Agilent AN 154 S-Parameter Design Application Note
Introduction The need for new high-frequency, solid-state circuit design techniques has been recognized both by microwave engineers and circuit designers. These engineers are being asked to design solid state circuits that will operate at higher and higher frequencies. The development of microwave transistors and Agilent Technologies’ network analysis instrumentation systems that permit complete network characterization in the microwave frequency range have greatly assisted these engineers in their work. The Agilent Microwave Division’s lab staff has developed a high frequency circuit design seminar to assist their counterparts in R&D labs throughout the world. This seminar has been presented in a number of locations in the United States and Europe. From the experience gained in presenting this original seminar, we have developed a four-part video tape, S-Parameter Design Seminar. While the technology of high frequency circuit design is ever changing, the concepts upon which this technology has been built are relatively invariant. The content of the S-Parameter Design Seminar is as follows: A. S-Parameter Design Techniques–Part I 1. Basic Microwave Review–Part I This portion of the seminar contains a review of: a. b. c. d. Transmission line theory S-parameters The Smith Chart The frequency response of RL-RC-RLC circuits 2. Basic Microwave Review–Part II This portion extends the basic concepts to: a. b. c. d. 2 Scattering-Transfer or T-parameters Signal flow graphs Voltage and power gain relationships Stability considerations B. S-Parameter Design Techniques Part II 1. S-Parameter Measurements In this portion, the characteristics of microwave transistors and the network analyzer instrumentation system used to measure these characteristics are explained. 2. High Frequency Amplifier Design The theory of Constant Gain and Constant Noise Figure Circles is developed in this portion of the seminar. This theory is then applied in the design of three actual amplifier circuits. The style of this application note is somewhat informal since it is a verbatim transcript of these video tape programs. Much of the material contained in the seminar, and in this application note, has been developed in greater detail in standard electrical engineering textbooks, or in other Agilent application notes. The value of this application note rests in its bringing together the high frequency circuit design concepts used today in R&D labs throughout the world. We are confident that Application Note 154 and the video taped S-Parameter Design Seminar will assist you as you continue to develop new high frequency circuit designs.
Chapter 1. Basic Microwave Review I Introduction This first portion of Agilent Technologies’ S-Parameter Design Seminar introduces some fundamental concepts we will use in the analysis and design of high frequency networks. These concepts are most useful at those frequencies where distributed, rather than lumped, parameters must be considered. We will discuss: (1) scattering or S-parameters, (2) voltage and power gain relationships, (3) stability criteria for two-port networks in terms of these S-parameters; and we will review (4) the Smith Chart. Network Characterization S-parameters are basically a means for characterizing n-port networks. By reviewing some traditional network analysis methods we’ll understand why an additional method of network characterization is necessary at higher frequencies. The only difference in the parameter sets is the choice of independent and dependent variables. The parameters are the constants used to relate these variables. To see how parameter sets of this type can be determined through measurement, let’s focus on the H-parameters. H11 is determined by setting V2 equal to zero—applying a short circuit to the output port of the network. H11 is then the ratio of V1 to I1—the input impedance of the resulting network. H12 is determined by measuring the ratio of V1 to V2—the reverse voltage gain-with the input port open circuited (Fig. 3). The important thing to note here is that both open and short circuits are essential for making these measurements. Figure 3 Moving to higher and higher frequencies, some problems arise: Figure 1 A two-port device (Fig. 1) can be described by a number of parameter sets. We’re all familiar with the H-, Y-, and Z-parameter sets (Fig. 2). All of these network parameters relate total voltages and total currents at each of the two ports. These are the network variables. 1. Equipment is not readily available to measure total voltage and total current at the ports of the network. 2. Short and open circuits are difficult to achieve over a broad band of frequencies. 3. Active devices, such as transistors and tunnel diodes, very often will not be short or open circuit stable. Some method of characterization is necessary to overcome these problems. The logical variables to use at these frequencies are traveling waves rather than total voltages and currents. Figure 2 3
Transmission Lines Let’s now investigate the properties of traveling waves. High frequency systems have a source of power. A portion of this power is delivered to a load by means of transmission lines (Fig. 4). Although the general techniques developed in this seminar may be applied for any characteristic impedance, we will be using lossless 50-ohm transmission lines. We’ve seen that the incident and reflected voltages on a transmission line result in a standing voltage wave on the line. The value of this total voltage at a given point along the length of the transmission line is the sum of the incident and reflected waves at that point (Fig. 6a). Figure 4 Voltage, current, and power can be considered to be in the form of waves traveling in both directions along this transmission line. A portion of the waves incident on the load will be reflected. It then becomes incident on the source, and in turn rereflects from the source (if ZS ≠ Zo), resulting in a standing wave on the line. If this transmission line is uniform in cross section, it can be thought of as having an equivalent series impedance and equivalent shunt admittance per unit length (Fig. 5). Figure 6 The total current on the line is the difference between the incident and reflected voltage waves divided by the characteristic impedance of the line (Fig. 6b). Another very useful relationship is the reflection coefficient, Γ. This is a measure of the quality of the impedance match between the load and the characteristic impedance of the line. The reflection coefficient is a complex quantity having a magnitude, rho, and an angle, theta (Fig. 7a). The better the match between the load and the characteristic impedance of the line, the smaller the reflected voltage wave and the smaller the reflection coefficient. Figure 5. A lossless line would simply have a series inductance and a shunt capacitance. The characteristic impedance of the lossless line, Zo, is defined as Zo = L/C. At microwave frequencies, most transmission lines have a 50-ohm characteristic impedance. Other lines of 75-, 90-, and 300-ohm impedance are often used. 4 Figure 7