In part one of this blog series, ADC Digital Downconverter: Decimation Filters and ADC Aliasing, Part 1 we began looking at the decimation filtering in the DDC when the complex to real conversion is enabled and the output data is real only. Now we will look at what happens when we place the DDC in complex mode and the output data is complex (I and Q).

We will continue looking at the AD9680 as an example just as we did in part 1. Similar to the real mode operation of the DDC the normalized decimation filter responses are the same regardless of speed grade. Once again, Iâ€™d like to mention that for the example filter response plots included here the specific insertion loss versus frequency is not given exactly but is figuratively shown to illustrate the approximate response of the filter. This should help give a high level understanding of how the filter responses are affected by the ADC aliasing.

Letâ€™s again look at the DDC block in the AD9680 which consists of an NCO, up to four cascaded half band (HB) filters (which we will also refer to as decimation filters), an optional 6 dB gain block, and an option complex to real conversion block as illustrated in the figure below. Recall that the AD9680 has four of these DDC blocks. For the case of the examples presented here the complex to real conversion block will be bypassed (disabled). To review, the signal from the ADC first passes through the NCO which shifts the input tones in frequency, then passes through the decimation filters, optionally through the gain block, and, if enabled, through the complex to real conversion (again, this block is bypassed for the examples here in this blog).

With the DDC in complex mode it is configured to have a complex output which consists of real and complex frequency domains commonly referred to as I and Q. Recall from part 1 the low pass response of the HB1 filter (illustrated in the figure below). The HB1 filter has a pass band of 38.5% of the real Nyquist zone. It also has a stop band that is 38.5% of the real Nyquist zone with transition band making up the remaining 23%. Likewise in the complex domain, the pass band and stop band each make up 38.5% (77% total) of the complex Nyquist zone with transition band making up the remaining 23%.

Letâ€™s continue to look at the HB1 filter and see the aliased response. When operating the DDC in complex output mode with the HB1 filter enabled the decimation ratio is equal to two and the output sample rate is half of the input sample clock. The pass band of the filter includes 38.5% of f_{S} /2 for I (real) data and 38.5% of f_{S} /2 for Q (complex) data. The solid blue line represents the actual filter response while the dotted blue line represents the effective aliased response of the filter due to the aliasing effects of the ADC. An input signal at 7 f_{S} /8 will alias into the first Nyquist zone at f_{S} /8 placing it in the pass band of the HB1 filter. The complex image of this same signal resides at â€“7 f_{S} /8 and will alias in the complex domain to â€“ f_{S} /8 placing it in the pass band of the HB1 filter in the complex domain.

Now letâ€™s look at the case where HB1 and HB2 are enabled. This results in a decimation ratio of four for each I and Q output. Once again, the actual frequency response of the HB1 + HB2 filters is given by the solid blue line. Enabling both HB1 and HB2 filters results in an available bandwidth of 38.5% of the decimated Nyquist zone in each of the real and complex domains (38.5% of f_{S} /4 where f_{S} is the input sample clock). Once again, notice the aliasing effects of the ADC and its impact on the combination of HB1 + HB2 filters. A signal that appears at 15 f_{S} /16 will alias into the first Nyquist zone at f_{S} /16. This signal has a complex image at â€“15 f_{S} /16 in the complex domain and will alias into the first Nyquist zone in the complex domain at â€“ f_{S} /16.

Now letâ€™s enable HB1, HB2, and HB3 filters and observer the result in complex DDC mode. In this case the decimation ratio is equal to eight. Here we see that the available bandwidth of 38.5% of f_{S} /8 in each the complex and the real domains. For simplicity and ease of viewing I have condensed the figure to more easily show the whole filter response. Just as in the two previous figures the effective aliased response of the HB1 + HB2 + HB3 filters is given by the dashed blue line while the solid blue line represents the actual filter response. Notice also that as we increase the number of decimation filters used the available bandwidth decreases. However, one benefit of the decimation filtering is the processing gain seen in the signal to noise ratio (SNR) of the ADC. For each decimation filter enabled in addition to HB1 there is approximately a 3 dB improvement in SNR (HB1 alone improves SNR by approximately 1 dB).

The last combination of filters that we will look at is HB1 + HB2 + HB3 + HB4 which has all the decimation filters in the AD9680 enabled and results in a decimation ratio of sixteen when operating the DDC in complex mode. This case is quite similar to the previous case but just scaled to reflect the larger decimation ratio. In this case we have an available bandwidth of 38.5% of f_{S} /8 for each the real and the complex domains. With all four half band decimation filters enabled we have approximately 100 dB of rejection from just past f_{S} /16 through the end of the first Nyquist zone. Once again, this response is effectively aliased into the upper Nyquist zones.

Last time we looked at the questions: â€śWhy do we decimate?â€ť and â€śWhat advantage does it offer?â€ť As we learned in the part one of this blog, different applications have different requirements that can benefit from decimation of the ADC output data. One motivation is to gain signal to noise ratio (SNR) over a narrow band of frequency that resides in an RF frequency band. Another reason we looked at was the fact that there is less bandwidth to process and results in lower output lane rates across the JESD204B interface which allows the use of a lower cost FPGA. By using all four decimation filters the DDC can realize processing gain and improve the SNR by up to 10 dB. In Table 1 below we can see the available bandwidth, decimation ratio, output sample rate, and the ideal SNR improvement offered by the different decimation filter selections when operating the DDC in complex mode.

**Table 1**

Now we have a pretty good insight into both the real and complex modes of operation for the DDC in the AD9680. We can see the advantages of the decimation filtering. Also we can get an idea of the flexibility of the DDC. The DDC can operate in real or complex mode and allow the user to use different receiver topologies depending on the needs of the particular application. Stay tuned for the next blog where we will continue looking at the DDC operation and dive a little deeper to look at the decimation filter responses and frequency folding due to the decimation. Coming soon in the next few months we will also look at using some updates to simulation tools and how they can be used to simulate the DDCs.

Hi.Â On the 2nd page of this article you wrote that “An “input signal at 7fs/8 will alias into the first Nyquist zone at fs/8 placing it in the pass band of the HB1 filter. The complex image of this same signal resides at â€“7fs/8 and will alias in the complex domain to â€“fs/8.” That is only true for real-valued inputs, not complex-valued inputs. I didn't understand your phrase “complex image.”Â By “complex image” did you mean “negative-frequency image?”

Hi DSPer, I guess it is a matter of semantics.Â You could refer to the negative frequency tone as the complex image or negative image.Â It resides in the complex or negative domain, depends on who you ask I guess.Â Technically negative domain and negative image are probably more accurate descriptions.Â However, whether the signal is real or complex there will be an image there.Â If using a purely real input the negativeÂ image would be nearly equal in magnitude to the fundamental.Â If using a complex signal the negative image would hopefully be lower since you'd like to have good quadrature balance, but as we know the quadrature balance won't always be exactly perfect.Â Thanks for the great question!!

Hi Jonathan. If I'm not mistaken, it appears that the frequency translation by fs/4 Hz in the ad9684's data sheet Figure 66 (Complex to Real Conversion) only works when the complex input signal contains no spectral energy outside the range of +/- fs/4 Hz.Â Something to think about. Also, kudos to those terrific high-tech geeks at Analog Devices for producing such a powerful and functional A/D converter!

Hi DSPer, another very good question.Â The diagram in Figure 66 in the AD9684 is a representative view of what is going on in that block, but is not the exact circuitry.Â The important ideas to garner from this figure is that the complex to real block will 1) remove the complex (Q), the spectrum gets shifted by +fs/4 in frequency, and 3) an option 6dB gain block can be enabled to offset the 6dB loss from the mixing process.

Thank you for the kind words as well.Â We have some very sharp analog and digital guys here at ADI designing ADCs.Â It is amazing to me how much more complex our ADC products have become in the last 5-6 years.Â The amount of digital processing has increased quite a bit!