Analog-to-digital converter, commonly referred to as ADC, is an electronic component that transforms analog signals into digital representations. In general, an ADC takes an input voltage signal and converts it into a digital output. Since digital signals themselves do not carry inherent meaning, they only represent relative values. ADCs are widely used in various fields such as signal acquisition, communication systems, automatic control, and multimedia technologies. This article outlines the testing methods for both static and dynamic parameters of ADCs.
**Definition of Static Parameters of ADC Performance**
Figure 1 illustrates the concept of Differential Nonlinearity (DNL), which is defined as the difference between the actual step voltage and the ideal step voltage in the transfer function of the ADC. The DNL value is calculated using the following formula:
$$ \text{DNL}(i) = \frac{V_{\text{actual}}(i+1) - V_{\text{actual}}(i)}{V_{\text{LSB-IDEAL}}} - 1 $$
Where:
- $ N $ is the number of bits of the ADC,
- $ D $ is the digital code output by the ADC,
- $ V_D $ is the minimum input voltage corresponding to the digital code $ D $,
- $ V_{\text{LSB-IDEAL}} $ is the ideal voltage change per least significant bit.
The maximum DNL value across all codes is typically considered as the differential nonlinearity error of the ADC.
Integral Nonlinearity (INL) is defined as the deviation of the actual transfer curve from the ideal one. The formula for INL is given as:
$$ \text{INL}(i) = \frac{V_{\text{actual}}(i) - V_{\text{ideal}}(i)}{V_{\text{LSB-IDEAL}}} $$
Other important static parameters include the offset error, gain error, and monotonicity. Gain error, for example, refers to the deviation of the last code’s voltage level from its ideal value.
$$ \text{Gain Error} = \frac{V_{2^N - 1} - V_{\text{ideal}}}{V_{\text{LSB-IDEAL}}} $$
**Definition of Dynamic Parameters**
Dynamic parameters of ADCs refer to performance metrics that describe the behavior of the ADC under varying input conditions. These parameters are usually measured under sinusoidal or other time-varying input signals and include things like Signal-to-Noise Ratio (SNR), Total Harmonic Distortion (THD), and Spurious Free Dynamic Range (SFDR). Table 1 provides a summary of key dynamic parameters and their definitions.
**Test Principles for Static Parameters**
Static parameter testing of ADCs is generally performed using two main techniques: ramp voltage testing and code density testing (also known as histogram testing).
The ramp voltage method involves applying a slowly increasing voltage to the ADC input and recording the resulting digital output. This allows the transfer function to be plotted and static parameters calculated. However, this method has several limitations, including the introduction of errors from DACs used in the test setup, limited precision due to the accuracy of the measuring instruments, and low efficiency because of the need to measure each code individually.
The code density method, on the other hand, uses a low-frequency sine wave slightly larger than the ADC’s full-scale range. By collecting the digital outputs and counting the frequency of each code, the transfer function can be reconstructed mathematically. This method offers higher precision, faster testing, and is more suitable for high-resolution ADCs.
Key considerations when performing code density testing include:
1. Ensuring the input signal amplitude is slightly larger than the ADC’s full-scale range to ensure all codes are represented.
2. Selecting an input frequency that is unrelated to the sampling rate of the data acquisition system to maintain statistical randomness.
3. Ensuring the total number of samples collected meets the required accuracy for the desired resolution.
Due to its high precision and efficiency, the code density method is widely used for testing the static characteristics of ADCs.
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