Short-range Wireless Communication

Engineering Worksheets

A number of radio engineering worksheets accompany this book. Their aim is to help you understand the technical explanations in the book, and to serve as a tool for your own work and study. In order to use the worksheets, you need to install a version of PTC Mathcad Prime, which supports *.mcdx files. All of our files run on the free (as this book is written) reduced functionality version, PTC Mathcad Express(opens in new tab/window). It is recommended that you become familiar with Mathcad Prime through tutorials and “Help” in order to benefit from the worksheets. Here are general comments on the style of the worksheets.

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  Names of variables on the worksheets are not necessarily the same as in the book text.

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  Assignments to variables may not be connected to the text. Change the assignments at will in the worksheets to solve the examples in the text and to suit your own interest and requirements.

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  Note that you can easily change the units of measurement of results to those you are most familiar with, for example from meters to feet or centimeters to inches.

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  In many worksheets, yellow marking of assignment terms are user entered given values and results are marked in blue.

Following is a synopsis of the individual worksheets. The files can be downloaded here.

Complex_numbers.mcdx : Complex Numbers Finds real and imaginary parts and argument of a complex number, for use with Mathcad Express. It shows how to create a constellation diagram on an x,y plot. This worksheet is not needed for fully functional Mathcad, which has built in complex number functions and polar plotting.

Conversion.mcdx: Impedance Transformations Complex This worksheet lets you convert capacitances and inductances between their values and their reactances. You can also find resonant frequencies and convert between serial and parallel impedances.

diffraction.mcdx : Diffraction Plots the formula for diffraction over a knife-edge barrier, and converts from the normalized distance of the barrier tip from the line-of-sight to the absolute value called height. The first Fresnel zone limit is also calculated.

diversity.mcdx : Transmit Diversity Demonstrates the use of the Alamouti algorithm for spatial diversity with two transmitter antennas and one receiving antenna. The known channel parameters are chosen with random amplitude and random phase. 8PSK modulation is assumed, with eight possible equal amplitude symbols. You can choose any two source symbols for the demonstration. Gaussian noise, with user determined standard deviation, is added to the received signal at each of the two consecutive reception times of the algorithm. The similarity of the resulting estimated transmitted symbols to the true values is easily recognized. You can see how the maximum likelihood decision rule works by comparing the detected symbols to each of the possible transmitted symbols. Finally, a constellation diagram shows the estimated symbols in relation to the noiseless constellation.

Helical.mcdx: Helical Antenna Use to design a helical antenna over a ground plane. You can specify turns per unit length to calculate the height, or the height to get number of turns.

Intermodulation.mcdx: Intermodulation Distortion This worksheet facilitates finding 3rd order spurious signal frequency and power given interfering signal frequencies and power and third order intercept. It also finds two tone dynamic range and 3rd order intercept of cascaded stages.

Loop.mcdx: Loop Antenna Use to design a printed circuit board or air small loop antenna. Calculates radiation and loss resistances, inductance and resonating capacitance. The loss resistance is apt to be greater than specified since board material and surroundings are not taken into account.

Loop_match.mcdx: Coupling Loop Match Facilitates designing coupling loop matching for a small resonant loop antenna with a given area. The worksheet shows design for square loops. For round loops use the circular perimeter for a given loop area to find inductance instead of the square perimeter as shown. The worksheet calculates the equivalent round coupling loop radius, given the required mutual inductance for the match and distance between loops and skew of loop centers. The fourth step in the worksheet shows adjustment of the radiating loop resonating capacitor to obtain a good match. Residual reactance in the match can be cancelled out with an inductor or capacitor in series with the coupling loop.

Matching.mcdx: Impedance Matching Calculates impedance matching circuit components, with different topographies. Terminations are resistive, but complex impedances can be dealt with by absorbing reactances in adjacent circuit components. Also designs an RF balun.

Microstrip.mcdx: Microstrip Transmission Lines Finds printed microstrip width or impedance according to frequency and board thickness and relative permittivity. Also calculates wavelength and effective relative permittivity in board.

MIMO.mcdx: MIMO Spatial Multiplex Demonstrates how using MIMO antennas, separate transmit data streams can be received without co-interference over a common channel resource. The condition is that the number of data streams is equal to or greater than the least number of antennas between the two terminals. A constellation diagram shows the estimated symbols in relation to the noiseless constellation.

Patch.mcdx: Microstrip Patch Antenna Use to design a square patch antenna. From frequency and board substrate thickness and dielectric constant, the worksheet finds the length of the sides and feed impedance at the center of the edge. By specifying the desired input impedance, often 50 ohms, the worksheet finds the point on the centerline of the patch for connecting a feed probe, the center wire of coax cable for example.

PLL.mcdx: Charge Pump PLL Calculates charge pump phase lock loop component values and displays loop and filter gain vs. frequency plots.

Probability.mcdx: Probability This worksheet shows how to find the probability of errors in a sequence of bits, dependent on the bit error rate. It also defines average, variance and standard deviation for a discrete function of a random variable and a for continuous Gaussian random variable.

Radiate.mcdx: Radio Wave Propagation This worksheet is used for finding the relationships between transmitting and receiving signal strengths, field strength, antenna gains and transmission distance in free space.

range.mcdx: Open Field Path Gain Plots path gain over an open field (wave reflection only from ground) for given frequency, antenna heights and polarization. A free space plot is also shown. From the plot you can find required receiver sensitivity for a given transmitter radiated power and range, or estimate range when transmitted and received power are known.

RFID_FF.mcdx: RFID Far Field

This worksheet finds the back-scattered power to a far field RFID reader, given the switched source impedances from the tag antenna during tag response modulation. It also calculates modulation and power efficiency factors which indicate link performance.

RFID_NF.mcdx: RFID Near Field This worksheet finds the magnetic flux density created by a near field RFID reader and uses it to calculate the induced voltage in a passive tag. Then it estimates the reflected voltage in the reader due to tag modulation.

Sensitivity.mcdx: Noise Figure and Sensitivity Calculates the cascaded noise figure which it uses to find receiver sensitivity. Also calculates sensitivity when the antenna is not at standard room temperature due to environmental noise.

Translines.mcdx: Transmission Lines This worksheet calculates various transmission line parameters at a given frequency. It defines VSWR, reflection coefficient and return loss and converts between them. It finds input impedance when load impedance is known, and load impedance for a given input impedance, taking into account the transmission line loss.