Impedance matching using two useful techniques

For maximum transfer of power from a source to a load, the source and load impedances must be conjugate matched. A number of techniques to do this have been developed. This post looks at two fairly simple and very popular ones. The L - section match and the cascade transmission line match. Simple analytical techniques are used to do this and described in the paper. The calculations can be done with a simple calculator. In order to access the detailed description, interested readers are directed to our website at www.signalpro.biz. Follow the links in the website to engineering pages>engineer's corner and then select the paper from the list on the page.

SFDR or Spurious free dynamic range

Someone asked a question about the significance of the SFDR. The answer to the question was as follows. ( For experienced receiver designers this is old hat of course.)

The SFDR is a specification which allows a reviewer to gauge the range of input/output signals that a receiver can handle while still in a linear range of operation.

The basic mathematical definition is:

SFDR = (2/3) x (IP3 - Noise floor)

The noise floor is defined as:

Pn(output) = kTBGF.

Where k = Boltzman's constant
T = Absolute temperature
IP3 = Third order intercept point at the output
G = Gain of the system
F = Noise factor.

Using this definition the SFDR can be calculated as:

SFDR = (2/3)(IP3 + 174 - 10logB - G - F).

Here the 174 represents the kT noise.

All quantities in dBm.

Thus if IP3 is known and gain is known , the input IP3 is known. The input signal should not exceed this as 3rd order distortion products will emerge from noise beyond this level at the input.

So an obvious conclusion is: Keep IP3 as high as possible and the noise floor as low as possible for high SFDR. Typically IP3 is about 11.6 dB above the 1 dB compression point of an amplifier.

Also it must be stressed that all components in a system, that have the potential of introducing distortion, should be assigned an IP3. Ultimately the final IP3 is the cascade of the individual IP3's.

FCC regulations for unlicensed transmitters

What does the term unlicensed transmitter actually imply? What is it that one can do with this frequency band/bands? In fact, to start a wireless system design in the unlicensed band this has to be the first step in the design. To understand this more fully we took a look at the FCC website. It is a vast website and in spite of a search engine it still takes a bit of doing to locate the relevant articles, regulations, rulings, tips etc. We did manage to locate a couple of papers which we believe are helpful for people who may want to understand this concept of the unlicensed frequency band in the US. These can be accessed through our website at www.signalpro.biz ( or, of course, through the FCC website!). Go to engineering_pages>engineer's corner and look for the unlicensed frequency band information. By the way, there are always updates to these, so it is a good idea to also check on the updates.

VSWR, refelection coeffcients, s11, etc

The basic quantities such as VSWR, return loss, reflection coefficients, s11 and s22 etc are all basic to design. Their interactions and relationships are also basic and a brief note to document these relationships can be both informative and useful. There are numerous descriptions of these individually on the web. We prefer to publish the note in our website at www.signalpro.biz>engineering pages>engineer's corner for interested parties.

The relationship of Tf ( forward transit time) and ft in a bipolar transistor model

Someone recently asked how the ft of a bipolar is related to tf, the forward transit time of the bipolar. The tf is a model parameter while ft is not. Yet we always talk about the ft of the transistor. The answer to this question can be found in the spg website ( www.signalpro.biz) under engineering pages>engineer's corner for interested parties.

IP3 -- third order intermodulation product

IP3 is an important quantity in systems analysis of wireless/RF systems. It is a measure of the performance of an amplifier and is related to the 1 dB compression point of an amplifier. To put it simply IP3 can be interpreted as an unwanted signal that comes out of the noise level in an amplifier system ( or a mixer ) and climbs at a rate of 3X the amplifier input - output characteristic. It is, as mentioned above, an unwanted signal and therefore care is taken to calculate it as it sets a boundary on achieveable performance of the circuit. A good paper on this and other related quantities ( such as 1 dB compression point, IP2 ) is presented in the "Engineer's Corner" in our website located at www.signalpro.biz>Engineering_Pages for interested readers. As young RF engineers it took us a while to completely understand the ramifications of IP3 and associated quantities. To be able to understand intermodulation intuitively is neccessary for good RF/wireless design.

The Harmonic Balance algorithm.

The Harmonic Balance algorithm is now an established technique for CAD programs of various types, specially for RF/MMIC and analog. We felt we needed to understand the algorithm. This would allow us to be better at using it in simulations and more importantly be able to say if we wanted to purchase it in a CAD tool we wanted or not.

The implementation of these algorithms in the circuit simulator are fairly involved. However, luckily, compared to a couple of decades ago we as circuit designers do not really need to know its intricacies. What we want to know is at a higher level of abstraction. The expectation is that, if we do this we can do better at simulation and know when to use it effectively and when to not use it!

As a result of discussions internal to our design and CAD group a better understanding was gained and we decided to write a brief paper on it. This paper is now available on our website at www.signalpro.biz. Interested readers may follow the links www.signalpro.biz>engineering pages>engineer's corner and read the paper if they wish.