Creating Missing/Extra Bits

The case of the missing or extra bits is straightforward. You can vertically scale the amplitude of a waveform segment using the AWG editor (Figure 10). In this example, the cursors select a 110 ns slice and the vertical scaling function decreases the amplitude of the entire segment by 50%. The AWG 2041's marker outputs are also shown in this example. The bits of two markers are associated with each waveform point. These provide two binary output signals that can assist in triggering instrumentation. Marker 1 was set to generate a pulse at each 20 ns bit interval, and Marker 2 was set to generate a pulse during the amplitude aberration. Marker 1 could be used to synchronize a scope to view the data recovery clock jitter, and Marker 2 can trigger the capture of a downstream signal in the read channel circuit.

Figure 10. The vertical cursors define the duration of the aberration. All points in the segment are scaled by 0.5 to simulate missing bits. The left (L) and right (R) cursor readouts show that the affected area falls between the 132^nd and 242^nd points in the 960-point waveform.

Building a 1M-Point Waveform Sequence

Since media defects are relatively infrequent, we use the AWG's sequence editor to generate this aberration with a low duty cycle. In this case we have two waveforms in our repertoire. The first is our 960-point (48-bit) test pattern waveform, CV-960.WFM, and the second is the same waveform plus the "missing" bits, CV-960M.WFM. The sequence editor creates a script for combining individual segments (Figure 11). In this example, we define a sequence where the basic test waveform repeats 1000 times, the version with the missing bits is inserted once, then the sequence repeats. Note that this simple script defines a new waveform with an equivalent size of 960,960 points!

Figure 11. The AWG's sequence editor provides a simple scripting procedure for concatenating waveform blocks.

Simulating Mechanical Shock

We need the sequence editor to generate long waveforms for applications that simulate mechanically induced amplitude modulations. Suppose we want to simulate a mechanical shock in a small laptop drive. We will use a damped sinusoid to model the shock's effect on the signal amplitude (Figure 12). Four lines in the equation editor implement the model. First, we define a 1 ms waveform using the range command. Then we define two constants that will simplify changes to the basic ring and decay parameters. The ring frequency is set to 5000 Hz using k0. The exponential decay constant is set to 200 µs using k1. The fourth line defines the damped sinusoid using these two constants. The DC term of 0.5 creates a positive-only multiplier so that the nominal level is non-zero.

Figure 12. An equation editor defines a damped sinusoid to amplitude modulate the read channel waveform.

Since the damped sinusoid will amplitude modulate the data waveform, we need to match the lengths of both waveforms. In this example we will use an AWG clock rate of 200 MS/s or 5 ns/point. The sequence editor was used to create an expanded data waveform consisting of 200 repetitions of the basic 960-point waveform. This is 192,000 points or just about 1 ms. We use the waveform editor to expand the damped sinusoid to the same record length of 192,000 points. The exact length of the two waveforms is 960 µs. Then we simply multiply the two waveforms together to perform the modulation (Figure 13).

Figure 13. The AWG's editor displays the two waveforms that will be multiplied together. The record lengths of the two waveforms must match.

A marker pulse was added to the final waveform at the beginning of the modulation envelope to simplify scope triggering. The TDS' peak detect acquisition readily captures the envelope (Figure 14). The cursors verify the 5000 Hz ring frequency.

Figure 14. The modulated read channel signal as captured by the TDS 744A oscilloscope.

Simulating Residual 1F Amplitude After 2F Overwrite

The next example simulates the residual 1F amplitude after a 2F overwrite. Since a typical 1F residual is attenuated by at least 30 dB, the approach is to add an attenuated 1F waveform to a 2F waveform. The editing procedure is similar to the previous example except we are adding instead of multiplying two waveforms (Figure 15). First, we attenuate the 1F waveform by using the editor's vertical scaling function. Then we simply add the two waveforms. The basic 1F and 2F patterns were created using the convolution procedure described above. As before, the record lengths must match in order to add the waveforms point-by-point. In this case, we could have used a common 80-point record, since the slower 1F pattern repeats in this interval. However, we used a 960-point common record length for consistency with our modulated data waveform.

Figure 15. The 1F waveform (upper) is scaled by 0.03 (­30.5 dB) before it is added to the 2F waveform (lower).

The TDS 744A display of the AWG overwrite signal is shown in Figure 16. The upper trace is the original 1F waveform. The time scale is 100 ns/div. The second trace is the FFT of the 1F waveform. The TDS' gated measurement function zooms in on the fundamental and measures a level of ­12 dBV centered at 12.5 MHz as expected. The absolute level is unimportant since we are interested in only the attenuation in the overwrite waveform. Note that the vertical scale of the FFT results are 40 dB/div and the horizontal scale is 10 MHz/div. The third and fourth traces are the overwrite waveform and its FFT. The 12.5 MHz fundamental is now ­44.8 dBV, so it has been attenuated by 32.8 dB. While the attenuation is not exactly 30 dB, the results are within allowable tolerances and are quite good given the finite 8-bit resolution of the 1 GS/s AWG generator. Note that the computational errors due to finite resolution occur only once. The 1F/2F relationships are not constant in the digital waveform record.

Figure 16. TDS 744A captured the original 1F and the calculated overwrite signal. The FFT calculates the levels of the 1F fundamental at 12.5 MHz.

Using a Filter to Modify Amplitude Characteristics

The previous example introduced the TDS 744A's FFT capability to provide a frequency domain view of an amplitude aberration. In fact, the residual 1F signal aberration was too small to observe directly in a time domain representation! This illustrates the need to modify the amplitude characteristics of test signals through the frequency domain. The AWG 2041 provides two basic methods for altering the amplitudes of the frequency components of a test signal. The first method is the straightforward hardware filter. The AWG provides a set of four Bessel low-pass filters: 10, 20, 50, and 100 MHz. The Bessel filter's linear phase response is particularly useful for preserving the peak characteristics of read channel test signals.

Figure 17 shows the Lorentzian pulse through three of the filters. This is the same 256 ns pulse we used to develop the modulated data waveform. The leftmost peak is the unfiltered pulse directly from the equation compiler. The next pulse was applied to the 100 MHz filter. There is a negligible peak amplitude reduction, and the signal is delayed relative to the unfiltered pulse by about 5 ns. If you synchronize the TDS on the AWG's marker pulse, enabling the AWG's 100 MHz filter will delay a modulated data waveform by 5 ns, in addition to filtering the output. The 50 MHz filter attenuates the peak slightly more and delays the peak by about 10 ns but nevertheless preserves the pulse shape. The 20 MHz filter attenuates the peak significantly and broadens the pulse shape, due to the attenuation of its higher frequency components. This filter is inappropriate for our original read channel pulse.

Figure 17. The unfiltered Lorentzian pulse output from AWG is the leftmost peak. The delayed pulses show the effect of the 100 MHz (shortest delay), 50 MHz, and 20 MHz (longest delay) Bessel low-pass filters.

The hardware low-pass filter is easy to apply, but the choices are fixed and may not match your application. In Figure 18, the TDS 744A captures a modulated data pattern with and without the AWG's 50 MHz low-pass output filter. The signal is delayed as predicted, but the attenuation above 50 MHz is barely noticeable in the frequency domain. We have already discovered that the 20 MHz hardware filter is unsuitable, so we need another solution to shape the frequency components in the data pattern.

Figure 18. The upper two overlayed waveforms show the modulated data pattern with and without the 50 MHz hardware low-pass filter. Since the marker pulse was used to trigger the TDS, the filtered waveform is delayed by about 10 ns. The TDS calculates the FFT spectra of the two signals in the lower two traces. The bottom trace is the filtered waveform, but the attenuation above 50 MHz is barely noticeable.

Using an FFT to Modify Amplitude Characteristics

The second method of altering frequency components is the AWG 2041's software based FFT editor option. The FFT editor lets you alter the magnitude and phase characteristics of a signal in the frequency domain. Figure 19 shows the AWG's filter editing menu applied to the modulated data pattern. We select the low-pass filter option and need to enter a break frequency and a rolloff rate. Here we enter 50.0 MHz and a brick wall rolloff of 400 dB/octave. The AWG editor uses the FFT to transform the original waveform into the frequency domain. It removes all the components above 50 MHz and transforms the altered frequency domain record back to a time domain record. Note that the editor also provides built-in high-pass, band-pass, and band-elimination filter templates.

Figure 19. The AWG 2041's FFT editor has built-in filtering functions to shape the frequency domain components of a waveform. Here the low-pass filter function is used to remove frequency components above 50 MHz in the modulated data pattern. The FFT editor is particularly useful in reshaping modulated patterns to verify the performance of channel filters.

The unfiltered waveform and the waveform filtered by the AWG's filter editor are captured by the TDS in Figure 20. The two traces exactly overlay in the time domain records. The two FFT traces reveal the superior filtering performance of the FFT-edited waveform. As in the overwrite example, traditional time-domain scope waveforms do not reveal that the frequency components above 50 MHz have been successfully removed. Thus, it is the combination of the AWG's time-domain and frequency-domain editing tools that provides the power and flexibility to create the signal aberrations required in modern disk drive applications.

Figure 20. The upper two overlayed waveforms show the modulated data pattern with and without the 50 MHz brick wall filter. The filtered waveform is not delayed relative to the unfiltered waveform. The TDS calculates the FFT spectra of the two signals in the lower two traces. The bottom trace is the spectrum of the filtered waveform.