Appendix G.Transformed frequency domain measurements using spice

				IMPULSE RESPONSE SPICE NET LIST MODIFICATION 315
Xcircuit		1	2	netname
RL	2	0	RLOAD
E21	21	0	VALUE=V(2)*2/N(R01,R02)

*n = SQRT(R02/R01)

*E21	21	0	2 0 ”2/n”
R21	21	0	1
*
.SUBCKT	netname		”first		node”	”last		node”

*Input side

*.

*.

*.

*Output side

.ENDS	netname
* Code	for S11	and S21
*.AC DEC ”num”		”f1” ”f2”
.PROBE	V(11)	V(21)
.END

G.7 IMPULSE RESPONSE SPICE NET LIST MODIFICATION

Time domain analysis with SPICE requires replacing the AC statement with a TRAN statement similar to the following:

.TRAN .01ps 250ps 0 .2ps

In addition the VIN statement should be replaced with one containing either the PULSE or the PWL transient function. The pulse statement has the form PULSE(initial volt, pulse volt, delay time, rise time, fall time, pulse width, period). The measured “impulse” from the time domain measurements from the network analyzer is approximated by the following PULSE statements. The 18 GHz pulse, with base width of 94.019 ps, is approximated as follows:

VIN 10 11 PULSE(0 1 0 39.482p 39.491p 15.05p)

The 26 GHz pulse, with a base width of 64.150 ps, is approximated as follows:

VIN 10 11 PULSE(0 1 0 26.395p 28.477p 9.278p)

Alternately, the more accurate piecewise linear fit could be used. The 18 GHz “impulse” is approximated using 81 points:

VIN 10 11 PWL(0ps 0, 1.5ps 0.0037, 3.0ps 0.0089, 4.5ps 0.0156,

316 TRANSFORMED FREQUENCY DOMAIN MEASUREMENTS USING SPICE

+6.0ps 0.0237, 7.5ps 0.0336, 9.0ps 0.0452, 10.5ps 0.0589,

+12.0ps 0.0745, 13.5ps 0.0922, 15.0ps 0.1121, 16.5ps 0.1342,

+18.0ps 0.1584, 19.5ps 0.1848, 21.0ps 0.2134, 22.5ps 0.2441,

+24.0ps 0.2767, 25.5ps 0.3111, 27.0ps 0.3472, 28.5ps 0.3848,

+30.0ps 0.4236, 31.5ps 0.4634, 33.0ps 0.5038, 34.5ps 0.5448,

+36.0ps 0.5858, 37.5ps 0.6267, 39.0ps 0.6671, 40.5ps 0.7065,

+42.0ps 0.7448, 43.5ps 0.7815, 45.0ps 0.8162, 46.5ps 0.8489,

+48.0ps 0.8789, 49.5ps 0.9062, 51.0ps 0.9304, 52.5ps 0.9513,

+54.0ps 0.9687, 55.5ps 0.9824, 57.0ps 0.9922, 58.5ps 0.9983,

+60.0ps 1.0002, 61.5ps 0.9982, 63.0ps 0.9922, 64.5ps 0.9823,

+66.0ps 0.9686, 67.5ps 0.9512, 69.0ps 0.9303, 70.5ps 0.9061,

+72.0ps 0.8788, 73.5ps 0.8487, 75.0ps 0.8161, 76.5ps 0.7813,

+78.0ps 0.7446, 79.5ps 0.7064, 81.0ps 0.6669, 82.5ps 0.6266,

+84.0ps 0.5857, 85.5ps 0.5446, 87.0ps 0.5037, 88.5ps 0.4633,

+90.0ps 0.4235, 91.5ps 0.3847, 93.0ps 0.3471, 94.5ps 0.3111,

+96.0ps 0.2767, 97.5ps 0.2441, 99.0ps 0.2135, 100.5ps 0.1849,

+102.0ps 0.1585, 103.5ps 0.1342, 105.0ps 0.1122, 106.5ps 0.0923,

+108.0ps 0.0746, 109.5ps 0.0591, 111.0ps 0.0455, 112.5ps 0.0338,

+114.0ps 0.0240, 115.5ps 0.0158, 117.0ps 0.0092, 118.5ps 0.0040,

+120.0ps 0)

The piecewise linear fit for the 26 GHz “impulse” is approximated using 77 points:

VIN 10 11 PWL(0ps 0,1ps .005, 2ps .015, 3ps .0267, 4ps .0402,

IMPULSE RESPONSE SPICE NET LIST MODIFICATION

317

+5ps .0556, 6ps .0731, 7ps .0925, 8ps .1140, 9ps .1375,

+10ps .1632, 11ps .1909, 12ps .2204, 13ps .2519, 14ps .2850,

+15ps .3198, 16ps .3560, 17ps .3933, 18ps .4318, 19ps .4709,

+20ps .5106, 21ps .5505, 22ps .5904, 23ps .6299, 24ps .6688,

+25ps .7067, 26ps .7433, 27ps .7784, 28ps .8116, 29ps .8427,

+30ps .8713, 31ps .8972, 32ps .9202, 33ps .9401, 34ps .9566,

+35ps .9697, 36ps .9792, 37ps .9850, 38ps .9871, 39ps .9855,

+40ps .9801, 41ps .9710, 42ps .9584, 43ps .9423, 44ps .9227,

+45ps .9001, 46ps .8745, 47ps .8462, 48ps .8155, 49ps .7825,

+50ps .7477, 51ps .7112, 52ps .6734, 53ps .6346, 54ps .5952,

+55ps .5553, 56ps .5154, 57ps .4756, 58ps .4363, 59ps .3979,

+60ps .3604, 61ps .3240, 62ps .2891, 63ps .2557, 64ps .2240,

+65ps .1942, 66ps .1663, 67ps .1404, 68ps .1166, 69ps .0948,

+70ps .0751,71ps .0575, 72ps .0418, 73ps .0279, 74ps .0160,

+75ps .0058, 76ps 0)

The piecewise linear fit for the 50 GHz “impulse” is approximated using 46 points:

VIN 10 11 PWL( 0ps -4.530E-03, 1ps -611.4E-06, 2ps 6.941E-03,

+3ps 0.019, 4ps 0.037, 5ps 0.061, 6ps 0.091, 7ps 0.130,

+8ps 0.175, 9ps 0.229, 10s 0.289, 11ps 0.355, 12ps 0.425,

+13ps 0.500, 14ps 0.576, 15ps 0.651, 16ps 0.724, 17ps 0.792,

+18ps 0.854, 19ps 0.906, 20ps 0.948, 21ps 0.979, 22ps 0.996,

+23ps 1.000, 24ps 0.990, 25ps 0.967, 26ps 0.931, 27ps 0.884,

318 TRANSFORMED FREQUENCY DOMAIN MEASUREMENTS USING SPICE

+28ps 0.828, 29ps 0.763, 30ps 0.693, 31ps 0.618, 32ps 0.542,

+33ps 0.467, 34ps 0.394, 35ps 0.325, 36ps 0.262, 37ps 0.204,

+38ps 0.155, 39ps 0.112, 40ps 0.077, 41ps 0.049, 42ps 0.028,

+43ps 0.013, 44ps 3.141E-03, 45ps -2.711E-03)

ACKNOWLEDGMENT

The authors wish to acknowledge the help of Terry Jamison in the analysis of the impulse response data.

REFERENCES

1.M. E. Hines and H. E. Stinehelfer Sr, “Time-Domain Oscillographic Microwave Network Analysis Using Frequency-Domain Data,” IEEE Trans. Microwave Theory Tech., Vol. MTT-22, pp. 276–282, 1974.

2.T. B. Mills, “S-Parameters in Spice,” RF Design, pp. 45–48, 1989.

3.K. B. Kumar and T. Wong, “Methods to Obtain Z, Y, H, G and S Parameters from the SPICE Program,” IEEE Circuits Devices, Vol. 4, pp. 30–31, 1988.

4.R. Goyal, “S-Parameter Output from the SPICE Program,”IEEE Circuits Devices, Vol. 4, pp. 28–30, 1988.

5.C. E. Smith, “Frequency Domain Analysis of RF and Microwave Circuits Using SPICE,” IEEE Trans. Microwave Theory Tech., Vol. MTT-42, pp. 1904–1909, 1994.

6.Ke Lu and T. J. Brazil, “A Systematic Error Analysis of HP8510 Time-Domain Gating Techniques with Experimental Verification,” 1993 IEEE MTT-S Microwave Theory Tech. Symp. Digest, pp. 1259–1262, 1993.