10.2 Some analogue performance metrics and test fundamentals

We introduce some of the analogue performance criteria for wireless communications devices in the context of the simplistic sample signals shown in Figure 10.1. Since many of the concepts presented in this section have been covered earlier, a qualitative description of this figure should suffice to review some of these concepts and describe their influence on test. For example, Figure 10.1a suggests that a radio receiver is expected to decipher a sometimes very weak user channel in the presence of large adjacent channels. The result is stringent linearity requirements not only at the frontend circuits but also downstream through the intermediate frequency circuits and/or the digitising circuitry. On the other hand (Figure 10.1b), a transmitter is ideally required to generate only the user signal without any spurious by-products due to circuit non-linearity. The goal of testing in both of these cases is to determine whether such signal discrimination is actually performed by the device under test (DUT). Figure 10.1 also suggests that frequency selectivity is an equally important function in radio transceiver ICs which are expected to selectively process the user channel while suppressing some strong interfering channels. Depending on the architecture used, frequency selectivity is performed at different places (and different frequency bands) within a single transceiver device, the ultimate goal being to separate the user channel from all other channels. Some other performance requirements for wireless communications devices, such as noise performance, can similarly be inferred from Figure 10.1.

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Figure 10.1: Sample signal spectra at (a) the input of a receiver and (b) the output of a transmitter. Linearity, frequency selectivity, noise performance and other performance requirements can easily be described through direct observation of such spectra

The above description of some of the behavioural requirements for wireless communications devices translate into corresponding circuit-specific requirements on linearity, spectral purity, noise, etc. Some of the metrics for these parameters are described in more detail here.

10.2.1 Linearity

When a signal passes through a non-linear system, it can get adversely modified by the input–output characteristic of the system. Assuming a memoryless system, a convenient method for representing the behaviour of the output signal is to expand it into a power series representation:

Linear and non-linear circuit behaviour is available directly from a frequency domain representation of the output signal of a circuit when excited by a sinusoidal signal. Specifically, consider a circuit that is described by the relation (10.1). If this circuit is excited by a sinusoid as

then its output can be expressed as

where only the first three terms of (10.1) are retained. Rearranging (10.3), the output can be written as

Equation (10.4) gives insights into many of the parameters that are usually sought in linear circuit specification. First, a single sine wave at the input of a non-linear system results in several waves at the output, the fundamental signal at the same frequency as the input and several harmonically related sine waves. The number and power of the extra harmonics is referred to as harmonic distortion, and it is one of the most important linearity tests for analogue circuits. Harmonic distortion, for example, is a key parameter in evaluating the baseband components such as D/A or A/D converters in a transceiver. Similarly, observation of (10.4) gives insights into how non-linearity modifies the amplitude of the original input signal. Apart from the desired gain introduced by the circuit, its non-linear nature introduces an additional term at the same frequency as that of the input signal. This phenomenon is known as gain compression, as this additional term usually acts to reduce the amplitude of the fundamental output signal. A common metric for gain compression is the 1 dB compression point, which is the input amplitude level that causes the circuit gain to decrease by 1 dB. From a test perspective, measuring this parameter requires delivering a spectrally pure sinusoidal signal of known amplitude to the linear component under test and extracting the output signal power. Another parameter that is related to gain compression is desensitisation, and it becomes important when more than just a sine wave is being processed. Specifically, when both a weak and a strong signal are input to the circuit, gain compression due to the strong signal acts to reduce the circuit's gain and, hence, the ability to amplify the weak signal.

Of special interest in narrowband systems is an intermodulation test, which is a yet more realistic measure of linearity. When more than just a single sine wave is applied to (10.1), it can be shown that the output exhibits sine wave components that are not harmonics of the input frequencies. Such components, which are called intermodulation products, can fall very close to the input signal frequencies and can, thus, reveal information about the non-linearity of the system in a narrow frequency band. Referring to Figure 10.1, intermodulation is actually the mechanism by which interfering channels affect an adjacent user channel. Again, from a test point of view, simultaneous sine wave generation with proper amplitude control is required. A typical parameter for measuring intermodulation is called the third-order intercept point. To obtain this point, a two-tone signal is applied to the circuit under test and the output fundamental two-tone signal as well as the third-order intermodulation products are measured. The third-order intercept point is defined as the input two-tone amplitude level for which the power in the intermodulation products exceeds the power in the fundamental output of the system.

Other linearity tests that are also important for analogue circuits include DC characteristics and common-mode and offset characteristics. Some of these are described briefly later in the text.

10.2.2 Frequency response

Different communication standards pose different requirements on the filtering properties of a radio system [4]. Similarly, different implementation choices also affect the filtering requirements in a radio transceiver. For example, Reference 5 describes recent trends in data converter design for radio applications that pose a wide range of analogue filter requirements. In general, both narrowband bandpass filters as well as lowpass anti-image or anti-alias filters are required.

The most important test for the frequency selective components of the radio IC is the magnitude and phase frequency response. Traditionally, a single sine wave with a swept frequency is applied to the filter under test, and the filter output magnitude and phase are recorded. With the recent application of DSP-based techniques in the test and measurement world, a much faster method for obtaining the same frequency response information is to excite the filter with several sine waves simultaneously and to digitise the output of the filter and process the magnitude and phase of each of the output sine waves. Several examples of this multitone test for analogue filters will be described in this chapter. With this approach, however, the choice of the input sine wave frequencies is important. Because of intermodulation due to the non-linearity of the filter, the filter output will contain not only the input component frequencies but also many other components due to the intermodulation terms. In order to avoid errors in the gain and phase measurement at the desired test signal frequencies, the latter have to be chosen to avoid the coexistence of intermodulation terms at the same frequencies as the test sine waves. Fortunately, several software methods for component frequency selection exist in the literature as described in Reference 6. The advantage of such an approach to filter response measurement is that other useful filter performance metrics, such as group delay, can easily be obtained through the application of DSP algorithms on the digitised filter output signal.

10.2.3 Noise

Because wireless transceiver circuits are required to operate on extremely low signal levels, the effects of noise due to the circuits themselves and due to external interference sources are given careful consideration in the design of wireless transceivers [4]. The treatment of noise is beyond the scope of this chapter and will not be included here. Instead, we introduce the concepts of the signal-to-noise ratio (SNR) and signal-to-noise and distortion ratio (SNDR). As can be expected from these terms, both are measures of the ratio of a certain desired signal's power to the power in noise (or noise plus distortion) that accompanies this signal. Such ratios are important at different locations within a circuit (e.g. input and output) or within a group of circuits (e.g. in a cascade of circuits), and they are especially challenging for test and characterisation. For example, in measuring the SNR at the output of a linear amplifier, care has to be taken so that the measurement instrument itself does not introduce excessive noise thus corrupting the estimate of the circuit's own noise generation properties. In modern test instruments, DSP methods are used to estimate noise power spectra in digitised circuit response signals. Such methods will be described briefly in subsequent sections.

Having the ability to compare signal levels to noise levels provides other useful information about analogue circuits and their ability to deal with random phenomena. For example, the ratio of the SNR at the input of a circuit to the SNR at its output is referred to as the noise figure, and it is a widely used metric in RF design. Similarly, by measuring the SNR at different power levels, the dynamic range of a circuit (or spurious-free dynamic range, SFDR) can be obtained as a measure of the range of signals that can be processed by a device [6].

10.2.4 Other performance metrics

The above sections introduced some of the important specification metrics for analogue and mixed-signal circuits. However, the complete specification set for such devices is more diverse [6]. For example, other important parameters include DC parametric performance, settling time, overshoot, cross-talk, jitter and substrate noise. Some of these parameters are increasingly important in a SOC environment in which large digital blocks are integrated alongside sensitive analogue blocks. These specifications also pose more diverse test requirements, and related signal delivery and extraction mechanisms, which are at the heart of the topics described in this chapter.