Talking about DDC (Digital Down Conversion) Technology of Oscilloscope

Nowadays, as the design of electronic products becomes more and more complex, the test content is also becoming more and more complex. People may not only need to know the time domain characteristics of the signal, but also want to understand the frequency domain characteristics of the signal, or the joint characteristics of multiple domains also need to be measured. As a result, it is very likely that the work test bench is filled with various instruments: oscilloscopes, spectrum analyzers, etc., and the work space is squeezed. What's more important is that the test work becomes complicated, and the complex connection of various instruments and the synchronization problems between instruments need to be solved. Therefore, for general debugging and measurement, people hope to have a multifunctional instrument that can not only meet the needs of time domain testing, but also perform frequency domain analysis, and even perform coherent joint debugging of time and frequency domain signals together, and even analyze some vector signals. Oscilloscopes are widely used as the most basic test and measurement instruments. If these analysis functions can be integrated, it will bring great convenience to engineers. At present, various oscilloscope manufacturers have also launched some all-in-one oscilloscopes, and the technologies are also different. They are either separate time domain and frequency domain channel measurements, or they are analyzed by software calculation, so they also face some problems. For example, in spectrum analysis, we know that RBW (resolution bandwidth) is inversely proportional to the capture time of the signal. If a smaller RBW is required (in layman's terms, a more detailed spectrum view), a longer capture time is required, and the sampling rate will inevitably be reduced, so high-frequency signals cannot be analyzed. On the contrary, if high-frequency signals are to be analyzed, the RBW will be larger and the frequency resolution will be weaker. In addition, in vector signal analysis, it will also be limited by the oscilloscope's storage space and sampling rate, resulting in the inability to analyze longer signals. So how can these measurement problems be solved through oscilloscope design? This article introduces the DDC (digital down-conversion) technology used by R&S oscilloscopes, which solves the above problems very well and gives full play to multi-domain joint testing.

2 DDC Introduction

DDC (Digital Down Converter) is a process in which a sine or cosine signal with the same frequency as the RF or IF signal carrier is generated by an NCO (numerically controlled oscillator), multiplied by the RF or IF signal, and finally the baseband signal is obtained by filtering and resampling.

Due to the huge advantages of digital signal processing, it has been widely used. In wireless communication systems, it is increasingly hoped that A/D (analog-to-digital) and D/A (digital-to-analog) conversion can be brought closer to the RF front end, so that various functions in communication can be realized through digital signal processing. However, due to the current limitations of the development level of ADC (analog-to-digital converter) and DSP (digital signal processor), it is very difficult to directly perform AD conversion and then digital signal processing at a very high frequency RF end - the same is true for digital oscilloscopes. For example, due to the limitation of processing power, if high-frequency signals are sampled at the RF end, a very high sampling rate is required. Once the capture time is extended, the number of sample points will be very large. At this time, it will be found that the oscilloscope processing time becomes longer and the response is very slow. In order to solve this contradiction between ADC and DSP, DDC is used to convert the signal to baseband, and then resample at a lower rate, which can reduce the amount of data and improve the efficiency of DSP.
 

Figure 1 DDC principle block diagram

Figure 1 is a block diagram of the DDC principle, which is mainly composed of NCO, mixer, low-pass filter and resampling modules. The RF signal is converted into a digital signal In(n) after passing through a high-speed ADC:
In(n) = s(n)×cos(wn) (1)

Where s(n) is the signal, cos(wn) is the carrier, and w is the carrier frequency. The NCO generates a local oscillator signal f(n) with the same frequency as the RF signal:
f(n) = cos(wn) (2)

The signal m(n) is obtained by mixing and multiplying the local oscillator signal and the RF signal:
m(n) = In(n)×f(n) = s(n)×cos(wn)×cos(wn)
          = 1/2s(n)[cos(2wn)+1] (3)

After low-pass filtering and resampling the signal m(n), the output signal Out(n) can be obtained:
Out(n) = 1/2s(n) (4)

It can be seen that through DDC, the real useful signal s(n) is retained, and the data volume is greatly reduced through resampling, which improves the efficiency of subsequent signal processing. Similarly, if DDC technology is used in a digital oscilloscope, it can not only retain the useful signal in the RF signal, but also greatly reduce the data volume and improve the processing speed of the oscilloscope.

Next we will discuss the DDC application in R&S oscilloscope.

3 DDC implemented in R&S oscilloscope hardware

Before discussing the application of DDC in R&S oscilloscopes, let's first compare the structural differences between R&S digital oscilloscopes and traditional digital oscilloscopes.

Figure 2 Block diagram of a traditional digital oscilloscope

Figure 2 is a basic block diagram of a traditional digital oscilloscope. The signal enters the oscilloscope through the analog channel, passes through the vertical gain amplifier and filtering, is converted into a digital signal by the ADC, is stored by the acquisition storage module, and then is processed by software, and finally displayed on the oscilloscope screen. Traditional digital oscilloscopes use software processing to process data, and there is no DDC structure in hardware. Therefore, when collecting or analyzing some high-frequency signals, it must be done at a high sampling rate. Since the storage space of the oscilloscope itself is limited, the time length of the signal collected or analyzed is also relatively short.

Figure 3 R&S digital oscilloscope structure block diagram

Figure 3 is a basic block diagram of the R&S digital oscilloscope. The signal processing flow is not much different from that of a traditional digital oscilloscope, but more hardware structures are used, including trigger systems, digital processing, DDC, etc. The characteristics and advantages of other hardware structures are not discussed in this article, but it can be clearly noticed that hardware-implemented DDC is used in this structure. Due to the use of hardware DDC structure, the signal can be down-converted to baseband first, and then resampled at a lower sampling rate. In the case of the same storage space, longer signals can be collected or analyzed. And because it is a hardware implementation, the speed will also be faster.

Next, the application of DDC in I/Q demodulation and spectrum analysis is discussed.  

3.1 DDC in I/Q Demodulation

Let's first look at a problem encountered in a real test: the signal to be tested is a modulated signal with a carrier frequency of 300MHz and a modulation bandwidth of 2MHz. If an oscilloscope is used to collect the signal, the acquisition time is expected to be as long as possible. How many seconds of signal can be collected at most? For this problem, we analyze it from the perspective of signal analysis.
First of all, for this type of modulated signal, the military uses radar signals (such as chirp signals) and the civilian uses general communication signals (such as QAM signals). Most of these signals are vector signals. For the analysis of this type of signal, orthogonal demodulation, i.e., I/Q demodulation, must be used. For this type of signal, traditional digital oscilloscopes can only directly collect the RF signal first, and after the data is stored, it is handed over to dedicated software or third-party software for processing (including I/Q demodulation and subsequent processing).

Figure 4: The process of modulated signal processing by a traditional digital oscilloscope

Figure 4 shows the processing flow of a traditional oscilloscope for this type of modulated signal. In response to the above problem, the carrier frequency is 300MHz, the modulation bandwidth is 2MHz, and the highest frequency of the signal is 301MHz. According to the Nyquist sampling theorem, the sampling rate used by the ADC must be twice or more than the highest frequency of the signal to truly restore the waveform. We assume that the traditional oscilloscope ADC uses a sampling rate of 602MSa/s, which is twice the highest frequency, for sampling (it is generally not recommended for the oscilloscope to use a sampling rate that is exactly twice the relationship. Generally, a relationship of 3 to 5 times can restore the waveform more realistically). Assuming that the oscilloscope storage depth is 10MSa, the longest time that can be collected is 10MSa / (602MSa/s) ≈ 16.6ms. Even if a traditional oscilloscope is used to collect this type of signal, only signals of more than 10 milliseconds can be collected. If the carrier frequency is higher, such as 2GHz, the acquisition time will be shorter.

To solve the above problems, R&S oscilloscopes use a hardware-implemented I/Q demodulation module, the most important part of which is DDC. By using this module, the modulated signal can be collected for as long as possible. [page]

Figure 5 R&S digital oscilloscope processing flow of modulated signals

FIG5 shows the processing flow of the modulated signal by the R&S oscilloscope, wherein the I/Q demodulation module is shown in FIG6 .
 

Some people are surprised and confused by the efficient use of storage space. They may think that even with the DDC structure, it is still digital signal processing and there is still an ADC at the front end. That is to say, the oscilloscope still needs to sample the RF signal at the front end and still needs to satisfy the 2x Nyquist theorem for the RF signal. Then, after calculation, only 16.6ms of signal can be stored. Where does the 2.5s come from? We can understand the reason by analyzing the signal processing flow in detail.

Figure 7 The generally accepted signal processing flow

 

The signal processing flow generally considered is shown in Figure 7. For this structure, as understood above, even if DDC is used in this case, the signal collected by the RF must be stored first, so it will still be affected by the high sampling rate. For the above example, only 16.6ms of signal can be stored. However, the actual processing flow of the R&S oscilloscope is shown in Figure 8.

Figure 8 R&S oscilloscope signal processing flow

 

In the RF front end, the ADC always maintains the highest real-time sampling rate, such as 10GSa/s, so that signal aliasing will not occur. The sampled digital signal is directly sent to the DDC for digital down-conversion. Since the DDC of the R&S oscilloscope is implemented in hardware and has a high speed, it can be processed in real time and directly stored after processing. Through this real-time DDC processing, storage space can be saved well, and the 2.5s signal storage mentioned in the above example can be achieved.

 

To this end, we conducted the following experiments.

 

First, a RF pulse signal with a carrier frequency of 3 GHz is generated by a signal source, a modulation pulse width of 0.4 ms, and a pulse repetition period of 1 ms. The settings are shown in Figure 9:

Figure 9 Pulse modulated RF signal setting with carrier frequency of 3 GHz

For the acquisition and analysis of the signal, if a traditional digital oscilloscope is used, the result of the signal length that can be acquired and analyzed is equivalent to that shown in Figure 10:
 

Figure 10: The equivalent result of RF pulse acquired by traditional digital oscilloscope

Since the RF signal frequency is 3GHz, the sampling rate must be at least 6GSa/s, which we set to 10GSa/s. The storage depth is still set to 10M. It can be seen that only 1ms of signal can be collected at this time, that is, only one pulse signal can be collected and analyzed.

If we use an R&S oscilloscope with an I/Q option with a DDC structure for acquisition analysis, we can first set the local oscillator frequency to 3 GHz. After converting the signal to baseband, we can acquire at a lower sampling rate, such as 100 MSa/s, and the storage depth is also set to 10M. The settings are shown in Figure 11:

Figure 11 R&S oscilloscope I/Q option settings

At this point, we can collect and analyze longer signals, that is, 100ms signals, which means we can collect and analyze up to 100 pulse signals! If the resampling rate is set lower, we can collect and analyze signals even longer. Figure 12 shows the test results of the R&S oscilloscope:
 

Figure 12 R&S oscilloscope acquisition of RF pulse results

In summary, the DDC technology in the R&S oscilloscope I/Q option enables efficient use of limited storage space in RF signal acquisition and analysis, and acquisition and analysis of signals of maximum time length.

3.2 DDC in Spectrum Analysis

The spectrum analysis function of an oscilloscope generally uses FFT (Fast Fourier Transformation). The spectrum analysis principle block diagram of a traditional digital oscilloscope is shown in Figure 13.

Figure 13 Block diagram of spectrum analysis of a traditional digital oscilloscope

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After the analog signal passes through the ADC, it becomes a digital signal. Then different window functions are selected for windowing processing, and finally the signal is directly transformed into the frequency domain by FFT. The spectrum range obtained by this processing method is from 0Hz to the maximum frequency (usually equal to half of the ADC sampling rate). For example, if the ADC sampling rate is 5GSa/s, the spectrum range obtained by FFT is from 0Hz to 2.5GHz. If you want to observe a certain section of the spectrum, you can zoom in the spectrum to the frequency band through software display zoom. The advantage of this traditional oscilloscope spectrum analysis method is that all processing processes are calculated by software, and the algorithm is simple, so it is easy to implement. However, if you pursue faster real-time spectrum measurement or higher-precision spectrum analysis, this traditional processing method will be very difficult. Because the full software processing method is used and the calculation is always performed on the entire frequency range (0Hz to the maximum frequency), the processing speed will be very slow, and real-time or quasi-real-time spectrum analysis cannot be achieved. In addition, the oscilloscope settings will be very complicated, and the time domain parameters (such as time base, sampling rate, etc.) need to be constantly adjusted to meet the required frequency domain parameter settings. Most importantly, due to the limitation of the oscilloscope's memory depth and the fact that the FFT points commonly used are only a few K, the frequency resolution, that is, the minimum distinguishable frequency, is very limited. It is usually difficult to achieve an ideal frequency resolution.

Generally speaking, there are two interpretations of frequency resolution. One interpretation is that it refers to the minimum frequency interval between two adjacent frequency points in FFT, as shown in formula (5):
∆f = fs / N = 1 / t (5)

Among them, ∆f represents the frequency resolution, fs represents the ADC sampling frequency, N represents the number of FFT calculation points, and t represents the time length of the acquired signal, that is, the capture time. It can be seen that the longer the signal acquisition time t, the smaller the frequency resolution ∆f, that is, the better the frequency resolution.

The second explanation is that frequency resolution can be expressed in terms of resolution bandwidth (RBW). RBW is defined as the 3dB bandwidth of the main lobe of the window function, as shown in Figure 14:
 

Figure 14 RBW definition

If the difference between the two signal frequencies is smaller than the defined bandwidth, ie, RBW, the two frequencies will be mixed together and cannot be distinguished.

Figure 15 Different spectra corresponding to different RBW settings

Figure 15 shows completely different spectra obtained by setting different RBWs for the same input signal. As the RBW increases from left to right, it can be seen that the main lobe width also increases and the frequency resolution capability also decreases. At the far right, the two frequencies in the signal cannot be distinguished at all.

Since the two interpretations of DDC on frequency resolution are similar, we will only discuss the second interpretation, namely RBW. The RBW calculation method is shown in formula (6):
RBW = RBWnorm × fs / N = RBWnorm / t (6)
Where RBWnorm is the normalization factor of the window function, such as 1.8962 for the Blackman-Harris window, fs is the sampling frequency, N is the number of FFT calculation points, and t is the length of the signal acquisition time. It can be seen from formula (6) that for a fixed window function, if you want to improve the frequency resolution, that is, reduce the RBW, you must increase the signal acquisition time, that is, the capture time. As can be seen from Figure 15, for a fixed rectangular window, the RBW is reduced from 1MHz to 100kHz, and the time base setting is increased from 100ns/div to 1μs/div. However, for digital oscilloscopes, the storage depth is limited. And there is the following relationship between the storage depth and the capture time and sampling rate:

Memory depth = sampling rate × capture time (7)

From formula (7), it can be seen that for a fixed storage depth, the sampling rate and the capture time are inversely proportional. If you want to increase the capture time, it means that the sampling rate will decrease. If the sampling rate decreases, it means the risk of signal aliasing. That is, for the spectrum analysis of traditional digital oscilloscopes, if you want to improve the frequency resolution, you will face the risk of signal aliasing, or you can only analyze low-frequency signals; if you want to analyze high-frequency signals, in order to ensure the sampling rate, the frequency resolution must not be improved.

To address this contradictory relationship, R&S oscilloscopes have introduced a series of processing methods such as DDC to effectively solve the problem.

Figure 16 Block diagram of spectrum analysis of R&S digital oscilloscope

Figure 16 shows the spectrum analysis flow of the R&S oscilloscope, and Figure 17 shows the spectrum analysis setup block diagram.

Figure 17 R&S digital oscilloscope spectrum analysis settings

Compared with traditional digital oscilloscopes, R&S oscilloscopes introduce DDC modules to down-convert the signal to baseband before FFT. Setting the center frequency is equivalent to setting the local oscillator frequency, so that the signal is down-converted to baseband. Therefore, when the baseband signal is resampled, even if a lower sampling frequency is used, it will not cause signal aliasing, so that the longest signal can be collected in a limited storage space, so the frequency resolution (RBW) can be effectively guaranteed. By setting the frequency span, the calculation range of FFT can be narrowed to the set bandwidth in hardware without performing FFT calculations on the entire frequency range, thereby improving the processing speed. In addition, the calculation method of FFT also adopts a segmented overlapping calculation method, which can better reflect the details of the spectrum. In summary, compared with the spectrum analysis of traditional digital oscilloscopes, the use of the R&S oscilloscope spectrum analysis structure has the following advantages:
• Due to the use of hardware processing and other methods, the spectrum analysis speed is fast and can achieve real-time spectrum analysis;
• The spectrum analysis settings are similar to those of a spectrum analyzer, and the spectrum parameters are directly set without the need for complex time domain parameter adjustments;
• It has a large dynamic range;
• This is the focus of this article. Due to the use of the DDC structure, the signal can be down-converted to baseband first, and then resampled at a lower sampling frequency, so that the longest signal can be collected within a limited storage space. According to formula (6), the frequency resolution (RBW) can be well guaranteed. That is, there is no need to worry about the compromise between signal frequency and RBW.

We conducted the following experiment.

Use a signal source to generate a single-frequency sine wave signal with a frequency of 3 GHz. If the traditional oscilloscope spectrum analysis method is used, the sampling rate must be set to above 6GSa/s to prevent the signal from aliasing. According to formulas (6) and (7), it is impossible to obtain a good RBW within the limited storage space. However, if the R&S oscilloscope spectrum analysis method is used, the settings are shown in Figure 18:

Figure 18 R&S digital oscilloscope spectrum analysis settings

The center frequency is set to 3GHz, the RBW is set to 5kHz, and the window function uses the Blackman Harris window. The spectrum analysis results are shown in Figure 19. We note that due to the use of the DDC structure, the sampling rate is set to 2.5GSa/s, and it does not need to meet the relationship of more than 2 times the signal frequency, because the sampling rate at this time is actually the resampling rate in the spectrum analysis. It can be seen from the frequency domain measurement results that the signal frequency is 3GHz, which is consistent with the output frequency of the signal source. Therefore, it can be seen that using the R&S oscilloscope spectrum analysis structure, even for high-frequency signals, it can still have good frequency resolution.

Figure 19 Spectrum analysis results of R&S digital oscilloscope

4 Summary

From the above discussion, it can be seen that the R&S digital oscilloscope adopts DDC technology, which can maximize the use of the oscilloscope's valuable storage space, whether in RF signal acquisition and analysis (I/Q demodulation) or in frequency domain analysis, and give full play to the multi-domain joint analysis of signals.