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.

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# 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 www.signalpro.biz.

# 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.

**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.

# 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.

# 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 www.signalpro.biz, 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 :https://www.amazon.com/VSWR-Impedance-matching-techniques-electronic/dp/1490902813 for more details on this and other matching topics.

# 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.

# 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.

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# Balun typical s parameters and their interpretation

The s parameters of a balun ( three port) are:

s12 = -s13 = s21 = -s31 and,

s11 = -infinity.

What does this mean in terms of conceptual understanding? The interpretation of these s parameter statements are:

- A balun is a three port device with a matched input and differential outputs.
- A balun is a three port power splitter
- The two outputs from a balun are equal in amplitude but opposite in phase.
- The voltage of one balanced output is the negative of the other balanced output.
- The input is matched to the input transmission line.
- The usual impedance is 50 Ohms. But it could be something else.
- A balun is a reciprocal device. Its output and inputs may be exchanged

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