When using a RF transformer, remember that the supplier specifies the impedance ratio of the transformer. The relationship of the impedance ratio to the voltage ratio of the transformer is:
20log[sqrt(Output impedance/input impedance)] = 20log(output voltage/input voltage). The currents are inverse 20log(Input current / output current)
As frequencies increase the chip resistor capacitance, inductance and pad parasitics start playing a significant role in the performance of the resistor . Sometimes at higher frequencies a chip resistor may start behaving capacitive sometimes inductive. A Signal Processing Group Inc., high frequency product was to be designed using chip resistors of value 75 Ohm. We investigated the chip resistor frequency response and found that for the highest frequency response the 0201 size is the best. However, assembling 0201 is quite challenging. The next best choice is 0402. This too has its difficulties in assembly. Going further down is the 0603 size, which is easier to use but has poorer frequency response generally than the 0201 and 0402 sizes. However, in our case the resistor value was 75 Ohm. From looking at the characterizations done by a well known chip resistor vendor it appears that if the resistor value is below 100 Ohm, 0603 and 0402 both behave about the same. The conclusion: We can use 0603 which is easier to use. Please visit our website for more information and publications and descriptions of services.
The characteristic impedance of microstrip changes at frequency owing to changes in the effective permittivity of the substrate. We analyzed this at 10 Ghz for a 0.062 inch substrate, with 1 oz copper and plotted the curve for Z0 ( characteristic impedance) change versus width of the microstrip. This is shown below. For more information on this and other interesting topics please visit the Signal Processing Group Inc. website.
This is an addendum to the original post on the current carrying capability of a PCB trace. The units of the width of the PCB trace were inadvertently left out. The units of the calculated width of the trace are mils.
A really fundamental parameter for PCB design is the copper weight to be used and the thickness of that copper. This post simply calls out these parameters for PCB designers who may need these constantly.
The thickness of 1 oz copper is 1.37 mils or 0.0347 mm
To determine the thickness of ( for example) 4 oz simply mutiply 1.37 mils by 4.0 ( or 0.0347 mm by 4.0). In terms of microns the thickness of 1 oz copper is 34.79 microns.
Please visit the Signal Processing Group Inc., website for more technical information, software, whitepapers etc.
s11 is the input reflection coefficient expressed in terms of s – parameters. It can be used as is in certain software programs to analyze the input characteristics of a 2 – port circuit. However, if these specialized programs are not available then a conversion between s11 can be carried out from the known ( measured) value of s11 using either the Smith Chart or by using a simple calculator for the conversion. The basic conversion algorithm is as follows:
Z = Zo * ((1 + Γ) / (1 – Γ))
Γ = (Z – Zo) / (Z + Zo)
S11 = 20 * Log10(mag)
Here Z is the impedance corresponding to the reflection coefficient, Zo is the characteristic impedance, Γ is the reflection coefficient. Obviously the calculations involve complex numbers as the impedances and the reflection coefficient are all complex numbers. Another way to do the conversion is to use the Smith Chart. As shown below. Just input the value of s11 or the reflection coefficient and read the impedance at that point..The example below converts a s11 magnitude of 0.6966 and angle 176.2 to an equivalent impedance directly.
The Smith Chart program used here is a freeware program developed by Prof. Fritz Dellsperger , Juerg Tschirren and Roger Wetzel of the Berne Institute of Engineering and Architecture.
The same function can be done using a calculator as mentioned above. The results of the calculator are shown below:
The calculator used for this function was from Le Leivre.com on the web. Please visit the Signal Processing Group Inc., website for more technical information, white papers, and general information for our cost – effective design, development and manufacturing services for Analog and RF/wireless ASICs and modules.
Impedance matching is a critical skill required for a large number of electronic circuit designs. A number of popular techniques are used over and over again and many are inbuilt into certain software packages. However, if one wishes to check out the matching using an independent package like PSPICE it becomes interesting to see what impedance matching means in the PSPICE domain. This allows the designer to check and re-check his design with a simple tool that is freely available in the industry, both as freeware and as a purchasable package with many “bells and whistles”. Ultimately though it is engineering judgement that counts and a simple way to check one’s work is always desirable. Please visit the Signal Processing Group Inc., website and check under the ” free articles…” menu item for an article addressing the impedance matching simulation technique and its interpretation.
It is interesting that the formula for calculating the inductance of a length of microstrip on a PCB has two different expressions. A majority of calculators use the ARRL expression shown below.
L = 0.00508*b*(ln[2b/(w+h)]+0.5+0.2235(w+h/b))
where h is the separation of the strip from the ground plane and w is the width of the microstrip. b is the length of the microstrip in inches However, we found that one company substitutes 0.12963 for 0.00508 in their calculations. It is not clear why this is so and answers were not forthcoming. In the absence of justification we continue to the use the original multiplier provided by ARRL i.e. 0.00508. Please visit the Signal Processing Group Inc., website for more technical and other information.
Rssi or received signal strength indication is a very popular circuit used in many radios to indicate the level of the received signal under various conditions. It typically consists of a series of limiting amplifiers followed by rectifiers and voltage to current converters that generate the rssi output signal. Recently Signal Processing Group Inc., released a rssi indicator IC that can work up to 450 Mhz.Its typical operation was tested at 70 Mhz and 300 Mhz and its rssi characteristic was published. This characteristic is reproduced below. Interested parties may contact us through our website for actual packaged silicon for purchase, design notes, application notes, IP etc.Modifications to the rssi design can be done as requested by interested customers and re-fabricated. The chip is designed in a 0.6 um BiCMOS process available from a popular foundry service.