Convert a complex number from polar to rectangular format.

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.

Microwave amplifier design: Calculate TIN using s parameters

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-parameter design: Conversion of rectangular to polar format

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.

Use Signal Processing Group Inc., for analog and RF/wireless ASICs and modules.

S parameter calculations for RF/Microwave design. Some comments on ARCTAN.

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.

Microwave and RF Design free CAD tools

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( . 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( 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 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. 

Microwave amplifier design: Difference between a MIC and MMIC

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.

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