When an RF engineer first calculates the noise figure of even the best low-noise high-speed ADC, the result may be relatively higher than the noise figure of a typical RF gain block, low noise amplifier, and so on. In order to interpret the results correctly, you need to understand the position of the ADC in the signal chain. Therefore, be careful when handling the noise figure of the ADC.
ADC noise figure definition
Figure 1 shows the basic model used to define the ADC noise figure. The noise factor F refers to the ratio of the total effective input noise power of the ADC to the noise power caused by the source resistance alone. Due to impedance matching, the square of the voltage noise can be used instead of the noise power. The noise figure NF is the noise factor expressed in dB, NF = 10log10F.
Figure 1: Noise figure of the ADC: Be careful!
The model assumes that the input to the ADC is from a source with a resistance of R. The input bandwidth is limited to fs/2 and the input has a filter with a noise bandwidth of fs/2. It is also possible to further limit the bandwidth of the input signal, resulting in oversampling and processing gain, which will be discussed later. The model also assumes that the input impedance of the ADC is equal to the source resistance. Many ADCs have high input impedance, so the termination resistor may be external to the ADC or used in parallel with the internal resistor to produce an equivalent termination resistance of R.
ADC noise figure derivation process
Full-scale input power is the power of a sine wave whose peak-to-peak amplitude just fills the ADC input range. The full-scale input sine wave given by the following equation has a peak-to-peak amplitude of 2VO, which corresponds to the peak-to-peak input range of the ADC:
The full-scale power of the sine wave is:
ADC noise figure derivation process
Full-scale input power is the power of a sine wave whose peak-to-peak amplitude just fills the ADC input range. The full-scale input sine wave given by the following equation has a peak-to-peak amplitude of 2VO, which corresponds to the peak-to-peak input range of the ADC:
The full-scale power of the sine wave is:
This power is usually expressed in dBm (based on 1 mW):
The noise bandwidth B of the filter needs to be further discussed. The noise bandwidth of a non-ideal brick wall filter refers to the bandwidth required for an ideal brick wall filter when the same noise power is passed. Therefore, the noise bandwidth of a filter is always greater than its 3 dB bandwidth, and the ratio of the two depends on the sharpness of the filter cut-off region. Figure 2 shows the noise bandwidth of a Butterworth filter with up to 5 poles as a function of 3 dB bandwidth. Note: For 2-pole, the noise bandwidth differs from the 3 dB bandwidth by 11%; after 2 poles, the two are essentially equal.
Figure 2: The relationship between the noise bandwidth of the Butterworth filter and the 3dB bandwidth
The first step in the NF calculation is to calculate its effective input noise based on the SNR of the ADC. The ADC data sheet gives the SNR at different input frequencies, ensuring that the value corresponding to the target IF input frequency is used. Also ensure that the harmonics of the fundamental signal are not included in the SNR value. Some ADC data sheets may confuse SINAD with SNR. Once you know the SNR, you can calculate the equivalent input rms voltage noise from the following equation:
This is the total effective input rms noise voltage measured over the entire Nyquist bandwidth (DC to fs/2), note that this noise includes the noise of the source resistance. The next step is to actually calculate the noise figure. In Figure 3, note that the amount of input voltage noise caused by the source resistance is equal to the source noise 4(4kTBR) voltage noise divided by 2, ie √(kTBR), because the ADC input termination resistor forms a 2:1 attenuator .
The expression of the noise factor F can be written as:
Convert F to dB and simplify to get the noise figure:
Where SNR is in dB, B is in Hz, T = 300 K, k = 1.38 &TImes; 10–23 J/K.
Figure 3: ADC noise figure based on SNR, sample rate, and input power
Oversampling and digital filtering produce processing gains that reduce the noise figure, as explained above. For oversampling, the signal bandwidth B is lower than fs /2. Figure 4 shows the correction factor, so the calculation formula for the noise figure becomes:
Figure 4: Effect of oversampling and processing gain on ADC noise figure
Calculation example for the 16-bit, 80/100 MSPS ADC AD9446
Figure 5 shows an example of NF calculation for the AD9446 16-bit, 80/105 MSPS ADC. A 52.3 Ω resistor in parallel with the 1 kΩ input impedance of the AD9446 results in a net input impedance equal to 50 Ω. The ADC operates under Nyquist conditions and the 82 dB SNR is the basis for the calculation using Equation 8 above, resulting in a noise figure of 30.1 dB.
Figure 5: Example of noise figure calculation for the 16944 80/100 MSPS ADC AD9446 operating in Nyquist conditions
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