou ld not be greatly excee ded and the bias current should he selected accordingly. We then obtain approximat ely 20m Vss at the output. for power matching. and twic e that for idle ope ration . For frequencies higher than about 10 • 15 MHz there arc no suitab le operationa l amplifiers . A transformer is required for phase reversa l now. so that finally a circuit like Ptg.aa or b is obtained. It is also wide-band, and can be used in the UF, VHF and UHr ranges with a suitable transformer.
VHF COM MUNICATIONS 2/95
Fig.5:
Out put Spect rum "f FiJ.:Ah Circuit wit h 2S0 M ll z/· IOdBm III lhe Input X: 100 Mlh:/d iv (0 I" 1 Gllz, zero marker on the left) Y: 10dn/di v (500 MII z line corres pon ds 10 .3OdBm)
If the two diodes in a circuit are largely identica l in their electrical properties, then the connections "an be as in Fig.aa. However, a circuit like Fig.a b also functions with considerable discrepancies in the characteristics of the individual diodes.
The circuits arc simple enough. and require only input power in the ranges which most signal generators can provide for them. A doub ling circuit thus make s it possible to double the application tuning range of a measuring mstrnment. Many commercia lly available signal generators make use of this application for the lOP octave of their tuning range (3). Unfortunately. this also doubles the original noise deviation of the generator, and any amplitude modulation is distorted in accord -
ance with Fig.J, unless the modulator is positioned after the doubler. Power matching is brought about by the selection of a suitable bias current. A 200n load should act at the output of the 1:(1+1) transformer. So each diode must have an AC resistance of lOon . This immediately results in output matching, for the diodes arc parallel for the doubled frequency and the effective internal resistance is j On. The bias curre nt values giv en apply for U,.=3OmV. Purists can vary the bias CUITCnt until a VSWR optimum is obtained on the input and output sides, or until the optimum conversion efficiency is obtained. A degree of efficiency of I % (conversion loss 20d H) is fairly typical for this circu it.
95
VHF CO MMUNICAT ION S 2195
3. FURT HER CHARACTERIST ICS
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- 40 Thin gs arc not ideal in technica l reali ty. The input curve form is not ideally sinuso idal. the diodes are not co mple tcly ident ical and the chara s..nerl suc s arc not exactly exponenti a l. Howeve r. it is 110I very difficult to obtain an output sign31 from such a doubler, which Is 20d H or mor e better tha n all other output prod ucts.
H g.S shows the spectrum obtai ned if circu it Fig .a h is used, with a bala nced to-unbalanced tran sformer from the UHF input of a c lapped -out television and the output volta ge o f a Marcon i 1": 20 15 signa l generator. A spurious suppre ssion o f heife r than 20dn is thorou ghly co nsistent with mo st highfrequ ency meas ure ment s on selective o bj ect s. Indeed. signal ge nerators which can be purchase d are offcn no bcucr than this.
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Some spurious respon,c~ at the OUl · put do not decrease quadratically. So when the input power decreases. th e suppression bec omes worse . Thi s can he remed ied by an au enuatc r after the double r.
Bec ause o f the quadrat ic relationship the output rises twice as steeply as the input. T his relat ionshi p is shown in Fig .6.
It is thu s possible. without any problem. to set ve ry low de fined ou tput vo ltages by va rying the input power level. On ly two speci al features need to be ta ke n into account:
If th e preci sion with which the input level can be set is, for example. t l dB. then th e output erro r ca n not he sma ller than ±2dB.
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4. APPLICATIONS I needed a doubl er of this type to generate a defi ned input volt age for the meteorologica l sate llite frequency (approx imat ely 1.7 G Hz). As I do not have a GHz signal generator th is was the
VHF CO MM UNICATIO NS 2/95
on ly way to obtain a half- way exact measu rem ent of the amplific ation of a convert er I had purchased.
If we position a 20dfi ampli fier lind anot her doubler aft er such a douh ler, the frequency coverage can be eve n increased by a factor of 4 . As the sweep o f a frequency mod ulation is also multiplied accordingly, a ci rcuit of this nature can be su itable for gcncrat ing unusually large frequency sweeps. If necessary. we can mix back into the origina l frequency position using a fixed standby frequency. Qu adratic amplitude mod ulat ion might be o f some intere st for spec ial purpose s. T am happy to leave that for the future . If you want to avoid quadratic distort ion and still mod ulate AM, a suitable modulator should be added to the doubler (c.g . PAS type from MiniCircuits) . Beca use o f the convers ion losses o f app roxim atel y 20d B and the differenti al freq uenci es at the input ami output. the two gates of a doubl er of th is type arc effectively decouplcd. Match ing to one is not spoil t by mismatching to the
s. LlTERATURI' (I)
D. Burchard (199 1): Basics of Rectificatio n of Low AC Voltages using Semi -Co nductor Diodes; VITf Communications 3/1991, pp.168-174.
(2)
D . Burchard ( 199 1): Absolute Calibration of a Noise Source; VI IP Com municatio ns 2/ 1992, pp .76*89.
(3) N .N. (1987): Series 2022 Signal Ge nerators Owners Manual. Marconi Instruments, IIcrtfordshire, U.K.
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