Harmonic cancellation

May 08, 2026 Last reply: 2 months ago 3 Replies
E

Can anyone explain to me how R10 almost completely cancels the third harmonic distortion in the circuit below? I'm aware that the distortion is caused by the limiter diodes and that the signals at U1 and U3 are in antiphase.



Remove R10 and it's 80dB down at 3 kHz.



Version 4.1 SHEET 1 3020 1796 WIRE -176 -208 -288 -208 WIRE -32 -208 -96 -208 WIRE 128 -208 -32 -208 WIRE 224 -208 128 -208 WIRE 400 -208 304 -208 WIRE -32 -176 -32 -208 WIRE 128 -176 128 -208 WIRE -32 -80 -32 -112 WIRE 48 -80 -32 -80 WIRE 128 -80 128 -112 WIRE 128 -80 48 -80 WIRE 48 -48 48 -80 WIRE -288 32 -288 -208 WIRE -176 32 -288 32 WIRE -32 32 -96 32 WIRE 48 32 -32 32 WIRE 208 32 128 32 WIRE 256 32 208 32 WIRE 400 32 400 -208 WIRE 400 32 320 32 WIRE 464 32 400 32 WIRE 608 32 544 32 WIRE 656 32 608 32 WIRE 800 32 720 32 WIRE -288 144 -288 32 WIRE -176 144 -288 144 WIRE 208 144 208 32 WIRE 256 144 208 144 WIRE 608 144 608 32 WIRE 656 144 608 144 WIRE -32 160 -32 32 WIRE -32 160 -112 160 WIRE 400 160 400 32 WIRE 400 160 320 160 WIRE 800 160 800 32 WIRE 800 160 720 160 WIRE 848 160 800 160 WIRE 976 160 928 160 WIRE 1024 160 976 160 WIRE 1152 160 1104 160 WIRE 1216 160 1152 160 WIRE 1360 160 1296 160 WIRE 1424 160 1360 160 WIRE 1456 160 1424 160 WIRE -176 176 -240 176 WIRE 256 176 224 176 WIRE 656 176 624 176 WIRE 224 208 224 176 WIRE 624 208 624 176 WIRE 976 272 976 160 WIRE 1024 272 976 272 WIRE 1152 272 1152 160 WIRE 1152 272 1088 272 WIRE 1216 272 1152 272 WIRE -240 288 -240 176 WIRE -176 288 -240 288 WIRE 400 288 400 160 WIRE 400 288 -96 288 WIRE 1360 288 1360 160 WIRE 1360 288 1280 288 WIRE 1216 304 1152 304 WIRE -240 336 -240 288 WIRE 1152 336 1152 304 WIRE -528 352 -528 320 WIRE -528 352 -576 352 WIRE -576 368 -576 352 WIRE -32 368 -32 160 WIRE 848 368 -32 368 WIRE 976 368 976 272 WIRE 976 368 928 368 WIRE -528 384 -528 352 WIRE -240 448 -240 416 WIRE -288 512 -288 144 WIRE 80 512 -288 512 WIRE 800 512 800 160 WIRE 800 512 160 512 FLAG 224 208 0 FLAG 624 208 0 FLAG -576 368 0 FLAG -528 240 vcc FLAG -528 464 vee FLAG -144 128 vcc FLAG -144 192 vee FLAG 288 128 vcc FLAG 288 192 vee FLAG 688 128 vcc FLAG 688 192 vee FLAG 48 -48 0 FLAG 1248 256 vcc FLAG 1248 320 vee FLAG 1152 336 0 FLAG 1424 160 vout FLAG -240 448 0 SYMBOL res -80 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value 10K SYMBOL res 144 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R5 SYMATTR Value 16K SYMBOL res 560 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R6 SYMATTR Value 16K SYMBOL res 176 496 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R4 SYMATTR Value 10K SYMBOL voltage -528 224 R0 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V3 SYMATTR Value 15 SYMBOL voltage -528 368 R0 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V4 SYMATTR Value 15 SYMBOL OpAmps\\LT1679 -144 160 R0 SYMATTR InstName U1 SYMBOL OpAmps\\LT1679 288 160 R0 SYMATTR InstName U2 SYMBOL OpAmps\\LT1679 688 160 R0 SYMATTR InstName U3 SYMBOL res -80 272 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 10k SYMBOL res -256 320 R0 SYMATTR InstName R1 SYMATTR Value 510 SYMBOL diode -48 -176 R0 SYMATTR InstName D1 SYMATTR Value BAV99HY SYMBOL diode 112 -112 M180 WINDOW 0 24 64 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName D2 SYMATTR Value BAV99HY SYMBOL res -80 -224 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R7 SYMATTR Value 47k SYMBOL res 320 -224 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 47k SYMBOL res 944 144 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R9 SYMATTR Value 1k SYMBOL res 944 352 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R10 SYMATTR Value 9.0k SYMBOL res 1312 144 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R11 SYMATTR Value 4.7k SYMBOL OpAmps\\LT1679 1248 288 R0 SYMATTR InstName U4 SYMBOL ind 1120 144 R90 WINDOW 0 5 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName L1 SYMATTR Value 68m SYMATTR SpiceLine Ipk=0.05 Rser=90 Rpar=709600 Cpar=15.406p mfg="Würth Elektronik" pn="7447452683 WE-TI 8012" SYMBOL cap 1088 256 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C3 SYMATTR Value 15n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0164 Lser=302p mfg="Würth Elektronik" pn="885012009006 WCAP-CSGP 1210" type="NP0" SYMBOL cap 720 16 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C2 SYMATTR Value 10n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0262 Lser=534p mfg="Würth Elektronik" pn="885012008030 WCAP-CSGP 1206" type="NP0" SYMBOL cap 320 16 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C1 SYMATTR Value 10n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0262 Lser=534p mfg="Würth Elektronik" pn="885012008030 WCAP-CSGP 1206" type="NP0" TEXT -456 576 Left 2 !.tran 0 10 0 100n startup TEXT -456 616 Left 2 !.options plotwinsize=0 numdgt=15 TEXT -280 -344 Left 2 ;1KHz 130dB based on

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Fig 5.1.2\nER May 2026



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J

Av of integrator stage proportional to 1/f. For 2 stages 2rd harmonic gain is 1/9th of fundamental. So 3rd at o/p of 2nd stage is 1/9 the amplitude of 3rd i/p to 1st stage (in antiphase). Sum in the ratio

9:1 to remove.
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E

Aha. Yes. All obvious now. Thank you.

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E

"JM" snipped-for-privacy@gmail.com wrote in message news: snipped-for-privacy@4ax.com...

By using the same trick to remove the 5th harmonic I can get below 140dB in a simulation. I wonder what reality would say.

Version 4.1 SHEET 1 3020 1796 WIRE -176 -208 -288 -208 WIRE -32 -208 -96 -208 WIRE 128 -208 -32 -208 WIRE 224 -208 128 -208 WIRE 400 -208 304 -208 WIRE -32 -176 -32 -208 WIRE 128 -176 128 -208 WIRE -32 -80 -32 -112 WIRE 48 -80 -32 -80 WIRE 128 -80 128 -112 WIRE 128 -80 48 -80 WIRE 48 -48 48 -80 WIRE 1424 -16 1184 -16 WIRE 2256 -16 1504 -16 WIRE -288 32 -288 -208 WIRE -176 32 -288 32 WIRE -32 32 -96 32 WIRE 0 32 -32 32 WIRE 96 32 80 32 WIRE 208 32 176 32 WIRE 256 32 208 32 WIRE 400 32 400 -208 WIRE 400 32 320 32 WIRE 432 32 400 32 WIRE 528 32 512 32 WIRE 640 32 608 32 WIRE 688 32 640 32 WIRE 832 32 752 32 WIRE 1184 112 1184 -16 WIRE 1248 112 1184 112 WIRE 1392 112 1328 112 WIRE 1424 112 1392 112 WIRE 1520 112 1504 112 WIRE 1632 112 1600 112 WIRE 1680 112 1632 112 WIRE 1824 112 1744 112 WIRE 1856 112 1824 112 WIRE 1952 112 1936 112 WIRE 2064 112 2032 112 WIRE 2112 112 2064 112 WIRE 2256 112 2256 -16 WIRE 2256 112 2176 112 WIRE -288 144 -288 32 WIRE -176 144 -288 144 WIRE 208 144 208 32 WIRE 256 144 208 144 WIRE 640 144 640 32 WIRE 688 144 640 144 WIRE -32 160 -32 32 WIRE -32 160 -112 160 WIRE 400 160 400 32 WIRE 400 160 320 160 WIRE 832 160 832 32 WIRE 832 160 752 160 WIRE 880 160 832 160 WIRE 1008 160 960 160 WIRE -176 176 -240 176 WIRE 256 176 224 176 WIRE 688 176 656 176 WIRE 224 208 224 176 WIRE 656 208 656 176 WIRE 1184 224 1184 112 WIRE 1248 224 1184 224 WIRE 1632 224 1632 112 WIRE 1680 224 1632 224 WIRE 2064 224 2064 112 WIRE 2112 224 2064 224 WIRE 1392 240 1392 112 WIRE 1392 240 1312 240 WIRE 1824 240 1824 112 WIRE 1824 240 1744 240 WIRE 2256 240 2256 112 WIRE 2256 240 2176 240 WIRE 2304 240 2256 240 WIRE 2432 240 2384 240 WIRE 2464 240 2432 240 WIRE 2496 240 2464 240 WIRE 1248 256 1184 256 WIRE 1680 256 1648 256 WIRE 2112 256 2080 256 WIRE -240 288 -240 176 WIRE -176 288 -240 288 WIRE 400 288 400 160 WIRE 400 288 -96 288 WIRE 1648 288 1648 256 WIRE 2080 288 2080 256 WIRE -240 336 -240 288 WIRE -528 352 -528 320 WIRE -528 352 -576 352 WIRE -576 368 -576 352 WIRE -32 368 -32 160 WIRE 880 368 -32 368 WIRE 1008 368 1008 160 WIRE 1008 368 960 368 WIRE 1056 368 1008 368 WIRE 1184 368 1184 256 WIRE 1184 368 1136 368 WIRE 1248 368 1184 368 WIRE 1824 368 1824 240 WIRE 1824 368 1328 368 WIRE -528 384 -528 352 WIRE -240 448 -240 416 WIRE 1392 448 1392 240 WIRE 2304 448 1392 448 WIRE 2432 448 2432 240 WIRE 2432 448 2384 448 WIRE -288 512 -288 144 WIRE 80 512 -288 512 WIRE 832 512 832 160 WIRE 832 512 160 512 FLAG 224 208 0 FLAG 656 208 0 FLAG -576 368 0 FLAG -528 240 vcc FLAG -528 464 vee FLAG -144 128 vcc FLAG -144 192 vee FLAG 288 128 vcc FLAG 288 192 vee FLAG 720 128 vcc FLAG 720 192 vee FLAG 48 -48 0 FLAG 2464 240 vout FLAG -240 448 0 FLAG 1648 288 0 FLAG 2080 288 0 FLAG 1280 208 vcc FLAG 1280 272 vee FLAG 1712 208 vcc FLAG 1712 272 vee FLAG 2144 208 vcc FLAG 2144 272 vee SYMBOL res -80 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value 10K SYMBOL res 96 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R5 SYMATTR Value 15k SYMBOL res 528 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R6 SYMATTR Value 15k SYMBOL res 176 496 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R4 SYMATTR Value 10K SYMBOL voltage -528 224 R0 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V3 SYMATTR Value 15 SYMBOL voltage -528 368 R0 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V4 SYMATTR Value 15 SYMBOL OpAmps\\LT1679 -144 160 R0 SYMATTR InstName U1 SYMBOL OpAmps\\LT1679 288 160 R0 SYMATTR InstName U2 SYMBOL OpAmps\\LT1679 720 160 R0 SYMATTR InstName U3 SYMBOL res -80 272 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 10k SYMBOL res -256 320 R0 SYMATTR InstName R1 SYMATTR Value 510 SYMBOL diode -48 -176 R0 SYMATTR InstName D1 SYMATTR Value BAV99HY SYMBOL diode 112 -112 M180 WINDOW 0 24 64 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName D2 SYMATTR Value BAV99HY SYMBOL res -80 -224 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R7 SYMATTR Value 47k SYMBOL res 320 -224 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 47k SYMBOL res 976 144 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R9 SYMATTR Value 1k SYMBOL res 976 352 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R10 SYMATTR Value 9k SYMBOL cap 752 16 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C2 SYMATTR Value 10n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0262 Lser=534p mfg="Würth Elektronik" pn="885012008030 WCAP-CSGP 1206" type="NP0" SYMBOL cap 320 16 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C1 SYMATTR Value 10n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0262 Lser=534p mfg="Würth Elektronik" pn="885012008030 WCAP-CSGP 1206" type="NP0" SYMBOL res 192 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R12 SYMATTR Value 910 SYMBOL res 624 16 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R13 SYMATTR Value 910 SYMBOL res 1344 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R11 SYMATTR Value 10K SYMBOL res 1520 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R14 SYMATTR Value 15k SYMBOL res 1952 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R15 SYMATTR Value 15k SYMBOL OpAmps\\LT1679 1280 240 R0 SYMATTR InstName U4 SYMBOL OpAmps\\LT1679 1712 240 R0 SYMATTR InstName U5 SYMBOL OpAmps\\LT1679 2144 240 R0 SYMATTR InstName U6 SYMBOL res 1344 352 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R17 SYMATTR Value 100k SYMBOL res 1152 352 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R18 SYMATTR Value 22k SYMBOL res 2400 224 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R19 SYMATTR Value 1k SYMBOL cap 2176 96 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C3 SYMATTR Value 10n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0262 Lser=534p mfg="Würth Elektronik" pn="885012008030 WCAP-CSGP 1206" type="NP0" SYMBOL cap 1744 96 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C4 SYMATTR Value 10n SYMATTR SpiceLine V=25 Irms=0 Rser=0.0262 Lser=534p mfg="Würth Elektronik" pn="885012008030 WCAP-CSGP 1206" type="NP0" SYMBOL res 1616 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R21 SYMATTR Value 910 SYMBOL res 2048 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R22 SYMATTR Value 910 SYMBOL res 1520 -32 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R16 SYMATTR Value 10k SYMBOL res 2400 432 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R23 SYMATTR Value 25k TEXT -456 576 Left 2 !.tran 0 10 0 100n startup TEXT -456 616 Left 2 !.options plotwinsize=0 numdgt=15 TEXT -280 -344 Left 2 ;1KHz 145dB based on

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Fig 5.1.2\nER May 2026

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