An electrical system normally has one or more input ports and one or more output ports. Figure 1-1 shows a system with a single input and a single output. Electrical devices such as filters, attenuators, and amplifiers fall into this category. Shown at the input is a signal, x(t) and at the output a signal, y(t). A more complex system (a phase lock loop) is shown in Figure 1-2. Although there is still only one input and one output, there are several blocks or subsections of the system, each having its own input and output. (Each block of the system may be considered as another system.) A design engineer thinks in terms of the individual blocks and signals while designing the system. Measurement instrumentation is used in the design phase when the engineer checks the performance of the individual blocks and signals. The signals and system blocks may also be measured in production, and later, when the system is maintained in the field.

The most familiar way of representing signals is in the time domain (i.e., a voltage or current represented as functions of time). An alternative representation which is extremely powerful and is inherent in spectrum and network measurements is the frequency domain representation, which describes the signal or system in terms of its frequency content (i.e., how much energy is present at each particular frequency). The frequency domain is related to the time domain by a body of knowledge generally known as Fourier theory, named for Jean Baptiste Joseph Fourier (1768-1830). This includes the series representation know as the Fourier series and the transform techniques known as the Fourier transform. Discrete (digitized) signals can be transformed into the frequency domain using the discrete Fourier transform.

The traditional method for implementing a spectrum analyzer is the swept heterodyne block diagram. Similar to a radio receiver, the spectrum analyzer is automatically tuned (swept) over the band of interest. This type of analyzer has been gradually replaced by the FFT analyzer at low frequencies, but the swept analyzer remains the dominant technology in the radio frequency range and above.

The preceding discussion was oriented toward understanding and measuring distortion in the device under test. However, the internal circuits of the analyzer are imperfect and will also produce distortion products. The distortion performance of the analyzer is specified by the manufacturer, either directly or lumped into a dynamic range specification. The instrument user can stretch the performance of the analyzer by understanding the nature of these distortion products. As shown in this chapter, distortion products can be reduced in amplitude by reducing the signal level. Not only do the absolute levels of the distortion products decrease, they decrease more than the decrease in signal level. So as the signal level decreases, the relative distortion level also decreases, depending on the order of the distortion product. Higher-order distortion products decrease the fastest. This implies that the distortion products internal to the analyzer can be reduced by reducing the signal level into the analyzer. The internal input attenuators of the analyzer may be used or an external attenuator may be attached, improving the distortion measurement range of the analyzer. The most obvious disadvantage of reduced signal level is reduced signal-to-noise ratio. The user may find that the low-level distortion products are buried in the noise. Reducing the resolution bandwidth of the analyzer will reduce the measured noise, but at the expense of a slower sweep rate.

Pulsed waveforms are an important class of signals in such systems as radar and digital radio. Pulsed signals can present a more difficult measurement problem than continuous waveforms. With a small-resolution bandwidth, the displayed spectrum has discrete spectral lines. With wide-resolution bandwidths, these line spectra are smeared together and the spectrum appears to be continuous. Under such measurement conditions, the settings of the spectrum analyzer greatly affect the measured results. The principles associated with the pulsed waveform (or pulse train) are also applicable to pulsed radio frequency signals. The envelope of the spectrum is the same and depends on the pulse width, but the spectrum is centered on the RF carrier frequency.

Transmission lines are commonly used to connect test and measurement instruments to circuits under test. Transmission lines are used to control the effects of inductance and capacitance which are unavoidable in high-frequency systems. Coaxial transmission lines are the most common and provide the best shielding of the signals being measured. Measurement error can be introduced due to impedance mismatch at either end of a transmission line. These errors must be understood and minimized in order to ensure an accurate measurement.

Two-port network theory provides the theoretical basis for making network measurements. Two-port network theory can be expanded to N-port theory for networks having more than two ports while one-port measurements are essentially a subset of two-port measurements. The simplest of two-port measurements is the gain or transfer function of the device. This assumes a fairly simple model of the device under test. More complete two-port models such as impedance parameters provide a better view of device behavior, while scattering parameters present a twoport model which is consistent with transmission line theory and measurements.

The most common network measurement is characterizing the transmission through a device. In many electronic systems, the response at the output of a system block due to a signal at the input is a critical parameter. For distortionless transmission through a device, the output signal must be identical to the input signal, perhaps delayed in time and scaled in amplitude. This implies the device must have a flat amplitude response and a linear phase response. These criteria are not usually completely met, but can be approached in practice. Measurement error is introduced into transmission measurements via a variety of mechanisms. These error mechanisms can be quantified so that the quality of the measurement is known.

Spectrum and network analyzer specifications are the instrument manufacturer's way of communicating to the user the level of performance which the user can expect from a particular instrument. Understanding and interpreting instrument specifications enables the instrument user to predict how the instrument will perform in a specific measurement situation. More specifically, the user can determine the overall accuracy of a measurement. The form and style of the specifications are usually related somewhat to the block diagram and measurement techniques internal to the instrument. These specifications will often appear to be more complex than necessary. Oversimplifying an instrument data sheet may force the manufacturer to understate the performance level of an instrument in order to cover all possible cases in a single specification. For instance, if the high-impedance input of an instrument exhibits poorer amplitude accuracy than the 50 Ω input, it makes sense to specify accuracy for the two inputs separately, rather than compromising the overall accuracy specification.