1.36 shows an isolator (left) and a circulator (right). Figure 1.37 shows the signal flow for a circulator. In the figure, the isolator on the left has an internal load mounted at the top, and the circulator on the right has three ports, with an SMA connector in place of the isolator load.
Figure 1.36 Isolator (left) and circulator (right).
Figure 1.37 Schematic representation of a circulator.
1.12 Antennas
As the air interface for all communications systems, antenna performance is the first (in a receiver) and the last (in a transmitter) characteristic that affects the overall system performance. An antenna can be small and simple, such as a whip antenna found on a handset, or quite complicated such as those found in phased‐array radar systems. Antennas have two key attributes: reflection and gain pattern.
Antenna reflection is essentially a measure of the power transfer efficiency from the transmitter to the over‐the‐air signal. Ideally, the antenna should be impedance matched to the transmitter's output impedance. In fact, it is typically the case that the antenna is matched to some reference impedance, typically 50 Ω, while the transmitter is likewise matched to the same reference impedance. This implies that while the two may be matched, in many cases they can be exactly mismatched if the phase of the antenna mismatch is not the conjugate of the phase of the transmitter's mismatch. The tighter the mismatch specification is for each, the less variation in transmitter power one sees when phasing causes the two mismatches to be on opposite sides of the reference impedance.
Further, simple antennas are matched to a rather narrow range of frequencies, and it is a significant aspect of antenna design to extend the impedance match across a broad range of frequencies. One common form is a bi‐conical antenna, often found for use in testing the radiated emissions from electrical components. On the other end of the spectrum is the desire for a narrowband antenna to have a low return loss over a small frequency range to minimize reflected power back to the high‐power transmitter.
Antenna gain, or antenna gain pattern, describes the efficiency of an antenna in radiating into the desired direction (or beam) relative to a theoretical omni‐directional antenna, often referred to as an isotropic radiator. This figure of merit is known as dBi, or decibels relative to an isotropic antenna.
Antenna pattern measurements are the measurement of the antenna radiation pattern, typically plotted as a contour of constant dBi on a polar plot, where the polar angle is relative to the main beam or “bore‐sight” of the antenna. Antenna pattern measurements can range from simple gain measurements on an antenna on a turntable to near‐field probing of complex multi‐element phased array structure. While these complex measurements are beyond the scope of the book, many aspects of antenna return loss measurement, including techniques to improve these measurements, will be covered.
1.13 PC Board Components
While a wide‐ranging topic, the measurement of passive PC board components is focused on the measurement of surface mount technology (SMT) resistors, SMT capacitors, and SMT inductors. These components comprise the majority of passive elements used in radio circuits and also create some of the most undesirable side effects in circuits because of the nature of their parasitic elements. Here is a review of the models of these elements; during measurement, the difficulty is in understanding the relative importance of aspects of these models and extracting the values of the model elements.
1.13.1 SMT Resistors
Resistors are perhaps the simplest of electronic elements to consider, and Ohms law is often the first lesson of an electronic text.
(1.91)
However, the model of an RF resistor becomes much more complex as frequencies rise and distributed effects and parasitic elements become dominant. In this discussion the focus will be on surface‐mount PC board components, as they are used almost exclusively today in modern circuits. Thin film or thick film hybrid resistors have similar effects, and although the parasitic and distributed effects tend to hold off until higher frequencies, much of this discussion applies to them as well.
A good model for a resistor consists of a resistive value in series with an inductance, both shunted by a capacitance. This is a reasonable model for an SMT resistor in isolation, but the values and effects of the model are modified greatly by the mounting scheme of the component. For example, if it is mounted in series with a microstrip transmission line and the impedance is such that the resistor is much narrower than the transmission line, then this model works well for predicting circuit behavior; on the other hand, if it is mounted on a narrow line, then the contact pads will provide additional shunt capacitance to ground, and the model must include some element to account for this effect. At lower frequencies, some shunt capacitance will do well, but at higher frequencies, a length of low impedance transmission line might be a better choice.
A resistor used in shunt mode to ground can have an entirely different model when it comes to parasitic effects from that of a series resistance. While the RF value of the resistive element may stay almost the same as the series value (close to the DC value), the effective inductance can be substantially higher as the inductance of the ground via adds to that of the resistor in a microstrip configuration. A larger pad on the ground via, surprisingly, can add even more effective inductance as it resonates with the inductance of the via to increase the apparent inductance of the pair. Meanwhile, the shunt capacitance of the resistor may be absorbed in the transmission line width. Figure 1.38 shows a model for a resistor mounted in the series and shunt configurations. Measurement examples to illustrate extracting these values will be shown in Chapter 11.
Figure 1.38 Models for a series resistor (left) and shunt resistor (right).
In many instances, one of the two parasitic elements will dominate the model for first‐order high‐frequency effects. In fact, one can use some simple calculations to estimate a rough order of magnitude for these parasitic elements. Take, for example, an 0603 resistor, which has dimensions of approximately 0.6 mm width, 0.4 mm height (considering some excess plating, and some edge effect), and 0.76 mm length. If one considers the contact of the resistor wrapped around the body, one might reasonably divide the effective length by 3, to about 0.25 mm. Remembering that SMT resistors are often constructed on ceramic substrates, with a relative dielectric constant of about 10, then the capacitance can be computed as
(1.92)
The actual value may be substantially greater or less depending upon the exact attributes of the electrodes, but
