Signals and characteristics

Of all the DWC signal types, ASK is one of the oldest. ASK is the oldest wireline digital communications signal, because the Morse telegraph was implemented simply as the presence or absence of current on the wire.

The popularity of ASK rises and falls over the decades. This signal type was very popular through the first half of the twentieth century through the use of Morse Code in wireless telegraphy. As commercial interest in greater bandwidth efficiency and power efficiency (see Section 2.8.1) grew through subsequent decades, ASK fell from favor and was replaced by signal types performing far better in these metrics. In more recent decades the need for extreme simplicity and absolute minimum cost in several DWC applications, such as remote keyless entry (RKE), is resulting in a resurgence in the application of ASK.

ASK clearly has its place in the pantheon of DWC signal types. This chapter explores the details of ASK, its advantages and disadvantages, leading to an understanding of where value does exist for this very simple signal type.

Amplitude shift keying definition

For all signals using digital amplitude modulation, the PAM signal (2.3) maps solely onto the amplitude parameter, leaving the frequency and phase parameters constant. One example waveform is shown in Figure 1.4. Mathematically this is written as where .

In Chapter 2, only introductory level details are presented for the many concepts listed. There are a few of these concepts that warrant a much more detailed discussion in this book. Usually this is because there is significant confusion on these topics even among well-experienced engineers, so that any new engineer to DWC technology is guaranteed to be even more confused. More often, however, I have found that many important aspects are simply missed in the literature – for example, the fact that the raised-cosine Nyquist filter is nearly the worst performing Nyquist filter option available.

DWC channel capacity – the fundamental work of Claude Shannon

In the middle of the twentieth century, Claude E. Shannon examined the theoretical capacity limit of a noise limited digital communications channel. From this work to today, the digital communications community has developed a set of “basic understandings” that, while being technically correct, contain enough unstated assumptions to lead to incomplete understandings. In this section the fundamental result of Shannon, as it has been further refined over the years, is examined in a number of different ways.

In 1948 Claude Shannon put forward a theorem, sometimes referred to as the Fundamental Theorem on Information Theory, which can be stated as [1]: (here repeated from Section 2.7)

An amplifier is a circuit designed to impose a specified voltage waveform, V(t), or, sometimes, a specified current waveform, I(t), upon the terminals of a device known as the “load.” The specified waveform is often supplied in the form of an analog “input signal” such as the millivolt-level signal from a dynamic microphone. In a public address system, an audio amplifier produces a scaled-up copy of the microphone voltage (the input signal) and this amplified voltage (the output signal) is connected to a loudspeaker (the load). An audio amplifier generally supplies more than a watt to the loudspeaker. The microphone cannot supply more than milliwatts, so the audio amplifier is a power amplifier as well as a voltage amplifier. The ability to amplify power is really the defining characteristic of an amplifier. Of course energy must be conserved; amplifiers contain or are connected to power supplies, usually batteries or power line-driven ac-to-dc converter circuits, originally known as “battery eliminators” but long since simply called “power supplies” (see Chapter 29). The amplifiers discussed in this chapter are the basic “resistance-controlled” circuits in which transistors (or vacuum tubes) are used as electronically variable resistors to control the current through the load. Such circuits span the range from monolithic op-amps to the output amplifiers in high-power microwave transmitters.

Single-loop amplifier

Figure 3.1 shows the simplest resistance-controlled amplifier. This circuit is just a resistive voltage divider. The manually variable resistor (rheostat) in (a) represents the electronically variable resistor (transistor) in (b).

Digital modulation is both the newest and the oldest radio technique. Morse code transmissions were strictly binary, with “key down” and “key up” equivalent to multiplying the carrier by one or zero. Many modern systems also use binary keying, but the zero state is usually signaled by reversing the polarity of the signal (binary phase-shift keying, BPSK) or by shifting the frequency (binary frequency-shift keying, BFSK). This improves the probability of distinguishing zeros from ones in the presence of noise.

In this chapter we look first at some of the methods used for binary and “m-ary” modulation. We then see how specially shaped pulses can be used with these methods in order to avoid intersymbol interference when the pulses, dispersed in time, partially overlap at the receiver. The “8-VSB” system used for digital television in the U.S. (see Chapter 19) provides an example of pulse amplitude modulation (PAM). Finally, we discuss two newer digital modulation systems: multicarrier and spread spectrum. A glossary is provided at the end of this chapter, listing the many common abbreviations used (BPSK, BFSK, 8-VSB, PAM, etc.).

Digital modulators

Digital modulation differs from analog modulation in that only a discrete set of states (in the space of amplitudes, phases, and frequencies) is used, and that the time devoted to any state is always an integral multiple of a basic time-step. The state during this time period constitutes a transmitted “symbol,” and the symbol rate is one of the parameters defining a modulation system.

We draw circuit diagrams with “lumped”components: ideal R's, C's, L's, transistors, etc., connected by lines that represent zero-length wires. But all real wires, if not much shorter than the shortest relevant wavelength, are themselves complicated circuit elements; the current is not the same everywhere along such a wire, nor is voltage uniform, even if the wire has no resistance. On the other hand, when interconnections are made with transmission lines, which are well-understood circuit elements, we can accurately predict circuit behavior. In this section we will consider two-conductor lines such as coaxial cables and open parallel wire lines. “Microstrip lines” (conducting metal traces on an insulation layer over a metal ground plane) behave essentially in the same way, but they have some subtle complications, which are mentioned in Appendix 10.1.

Characteristic impedance

The first thing one learns about transmission lines is that they have a parameter known as characteristic impedance, denoted Z0. How “real” is characteristic impedance? If we connect an ordinary dc ohmmeter to the end of a 50-ohm cable will it indicate 50 ohms? Yes, if the cable is very long, so that a reflection from the far end does not arrive back at the meter before we finish the measurement. Otherwise, the meter will simply measure whatever is connected to the far end, which could be short, an open circuit, or a resistance.

Spectrometry or spectral analysis is the statistical characterization of random (stochastic) signals such as the IF voltage in a radio astronomy receiver, as described in Chapter 26. The spectrometers discussed in this chapter are all multiplex spectrometers, meaning that they measure N points on the spectrum simultaneously. This is to be distinguished from swept-frequency spectrum analyzers, which measure spectral points sequentially. Multiplex spectrometers are used when long integration times are needed to pull a signal out of the noise, as in radio astronomy. They are also used for low-frequency spectrum analysis, where narrow channel bandwidths require long measurement times to process a sufficient number of independent samples. Most often the signal is Gaussian; if a fine-grained histogram of samples of the signal's amplitude is scaled to make the area below the curve equal to unity, the average curve will be the Gaussian probability density function, f(V) = (2πσ2)−1/2 exp(−V2/2σ2). You can verify (Problem 27.1) that σ is the rms value of V, i.e., σ2 is the power, 〈V2〉. But total power does not completely characterize the signal. A complete description is contained in the power spectral density function, S(ω), the distribution of power vs. frequency. A set of bandpass filters and power meters, i.e., a set of radiometers, serves to measure points on the spectral density function (usually called the PSD or simply the power spectrum). However, the simplest mathematical definition of the power spectrum uses the signal's autocorrelation function, R(τ), a function of time delay.

In RF work, as in low-frequency work, test instruments generally are designed either to analyze signals, or to determine parameters of components and systems. Signal analysis ranges from simple voltage, current, and power measurements to measurements of frequency, relative phase, frequency stability, modulation characteristics, RF field strength, and spectrum analysis. Parameter measurements range from simple resistance and reactance measurements through measurements of transfer characteristics of linear multiport devices (filter shapes, amplifier frequency response, etc.), and distortion (dynamic range, intermodulation). Parameter measurements require a signal generator to provide the stimulus whose response is measured. It is now common for measurement instruments to include built-in signal generators, but free-standing signal generators are widely used in specialized test setups.

Power measurements

Power measurements, as pointed out in Chapter 18, are best made with a square-law detector. If the waveform is unknown or noisy (i.e., has a random component), a square-law detector must be used, as power, by definition, is proportional to the average square of voltage. If the signal waveform is known, e.g., a sine wave, the power can also be calculated, for example, from a measurement of 〈|V(t)|〉. Commercial RF power meters normally present a 50-ohm impedance to source being measured, allowing a reflectionless connection to a 50-ohm cable.

Thermistor (temperature-dependent resistor) power meters are true square-law instruments and have a dynamic range typically from 1 μW (−30 dBm) to 100 mW (20 dBm). The power to be measured heats a thermistor which is one leg of a Wheatstone bridge circuit.

Class-C, D, and E RF power amplifiers are all about high efficiency. They are used in large transmitters and industrial induction heaters, where high efficiency reduces the power bill and saves on cooling equipment, and also in the smallest transmitters, such as cell phones, where high efficiency increases battery life. These amplifiers are so nonlinear (the output signal amplitude is not proportional to the input signal amplitude), they might better be called synchronized sine wave generators. They consist of a power supply, at least one switching element (a transistor or vacuum tube), and an LCR circuit. The “R” is the load, RL, often the radiation resistance of an antenna, equivalent to a resistor. The LC network is resonant at the operating frequency. The output sine-wave amplitude, while not a linear function of the input signal amplitude, is proportional to the power supply voltage. Thus, these amplifiers can be amplitude modulated by varying the supply voltage. Of course they can also be frequency modulated by varying the drive frequency (within a restricted bandwidth, determined by the Q of the LC circuit). Finally, they can be used as frequency multipliers by driving them at a subharmonic of the operating frequency.

The class-C amplifier

Figure 9.1 shows a class-C amplifier (a), together with an equivalent circuit (b). The circuit looks no different from the class-B amplifier ofFigure 3.15 or a small-signal class-A amplifier.

Oscillators are autonomous dc-to-ac converters. They are used as the frequency-determining elements of transmitters and receivers and as master clocks in computers, frequency synthesizers, wristwatches, etc. Their function is to divide time into regular intervals. The invention of mechanical oscillators (clocks) made it possible to divide time into intervals much smaller than the Earth's rotation period and much more regular than a human pulse rate. Electronic oscillators are analogs of mechanical clocks.

Negative feedback (relaxation) oscillators

The earliest clocks used a “verge and foliot” mechanism which resembled a torsional pendulum but was not a pendulum at all. These clocks operated as follows: torque derived from a weight or a wound spring was applied to a pivoted mass. The mass accelerated according to Torque = I d2θ/dt2 (the angular version of F = ma). When θ reached a threshold, θ0, the mechanism reversed the torque, causing the mass to accelerate in the opposite direction. When it reached −θ0 the torque reversed again, and so on. The period was a function of the moment of inertia of the mass, the magnitude of the torque, and the threshold setting. These clocks employed negative feedback; when the controlled variable had gone too far in either direction, the action was reversed. Most home heating systems are negative feedback oscillators; the temperature cycles between the turn on and turn off points of the thermostat. Negative feedback electronic oscillators are called “relaxation oscillators.”

In this chapter we examine rectangular metal waveguides and, in particular, their most common mode of operation, the fundamental “TE10” mode. We will also see how the concepts developed for two-conductor transmission lines apply to waveguides and look at waveguide versions of some low-frequency components.

The ability of a hollow metal pipe to transmit electromagnetic waves can be demonstrated by holding it in front of your eye. You can see through it, so, at least, it passes electromagnetic waves of extremely short wavelengths. From a purely dimensional analysis, you would guess correctly that the longest wavelength a pipe could transmit must be of the order of the pipe's transverse dimensions. It turns out that, for propagation in a rectangular pipe, the free-space wavelength, c/f, must be less than twice the longer transverse dimension and, for a circular pipe, less than 1.706 times the diameter. Waveguides have less loss and more power handling capacity than coaxial lines of the same size and they need no center conductor nor insulating structures to support a center conductor. Metal waveguides are used most often in the range from 1000 MHz to 100 GHz, where they have practical dimensions. Waveguides for optical frequencies are coated glass fibers.

Simple picture of waveguide propagation

A common RF engineering argument for the plausibility of transmitting electromagnetic waves through a hollow metal pipe is shown in Figure 16.1, where a two-conductor transmission line evolves into a waveguide. Quarter-wave shorted stubs are added to the line.