Case Study: How Much Does Amplifier Noise Contribute to the Total Noise in a Signal Chain?

Many real-world applications using high-speed ADCs require some kind of driver, amplifier, or gain block to scale the input signal to the full-scale analog input range1 to ensure the best signal-to-noise ratio (SNR) and spurious-free dynamic range (SFDR). In addition, a differential amplifier can also convert a single-ended signal to a differential signal to drive the ADC. These devices are active devices and thus contribute to the noise in the ADC front end. The integration of this noise within the operating bandwidth degrades the conversion performance.

The selection of the appropriate ADC for a specific application depends on many factors, including:

• Analog input range

• Input frequency/bandwidth

• Required resolution/SNR

• Required SFDR

Some applications require both high dynamic range and high resolution. The AD9268 is well suited for these applications, offering an SNR of 78.2 dBFS (dB relative to full scale) and an SFDR of 88 dBc at a 70 MHz IF.

At the system level, the ADC front end can use an amplifier, transformer, or balun, but the implementation using an amplifier is the most common. The reasons for using an amplifier may be one or more of the following:

• Provides gain to the input signal to increase ADC resolution

• Buffer or transform the impedance between the input source and the ADC

• Converts a single-ended input signal to a differential output signal

The AD8375 VGA can be used to convert single-ended signals to differential signals while maintaining high linearity and consistent noise performance at different gain settings. These features make it a good choice for driving ADCs at higher IFs. Unfortunately, active devices in the signal chain (i.e., amplifiers) can limit the performance of the ADC.

Figure 1 shows the circuit topology used for the noise calculations. The AD8375 has high impedance differential outputs (16 kΩ||0.8 pF). The amplifier interfaces to the ADC through a fifth-order, low-pass antialiasing filter (AAF) with 100 MHz bandwidth and 150 Ω input/output impedance. The frequency response of the circuit shown in Figure 1 is shown in Figure 2.

Figure 1. AD8375, AAF, and AD9268 signal chain.

Figure 2. Frequency response of the AD8375, AAF, and AD9268 signal chain.

System designers would not expect the amplifier driving the ADC input to degrade the overall dynamic performance of the system, but a driver and ADC combination selected for one application does not necessarily mean it will provide the same good performance in another application. Using the techniques described in this article, system engineers can estimate the expected performance before selecting an amplifier.

Figure 3 shows two different setups. Figure 3(a) uses passive coupling to connect the converter, which is the default option on the customer evaluation board. The passive front-end network uses a transformer or balun and a passive low-pass filter with a roll-off frequency of about 200 MHz to convert the single-ended signal to a differential signal. Figure 3(b) shows the optional amplifier path. The noise contribution of these two setups is compared below. A single-tone fast Fourier transform (FFT) at a low IF (10 MHz) is used to calculate the noise added by the amplifier.

Figure 3. Typical ADC front end: (a) passive; (b) active

There are two common techniques for noise analysis , but each is cumbersome. Noise spectral density (NSD) defines the noise power per unit bandwidth. For ADCs, its units are mean square dBm/Hz or dBFS/Hz; for amplifiers, its units are root mean square nV/√Hz. This inconsistency in units is an obstacle to system noise calculations when driving an ADC with an amplifier.

Noise figure (NF) is the logarithmic ratio of the input SNR to the output SNR, expressed in dB. This characteristic is commonly used by RF engineers and makes sense in a purely RF context, but using the NF calculation in a signal chain with an ADC can lead to misleading results.

Another more effective technique is to “denormalize” the noise density and express it as an rms noise voltage rather than a mean square voltage. This approach is straightforward and provides a clear analysis of system noise, as will be explained below.

The low-frequency single-tone FFTs of the two front ends are shown in Figure 4 and Figure 5, respectively. Note that the SNR of the passive front end is 77.7-dBFS, while the SNR of the active front end is 72.5-dBFS, which is 5.2 dBFS below the expected performance of the ADC.

Figure 4. FFT of a 10 MHz analog input tone for the circuit in Figure 3a.

Figure 5. FFT of a 10 MHz analog input tone for the circuit in Figure 3b.

The only difference between the setup shown in Figure 3a and Figure 3b is the addition of an amplifier to the signal chain, so it is safe to say that the performance degradation is due to the noise of the amplifier. The following calculation will help understand the noise introduced by the amplifier.

First, use the full-scale differential input voltage of the converter as specified in the data sheet. Divide the peak-to-peak voltage by 2√2 to get the rms voltage, which is 0.707 V rms.

Based on the typical SNR of the ADC at 10 MHz, the noise contribution of the converter is

V _{NOISE , ADC} = 92.2 μV rms, System SNR with amplifier front end = 72.5 dBFS, Calculating the system noise using Equation 3 yields 168 μV rms.

The system noise obtained from Equation 4 is the combined noise of the ADC and VGA. The amplifier noise can be calculated using Equation 5, which is 140 μV rms. This shows that the amplifier noise is at least 50% larger than the ADC noise, so it is the limiting factor in the system ac performance.

Note that one must determine whether the calculated V _{NOISE, AMP} value agrees with the amplifier’s data sheet. The specified noise spectral density is approximately 20 nV/√Hz at 150 Ω differential output impedance.

Although the data sheet states that the noise of the VGA is essentially constant with gain, this noise varies with load, so the noise spectral density should be scaled based on the total impedance driven by the amplifier output. The differential output impedance of the amplifier is large (16 kΩ||0.8 pF), so the impedance seen by the amplifier (see Figure 1) can be calculated as follows:

Using this value, the derated noise spectral density of the AD8375 in this application can be calculated using Equation 6:

Note that when calculating system noise with a real filter, the shape of the noise bandwidth is different from that of an ideal filter. This difference in frequency response is defined in terms of the “shape factor,” which reflects the noise in the roll-off region. The shape factor depends on the order of the filter and is the ratio of the noise bandwidth to the –3 dB bandwidth. The more poles a filter has, the closer the shape factor is to 1. This relationship can be seen in Table 1.

Table 1. Relationship between system order and shape factor

The shape factor for the example in Figure 1 is 1.02. The noise injected by the amplifier is calculated using Equation 6:

This estimated value of the noise injected into the system by the VGA agrees well with the measured value calculated using Equation 5, demonstrating that the performance of the signal chain consisting of the AD8375 and AD9268 is primarily determined by the amplifiers.