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Download this article in PDF format. (267 KB) Understanding How Amplifier Noise Contributes to Total Noise in ADC Signal Chains Introduction This article analyzes noise in a circuit that uses the AD9268 dual 16-bit, 125-/105-/80-MSPS, pipelined ADC, and the AD8375 ultralow distortion IF VGA. The signal chain includes a VGA—used at a gain setting of +6 dB, a 5th-order Butterworth low-pass filter with a –3-dB roll-off at 100 MHz, and the ADC. Noise calculations will be shown for the amplifier and filter, as they dictate the dynamic performance of the ADC over the band of interest. Problem The choice of an appropriate ADC for an application depends on many factors, including:
Some applications require both high dynamic range and high resolution. The AD9268 is very good choice for these applications, delivering 78.2-dBFS (dB relative to full-scale) SNR and 88-dBc SFDR at a 70-MHz intermediate frequency. At the system level, the ADC front-end could use an amplifier, a transformer, or a balun, but implementations using an amplifier are most common. An amplifier could be used for one or more of the following reasons:
The AD8375 VGA, which maintains high linearity and uniform noise performance over its various gain settings, can be used to convert single-ended signals to differential. These characteristics make it a good candidate for driving the ADC at higher intermediate frequencies. Unfortunately, the presence of an active device—the amplifier—in the signal chain can limit the ADC’s performance. Example Figure 1. The AD8375, AAF, and AD9268 signal chain.
Figure 2. Frequency response of the AD8375, AAF, and AD9268 signal chain. Performance Figure 3 shows two different setups: Figure 3(a), which uses passive coupling to the converter, is available as the default option on the customer evaluation board. The passive front-end network uses a transformer or balun to convert the single-ended signal to differential, along with a passive low-pass filter that rolls off at about 200 MHz. Figure 3(b) shows the optional amplifier path. A comparison of the noise contributed by these two setups follows. A single-tone fast Fourier transform (FFT) at a low intermediate frequency (10 MHz) is used to calculate the noise added by the amplifier. Figure 3. Typical ADC front-ends: (a) passive. (b) active. Two techniques are typically used for analyzing the noise, but each can be cumbersome. Noise spectral density (NSD) defines the noise power per unit bandwidth. It is represented in mean-square dBm/Hz or dBFS/Hz for ADCs and rms nV/√Hz for amplifiers. This incompatibility in units provides an obstacle to calculating system noise when an amplifier is driving an ADC. Noise figure (NF) is the log ratio of input SNR to the output SNR expressed in decibels. This specification, commonly used by RF engineers, makes sense in a purely RF world, but attempting to use NF calculations in a signal chain with an ADC can lead to misleading results.^{2} An alternate, but more effective, technique is to “de-normalize” the noise density, representing it as an rms noise voltage rather than a mean-square voltage. This method, as described here, is straightforward and allows a clear analysis of the system noise. Figure 4 and Figure 5 show the low-frequency single-tone FFTs of the two front ends. Note that the passive front end has Figure 4. FFT of a 10-MHz analog input tone for the circuit of Figure 3a.
Figure 5. FFT of a 10-MHz analog input tone for the circuit of Figure 3b. Analysis First, use the converter’s full-scale differential input voltage, as specified in the data sheet. Convert the peak-to-peak voltage to rms by dividing by 2√2 to get 0.707 V rms.
The contribution of the converter’s noise based on the ADC’s typical SNR at 10 MHz is
Using V_{NOISE, ADC} = 92.2 μV rms and system SNR with the amplifier front end = 72.5 dBFS, the system noise, using Equation 3, is 168 μV rms.
The system noise obtained from Equation 4 is the combined noise of the ADC and the VGA. The amplifier noise can be calculated from Equation 5 to be 140 μV rms. This calculation shows that the amplifier noise is at least 50% greater than the ADC noise, making it the limiting factor in determining the system’s ac performance. Note that we must determine whether the value of V_{NOISE, AMP} calculated above matches the amplifier’s data sheet. The specified noise spectral density is about 20 nV/√Hz with a 150-Ω differential output impedance. Although the data sheet specifies that the VGA’s noise is fairly constant with gain, this noise will change with the load, so the noise spectral density should be scaled to the total impedance driven by the amplifier outputs. Because the differential output impedance of the amplifier is large (16 kΩ||0.8 pF), the impedance seen by the amplifier (see Figure 1) can be calculated as Using this number, the derated noise spectral density for the AD8375 in this application can be found from Equation 6:
Note that when calculating system noise using a real filter, the noise bandwidth takes on a different shape than that of an ideal filter. This deviation in frequency response is characterized by the term, shape factor, and accounts for the noise in the roll-off region. The shape factor, which depends on the order of the filter, is the ratio of the noise bandwidth to the –3-dB bandwidth.^{3} The more poles in the filter, the closer the shape factor is to unity. This relationship can be seen in Table 1. Table 1. Relationship Between
In the example of Figure 1, the shape factor is 1.02. Using Equation 6, the noise injected by the amplifier will be; This estimated value of noise injected into the system by the VGA matches very well with the measured value using Equation 5, proving that the performance of the signal chain comprising the AD8375 and AD9268 is dominated by the amplifier. Conclusion I invite you to comment on noise in ADC signal chains in the Analog Dialogue Community on EngineerZone. References ^{2}The Data Conversion Handbook. ^{3}Reeder, Rob and Jim Caserta, “Ask The Application Engineer 36, Wideband A/D Converter Front-End Design Considerations II: Amplifier-or Transformer Drive for the ADC?” Analog Dialogue 41-02, 2007.
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