Greetings,

  I have been simulating a high dynamic range A/D Converter and had some questions/observations that I would like to share.

  The following analysis was performed using the standard Cadence tools: ADE, Spectre, and Calculator.

1) Philosophical question:
    It seems like Spectre's Fourier Integral based analysis
    is the best method for simulating the dynamic
    performance of D/A Converters. Since the FFT samples
    the D/A Converter output, it is difficult to evaluate the
    effect of glitch impulse on the output spectrum. While
    the Fourier Integral evaluates the entire data set it
    is more accurate. Is this observation correct?

2)  When simulating the dynamic response of a D/A
    Converter, SFDR, THD, SINAD, etc. the output response
    tends to suffer from the "picket fence" effect, that is,
    energy tends to be concentrated in the harmonics
    of the clock and input frequencies. This phenomena
    occurs even if the normal precautions are taken, that
    is, the input and clock frequencies are non-harmonically
    related. Is there a method to eliminate this phenomena
    from simulations?

3) For high dynamic range Data Converters, the  
   interpolation error is an issue. Strobing the output
   helps somewhat, so does setting the maxstep to < 1/2
    the FFT step size.  Are there any other approaches that
    can be used to improve the accuracy of the FFT?

4) A question on the difference between Nyquist rate
   ADCs and Delta-Sigma ADCs. When using synchronuos,
   non-coherent sampling to simulate SFDR/THD of a
    Nyquist rate ADC, the FFT "Rectangular" window has
    more dynamic range than the "Hanning" window.
    However, for Delta-Sigma Modulators, the "Rectangular"
    window gives inconsistent results, that is, the SFDR/
    THD are a function of the data window used for the FFT.
    while the "Hanning" gives consistent results.

    Is this difference because Nyquist converters have are
    "memoryless" while Delta-Sigma Modulators have
    "memory"?  Since the state of a Delta-Sigma Modulator
    is dependent on the previous state of the system there
    is effective spectral leakage DSM that does not occur
    for Nyquist-rate ADCs.

5) Some questions on the Fourier component from
   analogLib  and Spectre Fourier analysis:
   a) When using Fourier Analysis, the fundamental
        frequency is defined relative to the last simulation
        time point. If the simulation time is selected such that
        simulation stop time - (1/fundamental frequency),
        then the initial time points will be ignored and
        start-up effects will be ignored. Is this correct?
    b) Is there a parameter equivalent to refnormharm
        the numerator of the Fourier Integral? When
        testing Data Converters, the reference tone is
        seldom at the fundamental freuquency.
    c) When simulating a Delta-Sigma Modulator, what
        is the appropriate type of interpolation to use?
        Since there are a large number of points and
        the curve is highly non-linear, that is a stream
        of 1s and 0s, is linear or quadratic interpolation
        better?

        Looking forward to your comments.

                                                         Best Regards,

                                                            Sheldon

Ken,

   About #2

If you use coherent sampling with an ADC, for example,
fs=100M and fin=10M, then only 10 states get exercised
and the FFT shows the picket fence effect. That is, it  
looks like you are looking at "real" spectrum through a
picket fence. There are tones at 10M, 20M, 30M, ... and
nothing else. The solution for an ADC is to use
non-coherent sampling, for example, fs=100MHz and
fin=(3/256)*fs for a 256 point FFT.

The problem is that when simulating D/A Converter,
non-coherent sampling does not seem to work, that
is, the FFT always shows the picket fence effect even
when the input and sample frequencies are correctly
defined.

Have you ever run across this effect and do you have
any insight into how to eliminate it?

There seem to be two possible approaches:
1) Include the effect of DAC clock jitter in the simulation
2) Increase the number of points in the FFT to be
   greater than the DAC number of bits.

#1 seems to be the more reasonable approach, #2 is
painful because of the simulation time required.

                                              Best Regards,

                                                 Sheldon

Hi Sheldon,

Ref. 4 in your original post, the difference between the effects of the Rectangular window and the Hanning windown when applied to Nyquist-rate and oversampled delta-sigma converters is more due to the nature of the spectrum that they are applied to.

The rectangular window (in frequency domain) rolls off very slowly, and hence permits leakage of out-of-band signals into the signal band. While the problem is less severe in Nyquist-rate converters, in delta-sigma converters, the out-of-band shaped quantization noise has a considerable amount of energy concentrated in it, and even the least bit of leakage can ruin your FFT.

The only way to improve results with a rectangular window is to keep increasing the number of points to get a measly 3 dB improvement per octave. A Hanning window on the other hand has very good leakage properties and gives much better FFT results for a smaller number of points.

Your argument about the "memory" inherent in the state of these converters is correct to a certain extent. However, it is the nonlinearity introduced by the quantizer, coupled with this memory that causes much of the misery. If you just removed that quantizer leaving behind a discrete-time filter, the effect would not be as severe.

Essentially, all that "random" switching between the 1s and 0s causes the problem. I would conjecture that the output of a delta-sigma ADC with a multi-bit quantizer would be a bit better behaved, although there too, the Hanning window is superior.

For more, please refer the Appendix A of "Understanding Delta-Sigma Converters" by Temes & Schreier.

Regards
Vivek