Double stub impedance matching for RF and Microwave design


Its interesting how many techniques exist today for impedance matching of complex loads to transmission lines. A really interesting one is the technique of double stub matching which is a popular one. Its simpler cousin is single stub matching which can be used but runs out of steam under some circumstances

Double stub impedance matching is more involved than single stub matching. First of all we need to discuss the rationale for using double stub matching. In order to understand all this, consider the points below:

1.0 A single stub match involves the use of a stub of fixed length placed at a fixed position on the transmission line from the load for a specific load.

2.0 If the value of the load changes then the length of the stub and the position at which it is placed must also change.

3.0 A better technique would be where we could fix the positions of the stubs in relation to each other and only change the lengths of the stubs to match varying loads. This is done using the techniques of double and triple stub matching.

4.0 Both analytic and graphical techniques are available to do double stub matching. The graphical method is usually the Smith Chart method and that is what we have focused on. However analytical techniques can be enlightening as well, and are recommended if you are mathematically minded.

5.0 In order to further understand the technique of double stub matching you need a reasonable amount of the understanding of how the Smith Chart works.

6.0 There are some loads that cannot be matched using double stub matching by simply altering the length of the stubs. However if we are willing and able, to move the stubs together a distance away (or towards the load) from the load then we can accommodate the load. This can be discussed and illustrated using the Smith Chart method. These loads form an area of the Smith Chart collectively known as the forbidden zone for double stub matching.

7.0 Additional techniques can be used to overcome the limitations of double stub matching if needed. Similar techniques to that of double stub matching are used for triple stub matching.

The interesting situation as far as learning about double stub matching is that there are very few articles available that really discuss the technique for the newbie. We know as we did a web search and came up with very few articles that deal with this.

A forthcoming book from Ain Rehman of Signal Processing Group Inc, addresses these techniques in some detail with a minimum of math. The title is VSWR and Impedance matching techniques. This book will be available on Amazon both as a paperback and as a Kindle book shortly for interested readers.

Please visit our website for more information and other articles of interest.

Signal Processing Group Inc., delivers RF Design, RF IC design, rf circuit design, ic design, analog design, rf technology, analog circuit design, asic chip, integrated circuit design and various rf devices

This is low noise RF Amplifier by Signal Processing Group Inc., available from Amazon

A low noise RF amplifier by Signal Processing Group Inc.

SPG designs, develops and delivers custom analog and RF/wireless asics and modules.

RF/microwave design freeware

Its so impressive to see the amount of freeware now available to do RFMW design and development. From the “free-est” of freeware for RFMW ( APPAD) to many other packages. A harmonic balance tool is also available as freeware. The consequence is that we as design engineers do not always have to pay an arm and a leg to get the commercial packages ( of which there are few) and be hostages to these vendors. A lot of work can be done prior to spending umpteen dollars so that the cost can be lowered significantly.  Currently we have a few of these freeware tools under assessment and will be reporting on their performance in this blog.

RF/Microwave design: The inductance and capacitance equivalents of microstrip/transmission lines


Microstrip ( or transmission lines) are used extensively in high frequency design of MMICs or PCB level circuits. In many cases it is simpler just to use a piece of microstrip as an inductance or a capacitance. ( Especially in microwave design). However we need to calculate what the microstrip dimensions should be to realize an inductor or a capacitor or both. ( There is much more information in the second edition of the forthcoming book on VSWR and matching techniques for the interested reader). Here then are the expressions for these types of structures:

XL = reactance of an inductive line = XL= ZoSin( 2*pi*length/lambdag). From this expression one can extract what the length should be as well. Here length is the length of the microstrip ( generally higher resistance e.g 100 Ohms), lambdag = wavelength in air/square root ( relative permittivity) also known as guide wavelength in some texts. Zo is the characteristic impedance of the microstrip line.

Capacitors can also be realized by microstrip structures. In this case the susceptance is given by:

B = (1/Zo)Sin2.0*pi*length/lambda. It should be noted that the line lengths for a capacitance are usually short and of low impedance.

In each of these structures there are accompanying parasitic elements also, In the case of an inductance there are parasitic capacitors at the two ends. forming a pi circuit, See the diagrams below. In the case of a capacitor there are series inductances in its leads,

Please see the reference on these expressions: Foundations of Interconnect and microstrip design by T.C Edwards and M.B Steer. John Wiley and Sons LTD, publisher.

For more and other interesting information and articles visit our website.


Integrate a board based prototype design using SPG's custom design and delivery services

RF Power amplifier design: small signal and large signal s-parameter comparison

Small signal s parameters are a well known set of parameters in small signal RF amplifier design. However, if the amplifier is a RF Power amplifier then small signal s parameters will not accurately reflect its operation. In this case large signal s parameters are required. So what is the difference in values between small signal s parameters and large signal s parameters for a particular circuit? To answer this question we ran a simulation using a well known industry standard simulator to derive both small signal and large signal s parameters at a particular frequency and particular bias conditions. The results are shown below.

The frequency is 2.5 Ghz. The small signal parameters found were: s11=0.184/-45.56, s12=0.019/-37.358, s21=4.306/24.992 and s22=0.465/35.422.

The large signal s parameters at the same frequency were: s11=0.691/13.914, s12=0.148/11.864, s21=0.148/11.864 and s22=0.965/-170.913.


Please note the difference Please visit our website for more articles and information.

RF amplifier design: Velocity factor for a transmission line.

A velocity factor ( VF) is frequently quoted by vendors and used extensively in matching calculations. Here is the definition of the velocity factor for the uninitiated. The velocity factor is simply = 1/sqrt(relative permeability of the media X relative permittivity of the media). Generally the relative permeability is unity. So the velocity factor can said to be simply 1/sqrt( relative permittivity of the media). In other terms the VF of the media defines how a traveling wave is slowed down in the media compared to free space. More info please visit our website at 

RF Power amplifier: two tone testing

Two tone testing is used most often to test the linearity of a RF power amplifier ( or other amplifiers for that matter). The technique is fairly simple in principle but can have its little “gotchas”. First off, choice of frequencies. If you have 2.5 Ghz S band RFPA you are going to test, what frequencies do you use? Use frequencies close to 2.5 Ghz, say a few Mhz above and below or whatever provides the test results accurately ( simulations can be used to do this).Then the second issue is how do you generate the two tones to be input into the amplifier and not generate significant other IM products that will certainly destroy the test. ( A handy rule of thumb is to keep these input IMPs at least 6 dB below the test tones). Simple things like this can cause a real headache. My take is that if you are testing a 2.5 Ghz amplifier then you should place the two tones close to that frequency. Drive the amplifier so that the output at the tone will be close its rated output. Then measure using a good spectrum analyzer. ( Somewhat of a problem if you are a small company or hobbyist). Generally what will happen is that if the two tones are separated by f0 then the strongest two products will appear at f0 below the lower test tone and f0 above the higher test tone. Obviously there will be many more IM products that will be generated.

Industry standard  measures the ratio of the weakest desirable output (they both should be the same) to the strongest undesirable frequency (closest to one of the desirable frequencies) as a ratio in decibels (dB) and calls this number the IMD value.  However the American Radio Relay League refers to the undesirable strongest output
to the peak power in both desirable outputs resulting in a number that is 6dB larger than industry numbers.
Signal processing Group Inc., design and delivers analog and RF/Wireless ASICs and modules.


RF Power Amplifiers: Noise Power Ratio, NPR

Noise power ratio or NPR is a measure for a RF power amplifier ( among other analog circuits) that is usually used in the case of multicarrier power transmission using RFPAs. In order to understand NPR, it is instructive to basically describe how it is measured. First a white noise source is used and its output is passed through a band pass filter in the frequency band of interest. This represents multiple carriers with random amplitudes and phases. Then the resulting filtered signal is passed through a narrow, steep notch filter which is tuned to the frequencies of interest at the current measurement. First the output of this filter is passed through the DUT ( device under test) and the noise power is measured in the notch by using a narrow band receiver. Then the notch filter is bypassed and the noise power is again measured in the frequencies where the notch is using the narrow band receiver. The ratio of the two readings in dB is the NPR.

SPG designs, develops and delivers custom analog and RF/wireless asics and modules.

RF Power Amplifier Design: Conjugate matching and load line matching

A power amplifier device is characterized for a maximum operating current and a maximum operating voltage ( also see the safe operating areas of the device). A load line match is simply using the calculation: Vmax ( operating)/Imax(operating). This is the impedance that needs to be matched to if you want maximum performance out of the device. This is referred to in many books as the load line match. See also the paper in this blog on RF power amplifier design for a discussion of the load line. ( Go to, go to complementary menu item, go to more reports, select RF Amp 1 paper), Conjugate match on the other hand refers to matching of the real parts of the generator and load with the reactance tuned out. See the book at : for more details on this and other matching topics.

SPG designs, develops and delivers custom analog and RF/wireless asics and modules.

LC balun calculator

A LC balun balun calculator is now available for interested users on the Signal Processing Group Inc.’s website under the complementary menu item. Please scan through the items listed until you can select your choice. For background on LC baluns please read the post on LC baluns on the SPG blog. Use search to find it.

Use SPG's services

Balun design: A simple LC balun

One of the simplest baluns can be designed using L and C elements as shown below:

The design equations have been embodied in a Javascript calculator that will be provided in this blog for free download in the next post. Check back in a day or two to download the calculator. The input of this circuit is a balanced waveform and the impedance is set by the values of the L/C combinations. The output is another balanced signal with the required output impedance also calculated using the input and output impedances. This circuit may be implemented using discrete elements for use as a impedance transformer or a balun.

Please visit our website at for more technical articles of interest and a description of our services.