Analog-to-digital converter, commonly referred to as ADC, is an electronic component that converts analog signals into digital form. Typically, it takes an input voltage and produces a corresponding digital output. Since digital signals do not carry intrinsic meaning on their own, they only represent relative values. ADCs are widely used in signal acquisition, communication systems, automatic control, and multimedia applications. This article explores the testing methods for both static and dynamic parameters of ADCs.
**Definition of Static Parameters**
Static parameters are key performance metrics that describe the accuracy and linearity of an ADC under steady-state conditions. One such parameter is Differential Nonlinearity (DNL), which measures the deviation between the actual step size and the ideal step size. The formula for DNL is:
$$ \text{DNL} = \frac{V_{\text{actual}} - V_{\text{ideal}}}{V_{\text{LSB-IDEAL}}} $$
Where N represents the number of bits, D is the digital code, $ V_D $ is the minimum input voltage corresponding to code D, and $ V_{\text{LSB-IDEAL}} $ is the ideal voltage change per bit. The maximum DNL value across all codes defines the overall differential nonlinearity error of the ADC.
Integral Nonlinearity (INL) measures the deviation of the actual transfer function from the ideal one. It can be expressed as:
$$ \text{INL} = \frac{V_{\text{actual}} - V_{\text{ideal}}}{V_{\text{LSB-IDEAL}}} $$
Other important static parameters include offset error, gain error, and quantization error. Gain error, for example, is defined as the difference between the actual and ideal value at the maximum digital code:
$$ \text{Gain Error} = V_{2^N - 1} - V_{\text{ideal}} $$
**Definition of Dynamic Parameters**
Dynamic parameters evaluate the performance of an ADC under varying input conditions. These include parameters such as Signal-to-Noise Ratio (SNR), Total Harmonic Distortion (THD), and Spurious-Free Dynamic Range (SFDR). Table 1 provides a detailed overview of these dynamic parameters.
**Test Principles for Static Parameters**
There are two common methods for testing static parameters: the ramp voltage test and the code density test (also known as histogram test).
The **ramp voltage test** involves applying a slowly increasing voltage to the ADC input and recording the resulting digital output. While this method is straightforward, it has several limitations. First, the use of a DAC to generate the ramp introduces errors, making it unsuitable for high-resolution ADCs above 16 bits. Second, the precision of the test is limited by the resolution of the digital voltmeter used. Third, the process is time-consuming, as each digital code must be measured individually, making it more suitable for lower-precision ADCs.
The **code density test**, on the other hand, uses a low-frequency sine wave slightly larger than the ADC’s input range. By collecting and analyzing the frequency of each digital code, the transfer function of the ADC can be reconstructed. This method is more efficient and accurate, making it ideal for high-precision ADC testing.
Key considerations for this method include ensuring that the input signal amplitude exceeds the full-scale range to capture all possible digital codes, selecting an input frequency that avoids aliasing, and ensuring sufficient sampling points to meet statistical requirements. The total number of samples should satisfy:
$$ N_t = \frac{1}{\alpha} \cdot 2^n $$
Where $ N_t $ is the number of samples, $ n $ is the ADC resolution, and $ \alpha $ is the required accuracy.
Due to its high precision, speed, and ease of implementation, the code density test is widely used for evaluating the static characteristics of ADCs.
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