Agilent AN 154
S-Parameter Design Application Note
句子翻译
The need for new high-frequency, solid-state circuit design techniques has been recognized both by micro-wave engineers and circuit designers. The engi-neers 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 instrumen-tation systems that permit complete network char-acterization in the microwave frequency range have greatly assisted the engineers in their work. The Agilent Microwave Division’s lab staff has developed a high frequency circuit design minar to assist their counterparts in R&D labs through-out the world. This minar has been prented
in a number of locations in the United States and Europe.
From the experience gained in prenting this orig-inal minar, we have developed a four-part video tape, S-Parameter Design Seminar.While the tech-nology 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
(Part No. 90i030A586, VHS; 90030D586, 3/4”)
1.Basic Microwave Review–Part I
This portion of the minar contains a review of:
a.Transmission line theory
b.S-parameters
c.The Smith Chart
d.The frequency respon of RL-RC-RLC
circuits
2.Basic Microwave Review–Part II
This portion extends the basic concepts to:
a.Scattering-Transfer or T-parameters
b.Signal flow graphs
c.Voltage and power gain relationships
d.Stability considerations B.S-Parameter Design Techniques Part II
(Part No. 90030A600, VHS; 90030D600, 3/4”)
青蛙的种类1.S-Parameter Measurements
In this portion, the characteristics of
microwave transistors and the network ana-
lyzer instrumentation system ud to meas-
ure the characteristics are explained.
2.High Frequency Amplifier Design
The theory of Constant Gain and Constant
Noi Figure Circles is developed in this por-
tion of the minar. 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 the video tape programs.
Much of the material contained in the minar, 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 ud 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 fre-quency circuit designs.
Introduction
2
3
Introduction
This first portion of Agilent Technologies’ S-Para-meter Design Seminar introduces some fundamen-tal concepts we will u in the analysis and design of high frequency networks.
The concepts are most uful at tho frequencies where distributed, rather than lumped, parameters must be considered. We will discuss: (1) scattering or S-parameters, (2) voltage and power gain rela-tionships, (3) stability criteria for two-port net-works in terms of the S-parameters; and we will review (4) the Smith Chart.
索朗扎西Network Characterization
S-parameters are basically a means for characteriz-ing 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.
Figure 1
A two-port device (Fig. 1) can be described by a number of parameter ts. We’re all familiar with the H-, Y-, and Z-parameter ts (Fig. 2). All of the network parameters relate total voltages and total currents at each of the two ports. The are the network variables.
Figure 2
The only difference in the parameter ts is the choice of independent and dependent variables.The parameters are the constants ud to relate the variables.
To e how parameter ts of this type can be determined through measurement, let’s focus on the H-parameters. H 11is determined by tting V 2equal to zero—applying a short circuit to the output port of the network. H 11is then the ratio of V 1to I 1—the input impedance of the resulting network.H 12is determined by measuring the ratio of V 1to V 2—the rever voltage gain-with the input port open circuited (Fig. 3). The important thing to note here is that both open and short circuits are esn-tial for making the measurements.
Figure 3
Moving to higher and higher frequencies, some problems ari:
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 the problems. The logical variables to u at the frequencies are traveling waves rather
整式的加减教案
than total voltages and currents.
4
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).
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 re-reflects from the source (if Z S ≠Z o ), resulting in a standing wave on the line.
If this transmission line is uniform in cross c-tion, it can be thought of as having an equivalent ries impedance and equivalent shunt admittance per unit length (Fig. 5).
Figure 5.
A lossless line would simply have a ries induc-tance and a shunt capacitance. The characteristic
impedance of the lossless line, Z o , is defined as Z o =L/C. At microwave frequencies, most trans-mission lines have a 50-ohm characteristic imped-ance. Other lines of 75-, 90-, and 300-ohm imped-ance are often ud.
Although the general techniques developed in this minar may be applied for any characteristic
impedance, we will be using lossless 50-ohm trans-mission lines.
We’ve en 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 6
The total current on the line is the difference
林彪是怎么死的between the incident and reflected voltage waves divided by the characteristic impedance of the line (Fig. 6b).
Another very uful relationship is the reflection coefficient, Γ. This is a measure of the quality of the impedance match between the load and the charac-teristic impedance of the line. The reflection coeffi-cient 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 7
5
This can be en more clearly if we express the reflection coefficient in terms of load impedance or load admittance. The reflection coefficient can be made equal to zero by lecting a load, Z L , equal to the characteristic impedance of the line (Fig. 7b).To facilitate computations, we will often want to normalize impedances to the characteristic imped-ance of the transmission line. Expresd in terms of the reflection coefficient, the normalized imped-ance has this form (Fig. 8).
Figure 8
S-Parameters
Having briefly reviewed the properties of transmis-sion lines, let’s inrt a two-port network into the line (Fig. 9). We now have additional traveling waves that are interrelated. Looking at E r2, we e that it is made up of that portion of E i2reflected from the output port of the network as well as that portion of Ei 1that is transmitted through the net-work. Each of the other waves are similarly made up of a combination of two waves.
幼儿园师德培训
Figure 9
2017日历It should be possible to relate the four traveling waves by some parameter t. While the derivation of this parameter t will be made for two-port net-works, it is applicable for n-ports as well. Let’s start with the H-parameter t (Fig. 10).
Figure 10
Figure 11
By substituting the expressions for total voltage and total current (Fig. 11) on a transmission line into this parameter t, we can rearrange the equations such that the incident traveling voltage waves are the independent variables; and the
reflected traveling voltage waves are the dependent variables (Fig. 12).
Figure 12
蒜蓉粉丝蒸生蚝The functions f 11, f 21and f 12, f 22reprent a new t of network parameters relating traveling voltage waves rather than total voltages and total currents.In this ca the functions are expresd in terms of H-parameters. They could have been derived from any other parameter t.
It is appropriate that we call this new parameter t “scattering parameters,” since they relate tho waves scattered or reflected from the network to tho waves incident upon the network. The
scattering parameters will commonly be referred to as S-parameters.
Let’s go one step further. If we divide both sides of the equations by Z o , the characteristic imped-ance of the transmission line, the relationship will not change. It will, however, give us a change in variables (Fig. 13). Let’s now define the new vari-ables:
Figure 13
