This time, I'll be talking about the basics of A/D converters. It's a tutorial-style presentation, so please bear with me.
A/D converters, which convert analog signals to digital signals, are used in digital measuring instruments.
It is a very important device. The main factor that determines the performance of its A/D converter is the sample
These are the sampling frequency and resolution. The sampling frequency is the maximum frequency of the analog signal that can be input.
The bandwidth is determined by the number of bandwidths, and the resolution is determined by how small a signal can be reproduced from the input analog signal.
This represents the capability and is determined by the number of bits in the digital data.
Generally, the process of converting an analog input voltage into a discrete digital value is called quantization, and
The degree to which it is divided depends on the number of bits in the binary number. For example, bit
If the number is 8, the input voltage will be divided into 256 parts (= 2 to the power of 8).
The sampling frequency (conversion speed) and bit depth are the main factors used in digital measuring instruments.
A/D converters can be classified as follows:
| Conversion speed (sampling frequency) | Number of bits | Main methods | Main applications |
| For low speed (Several Hz to several kHz) |
8 〜 20 | double integral type | Panel meters, scales thermometer |
| For medium speed (Several kHz to several hundred kHz) |
16 〜 24 | ΔΣ modulation type | Audio equipment, measuring instruments |
| For medium and high speeds (Several tens of kHz to several MHz) |
8 〜 16 | Sequential comparison type | Measuring instruments, numerical control |
| For high speed (Several MHz to several GHz) |
4 〜 8 | Parallel comparison type (Flash type) |
Oscilloscope, video |
The double integration method, a typical method for low-speed A/D converters, has the configuration shown in Figure 1, and the input voltage
Vin is integrated over a fixed time (mΔt; m is a fixed value), and then the integrated voltage value is used as the base.
The voltage VRef is integrated again (discharged) until it reaches 0V, and the time taken is counted with a counter.
Let's call that count value n;
This allows us to obtain a digital value n that is proportional to the input voltage Vin.
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Figure 1 Block diagram of a double-integration A/D converter
This method is;
- Unaffected by variations in component parts (such as R and C).
- Unaffected by long-term fluctuations in clock pulses
- Since the input voltage is integrated, superimposed noise can be removed.
These features allow for the inexpensive manufacture of high-precision A/D converters, making them suitable for digital panel displays.
It is widely used in fields such as data entry.
Successive approximation A/D converters have a configuration as shown in Figure 2 and have been widely used for measurement and control purposes.
This is a method that, as the name suggests, converts a predetermined digital value to an input voltage using a D/A converter.
The analog value is converted, and then the bits are compared sequentially from the most significant bit to determine whether each bit is 1 or 0.
The conversion is terminated by comparing the least significant bit. Thus, this method is fundamentally based on the conversion process.
Because it takes time and the input voltage needs to remain constant during that time, a sample-and-hold circuit is placed before it.
It is essential.
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Figure 2 Block diagram of a successive approximation A/D converter
This method is;
- It is simple in principle, relatively fast, and can achieve high resolution.
- It can be easily configured even with a microcontroller.
- It is highly dependent on variations in components (especially D/A converters).
It possesses these characteristics and is still widely used today.
The ΔΣ modulation type A/D converter is a method recently developed in Japan (configuration shown in Figure 3), and is a recent development in Japan.
It is widely used in the field of digital audio (so-called 1-bit audio).
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Figure 3 Block diagram of a ΔΣ modulation type A/D converter (first order)
A major feature of this method is that it uses oversampling and noise shaping techniques, and in practice
The frequency band used (the so-called Nyquist frequency, half the sampling frequency fs in Figure 3)
In this region, quantization noise can be significantly reduced. Figure 3 shows a first-order quantization, but this can be increased.
A configuration where stages are connected in a dependent manner is sometimes specifically called MASH (Multi-Stage Noise Shaping).
Furthermore, because this method uses a very simple analog circuit, it is easy to integrate it into a single chip.
As described above, this method uses oversampling technology, so the sample clock is k times the actual sampling frequency fs (for example, 64 or 128). A 1-bit data sequence with a frequency of k fs is output, which is then passed through a digital filter (such as an FIR) and downsampled to 1/k, ultimately yielding N bits of digital data at the sampling frequency fs.
Another major feature of this method is that the sampling frequency kfs used for digitization is actually analyzed.
Because it is much higher than the desired frequency band (1/2fs), an anti-aliasing filter is used to prevent aliasing.
A single filter (compared to a successive approximation filter) can be a simpler low-pass filter.
And so.
Thus, the ΔΣ modulation type has many advantages compared to the conventional successive approximation type, so measurement
Even in the field of tableware, replacements are becoming increasingly common.
The biggest drawback of the ΔΣ modulation type is that it includes a digital filter internally, resulting in a large output latency.
This is a problem. Therefore, it is unsuitable for control system applications that require high-speed response. Also,
Compared to successive approximation converters, it can also be used in applications such as time-division multiplexing of channels to create a single A/D converter.
It's not very suitable.
The parallel compare A/D converter has the configuration shown in Figure 4, and in an N-bit A/D converter, (2N-1)
The reference voltage is compared with the voltage value obtained by dividing the reference voltage by a resistor using a comparator, and the result is coded.
This is a method for obtaining N bits of digital data. It is, so to speak, a method of conversion by force, and very
Since it can be converted instantly at high speed, a sample-and-hold circuit is not necessary, but increasing the number of bits
Attempting to do so would require a large circuit size, making it practically difficult to implement.
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Figure 4 Block diagram of a parallel approximation A/D converter
Now, an A/D converter quantizes an analog time signal with a certain resolution, so in principle,
Child-size errors are unavoidable. Currently, the full-scale value of the input voltage is FS (V), and the number of bits is N.
If we assume that the minimum decomposition voltage value q (which we call 1LSB, and q = 1LSB) is:
; Considering the quantization error in Figure 5 as a function of time e(t), and calculating the effective value of e(t),
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Figure 5 Analog-to-digital conversion characteristics and quantization error
Next, if the input signal is a sine wave with both amplitudes equal to FS, its RMS value is / 2 FS, so the signal-to-noise ratio (SNR) is:
For example, when a 16-bit A/D converter is input to a full-scale sine wave:
The ideal signal-to-noise ratio (SNR) is approximately 98 dB, but in reality, for the following reasons, the value is higher than this.
It's normal for them to get smaller.
- These include nonlinearity errors, offset errors, and gain errors in A/D conversion.
- The crest factor of an actual signal is usually smaller than that of a sine wave, so the signal-to-noise ratio (SNR) will also be smaller than the one shown above.
The specifications of actual measuring instruments such as FFT analyzers, including the signal-to-noise ratio and dynamic range, are as follows:
Not only the performance of the A/D converter, but also the self-noise of the analog section and the processing accuracy after digitization.
It is greatly influenced by the degree as well. The combined capabilities of these factors constitute the specifications.
(Excerpt from the email newsletter issued on October 23, 2008)
