897:, effectively resulting in a multiplier with both whole number and fractional component. Such a multiplier is called a fractional-N synthesizer after its fractional component. Fractional-N synthesizers provide an effective means of achieving fine frequency resolution with lower values of N, allowing loop architectures with tens of thousands of times less phase noise than alternative designs with lower reference frequencies and higher integer N values. They also allow a faster settling time because of their higher reference frequencies, allowing wider closed and open loop bandwidths.
838:, which can provide a high Q and narrow bandpass filtering function. The inherent square-law nonlinearity of the voltage-to-force transfer function of a cantilever resonator's capacitive transducer can be employed for the realization of frequency doubling effect. Due to the low-loss attribute (or equivalently, a high Q) offered by MEMS devices, improved circuit performance can be expected from a micromechanical frequency doubler than semiconductor devices utilized for the same task.
670:. The ideal (but impractical) impulse train generates an infinite number of (weak) harmonics. In practice, an impulse train generated by a monostable circuit will have many usable harmonics. YIG multipliers using step recovery diodes may, for example, take an input frequency of 1 to 2 GHz and produce outputs up to 18 GHz. Sometimes the frequency multiplier circuit will adjust the width of the impulses to improve conversion efficiency for a specific harmonic.
683:
66:
25:
168:
877:
voltage is fed to the VCO to adjust the frequency. This adjustment increases the frequency as the phase of the VCO's signal lags that of the reference signal and decreases the frequency as the lag decreases (or lead increases). The VCO will stabilize at the desired frequency multiple. This type of PLL is a type of
807:
Frequency multipliers use circuits tuned to a harmonic of the input frequency. Non-linear elements such as diodes may be added to enhance the production of harmonic frequencies. Since the power in the harmonics declines rapidly, usually a frequency multiplier is tuned to only a small multiple (twice,
663:. A full wave rectifier, for example, is good for making a doubler. To produce a times-3 multiplier, the original signal may be input to an amplifier that is over driven to produce nearly a square wave. This signal is high in 3rd order harmonics and can be filtered to produce the desired x3 outcome.
658:
From a conversion efficiency standpoint, the nonlinear circuit should maximize the coefficient for the desired harmonic and minimize the others. Consequently, the transcribing function is often specially chosen. Easy choices are to use an even function to generate even harmonics or an odd function
876:
by the multiplication factor. The divided signal and the reference frequency are fed into a phase comparator. The output of the phase comparator is a voltage that is proportional to the phase difference. After passing through a low pass filter and being converted to the proper voltage range, this
726:
Efficiently generating power becomes more important at high power levels. Linear Class A amplifiers are at best 25 percent efficient. Push-pull Class B amplifiers are at best 50 percent efficient. The basic problem is the amplifying element is dissipating power. Switching Class C amplifiers are
799:) produced by the nonlinear device drops off rapidly at the higher harmonics, so most frequency multipliers just double or triple the frequency, and multiplication by higher factors is accomplished by cascading doubler and tripler stages.
815:
Since the tuned circuits have a limited bandwidth, if the base frequency is changed significantly (more than one percent or so), the multiplier stages may have to be adjusted; this can take significant time if there are many stages.
646:
755:
that is tuned with a magnetic field. The step recovery diode impulse generator is driven at a subharmonic of the desired output frequency. An electromagnet then tunes the YIG filter to select the desired harmonic.
516:
889:
In some PLLs the reference frequency may also be divided by an integer multiple before being input to the phase comparator. This allows the synthesis of frequencies that are N/M times the reference frequency.
285:
circuits. It can be more economical to develop a lower frequency signal with lower power and less expensive devices, and then use a frequency multiplier chain to generate an output frequency in the
384:
1173:
Wang, Zhenxing; Zhang, Zhiyong; Xu, Huilong; Ding, Li; Wang, Sheng; Peng, Lian-Mao (2010). "A high-performance top-gate graphene field-effect transistor based frequency doubler".
1208:
Wang, Zhenxing; Liang, Shibo; Zhang, Zhiyong; Liu, Honggang; Zhong, Hua; Ye, Lin-Hui; Wang, Sheng; Zhou, Weiwei; Liu, Jie; Chen, Yabin; Zhang, Jin; Peng, Lian-Mao (2014).
666:
YIG multipliers often want to select an arbitrary harmonic, so they use a stateful distortion circuit that converts the input sine wave into an approximate
538:
193:
83:
38:
988:
856:
can be used for designing frequency multiplier circuits. Graphene can work over a large frequency range due to its unique characteristics.
427:
931:
229:
211:
149:
52:
130:
651:
So a frequency multiplier can be built from a nonlinear electronic component which generates a series of harmonics, followed by a
955:
102:
1307:
872:(VCO) is initially tuned roughly to the range of the desired frequency multiple. The signal from the VCO is divided down using
835:
825:
87:
109:
869:
1114:
791:
or transistors) operate nonlinearly and create harmonics, so an amplifier stage can be made a multiplier by tuning the
183:
116:
1021:
Basu, Joydeep; Bhattacharyya, Tarun K. (2013). "Microelectromechanical system cantilever-based frequency doublers".
727:
nonlinear, but they can be better than 50 percent efficient because an ideal switch does not dissipate any power.
528:
represent the generated harmonics. The
Fourier coefficients are given by integrating over the fundamental period
76:
1210:"Scalable Fabrication of Ambipolar Transistors and Radio-Frequency Circuits Using Aligned Carbon Nanotube Arrays"
274:
selects the desired harmonic frequency and removes the unwanted fundamental and other harmonics from the output.
98:
44:
909:
of the fractional-N synthesizer. This is done to shrink sidebands created by periodic changes of an integer-N
270:
circuit that distorts the input signal and consequently generates harmonics of the input signal. A subsequent
397:, the output is still a sine wave (but may acquire a phase shift). However, if the sine wave is applied to a
329:
893:
This can be accomplished in a different manner by periodically changing the integer value of an integer-N
660:
812:
are inserted in a chain of frequency multipliers to ensure adequate signal level at the final frequency.
878:
278:
1264:
1221:
1182:
1129:
853:
780:
730:
A clever design can use the nonlinear Class C amplifier for both gain and as a frequency multiplier.
298:
294:
255:
189:
849:
based FETs have also been employed for frequency doubling with more than 90% converting efficiency.
178:
741:
1209:
123:
1284:
1245:
1155:
1095:
1048:
1030:
997:
796:
251:
1237:
1087:
927:
910:
906:
894:
873:
865:
398:
1276:
1229:
1190:
1145:
1137:
1079:
1040:
305:
747:
Microwave generators may use a step recovery diode impulse generator followed by a tunable
772:
652:
290:
271:
308:. The nonlinear distortion in crystals can be used to generate harmonics of laser light.
1225:
1186:
1133:
960:
414:
390:
282:
267:
682:
1301:
792:
1288:
1249:
1159:
1099:
1052:
788:
738:
Generating a large number of useful harmonics requires a fast nonlinear device.
243:
65:
1280:
1083:
1067:
942:
936:
828:
776:
752:
748:
667:
641:{\displaystyle c_{k}={\frac {1}{2\pi }}\int _{0}^{T}x(t)\,e^{-j2\pi kt/T}\,dt}
1141:
1044:
868:(PLL) uses a reference frequency to generate a multiple of that frequency. A
831:
809:
394:
317:
286:
259:
1241:
1233:
1091:
297:, survive the nonlinear distortion without ill effect (but schemes such as
846:
402:
263:
1150:
795:
at the output to a multiple of the input frequency. Usually the power (
765:
655:
which passes one of the harmonics to the output and blocks the others.
266:(multiple) of its input frequency. Frequency multipliers consist of a
1194:
1072:
IEEE Transactions on
Ultrasonics, Ferroelectrics and Frequency Control
511:{\displaystyle x(t)=\sum _{k=-\infty }^{\infty }c_{k}e^{j2\pi kft}.}
1265:"A frequency multiplier using three ambipolar graphene transistors"
1035:
784:
1068:"1.156-GHz self-aligned vibrating micromechanical disk resonator"
905:
A delta sigma synthesizer adds a randomization to programmable-N
834:
is one of the most fundamental and widely studied structures in
937:
Fractional N frequency synthesizer with modulation compensation
677:
161:
59:
18:
808:
three times, or five times) of the input frequency. Usually
787:. In transmitting circuits many of the amplifying devices (
775:, and some of the same nonlinear devices are used for both:
945:
U.S. Patent 5,224,132, Bar-Giora
Goldberg, (1993, June 29)
939:
U.S. Patent 4,686,488, Attenborough, C. (1987, August 11)
1113:
Wang, Han; Nezich, D.; Kong, Jing; Palacios, T. (2009).
1263:
Kabir, Hussain
Mohammed Dipu; Salahuddin, S.M. (2017).
694:
1023:
541:
430:
332:
996:, Fremont, CA: Micro Lambda Wireless, archived from
90:. Unsourced material may be challenged and removed.
640:
510:
378:
943:Programmable fractional-N frequency synthesizer
820:Microelectromechanical (MEMS) frequency doubler
771:Frequency multipliers have much in common with
990:Technology Description: YIG Tuned Oscillators
718:Clipping circuits. Full wave bridge doubler.
413:. The distorted signal can be described by a
8:
1066:Jing Wang; Ren, Z.; Nguyen, C.T.-C. (2004).
978:For example, the old Hewlett Packard 83590A.
405:; frequency components at integer multiples
53:Learn how and when to remove these messages
860:Phase-locked loops with frequency dividers
1149:
1034:
631:
621:
602:
597:
579:
574:
555:
546:
540:
484:
474:
464:
450:
429:
375:
331:
304:Frequency multiplication is also used in
230:Learn how and when to remove this message
212:Learn how and when to remove this message
150:Learn how and when to remove this message
293:range. Some modulation schemes, such as
277:Frequency multipliers are often used in
971:
379:{\displaystyle x(t)=A\sin(2\pi ft)\,}
7:
842:Graphene based frequency multipliers
768:. Regenerative varactors. Penfield.
88:adding citations to reliable sources
401:, the resulting distortion creates
926:, 2nd Ed., John Wiley & Sons,
465:
460:
14:
924:Frequency Synthesis by Phase-lock
389:If the sine wave is applied to a
34:This article has multiple issues.
1115:"Graphene Frequency Multipliers"
956:Heterostructure barrier varactor
722:Class C amplifier and multiplier
681:
661:Even and odd functions#Harmonics
192:has been specified. Please help
166:
64:
23:
75:needs additional citations for
42:or discuss these issues on the
594:
588:
440:
434:
372:
357:
342:
336:
1:
870:voltage controlled oscillator
409:of the fundamental frequency
1122:IEEE Electron Device Letters
393:, such as a non–distortion
1326:
1281:10.1016/j.mejo.2017.10.002
1084:10.1109/TUFFC.2004.1386679
753:yttrium iron garnet sphere
182:to meet Knowledge (XXG)'s
824:An electric-field driven
254:that generates an output
1269:Microelectronics Journal
1142:10.1109/LED.2009.2016443
1045:10.1177/1045389X12461695
885:Fractional-N synthesizer
751:. The YIG filter has a
1175:Applied Physics Letters
922:Egan, William F. 2000.
901:Delta sigma synthesizer
659:for odd harmonics. See
320:has a single frequency
1308:Communication circuits
1234:10.1002/adma.201302793
642:
512:
469:
380:
279:frequency synthesizers
99:"Frequency multiplier"
879:frequency synthesizer
854:ambipolar transistors
643:
513:
446:
381:
742:Step recovery diodes
539:
428:
330:
299:amplitude modulation
295:frequency modulation
248:frequency multiplier
194:improve this article
84:improve this article
1226:2014AdM....26..645W
1187:2010ApPhL..96q3104W
1134:2009IEDL...30..547H
1003:on 23 February 2012
734:Step recovery diode
584:
1214:Advanced Materials
874:frequency dividers
693:. You can help by
638:
570:
508:
376:
252:electronic circuit
16:Electronic circuit
1195:10.1063/1.3413959
1078:(12): 1607–1628.
911:frequency divider
907:frequency divider
895:frequency divider
866:phase-locked loop
764:Resistive loaded
711:
710:
568:
399:nonlinear circuit
240:
239:
232:
222:
221:
214:
184:quality standards
175:This article may
160:
159:
152:
134:
57:
1315:
1293:
1292:
1260:
1254:
1253:
1205:
1199:
1198:
1170:
1164:
1163:
1153:
1119:
1110:
1104:
1103:
1063:
1057:
1056:
1038:
1018:
1012:
1011:
1010:
1008:
1002:
995:
985:
979:
976:
773:frequency mixers
706:
703:
685:
678:
647:
645:
644:
639:
630:
629:
625:
583:
578:
569:
567:
556:
551:
550:
517:
515:
514:
509:
504:
503:
479:
478:
468:
463:
385:
383:
382:
377:
306:nonlinear optics
258:and that output
235:
228:
217:
210:
206:
203:
197:
170:
169:
162:
155:
148:
144:
141:
135:
133:
92:
68:
60:
49:
27:
26:
19:
1325:
1324:
1318:
1317:
1316:
1314:
1313:
1312:
1298:
1297:
1296:
1262:
1261:
1257:
1207:
1206:
1202:
1172:
1171:
1167:
1117:
1112:
1111:
1107:
1065:
1064:
1060:
1020:
1019:
1015:
1006:
1004:
1000:
993:
987:
986:
982:
977:
973:
969:
952:
919:
903:
887:
862:
844:
826:micromechanical
822:
805:
762:
736:
724:
716:
707:
701:
698:
691:needs expansion
676:
653:bandpass filter
598:
560:
542:
537:
536:
526:
480:
470:
426:
425:
328:
327:
314:
291:millimeter wave
272:bandpass filter
236:
225:
224:
223:
218:
207:
201:
198:
187:
171:
167:
156:
145:
139:
136:
93:
91:
81:
69:
28:
24:
17:
12:
11:
5:
1323:
1322:
1319:
1311:
1310:
1300:
1299:
1295:
1294:
1255:
1220:(4): 645–652.
1200:
1181:(17): 173104.
1165:
1128:(5): 547–549.
1105:
1058:
1029:(2): 240–246.
1013:
980:
970:
968:
965:
964:
963:
961:CPU multiplier
958:
951:
948:
947:
946:
940:
934:
918:
917:PLL References
915:
902:
899:
886:
883:
861:
858:
843:
840:
821:
818:
804:
801:
761:
760:Varactor diode
758:
735:
732:
723:
720:
715:
712:
709:
708:
688:
686:
675:
672:
649:
648:
637:
634:
628:
624:
620:
617:
614:
611:
608:
605:
601:
596:
593:
590:
587:
582:
577:
573:
566:
563:
559:
554:
549:
545:
524:
519:
518:
507:
502:
499:
496:
493:
490:
487:
483:
477:
473:
467:
462:
459:
456:
453:
449:
445:
442:
439:
436:
433:
415:Fourier series
391:linear circuit
387:
386:
374:
371:
368:
365:
362:
359:
356:
353:
350:
347:
344:
341:
338:
335:
313:
310:
283:communications
238:
237:
220:
219:
190:cleanup reason
174:
172:
165:
158:
157:
72:
70:
63:
58:
32:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
1321:
1320:
1309:
1306:
1305:
1303:
1290:
1286:
1282:
1278:
1274:
1270:
1266:
1259:
1256:
1251:
1247:
1243:
1239:
1235:
1231:
1227:
1223:
1219:
1215:
1211:
1204:
1201:
1196:
1192:
1188:
1184:
1180:
1176:
1169:
1166:
1161:
1157:
1152:
1147:
1143:
1139:
1135:
1131:
1127:
1123:
1116:
1109:
1106:
1101:
1097:
1093:
1089:
1085:
1081:
1077:
1073:
1069:
1062:
1059:
1054:
1050:
1046:
1042:
1037:
1032:
1028:
1024:
1017:
1014:
999:
992:
991:
984:
981:
975:
972:
966:
962:
959:
957:
954:
953:
949:
944:
941:
938:
935:
933:
932:0-471-32104-4
929:
925:
921:
920:
916:
914:
912:
908:
900:
898:
896:
891:
884:
882:
880:
875:
871:
867:
859:
857:
855:
852:In fact, all
850:
848:
841:
839:
837:
833:
830:
827:
819:
817:
813:
811:
803:Previous uses
802:
800:
798:
794:
793:tuned circuit
790:
786:
782:
778:
774:
769:
767:
759:
757:
754:
750:
745:
743:
739:
733:
731:
728:
721:
719:
713:
705:
696:
692:
689:This section
687:
684:
680:
679:
673:
671:
669:
668:impulse train
664:
662:
656:
654:
635:
632:
626:
622:
618:
615:
612:
609:
606:
603:
599:
591:
585:
580:
575:
571:
564:
561:
557:
552:
547:
543:
535:
534:
533:
531:
527:
505:
500:
497:
494:
491:
488:
485:
481:
475:
471:
457:
454:
451:
447:
443:
437:
431:
424:
423:
422:
420:
416:
412:
408:
404:
400:
396:
392:
369:
366:
363:
360:
354:
351:
348:
345:
339:
333:
326:
325:
324:
323:
319:
311:
309:
307:
302:
300:
296:
292:
288:
284:
280:
275:
273:
269:
265:
261:
257:
253:
249:
245:
234:
231:
216:
213:
205:
195:
191:
185:
181:
180:
173:
164:
163:
154:
151:
143:
132:
129:
125:
122:
118:
115:
111:
108:
104:
101: –
100:
96:
95:Find sources:
89:
85:
79:
78:
73:This article
71:
67:
62:
61:
56:
54:
47:
46:
41:
40:
35:
30:
21:
20:
1272:
1268:
1258:
1217:
1213:
1203:
1178:
1174:
1168:
1151:1721.1/54736
1125:
1121:
1108:
1075:
1071:
1061:
1026:
1022:
1016:
1005:, retrieved
998:the original
989:
983:
974:
923:
904:
892:
888:
863:
851:
845:
823:
814:
806:
789:vacuum tubes
779:operated in
770:
763:
746:
740:
737:
729:
725:
717:
699:
695:adding to it
690:
665:
657:
650:
529:
522:
521:The nonzero
520:
418:
410:
406:
388:
321:
315:
303:
276:
247:
241:
226:
208:
199:
176:
146:
137:
127:
120:
113:
106:
94:
82:Please help
77:verification
74:
50:
43:
37:
36:Please help
33:
777:transistors
244:electronics
196:if you can.
967:References
829:cantilever
810:amplifiers
749:YIG filter
110:newspapers
39:improve it
1275:: 12–15.
1036:1210.3491
832:resonator
766:varactors
613:π
604:−
572:∫
565:π
492:π
466:∞
461:∞
458:−
448:∑
403:harmonics
395:amplifier
364:π
355:
318:sine wave
301:do not).
287:microwave
268:nonlinear
260:frequency
202:July 2011
140:July 2011
45:talk page
1302:Category
1289:31657795
1250:20376132
1242:24458579
1092:15690722
950:See also
847:Graphene
702:May 2019
674:Circuits
264:harmonic
177:require
1222:Bibcode
1183:Bibcode
1160:9317247
1130:Bibcode
1100:9498440
1053:1266952
781:Class C
316:A pure
179:cleanup
124:scholar
1287:
1248:
1240:
1158:
1098:
1090:
1051:
1007:18 May
930:
785:diodes
312:Theory
256:signal
250:is an
126:
119:
112:
105:
97:
1285:S2CID
1246:S2CID
1156:S2CID
1118:(PDF)
1096:S2CID
1049:S2CID
1031:arXiv
1001:(PDF)
994:(PDF)
714:Diode
262:is a
131:JSTOR
117:books
1238:PMID
1088:PMID
1009:2012
928:ISBN
836:MEMS
797:gain
783:and
281:and
246:, a
103:news
1277:doi
1230:doi
1191:doi
1146:hdl
1138:doi
1080:doi
1041:doi
697:.
417:in
352:sin
289:or
242:In
188:No
86:by
1304::
1283:.
1273:70
1271:.
1267:.
1244:.
1236:.
1228:.
1218:26
1216:.
1212:.
1189:.
1179:96
1177:.
1154:.
1144:.
1136:.
1126:30
1124:.
1120:.
1094:.
1086:.
1076:51
1074:.
1070:.
1047:.
1039:.
1027:24
1025:.
913:.
881:.
864:A
744:.
532::
421:.
407:nf
48:.
1291:.
1279::
1252:.
1232::
1224::
1197:.
1193::
1185::
1162:.
1148::
1140::
1132::
1102:.
1082::
1055:.
1043::
1033::
704:)
700:(
636:t
633:d
627:T
623:/
619:t
616:k
610:2
607:j
600:e
595:)
592:t
589:(
586:x
581:T
576:0
562:2
558:1
553:=
548:k
544:c
530:T
525:k
523:c
506:.
501:t
498:f
495:k
489:2
486:j
482:e
476:k
472:c
455:=
452:k
444:=
441:)
438:t
435:(
432:x
419:f
411:f
373:)
370:t
367:f
361:2
358:(
349:A
346:=
343:)
340:t
337:(
334:x
322:f
233:)
227:(
215:)
209:(
204:)
200:(
186:.
153:)
147:(
142:)
138:(
128:·
121:·
114:·
107:·
80:.
55:)
51:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
