In an earlier post the differential impedance of edge coupled microstrip was described. A calculator for the differential impedance is also available. The differential impedance is also dependent on the characteristic impedance of the microstrip used . Therefore a calculator was developed to find the characteristic impedance of the microstrip. . All of these resources and tools can be accessed from the Signal Processing Group Inc., website by using the “complementary” link.
When two parallel, closely spaced, microstrip lines are used to deliver a differential signal to a load, the differential impedance between them can be calculated using a closed form expression. This impedance is not the characteristic impedance of the individual lines. The differential impedance is modified by the proximity of the two lines to each other. A calculator has been developed by Signal Processing Group Inc., to do this using javascript.
The input to the program is:
1) Characteristic impedance of the lines – Zo
2) The thickness of the PCB – h
3) The spacing of the lines on the PCB—s
It is recommended that when adjusting the dimensions of the lines to get the required differential impedance ( Zdiff) the width of the lines be adjusted, not the spacing.
Another javascript provides a calculator to do this adjustment. This calculator requires the following inputs:
4) εr the dielectric constant of the substrate
5) t, the thickness of copper
6) W, the width of the strip
7) h, the thickness of the substrate.
The javascripts are interactive and these constants can be inserted as it runs. Both the scripts can be accessed from the SPG website by interested users.under the complementary menu i
Here are some design rules for the use of differential microstrip lines.
Design Rule 1 The traces should be of equal length.
Design Rule 2: Route differential traces close together.
Design Rule 3: Differential impedance calculations are necessary with differential signals and traces.
Design Rule 4: The separation between the two traces (of the differential pair) must remain constant over the entire length.
Check out this impedance matching book available from Amazon.
Its wonderful to see the progress made by the III-V technology companies in providing the foundry services and products for really high performance products and MMICs. When I started in GaAs the maximum wafer size for a GaAs wafer was about the size of my thumbnail. Today there are Si-GaAs wafers 12 inches across! Design tools for simulation and characterization have also come a long way. Before these developments we were designing MICs and there were none or very few design tools. We matched the input and out reflection coefficients using tiny gold disks of various radii to achieve the optimum matching. I remember getting 1 Watt out of a GaAs FET. It was unknown during those days. It took a thermal bonder, much sweat ( and tears) and precise bondwire matching and the rest of the work to achieve this. Today I work with ADS and similar tools to seriously reduce risk before layout and post layout of the MMICs. MMIC packages have come a long way too. During the days I was learning MMIC design, no packages were available. The die was mounted directly on the Alumina substrate. Now we can get touchstone files for packages and along with the s – parameters of the device itself, a reasonable match can be done a priori. Devices such as pHEMTs were not available then. They are available now. By the way we used TWT’s to test the devices. These were the test boxes provided by HP to test those high frequencies ( mostly X Band) we were designing in. So with the foundry services, the CAD tools, the package data and test equipment available today, MMIC development is much less of a risk today than it used to be. Good job and kudos to all the companies who have made it possible. By the way the accompanying image of the Smith Chart is a reflection ( no pun intended) of the workhorse tool of those early days of MMIC design. By Ain Rehman, Signal Processing Group Inc.
In 1962 John Rollet published a paper in the IRE called Stability and Power – Gain invariants of Linear two ports. In this he described the K – factor for an amplifier. When designing an amplifier or selecting one from a catalog, check the K factor. If the K – factor is greater than 1, then the amplifier is unconditionally stable, if not then it should be checked for stability. It could be conditionally stable, or in the worst case, unstable. You can access a javascript calculator from the Signal Processing Group Inc,. website to calculate K. Just select the complementary menu item and choose the calculator link,
An earlier post dealt with a calculator for a rectangular to a polar format converter for complex numbers. In many cases — addition and subtraction is only one of them– complex number arithmetic needs to be done in rectangular format. Therefore complex numbers, ( and s parameters are complex numbers) should be converted to the rectangular format. The calculator can be found under the complementary items menu on the Signal Processing Group Inc., website.
TIN is the input reflection coefficient of a two port that is terminated with a terminating impedance Zs on the signal side and a terminating impedance ZL on the output side. When this is done the input and output reflection coefficients are modified from s11 and s22. Here s11 and s22 are the reflection coefficients seen looking into the input and output of the two port ( or amplifier) before the terminating impedances are connected. TIN and TOUT ( addressed in another post) have a direct and significant effect on the design of a microwave amplifier. It is important therefore, to calculate these as part of the overall design.
Signal Processing Group Inc has published a calculator using javascript to allow a user to do these calculations quickly and efficiently. The calculator may be found on the SPG website under the complementary menu item.
S – parameters are complex numbers. S – parameters are used extensively in the design of many high frequency functions such as amplifiers, mixers, oscillators etc. Some engineers prefer using them in rectangular format, while others prefer the polar format. In some ways the polar format is easier to deal with. This is the case when multiplying or dividing. The rectangular format is better ( or essential) when adding or subtracting). Although there appear to be one or two converters on the web, we were not too sure of their results so we designed a rectangular to polar converter in javascript ( a polar to rectangular one is in the works). Please visit our website and select the complementary items link to access the calculator.
S parameters are usually used in calculations of RF/wireless/microwave design and development. S parameters are complex numbers that can be written in a rectangular form with real and imaginary components, as well as in the polar form, with a radius ( magnitude) and angle.
Conversions between the polar form and the rectangular form are common . Some engineers like the polar form others like the rectangular form. When converting from the rectangular form to the polar form, the magnitude is calculated by taking the square root of the sum of the squares of the real and imaginary component. Associated with this calculation is the angle.
The angle is calculated by taking the ARCTAN ( imaginary/real). This is easy to do but there is a wrinkle in this calculation that needs to be understood, and taken care of, when calculating the angle. We have found that some calculators on the web do not take care of this issue.
The value of the angle is also dependent on the quadrant the angle lies in. For example, lets say that the real component is negative and the imaginary component is negative. When the imaginary is divided by the real in this case, the quotient is positive. When the ARCTAN is taken of this positive quantity the result can be ( if care is not taken) an angle in the first quadrant. This is misleading.
The correct result of such a calculation, must take account of which quadrant the angle lies in. In the above example the angle really lies in the third quadrant. The ARCTAN calculator can calculate the angle in the first quadrant. To get the correct answer one should subtract 180 degrees from the result.
Please see the Wikipedia for a detailed explanation of this. The search term is Inverse trigonometric functions.
At Signal Processing Group Inc., most of our RF/wireless/microwave designs use the s-parameter approach as routine. Please visit our website and check out other articles and information.
If you are not wealthy enough to buy the extravagantly priced CAD tools for RF and Microwave design then there are a few public domain freeware tools available on the web. You will have to register and then a download can be done. They are fairly user friendly and simple to use. The first of these tools is GNUPLOT( gnuplot.info) . A really nice plotting program which allows various types of plots to be made. It allows mathematical expressions to be evaluated and plotted. Then there is APPCAD(www.avagotech.com/appcad). This is a very nice tool that is available from ACAGO. It is great for microwave and RF design with a multitude of features dear to an RF/microwave design engineer’s heart. Finally I must mention the TXLINE tool from National Instruments( formerly AWR).It has a large number of features dealing with transmission lines and materials. It is available from http://www.awrcorp.com/products/optional-products/tx-line-transmission-line-calculator. Finally there are a large number of javascripts available on the Signal Processing Group Inc.’s website under the “complementary” menu item. These are small scripts that allow one to calculate a large number quantities such as reflection coefficients, transmission line parameters etc. If you are interested in impedance matching then you can get the VSWR and Impedance matching book from Signal Processing Group’s “products for sale” section. The price is minimal compared to the information contained in the 122 pages or so.
There are two types of similar microwave integrated circuits. Microwave integrated circuits ( MIC) and monolithic microwave circuits ( MMIC) sometimes get confused. A typical MIC is a hybrid device with one layer of metallization for conductors and transmission lines, with discrete components (resistors, capacitors, integrated circuit chips, transistors, diodes, etc.) placed and bonded to a substrate which can be a high performance PCB or Alumina.
Some of the simpler components can be deposited on the substrate. MICs were originally developed in the 1960s, and even now deliver a very cost-effective solution. Monolithic microwave integrated circuits (MMIC) on the other hand, are a semiconductor integrated circuit technique, where the active and passive circuit elements are implemented on a semiconductor substrate. Typically Bipolar, SiGe, GaAs, GAN substrates are used.
