1
Introduction

1.1 Background

During 1864 and 1867, James Clerk Maxwell established his theory of electromagnetism, which predicted that electric and magnetic fields travel through space as waves moving at the speed of light.1 Between 1886 and 1889, Heinrich Rudolf Hertz conducted a series of experiments that demonstrated the existence of electromagnetic waves and validated Maxwell’s theory.2 By the mid‐1890s, the scientific and technical foundation had been laid for Guglielmo Giovanni Maria Marconi to develop wireless telegraphy systems.3 At the turn of the 20th century, wireless telegraphy began to be used commercially and wireless telephony was also demonstrated, indicating that the wireless age came.4 Since then, antennas that made wireless communication possible have opened up many other possibilities.

1.2 Balanced and Unbalanced Antennas

A dipole antenna commonly consists of two identical conductive elements such as metal wires or rods. A loop antenna is usually made of a coil of metal wire or another electrical conductor. A dipole antenna was used as a transmitting antenna and a loop antenna as a receiving antenna by Hertz for the discovery of electromagnetic waves. Hence, the dipole and loop antennas are the earliest antennas. Figure 1.1 shows photos of Hertz’s sphere‐loaded dipole and loop antennas [1].

Figure 1.1 Photos of (a) Hertz’s dipole and (b) loop antennas.

Sources: (a) Heinrich Hertz/Public Domain. (b) Rollo Appleyard/Wikimedia Commons/Public domain.

A monopole antenna normally consists of a straight metal wire or rod, often mounted perpendicularly over a conductive surface, called a ground plane. The monopole antenna was invented in 1895 and patented in 1896 by Marconi [2]. He found that the monopole antenna could cover longer distances than the dipole antenna in his radio transmission experiments. Figure 1.2 shows a photo of the monopole antenna setup by Marconi himself at Shanghai Jiaotong University (SJTU) on 8 December 1933.5

Antennas can be balanced or unbalanced. A dipole antenna is balanced for its structural symmetry about the feed point, while a monopole antenna is unbalanced for its structural asymmetry about the feed point. It is noted that the old terms of balanced and unbalanced antennas cause confusion. For example, if a dipole antenna is installed parallel to the Earth’s surface, it is indeed balanced. However, if the dipole antenna is installed vertically to the Earth’s surface, it is unbalanced because one arm of the dipole antenna is closer to the Earth’s surface than the other. In addition, if a dipole antenna is fed off‐center, the dipole antenna is obviously unbalanced, but the feeding source is balanced. To avoid confusion, the new terms of differential and single‐ended antennas are adopted in this book. The new terminology is based on feeding sources rather than antenna structures. A differential antenna is an antenna fed with a differential or an equivalently differential signal source. A dipole antenna is a differential antenna. A single‐ended antenna is an antenna fed with a single‐ended signal source. A monopole antenna is a single‐ended antenna.

Figure 1.2 Photo of Marconi and his monopole antenna taken at SJTU on 8 December 1933.

Source: Shanghai Jiao Tong University/Wikimedia Commons/Public domain.

1.3 Even and Odd Modes

Three principal types of transmission lines are microstrip, stripline, and coplanar waveguide (CPW). They are widely used in modern wireless systems. A transmission line pair can be formed with any of them. Figure 1.3 shows the transmission line pair in a microstrip structure. We use it as an example to describe the even and odd modes of propagation.

Figure 1.3 Illustration of the transmission line pair in a microstrip structure. (a) Even and (b) odd modes.

Figure 1.4 Illustration of the electric field distributions (a) for the even and (b) for the odd modes.

The even mode is the mode corresponding to both lines having the same potential V to the ground plane and carrying the identical current in the same direction. The odd mode is the mode corresponding to both lines having opposite potentials V and –V, relative to the ground plane and carrying the identical current in the opposite directions. Figure 1.4 shows a sketch of electric field lines for the two modes. Note a magnetic wall exists in the even mode whereas an electric wall exists in the odd mode. The wall separates the whole structure into two identical half structures.

The even mode has an associated characteristic impedance Z0e, which can be calculated from the half structure of the even mode. Similarly, the odd mode corresponds to a characteristic impedance Z0o, which can be calculated from the half structure of the odd mode. It should be able to figure out from the field distributions in Figure 1.4 that Z0e is larger than Z0o.

1.4 Differential and Single‐Ended Circuits

A differential circuit deals with the difference between two input signals, while a single‐ended circuit accepts a single input signal. Figure 1.5 shows the schematic diagrams of differential and single‐ended bipolar junction transistor (BJT) amplifiers. We will use them as examples to illustrate the responses of differential and single‐ended circuits to differential and common‐mode signals.

Note that both V1 and V2 are two input signals. The differential‐mode input signal is defined as

and the common‐mode input signal as

Figure 1.5 Schematic diagrams of (a) differential and (b) single‐ended BJT amplifiers.

Thus, the two input signals V1 and V2 can be expressed as

and

Assuming that the common‐mode signal is an interference, and the differential‐mode signal is desirable, the single‐ended amplifier will amplify both the interference and desirable signal, while the differential amplifier has the advantage of amplifying only the desirable signal and rejecting the interference.

1.5 An Important Ratio

There exists an important ratio between many differential and single‐ended structures. For a differential antenna such as a half‐wavelength dipole, it has an input impedance

while for a single‐ended antenna such as a quarter‐wavelength monopole, it has an input impedance

Hence, the impedance ratio of the differential dipole to the single‐ended monopole is 2 : 1, and so is the size ratio.

Let us turn to the differential and single‐ended amplifiers as shown in Figure 1.5. The differential amplifier consists of two transistors and two resistors. The area is assumed to be Ad. The input resistance Rd is given by

where VT is the thermal voltage and IB is the base bias current. The single‐ended amplifier consists of one transistor and one resistor. The area is assumed to be As. The input resistance Rs is given by

Hence, the ratio of 2 : 1 is also true for the circuits. In Chapter 4, we will show that this important ratio is not always correct.

1.6 Mixed‐Mode S‐Parameters

S‐parameters refer to the scattering parameters of a microwave network. Taking a three‐port network as an example, the S‐parameters in a matrix form are expressed as

where the variable ai represents a power wave incident to port i and the variable bj a power wave reflected from port j. If each port is terminated in the reference impedance Z0, the S‐parameters of the three‐port vector network are defined as

where i and j are from 1 to 3 and aj−1 and aj−2 should be set to zero. S‐parameters are measured with a two‐port vector network analyzer.

Mixed‐mode S‐parameters are used for the characterization of differential structures [3]. Let us reconfigure the three‐port network as one single‐ended port (port 1) and one differential port (ports 2 and 3). Assuming that a single‐ended signal exists at the single‐ended port, a differential‐mode signal, and a common‐mode signal exist at the differential port, we use the nomenclature s, d, and c to represent the single‐ended, differential, and common modes, respectively, and we obtain the mixed‐mode S‐parameters in a matrix form as

Mixed‐mode S‐parameters are measured with a four‐port vector network analyzer. They can also be calculated using the single‐ended S‐parameters measured by a...