Application Notes

**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 the Keysight Technologies, Inc. network analysis instrumentation systems that permit complete network characterization in the microwave frequency range have greatly assisted these engineers in their work.

The Keysight 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 videotape, 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.

**Table of content**

__S-Parameter Design Techniques–Part I __

__Basic Microwave Review–Part I__

- Transmission line theory
- S-parameters
- The Smith Chart
- The frequency response of RL-RC-RLC circuits

__Basic Microwave Review–Part II__

- Scattering-Transfer or T-parameters
- Signal low graphs
- Voltage and power gain relationships
- Stability considerations

__S-Parameter Design Techniques Part II __

S-Parameter Measurements: In this portion, the characteristics of microwave transistors and the network analyzer instrumentation system used to measure these characteristics are explained.

- 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 videotape 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 Keysight 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 this application note and the videotaped 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 the Keysight 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.

A two-port device can be described by a number of parameter sets. We’re all familiar with the H-, Y-, and Z-parameter sets. All of these network parameters relate to total voltages and total currents at each of the two ports. These are the network variables.

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. The important thing to note here is that both open and short circuits are essential for making these measurements.

Moving to higher and higher frequencies, some problems arise:

- Equipment is not readily available to measure total voltage and total current at the ports of the network.
- Short and open circuits are difficult to achieve over a broadband of frequencies.
- 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.

__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.

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 re-reflects 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.

A lossless line would simply have a series inductance and 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.

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.

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