Problem 14.3 - The Fourier Series of a Periodic Sawtooth Waveform
*
* NOTE: This is a two-part problem.
* 1. The PWL function and the .TRAN command define an analysis of a
* symmetric sawtooth waveform over one period of the waveform.
* 2. The PWL function is used to describe 10 cycles of a symmetric
* sawtooth waveform for .FOUR and Fourier Transform analysis.
*
* Draw on paper the waveform described by the PWL function in the
* program listing below. Check to make sure that the waveform has the
* same value at t=T as it does at t=0. This is to insure that the
* waveform is one cycle of a periodic waveform that does not have
* a discontinuity (sometimes called a double value) at t=T.
*
* Use PROBE to display the graphs of the waveforms and to perform the
* Fourier analysis. Select the waveforms for analysis one at a time,
* instead of displaying them simultaneously. Obtain hard copies of the
* PROBE graph of the frequency spectrum for each part of the problem.
*
* You can observe the effect of the increased resolution obtained when
* 10 cycles are sampled if you take the two frequency-spectrum graphs
* and superimpose them (put one on top of the other). You can see that
* the tips of the spectral components at multiples of the fundamental
* frequency have the same value. This comparison confirms that only
* the values shown on the graph at multiples of the fundamental
* frequency have any meaning.
*
.OPT NOPAGE NOBIAS
V1 1 0 PWL(0,0,1E-7,-7,999.9E-6,7,1E-3,0)
R1 1 0 1K
.TRAN ; Complete the .TRAN command for an analysis
; period of 1 millisecond.
.FOUR 1000 V(1)
.PROBE
.END
Problem 14.3, Part 2. The Fourier Series of a Periodic Sawtooth Waveform
*
* Fourier series with 10 periods of the periodic waveform
* in the sampling window. This gives better resolution for
* the PROBE Fourier Transform function, but much poorer
* resolution for the .FOUR command. The reason for the poor
* resolution is that there are fewer samples taken over the
* one cycle of the waveform used for the .FOUR calculation.
*
.OPT NOPAGE NOBIAS
V1 1 0 PWL(0,0,1E-7,-7,999E-6,7,1001E-6,-7,1999E-6,7,2001E-6,
+ -7,2999E-6,7,3001E-6,-7,3999E-6,7,4001E-6,-7,4999E-6
+ ,7,5001E-6,-7,5999E-6,7,6001E-6,-7,6999E-6,7,7001E-6,
+ -7,7999E-6,7,8001E-6,-7,8999E-6,7,9001E-6,-7,
+ 9999E-6,7,10E-3,0)
R1 1 0 1K
.TRAN ; Complete the .TRAN command for an analysis
; period of 10 milliseconds.
.FOUR 1000 V(1)
.PROBE
.END