Version 4 SHEET 1 2816 2596 WIRE 16 336 16 304 WIRE 16 416 16 464 WIRE 16 304 240 304 WIRE 1568 -192 1632 -192 WIRE 736 1408 784 1408 WIRE 288 1408 352 1408 WIRE 608 1408 672 1408 WIRE 832 1408 896 1408 WIRE 960 1408 1008 1408 WIRE 1056 1408 1104 1408 WIRE 352 1408 400 1408 WIRE 1168 1408 1216 1408 WIRE 1216 1408 1264 1408 WIRE 224 1408 160 1408 WIRE 608 1408 608 1472 WIRE 608 1504 608 1600 WIRE 832 1472 832 1408 WIRE 1056 1472 1056 1408 WIRE 1264 1472 1264 1408 WIRE 1264 1504 1264 1632 WIRE 1056 1504 1056 1600 WIRE 832 1504 832 1600 WIRE 400 1328 400 1408 WIRE 400 1408 448 1408 WIRE 400 1296 400 1184 WIRE 608 1328 608 1408 WIRE 608 1296 608 1216 WIRE 832 1296 832 1216 WIRE 1056 1296 1056 1216 WIRE 1264 1296 1264 1216 WIRE 1088 1184 1232 1184 WIRE 1056 1328 1056 1408 WIRE 832 1328 832 1408 WIRE 1296 1184 1376 1184 WIRE 1264 1408 1264 1328 WIRE 128 1408 80 1408 WIRE 560 1408 608 1408 WIRE 784 1408 832 1408 WIRE 1008 1408 1056 1408 WIRE 640 1184 800 1184 WIRE 864 1184 1024 1184 WIRE 400 1184 576 1184 WIRE 1264 1632 1088 1632 WIRE 800 1632 640 1632 WIRE 1024 1632 864 1632 WIRE 576 1632 256 1632 WIRE 256 1440 256 1632 WIRE 416 2192 464 2192 WIRE 688 2192 736 2192 WIRE 256 2192 304 2192 WIRE 464 2192 512 2192 WIRE 960 2192 1008 2192 WIRE 1008 2192 1056 2192 WIRE 1232 2192 1280 2192 WIRE 224 1968 144 1968 WIRE 544 2336 544 2416 WIRE 1440 2416 1440 2192 WIRE 1088 2336 1088 2416 WIRE 816 2336 816 2416 WIRE 816 2064 816 1968 WIRE 1088 2064 1088 1968 WIRE 1360 2064 1360 1968 WIRE 224 1968 544 1968 WIRE 1440 2192 1488 2192 WIRE 112 1968 48 1968 WIRE 1440 2416 1088 2416 WIRE 544 2416 224 2416 WIRE 224 2224 224 2320 WIRE 224 2352 224 2416 WIRE 304 2192 352 2192 WIRE 576 2192 624 2192 WIRE 848 2192 896 2192 WIRE 224 2064 224 1968 WIRE 816 1968 1088 1968 WIRE 1088 1968 1360 1968 WIRE 544 2064 544 1968 WIRE 544 1968 816 1968 WIRE 544 2096 544 2160 WIRE 224 2096 224 2160 WIRE 816 2096 816 2160 WIRE 1088 2096 1088 2160 WIRE 1088 2304 1088 2224 WIRE 816 2304 816 2224 WIRE 544 2304 544 2224 WIRE 1088 2416 816 2416 WIRE 816 2416 544 2416 WIRE 192 2192 160 2192 WIRE 160 2192 160 2208 WIRE 1392 2192 1440 2192 WIRE 1360 2096 1360 2160 WIRE 736 2192 784 2192 WIRE 1120 2192 1168 2192 WIRE 1280 2192 1328 2192 WIRE 512 1408 560 1408 WIRE 192 720 256 720 WIRE 384 720 448 720 WIRE 16 880 16 848 WIRE 16 768 16 720 WIRE 16 720 48 720 WIRE 256 720 320 720 WIRE 448 720 512 720 WIRE 880 880 880 848 WIRE 880 768 880 720 WIRE 640 720 688 720 WIRE 880 720 960 720 WIRE 48 720 128 720 WIRE 752 720 800 720 WIRE 800 720 816 720 WIRE 576 720 640 720 FLAG 16 464 0 FLAG 240 304 in IOPIN 240 304 Out FLAG 560 1408 z_1_ FLAG 784 1408 z_2_ FLAG 1008 1408 z_3_ FLAG 352 1408 sum_ FLAG 1376 1184 out_ IOPIN 1376 1184 Out FLAG 1216 1408 z_4_ FLAG 80 1408 in IOPIN 80 1408 In FLAG 464 2192 z_1_t FLAG 736 2192 z_2_t FLAG 1008 2192 z_3_t FLAG 304 2192 sum_t FLAG 1488 2192 out_t IOPIN 1488 2192 Out FLAG 1280 2192 z_4_t FLAG 48 1968 in IOPIN 48 1968 In FLAG 160 2208 0 FLAG 16 880 0 FLAG 256 720 z_1 FLAG 448 720 z_2 FLAG 640 720 z_3 FLAG 880 880 0 FLAG 48 720 sum FLAG 960 720 out IOPIN 960 720 Out FLAG 800 720 z_4 SYMBOL voltage 16 320 R0 WINDOW 123 24 132 Left 0 WINDOW 39 0 0 Left 0 SYMATTR Value2 AC 1 SYMATTR InstName V1 SYMATTR Value "" SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 1264 1504 R0 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A4 SYMATTR InstName X5 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 1056 1504 R0 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A3 SYMATTR InstName X6 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 832 1504 R0 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A2 SYMATTR InstName X7 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 608 1504 R0 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A1 SYMATTR InstName X8 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 400 1296 M180 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B0 SYMATTR InstName X9 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 608 1296 M180 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B1 SYMATTR InstName X10 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 832 1296 M180 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B2 SYMATTR InstName X11 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 1056 1296 M180 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B3 SYMATTR InstName X12 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 1264 1296 M180 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B4 SYMATTR InstName X13 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 160 1408 M90 WINDOW 39 34 7 VLeft 0 SYMATTR SpiceLine G=G1 SYMATTR InstName X14 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 608 1184 R0 SYMATTR InstName X15 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 1056 1184 R0 SYMATTR InstName X16 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 1264 1184 R0 SYMATTR InstName X17 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 832 1184 R0 SYMATTR InstName X18 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 1056 1632 R180 SYMATTR InstName X19 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 832 1632 R180 SYMATTR InstName X20 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 608 1632 R180 SYMATTR InstName X21 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum1p1n 256 1408 R0 SYMATTR InstName X22 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 224 2320 M180 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A4 SYMATTR InstName X27 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 544 2304 M180 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A3 SYMATTR InstName X28 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 816 2304 M180 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A2 SYMATTR InstName X29 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Z_gain 1088 2304 M180 WINDOW 39 13 -2 Left 0 SYMATTR SpiceLine G=A1 SYMATTR InstName X30 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 1360 2096 R0 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B0 SYMATTR InstName X31 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 1088 2096 R0 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B1 SYMATTR InstName X32 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 816 2096 R0 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B2 SYMATTR InstName X33 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 544 2096 R0 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B3 SYMATTR InstName X34 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 224 2096 R0 WINDOW 39 12 -9 Left 0 SYMATTR SpiceLine G=B4 SYMATTR InstName X35 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_gain 144 1968 M90 WINDOW 39 34 7 VLeft 0 SYMATTR SpiceLine G=G1 SYMATTR InstName X36 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p1n 544 2192 R0 SYMATTR InstName X37 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p1n 816 2192 R0 SYMATTR InstName X38 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p1n 1088 2192 R0 SYMATTR InstName X39 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p1n 224 2192 R0 SYMATTR InstName X40 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\z_sum2p 1360 2192 M180 SYMATTR InstName X41 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 480 1408 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X1 SYMBOL bv 16 752 R0 SYMATTR InstName SUM3 SYMATTR Value V={G1}*V(in) -(A1*V(z_1)+A2*V(z_2)+A3*V(z_3)+A4*V(z_4)) SYMBOL bv 880 752 R0 SYMATTR InstName SUM4 SYMATTR Value V=B0*V(sum) + B1*V(z_1) + B2*V(z_2) + B3*V(z_3) + B4*V(z_4) SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 704 1408 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X2 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 928 1408 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X3 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 1136 1408 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X4 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 160 720 R0 WINDOW 39 -45 56 Left 0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X42 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 352 720 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X43 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 544 720 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X44 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 720 720 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X45 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 384 2192 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X23 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 656 2192 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X24 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 928 2192 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X25 SYMBOL D:\\WUTemp\\Z-transform\\Yahoo\\Laplace_st 1200 2192 R0 SYMATTR SpiceLine TS={TS} SYMATTR InstName X26 TEXT -48 -296 Left 0 !.PARAM FS=10k TEXT -48 -264 Left 0 !.PARAM TS=1/FS TEXT -48 -344 Left 0 !.AC LIN 1000 10 {FS/2} TEXT -48 -480 Left 0 !.PARAM G1=0.00482434336 \n.PARAM B0=1 B1=4 B2=6 B3=4 B4=1\n.PARAM A0=1.0 A1=-2.369513 A2=2.3139884 A3=-1.0546654 A4=0.187379492 TEXT -48 -512 Left 0 ;Example: 4th order Butterworth lowpass, fg=0.1*fs TEXT 184 -296 Left 0 ;sampling frequency TEXT -24 248 Left 0 ;Source for step response and AC TEXT -40 -728 Left 0 ;AC Simulation Of Sampled Systems with Z-Transform, Helmut Sennewald V2.0 \n \nInstead of the delay element z^-1, the Laplace equivalent e^-sT is used.\nClick the right hand mouse button over the symbols to see the passed parameters.\n \nH(z) = G1 * ( B0 + B1*z^-1 + B2*z^-2 + .... Bn*z^-n) / (1 + A1*z^^-1 + A2*z^-2 + A3*z^-3 + ... Am*z^-m) B0 = 1 TEXT 672 640 Left 0 ;Delay with Laplace exp(-sT) TEXT 1096 120 Left 0 ;Z TEXT 1112 104 Left 0 ;-1 TEXT 1272 120 Left 0 ;Z TEXT 1288 104 Left 0 ;-1 TEXT 920 120 Left 0 ;Z TEXT 936 104 Left 0 ;-1 TEXT 744 120 Left 0 ;Z TEXT 760 104 Left 0 ;-1 TEXT 1008 240 Left 0 ;A2 TEXT 832 240 Left 0 ;A1 TEXT 1184 240 Left 0 ;A3 TEXT 1360 240 Left 0 ;A4 TEXT 464 112 Left 0 ;G1 TEXT 568 112 Left 0 ;+ TEXT 408 96 Left 0 ;IN TEXT 688 304 Left 0 ;+ TEXT 688 336 Left 0 ;+ TEXT 688 368 Left 0 ;+ TEXT 688 400 Left 0 ;+ TEXT 592 128 Left 0 ;- TEXT 1008 -48 Left 0 ;B2 TEXT 832 -48 Left 0 ;B1 TEXT 1184 -48 Left 0 ;B3 TEXT 1360 -48 Left 0 ;B4 TEXT 1512 -224 Left 0 ;+ TEXT 1512 -192 Left 0 ;+ TEXT 1512 -160 Left 0 ;+ TEXT 1512 -128 Left 0 ;+ TEXT 656 -48 Left 0 ;B0 TEXT 1512 -256 Left 0 ;+ TEXT 1592 -216 Left 0 ;OUT TEXT 648 128 Left 0 ;sum TEXT 1072 -304 Left 0 ;Direct Form II 4th Order System TEXT -8 1128 Left 0 ;Direct Form II TEXT -24 1904 Left 0 ;Transposed Direct Form II TEXT 0 632 Left 0 ;Direct Form II TEXT 184 -264 Left 0 ;sampling period TEXT -56 -144 Left 0 ;Used symbols:\n laplace_st.asy\n z_gain.asy\n z_sum_2p.asy\n z_sum_1p1n.asy\n z_sum_2p1n.asy\n \nThis is a hierarchical schematic.\nEach symbol has a corresponding \nschematic xxx.asc . LINE Normal 896 112 800 112 LINE Normal 896 112 896 112 LINE Normal 1072 112 976 112 LINE Normal 1072 112 1072 112 LINE Normal 1248 112 1152 112 LINE Normal 1376 112 1328 112 LINE Normal 848 112 848 208 LINE Normal 1024 112 1024 208 LINE Normal 1200 112 1200 208 LINE Normal 1376 112 1376 208 LINE Normal 848 304 848 272 LINE Normal 704 304 848 304 LINE Normal 1024 336 1024 272 LINE Normal 704 336 1024 336 LINE Normal 1200 368 1200 272 LINE Normal 704 368 1200 368 LINE Normal 1376 400 1376 272 LINE Normal 704 400 1376 400 LINE Normal 608 352 640 352 LINE Normal 592 352 608 352 LINE Normal 592 144 592 352 LINE Normal 720 112 672 112 LINE Normal 720 112 720 112 LINE Normal 624 112 672 112 LINE Normal 448 112 416 112 LINE Normal 448 112 448 112 LINE Normal 560 112 512 112 LINE Normal 560 112 560 112 LINE Normal 1024 -16 1024 112 LINE Normal 848 -16 848 112 LINE Normal 1200 -16 1200 112 LINE Normal 1376 -16 1376 112 LINE Normal 672 -16 672 112 LINE Normal 848 -176 848 -80 LINE Normal 848 -224 848 -176 LINE Normal 1504 -224 848 -224 LINE Normal 1024 -160 1024 -80 LINE Normal 1024 -192 1024 -160 LINE Normal 1200 -160 1200 -80 LINE Normal 1200 -160 1200 -160 LINE Normal 1376 -96 1376 -80 LINE Normal 1376 -128 1376 -96 LINE Normal 672 -160 672 -80 LINE Normal 672 -256 672 -160 LINE Normal 1504 -192 1024 -192 LINE Normal 1504 -160 1200 -160 LINE Normal 1504 -128 1376 -128 LINE Normal 1504 -256 672 -256 RECTANGLE Normal 352 512 -64 208 2 RECTANGLE Normal 1152 144 1072 80 RECTANGLE Normal 1328 144 1248 80 RECTANGLE Normal 976 144 896 80 RECTANGLE Normal 800 144 720 80 RECTANGLE Normal 704 416 640 288 RECTANGLE Normal 1568 -112 1504 -272 RECTANGLE Normal 1648 1728 -64 1072 2 RECTANGLE Normal 1648 2496 -64 1856 2 RECTANGLE Normal 1648 944 -64 592 2 CIRCLE Normal 1056 272 992 208 CIRCLE Normal 880 272 816 208 CIRCLE Normal 1232 272 1168 208 CIRCLE Normal 1408 272 1344 208 CIRCLE Normal 512 144 448 80 CIRCLE Normal 624 144 560 80 CIRCLE Normal 1056 -16 992 -80 CIRCLE Normal 880 -16 816 -80 CIRCLE Normal 1232 -16 1168 -80 CIRCLE Normal 1408 -16 1344 -80 CIRCLE Normal 704 -16 640 -80