Entering the RF signal chain, ADI takes you to deeply understand its characteristics and performance indicators

Before we dive in, let's first understand what RF actually means. At first glance, this seems like a simple question. We all know that RF stands for radio frequency, and the common definition of this term specifies a specific frequency range: the MHz to GHz electromagnetic spectrum. However, if we look at their definitions more closely and compare them, we'll see that they only differ in their definition of the actual boundaries of the RF spectrum. This term becomes even more confusing given that we may often use this term in a broad range of other contexts that have nothing to do with a specific frequency. So, what is RF?

By focusing on the salient characteristics of RF, including phase shift, reactance, dissipation, noise, radiation, reflection, and nonlinearity, a consistent definitional foundation can be established that covers a wide range of meanings. This foundation represents a modern, all-encompassing definition that does not rely on a single aspect or specific numerical value to distinguish RF from other terms. The term RF applies to any circuit or component that has many of the characteristics that make up this definition.

Now that we have set the context for this discussion, we can get down to business and analyze the generic RF signal chain in Figure 1. A distributed element circuit model is used to represent the phase shift in the circuit, which is not negligible at shorter RF wavelengths, so the approximate representation of the lumped circuit is not applicable to these types of systems. An RF signal chain may include a variety of discrete components such as attenuators, switches, amplifiers, detectors, synthesizers, and other RF analog devices, as well as high-speed ADCs and DACs. When all of these components are combined for a specific application, the overall nominal performance will depend on the combined performance of these discrete components.

Figure 1. A generic RF signal chain.

Therefore, in order to design a specific system that can meet the target application, RF system engineers must be able to truly think from a system-level perspective and have a consistent understanding of the key concepts and principles that underlie it. This knowledge is so important that we have written this discussion article, which consists of two parts. The goal of the first part is to briefly introduce the main characteristics and indicators used to determine the characteristics of RF devices and quantify their performance. The goal of the second part is to provide an in-depth introduction to the various individual components and their types that can be used to develop an RF signal chain for the desired application. In this article, we will focus on the first part and consider the main characteristics and performance indicators related to RF systems.

There are a variety of parameters used to characterize the overall RF system and its discrete modules. Depending on the application or use case, some of these characteristics may be extremely important, while others may be less important or insignificant. It is certainly not possible to conduct a comprehensive analysis of such a complex topic in this article alone. However, we will attempt to provide a concise and comprehensive overview of the most common RF performance by following the common thread of transforming a complex and interrelated set of topics into a balanced, easy-to-understand guide to RF system attributes and characteristics.

The scattering matrix (or S-matrix) is a fundamental term used when describing the behavior of an RF system. We can use the S-matrix to represent a complex RF network as a simple N-port black box. An example of a common 2-port RF network (such as an amplifier, filter, or attenuator) is shown in Figure 2, where Vn ⁺ is the complex amplitude of the voltage of the incident wave at the n-port and Vn ^– is the complex amplitude of the voltage of the reflected wave at the n-port. ² When all its ports are terminated with matched loads, we can describe this network by a scattering matrix, where the elements (or S-parameters) quantify how the RF energy propagates through the system based on the relationship between these voltage waves. Now, we use S-parameters to represent the main characteristics of a typical RF network.

Figure 2. A 2-port network represented by an S-matrix.

In the case of a matched network, S ₂₁ is equivalent to the transmission coefficient from port 1 to port 2 (S _{12 can also be defined in a similar way). The magnitude |S 21} | expressed in a logarithmic scale represents the ratio of output power to input power and is called gain or scalar logarithmic gain. This parameter is an important specification for amplifiers and other RF systems and can also take negative values. Negative gain indicates inherent loss or mismatch loss, which is usually expressed as its reciprocal, namely insertion loss (IL), which is a typical specification for attenuators and filters.

_{If we now consider the incident and reflected waves at the same port, S 11} and S ₂₂ can be defined as shown in Figure 2. These terms are equivalent to the reflection coefficient |Γ| of the corresponding port when the other port is terminated with a matched load. We can relate the magnitude of the reflection coefficient to the return loss (RL) from Equation 1:

Return loss is the ratio of the incident power at a port to the reflected power at the source. Depending on the port we use to estimate this ratio, we can differentiate between input and output return loss. Return loss is always a non-negative value and indicates how well the input or output impedance of the network matches the impedance of the port towards the source.

It is important to note that this simple relationship of IL and RL to S parameters is only valid if all ports are matched, which is a prerequisite for defining the S matrix of the network itself. If the network is not matched, it will not change its intrinsic S parameters, but it may change the reflection coefficient of its ports and the transmission coefficient between ports.

All of these fundamental quantities we have described will vary over frequency, a fundamental characteristic common to all RF systems. It defines the frequency range supported by these systems and gives us one more critical performance metric - bandwidth (BW).

While this term may refer only to signal characteristics, some form of it can be used to describe the RF systems that process those signals. Bandwidth generally defines the frequency range that is limited by a standard. However, it can have different meanings depending on the specific application context. To make our discussion more comprehensive, let's briefly define the different meanings:

• The 3 dB bandwidth is the frequency range over which the signal power level exceeds half of its maximum value.

• Instantaneous bandwidth (IBW) or real-time bandwidth is the maximum continuous bandwidth that a system can generate or acquire without requiring retuning.

• Occupied bandwidth (OBW) is the frequency range that contains a certain percentage of the total integrated signal power.

• Resolution bandwidth (RBW) generally refers to the minimum spacing between two frequency components that can be further resolved. For example, in a spectrum analyzer system, it is the frequency range of the final filter stage.

These are just a few examples of various bandwidth definitions; however, regardless of their meaning, the bandwidth of an RF signal chain is largely determined by its analog front end and the sampling rate and bandwidth of its high-speed analog-to-digital converter or digital-to-analog converter.

It is important to note that the characteristics of RF systems vary not only with frequency, but also with signal power level. The basic characteristics we described at the beginning of this article are usually expressed in small signal S parameters without considering nonlinear effects. However, in general, the continued increase in power levels through the RF network usually leads to more obvious nonlinear effects, eventually causing its performance to degrade.

When we talk about an RF system or component having good linearity, we are usually referring to the key metrics used to describe its nonlinear performance to meet the requirements of the target application. Let’s look at these key metrics that are commonly used to quantify the nonlinear behavior of RF systems.

The first parameter we need to consider is the output 1 dB compression point (OP1dB), which defines the inflection point where a generic device transitions from linear mode to nonlinear mode, i.e. the output power level at which the system gain decreases by 1 dB. This is a fundamental characteristic of a power amplifier and is used to set the operating level of the device towards the saturation level defined by the saturated output power (P _SAT ). The power amplifier is usually the last stage in the signal chain, so these parameters usually define the output power range of the RF system.

Once a system is in nonlinear mode, it distorts the signal and produces spurious frequency components, or spurs. Spurs are measured relative to the carrier signal (in dBc) and can be divided into harmonics and intermodulation products (see Figure 3). Harmonics are signals that are integer multiples of the fundamental frequency (for example, H1, H2, H3 harmonics), while intermodulation products are signals that appear when two or more fundamental signals are present in a nonlinear system. If the first fundamental signal is at frequency f1 _and the second at f2 _, the second-order intermodulation products appear at the sum and difference frequencies of the two signals, i.e., f1 ₊ f2 _and f2 _– f1 _, as well as f1 ₊ f1 _and f2 ₊ f2 ₍ the latter are also called H2 harmonics). The second-order intermodulation products combine with the fundamental signal to produce third-order intermodulation products, two of which (2f1 _– f2 _and 2f2 _– f1 ₎ are particularly important and difficult to filter out due to their proximity to the original signal. The output spectrum of a nonlinear RF system containing spurious frequency components represents intermodulation distortion (IMD), an important term to describe the nonlinearity of the system.

Figure 3. Harmonics and intermodulation products.

Spurious components related to second-order intermodulation distortion (IMD2) and third-order intermodulation distortion (IMD3) can interfere with the desired signal. An important indicator for quantifying the severity of interference is the intercept point (IP). We can distinguish between second-order (IP2) and third-order (IP3) intercept points. As shown in Figure 4, they define hypothetical points of input (IIP2, IIP3) and output (OIP2, OIP3) signal power levels at which the power of the corresponding spurious components will reach the same level as the fundamental component. Although the intercept point is a purely mathematical concept, it is an important indicator for measuring the tolerance of RF systems to nonlinearities.

Figure 4. Definition of nonlinear characteristics.

Now let’s look at another important characteristic inherent in every RF system – noise. Noise is the fluctuation of electrical signals and has many different aspects. Noise can be classified into many different types and forms, depending on its spectrum and how it affects the signal, as well as the mechanism that creates it. However, despite the many different sources of noise, we do not need to delve into their physical characteristics in order to describe their ultimate impact on system performance. We can start with a simplified model of system noise, which uses a single theoretical noise generator and is described by an important metric called noise figure (NF). It quantifies the degradation of the signal-to-noise ratio (SNR) caused by the system and is defined as the logarithm of the output SNR to the input SNR. The noise figure, expressed on a linear scale, is called the noise factor. This is a key characteristic of an RF system that controls its overall performance.

For simple linear passive devices, the noise figure is equal to the insertion loss defined by |S ₂₁ |. In more complex RF systems consisting of multiple active and passive components, the noise is described by their respective noise factors F _i and power gains G _i , and the effect of noise is reduced at each stage in the signal chain according to the Friis formula (assuming impedance matching at each stage):

It can be concluded that the first two stages of the RF signal chain are the main contributors to the overall system noise figure. This is why it is important to place the components with the lowest noise figure, such as low noise amplifiers, at the front end of the receiver signal chain.

If we now consider a dedicated device or system that generates a signal, when we talk about its noise performance characteristics, we generally refer to the signal characteristics affected by the noise source. These characteristics are phase jitter and phase noise, which are used to represent the stability of the signal in the time domain (jitter) and frequency domain (phase noise). The choice of which one to use generally depends on the application, for example, in RF communication applications, phase noise is generally used, while in digital systems, jitter is usually used. Phase jitter refers to small fluctuations in the phase of the signal, while phase noise is its spectral representation, defined as the noise power in a 1Hz bandwidth at different frequency offsets from the carrier frequency, and the power is considered to be balanced within this bandwidth (see Figure 5).

Figure 5. Phase noise characteristics example.

So far, we have considered a number of important coefficients and derived many parameters based on these coefficients that can be used to quantify the performance of RF signal chains in various application areas. For example, the term dynamic range (DR) is derived from noise and spurs to describe the operating range within which a system achieves the desired characteristics. As shown in Figure 4, if the lower limit of this range is determined by noise and the upper limit is determined by the compression point, we call it linear dynamic range (LDR); if its upper limit is determined by the maximum power level (the level at which intermodulation distortion becomes unacceptable), we call it spurious-free dynamic range (SFDR). It is important to note that the actual definition of LDR and SFDR may vary depending on the specific application.

The lowest signal level that the system can handle to generate an output signal with a specified SNR defines another important characteristic of the receiver system, namely sensitivity. It is mainly determined by the system noise figure and the signal bandwidth. The noise of the receiver itself will limit the sensitivity and other system specifications. For example, phase noise or jitter in a data communication system will cause the constellation points in the eye diagram to deviate from their ideal positions, which will reduce the error vector magnitude (EVM) of the system and increase the bit error rate (BER).

There are many characteristics and performance metrics that can be used to characterize an RF signal chain. They refer to different system aspects, and their importance and relevance may vary depending on the application. Although it is impossible to fully cover all of these factors in one article, if RF engineers have a deep understanding of the basic characteristics discussed in this article, they can easily translate them into key requirements and technical specifications in target applications such as radar, communication, measurement, or other RF systems.

ADI can meet a variety of demanding RF application requirements with the industry's broadest portfolio of RF, microwave and millimeter wave solutions and deep system design expertise. These extensive discrete and fully integrated ADI solutions from antenna to bit help open the entire spectrum from DC to over 100 GHz and provide excellent performance, supporting a variety of RF and microwave designs in applications such as communications, test and measurement instruments, industry, aerospace and defense.