Understanding the Significance of Dynamic Range and Spurious-Free Dynamic Range


The concepts of dynamic range and spurious-free dynamic range (SFDR) appear in a variety of engineering contexts. Even so, many EEs may not fully grasp the importance of these performance metrics. In this article, we’ll examine how dynamic range and SFDR are defined and used in multiple applications, paying particular attention to aspects that are relevant to vector network analyzers (VNAs).

First, though, we’ll take a look at the noise vs. linearity trade-off in analog design. This trade-off limits the dynamic range of many circuits; it will also help us understand why the dynamic range and SFDR specifications are important.

 

The Linearity-Noise Trade-Off in Analog Design

When trying to improve the linearity of an analog circuit, we face several trade-offs between linearity and other performance dimensions of the circuit—gain, bandwidth, and noise characteristics, to name a few. While all of these are important, the trade-off between linearity and noise will be our focus in this article.

 

Source Degeneration in a Common-Source Amplifier

To understand the linearity-noise trade-off, let’s look at a basic linearization technique: adding a resistor (RS) in series with the source terminal of a common-source stage (Figure 1).

 

Figure 1. A MOSFET common-source amplifier with source resistor. Image used courtesy of Steve Arar

 

Known as the degeneration resistor, RS acts as a source of local negative feedback to the gate-source voltage of the MOSFET. The voltage drop across RS is proportional to the drain current. As the drain current increases, the voltage drop across RS also increases. This reduces the gate-source voltage of the MOSFET, which reduces the drain current.

This local feedback improves the linearity of the circuit. However, the added resistor increases the circuit complexity and contributes additional noise to the circuit, degrading the overall noise performance.

 

Analog Sample-And-Hold Circuits

The trade-off between noise and linearity also manifests itself in the design of analog-to-digital converters (ADCs), which are important components in radio receivers and test and measurement systems. Consider the basic block diagram of a sample-and-hold (S/H) circuit in Figure 2.

 

Block diagram of a sample-and-hold circuit.

Figure 2. Block diagram of a sample-and-hold circuit for analog signals. Image used courtesy of Analog Devices

 

If we increase the hold capacitance (CH), the system bandwidth—and, by extension, the noise—drops. However, in this case, the first amplifier needs to drive a larger capacitor. The current that a practical amplifier can provide is finite. As a result, with a larger capacitor, the S/H might not be able to follow the input signal quickly enough, especially for signals with large amplitudes or high frequencies.

The limited slew rate of S/H circuits is a key reason why building highly linear ADCs with good noise performance is a challenging task beyond several megahertz of signal bandwidth.

 

Radio Receiver Signal Paths

As a last example of the noise vs. linearity trade-off, I’d like to explore the radio receiver signal chain. Figure 3 is a simplified block diagram of a VNA’s reference and test channels.

 

Simplified block diagram of a VNA's reference and test channels.

Figure 3. Reference and test channel signal paths for a vector network analyzer. Image used courtesy of Steve Arar

 

If we add low-noise amplifiers (LNAs) before the RF mixers, we can make the noise contributed by the following stages relatively small in comparison to the desired signal. In this way, the receiver becomes less sensitive to the noise of the stages after the LNA. However, this requires mixers with higher linearity to successfully downconvert the relatively larger signals produced by the LNA. Once again, we see the familiar noise and linearity trade-off!

 

Introducing the Dynamic Range

Linearity is the primary limiting factor in the measurement of large signals. As the input signal amplitude increases, real-world circuits become more nonlinear and start to produce unacceptable levels of distortion. This reduces measurement accuracy. Therefore, to measure larger signals, we need to linearize the system.

However, as we saw in the previous section, linearization is usually achieved at the cost of higher noise. With higher noise levels, small signals can be buried in the noise floor and might not be detectable. This makes it challenging to design a circuit that can accurately measure both high- and low-amplitude signals.

To characterize this important property of the circuit, we use the dynamic range metric, which is defined as the difference between the highest and the lowest amplitude signals that the system can measure. This is illustrated by an example spectrum in Figure 4.

 

An illustration of dynamic range.

Figure 4. Dynamic range is the difference between the maximum measurable signal and the noise floor. Image used courtesy of Steve Arar

 

The dynamic range determines the range of signal amplitudes that the system can measure. For signal amplitudes within this range, we can assume that the circuit is acceptably linear and deterministic (meaning that the output isn’t an unpredictable signal produced by noise).

The dynamic range is an important parameter of spectrum analyzers and VNAs, as we’ll discuss shortly. The upper end of the dynamic range in spectrum analyzers and VNAs is usually limited by the compression point of the amplifiers and mixers within the analyzer. Figure 5 shows how a typical amplifier becomes excessively nonlinear when the input power approaches the amplifier’s compression point.

 

An example of a power amplifier's gain curve.

Figure 5. Example gain curve for a power amplifier. Image used courtesy of David M. Pozar

 

Why Is Dynamic Range Important?

To capture the DUT’s response at different frequencies, you need measurement equipment with a sufficiently high frequency range. In just the same way, your equipment should have a high enough dynamic range to accurately measure the different power levels produced by the DUT.

To illustrate the importance of having a high dynamic range, let’s examine a common application: measuring the frequency response of a filter. Consider a band-pass filter with 90 dB of stopband rejection. Figure 6 shows the measured response obtained by two different VNAs when sweeping a single-tone sinusoidal input across the frequency range of interest.

 

Frequency spectrum of a band-pass filter on two different measurement systems.

Figure 6. Frequency spectrum of a band-pass filter on two different measurement systems. Image used courtesy of Agilent Technologies

 

The response in the figure’s left-hand portion is the result of using a VNA with a low dynamic range. In this case, the VNA’s receiver has a sensitivity of about –60 dBm. As a result, in the stopband of the filter where the filter’s output signal is very small, the VNA measures its own noise floor rather than the signal produced by the filter.

The right-hand response was obtained by a VNA with a sensitivity of –100 dBm. This represents a much wider dynamic range, and the improvement allows us to properly characterize the filter’s stop-band behavior. Note how the traces become noisy at frequencies where the filter’s output power becomes comparable with the noise floor of the VNAs.

In this example, the large and small signals were measured by the test equipment at different times—they weren’t simultaneously applied to the VNAs. To investigate system performance when both small and large signals are present, we use the spurious-free dynamic range (SFDR).

 

Defining the Spurious-Free Dynamic Range

Even with a single-tone input, a nonlinear circuit can produce different frequency components (spurs) at the output. These spurs may or may not be harmonically related to the input, as illustrated in Figure 7.

 

Dynamic range and spurious-free dynamic range.

Figure 7. Spurious-free dynamic range compared to dynamic range. Image used courtesy of Steve Arar

 

In Figure 7, the orange component is the fundamental, or desired, output component. In this example, the fundamental component is smaller than the maximum measurable signal. However, we’re assuming it’s large enough to produce several spurs (the purple components).

To quantify the effect of the spurs, we use the SFDR specification. There are multiple definitions of SFDR, which can be confusing at times. We’ll define it here as the difference between the desired signal amplitude and the largest spur over the bandwidth of interest.

When using this definition, the maximum spur amplitude is specified in reference to the signal (or carrier) level. We therefore express the SFDR in dBc (dB relative to the carrier). Note that even in the presence of spurs, the dynamic range is still defined as the difference between the maximum measurable signal and the noise floor of the system.

 

When to Use Spurious-Free Dynamic Range

Let’s examine a scenario where a circuit receives both small and large signals simultaneously. The small signal is the one that needs to be measured; the large signal is an interferer. This is the situation for our everyday radio receivers.

We can see this in Figure 8, which shows a radio receiver operating at typical signal levels. The antenna receives two signals in its frequency range of interest: a low-power desired signal and a high-power, in-band blocker.

 

Example radio receiver with a small desired input signal and a large blocking signal.

Figure 8. Example radio receiver with a small desired input signal and a large blocking signal. Image used courtesy of Steve Arar

 

Note that an in-band blocker has a different effect than one that’s out-of-band. Out-of-band blockers are usually sufficiently suppressed by a band-select filter in the receiver front end.

By comparison, the frequency of an in-band interferer is closer to the desired signal. Generally, it’s not removed until the end of the receiver chain. The RF mixer in Figure 8 will therefore downconvert both the desired signal and the in-band blocker to an intermediate frequency (fIF).

The RF signal chain and ADC need to measure the desired small signal in the presence of the large interferer. However, the high-power blocker can make the system operate nonlinearly, leading to spurs at frequencies very close to the desired signal. Figure 9 shows how the nonlinearities can produce such spurs (the purple components).

 

Spurs created by system nonlinearities.

Figure 9. System nonlinearities can create in-band spurs from high-power input signals. Image used courtesy of Steve Arar

 

If a spur close to the desired signal is large enough, it can degrade the receiver’s signal-to-noise ratio. We need to know the SFDR of the receiver to determine the maximum spur level that can show up in the spectrum.

 

Selecting the Right Dynamic Range Metric

The dynamic range characterizes the difference between the highest and the lowest amplitude signals that the system can measure. However, as we’ve now seen, dynamic range only provides limited information about system performance. It’s most useful when we have input signals with amplitudes in the system’s linear region.

For high-power input signals that result in nonlinear system operation, we need to also look at the spurious-free dynamic range. The SFDR specification is particularly helpful in applications where both large and small signals need to be measured simultaneously, such as communications systems.

Now that we understand the importance of dynamic range, we can start looking for ways to improve it. In the next article of this series, we’ll discuss ways to increase the dynamic range of a VNA.



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