Small Signal Calculation of a SW RF Stage

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1 Small Sinal alculation of a SW F Stae amon ara Patron rvara@inictel.ob.e INITE-UNI Our article The Modern Armtron eenerative eceiver reented a 53kHz~7kHz MW reenerative detector baed on the J3 N-channel JFET a a counterart of the famou vacuum-tube homoloou. The receiver there decribed wa found to be very elective and enitive. Tet conducted with different coil arranement and an outide aerial ueted alo excellent erformance throuhout the entire hort wave ectrum. When tetin the receiver, the lanetary reduction drive ued in conunction with the 475-F broadcat variable roved to be very ueful when tunin adacent tation in the crowded SW band. Althouh the author SW rototye worked imreively well, ome variation were devied thinkin of exerimenter wihin to relicate the receiver but lackin maybe ace for a decent antenna. uly attention wa iven for a minimum art count. There i the ayin that a workin receiver will be a ood a it aociated antennaround ytem. Situation exit where local condition will render an outide randomwire antenna uele for endin ood inal to a receiver. In thi cae, an F-amlifier tae ahead of the reenerative detector will ive the extra voltae ain required for a ucceful erformance. Fi. SW reenerative receiver

2 Fi. how the chematic of the author initial SW receiver rototye. Tetin for better enitivity, a very imle untuned F amlifier uin the MPF N-channel JFET in common-ate confiuration wa added to the J3-baed SW receiver. Thi tae wa caacitively couled to the tunin tank of the reenerative detector. In order to take advantae of the maximum available voltae ain a.-mh F choke wa connected between the JFET drain electrode and the ower uly. It wa found that tiht coulin to the detector tae would ive the bet noie / interference reection. A low ditributed-caacitance three-ection ie-wound F choke wa elected for thi alication. ow-cot ile-wound choke affected the uer end of the tuned band, recludin their ue. Fi. how the chematic of the F tae. The uh F choke in erie with the antenna lead-in effectively block FM / T interference and a ower rid-like annoyinly tron interference at the author location. The erie connected F variable caacitor hel attenuatin very tron inal and will alo imrove electivity. The outut imedance of the F tae deend on the imedance connected to it inut. Havin ome ain control throuh the ue of a variable inut attenuator i adviable, iven the dynamic rane of available SW radio inal. However, thi will brin about chane in the outut imedance of the amlifier, which in turn will caue ome receiver detunin. In order to have ome quantitative knowlede of the factor affectin the outut imedance of the amlifier, the author conducted ome calculation aumin oeration in the mid band, o the device arameter could be conidered real quantitie. For hiher frequencie comlex number would have to be ued. However, the theoretical reult obtained were coherent with the exerimental obervation at SW frequencie. Fi. JFET-baed F tae The mall-inal model emloyed for ain and imedance calculation can be een in Fi.3. i the enerator inal voltae and i the enerator outut reitance. i the drain dynamic reitance and i the ource bia external reitor. The JFET mall-inal model ue a vacuum tube-like circuit model. Hence, we need

3 definin a the amlification factor, bein m. The quantity m i the JFET forward tranfer conductance for frequencie in the mid band. Fi.3 Small-inal model In the fiure above, // Solvin for I ive: I Knowin that o I o, where I o -I, we arrive at: [ ] I The outut reitance i then: //

4 o in term of yield an exreion for the voltae ain Av o / : [ ] v A // which can alo be written a: v A The inut reitance of the tae a een toward the JFET ource may be found to be: in I For the cae the enerator i an antenna, if we let a be the voltae induced on the antenna by the radio wave, r the antenna-round ytem reitive loe lu the antenna radiation reitance, the variable inut attenuator total reitance and K the fraction of thi reitance exitin between the lider and the round end, we et (Fi. 4): r a K K K r // The voltae ain from enerator to load i : v r a a T A K Av

5 Numerical examle Fi.4 Antenna and inut equivalent The followin examle aume a JFET havin the followin mall-inal mid-band arameter: m 4mS, 4k ohm, m 6. The antenna-round ytem lo reitance lu the antenna radiation reitance i r ohm. The ource reitor i k ohm. The inut attenuator total reitance i.47k ohm and the outut load imedance i reitive and equal to 4k ohm. K K r Av Av T o..8.43kω kΩ kΩ kΩ kΩ kΩ kΩ kΩ.84.8kΩ kΩ Modification of formulae for the biolar cae The biolar cae (in a common-bae confiuration) require that be made equal to m / h oe and /h oe ubtituted for. Alo, e hould be ubtituted for. So we now have:, m /h oe h ( )( // ) e The formula for remain the ame. Exlanation for why the receiver detune when the ain control i aduted The tunin tank ha erie loe, motly attributed to the coil, if the tunin caacitor i of a hih-quality tye. The loy coil can be converted into an equivalent ideal lole coil with a arallel lo r : oe Q r r ( Q )

6 where Q πf r r The coil now tune with the caacitor to the ame frequency the loy coil wa tunin in conunction with the ca: f π When a coil ha erie loe, the tuned frequency i affected and will be iven by a different formula. A can be een i reater than, o, iven, the loy inductor will tune to a lower frequency than that obtained with a lole. Now, the total arallel lo i r t o // r. A ha been een, a manual chane in the F tae voltae ain will caue variation in the outut reitance o of the amlifier. Hence, the net arallel lo r t will chane, drivin u to accommodate reeneration value to the new ituation. eeneration artially cancel out arallel lo, which i a rereentation of the oriinal erie loe of the coil. When cancellation i occurrin, tend to the value, o the tuned frequency chane. A new reeneration level imlie a new value for. Selectin a low value for // will hel reducin frequency detunin due to o variation. Bia iue uually imoe contraint on the oible value for the ource reitor. So we are forced to minimize, either by reducin r or electin lower value for. It much eaier (and le exenive) to chane the attenuator total reitance than chanin a comlete antenna-round ytem lookin for a lower r.

7 APPENIX Tye-I oy - eonant ircuit onider an - arallel reonant circuit with erie loe in the inductive branch. The inut admittance Y i iven by: Y ()...() eonance i attained when the admittance function hae i zero. Thi i, when:

8 (3) The reonant frequency i iven then by: <...(4) The admittance at reonance i: Y (5) The inut imedance at reonance i Z / Y. Then: Z ( Q ) where: ( Q ) (6) Q (7) i the inductor Q factor at frequency. Eq.(3) can be written a: or Then, ( ) ( Q ) Q

9 Subtitutin into Eq.(4) yield: Q Q (8) Q The above exreion uet that arallel reonance i between caacitor and an inductor (9) Q Thu, the equivalent arallel reonant circuit i a hown in the fiure below, for frequencie in the vicinity of. amon ara Patron rvara@inictel.ob.e ima Peru, South America July 3rd, 7

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